STIGMATIC SPECTROSCOPY OF THE SOLAR ATMOSPHERE IN THE
VACUUM-ULTRAVIOLET
by
Hans Thomas Courrier
A dissertation submitted in partial fulfillment
of the requirements for the degree
of
Doctor of Philosophy
in
Physics
MONTANA STATE UNIVERSITY
Bozeman, Montana
May 2020
©c COPYRIGHT
by
Hans Thomas Courrier
2020
All Rights Reserved
ii
DEDICATION
To my parents, Thomas J. and Marilyn S. Courrier, for their unfailing support
and presence.
To Lindsay Ryder, for your unconditional love and support.
iii
ACKNOWLEDGEMENTS
This work would not have been possible without the generous support and
guidance of Dr. Charles Kankelborg. Thank you for your valuable insight and wisdom
that you were always willing to impart and your encouragement that kept me going.
Thanks also go to my graduate committee for their efforts, advice, and guidance: Dr.
John Carlsten, Dr. Rufus Cone, Dr. Dana Longcope, Dr. David McKenzie, and Dr.
Jiong Qiu. Sounding rocket and satellite missions are a collective effort and would
not be possible without the work of many hands. I would like to extend my gratitude
to my MSU team members: Dr. J. L. Fox, Dr. T. Rust, R. Smart, J. Parker, K.
Mashburn, J. Plovanic, M. Norton, J. Maxwell, S. Atwood, J. Knoll, and J. Hartman,
for their contributions. Neither launch of the MOSES instrument would have been
possible without the professional and excellent work of the NSROC team and WSMR
staff. It was also a great privilege to work with the members of the LMSAL IRIS
team, including Dr. B. De Pontieu and Dr. J. P. Wülser. I am fortunate to have found
many good friends in the MSU Physics Department staff. Thanks to N. Williams for
your above and beyond technical assistance and the many entertaining conversations
around a milling machine. I am certain I would have lost my way long ago if not for
the guidance and wisdom of M. Jarret. Thank you, Margaret.
Thanks to my parents, T. and M. Courrier, for providing a loving home and good
education. L. Ryder has been a supportive partner and friend through all consuming
work; may I always be there for her.
iv
TABLE OF CONTENTS
1. INTRODUCTION ........................................................................................1
Spectroscopy and the Solar Atmosphere ...........................................................1
Stigmatic Solar Spectroscopy...........................................................................5
Magnetic Reconnection..............................................................................8
Alfvén Waves.......................................................................................... 12
The IRIS PSF......................................................................................... 13
Limitations of Slit-Spectrographs ................................................................... 16
Slitless Solar Spectroscopy............................................................................. 21
Challenges of Slitless Spectroscopy ........................................................... 25
Summary of Dissertation Chapters................................................................. 27
2. USING LOCAL CORRELATION TRACKING TO RECOVER
SOLAR SPECTRAL INFORMATION FROM A SLITLESS SPEC-
TROGRAPH.............................................................................................. 29
Contribution of Authors and Co–Authors ....................................................... 29
Manuscript Information ................................................................................ 30
Introduction ................................................................................................. 32
Methodology ................................................................................................ 35
FLCT Parameters ................................................................................... 36
Inverting Synthetic Data ......................................................................... 44
Inverting MOSES Data ................................................................................. 50
Discussion and Conclusions ........................................................................... 54
Acknowledgements........................................................................................ 57
3. AN ON ORBIT DETERMINATION OF POINT SPREAD FUNC-
TIONS FOR THE INTERFACE REGION IMAGING SPECTRO-
GRAPH ..................................................................................................... 58
Contribution of Authors and Co–Authors ....................................................... 58
Manuscript Information ................................................................................ 59
Introduction ................................................................................................. 61
Instrument and Data Selection ...................................................................... 63
NUV Data Reduction.............................................................................. 67
Estimation of Mercury’s limb ........................................................... 69
FUV Data Reduction .............................................................................. 70
PSF Estimation............................................................................................ 71
Initial Guesses ........................................................................................ 73
Mercury’s Shadow ........................................................................... 73
v
TABLE OF CONTENTS – CONTINUED
Model PSFs..................................................................................... 74
Semi-blind Deconvolution ........................................................................ 78
Stopping Criterion .................................................................................. 79
Results and Discussion.................................................................................. 80
Effect of the Initial Guess on the PSF ...................................................... 94
PSF Effect on Data................................................................................. 95
Concluding Remarks ..................................................................................... 97
Acknowledgements...................................................................................... 100
4. THE EUV SNAPSHOT IMAGING SPECTROGRAPH (ESIS) ................... 102
Contribution of Authors and Co–Authors ..................................................... 102
Manuscript Information .............................................................................. 104
Introduction ............................................................................................... 106
The ESIS Concept ...................................................................................... 109
Limitations of the MOSES Design.......................................................... 109
ESIS Features ....................................................................................... 113
Science Objectives ...................................................................................... 116
Magnetic Reconnection Events............................................................... 117
Energy Transfer .................................................................................... 118
Science Requirements ............................................................................ 121
The ESIS Instrument .................................................................................. 121
Optics .................................................................................................. 122
Optimization and Tolerancing................................................................ 126
Coatings and Filters.............................................................................. 129
Sensitivity and Cadence ........................................................................ 133
Alignment and Focus ............................................................................ 134
Apertures and Baffles ............................................................................ 136
Cameras ............................................................................................... 139
Avionics ............................................................................................... 141
Pointing System.................................................................................... 143
Mechanical ........................................................................................... 143
Mission Profile............................................................................................ 143
ESIS Mission Update ............................................................................ 144
Conclusion and Outlook.............................................................................. 145
Acknowledgements...................................................................................... 146
5. CONCLUSION......................................................................................... 147
MOSES Doppler Inversion........................................................................... 148
vi
TABLE OF CONTENTS – CONTINUED
Future Directions for LCT Doppler Maps ............................................... 150
PSFs for IRIS ............................................................................................ 152
Future Directions for IRIS PSF Characterization .................................... 153
ESIS .......................................................................................................... 154
ESIS Objectives .................................................................................... 156
REFERENCES CITED.................................................................................. 157
APPENDICES .............................................................................................. 174
APPENDIX: Error Estimation...................................................................... 175
APPENDIX: Diffraction from Mercury’s Limb ............................................... 178
Mercury Diffraction Model .......................................................................... 179
IRIS -Specific Assumptions .................................................................... 179
Fresnel Diffraction Model ...................................................................... 180
Mercury Limb Diffraction at IRIS ............................................................... 182
vii
LIST OF TABLES
Table Page
3.1 IRIS Mercury transit observations .................................................... 65
3.2 PSF energy distribution................................................................... 82
3.3 Residual intensity after PSF deconvolution ....................................... 87
3.4 Correlation between Mg ii Features and Atmospheric Properties......... 97
4.1 ESIS instrument requirements. AR is active region, QS
quiet sun, and CH coronal hole. ..................................................... 122
4.2 ESIS Design Parameters. ............................................................... 123
4.3 Figure and surface roughness requirements compared to
metrology for the ESIS optics. Slope error (both the
numerical estimates and the measurements) is worked out
with integration length and sample length defined per ISO 10110. .... 127
4.4 Imaging error budget and tolerance analysis results. MTF
is given at 0.5 cycles/arcsecond....................................................... 129
4.5 Estimated signal statistics per channel (in photon counts)
for ESIS lines in coronal hole (CH), quiet Sun (QS), and
active region (AR)......................................................................... 134
4.6 ESIS Camera properties. ............................................................... 142
A.1 Error model parameters at 30.4 nm. .............................................. 177
viii
LIST OF FIGURES
Figure Page
1.1 Loops over NOAA Active Region 12740 as viewed by AIA...................4
1.2 Zeeman splitting in sunspot ...............................................................6
1.3 Stigmatic HRTS spectra of an Explosive Event ...................................9
1.4 Petschek and Tearing Mode Spectra ................................................. 11
1.5 Point spread and line spread function effects on slit spectrum ............ 15
1.6 Standard Model of Reconnection in a flaring region........................... 18
1.7 Spectrum form NRL slitless spectrograph ......................................... 22
2.1 Schematic diagram of MOSES instrument......................................... 35
2.2 Image with FLCT-generated displacement vectors............................. 38
2.3 FLCT-recovered displacements from a pair of symmetri-
cally displaced Gaussian functions. Fig. 2.2. ..................................... 39
2.4 Estimates of MOSES PSFs .............................................................. 41
2.5 Estimates of MOSES MTFs ............................................................. 42
2.6 Systematic error of FLCT method from MOSES PSFs....................... 43
2.7 Dopplergrams of closely spaced spectral point sources ....................... 45
2.8 Dopplergrams of point sources with increased separation ................... 48
2.9 FLCT-generated Dopplergrams of MOSES data ................................ 52
2.10 Dopplergram of bi-directional explosive event.................................... 53
2.11 Dopplergram of compact explosive event........................................... 55
3.1 IRIS slit-jaw image and NUV spectra of Mercury transit ................... 64
3.2 Reduced spectra from IRIS data set 4 .............................................. 68
3.3 Mercury transit in FUV................................................................... 71
3.4 Diffraction-limited model PSFs for the IRIS telescope........................ 75
3.5 Deconvolution of model PSFs from reduced data ............................... 76
ix
LIST OF FIGURES – CONTINUED
Figure Page
3.6 Cost functions for the semi-blind deconvolution routine ..................... 79
3.7 PSF estimates from the semi-blind deconvolution routine .................. 81
3.8 PSF total energy vs. radius from center............................................ 83
3.9 PSF estimates deconvolved from reduced data .................................. 86
3.10 Modulation Transfer Functions of the IRIS SG.................................. 88
3.11 Comparison of deconvolved IRIS spectra .......................................... 90
3.12 Comparison of deconvolved IRIS spectra .......................................... 91
3.13 Intensity variation along a single spectral cut.................................... 92
3.14 PSF estimates from an alternate initialization................................... 93
3.15 Isolated Explosive Event observed by IRIS........................................ 98
3.16 Mg ii k wing EE spectra .................................................................. 99
3.17 Si iv EE spectra .............................................................................. 99
4.1 MOSES instrument schematic........................................................ 110
4.2 ESIS instrument schematic ............................................................ 113
4.3 ESIS optical layout and apertures .................................................. 124
4.4 ESIS CCD dispersion schematic ..................................................... 125
4.5 Ray traced and RMS spot diagrams ............................................... 128
4.6 ESIS grating efficiency................................................................... 130
4.7 ESIS Primary mirror reflectivity .................................................... 132
4.8 ESIS filter transmissivity ............................................................... 133
4.9 Alignment transfer GSE ................................................................ 135
4.10 ESIS stray light baffles .................................................................. 137
4.11 ESIS camera assembly ................................................................... 139
x
LIST OF FIGURES – CONTINUED
Figure Page
B.1 Schematic diagram of complex field immediately behind
Mercury’s limb.............................................................................. 180
B.2 Solar point source diffraction pattern from Mercury’s limb
at the position of IRIS................................................................... 182
B.3 Schematic diagram showing geometry for diffraction pat-
terns from multiple sources. ........................................................... 183
B.4 Solar diffraction pattern from Mercury’s limb as seen by IRIS.......... 184
xi
ABSTRACT
The solar atmosphere presents a complicated observing target since tremendous
variability exists in solar features over a wide range of spatial, spectral, and temporal
scales. Stigmatic spectrographs are indispensable tools that provide simultaneous
access to spatial context and spectroscopy, enabling the diagnosis of solar events
that cannot be accomplished by imaging or spectroscopy alone. In this dissertation
I develop and apply a novel technique for on orbit spectrograph calibration, recover
co-temporal Doppler shifts of widely spaced solar features, and describe a new design
for a slitless solar spectrograph.
The Interface Region Imaging Spectrograph, (IRIS) is currently the highest
spatial and spectral resolution, space based, solar spectrograph. Ongoing calibration
is important to maintaining the quality of IRIS data. Using a Mercury transit against
the backdrop of the dynamic solar atmosphere, I characterize the spatial point spread
functions of the spectrograph with a unique, iterative, blind, deconvolution algorithm.
An associated deconvolution routine improves the ability of IRIS to resolve spatially
compact solar features. This technique is made freely available to the community for
use with past and future IRIS observations.
The Multi-Order Extreme Ultraviolet Spectrograph (MOSES) is a slitless
spectrograph that collects co-temporal, but overlapping spatial and spectral images of
solar spectral lines. Untangling these images presents an ill-posed inversion problem. I
develop a fast, automated method that returns Doppler shifts of compact solar objects
over the entire MOSES field of view with a minimum of effort and interpretation bias.
The Extreme ultraviolet Snapshot Imaging Spectrograph (ESIS) is a slitless
spectrograph that extends the MOSES concept. I describe this new instrument, which
is far more complex and distinct as compared to MOSES, and the contributions I
made in the form of optical design and optimization. ESIS will improve the quality of
spatial and spectral information obtained from compact and extended solar features,
and represents the next step in solar slitless spectroscopy.
Taken together, these contributions advance the field by supporting existing
instrumentation and by developing new instrumentation and techniques for future
observations of the solar atmosphere.
1
CHAPTER ONE
INTRODUCTION
1.1 Spectroscopy and the Solar Atmosphere
The Sun, as observed from Earth, can be decomposed into several layers. The
photosphere is the layer that is observed in the visible continuum. In broad terms,
temperature and density increase from the top of the photosphere inward, which
correlates to a rapid increase in optical density. For this reason, the photosphere
represents the “surface” of the Sun as visible to our eyes. The radiation spectrum
from the photosphere is roughly approximated by that of a blackbody at ∼5800 K,
superimposed by Fraunhofer absorption lines from the photosphere and chromosphere
in the foreground.
The solar interior comprises the layers below the photosphere. Moving inward
the next layer encountered is the convective zone, followed by the radiative zone.
Both of these layers are named for their dominant processes of energy transport. The
innermost layer is the core, where nuclear fusion powers the entire star. Starting
from the ∼4000 K temperature minimum at a position about 500 km above the
photosphere, both temperature and density increase by orders of magnitude as radius
decreases [e.g. Model S, Christensen-Dalsgaard et al., 1996].
The solar atmosphere consists of the top of the photosphere and the layers
above. The chromosphere sits directly above the photosphere, while the corona
is the outermost layer that can extend well beyond the Earth. In between the
chromosphere and corona is the transition region (TR). The simplest models describe
2
the TR as a thin interface layer, even though observations present a more complicated
picture. In the solar atmosphere, density continues to decrease as height above
the photosphere increases. This correlates with a decrease in optical depth. From
the upper chromosphere outward, the solar atmosphere is well approximated as
an optically transparent1 medium, so that there is little absorption or scattering
of outgoing radiation. Somewhat curiously, however, the temperature in the solar
atmosphere increases with height above the photosphere; a relatively gradual rise from
the the temperature minimum above photosphere is observed in the chromosphere,
before rapidly increasing through the TR to ∼1 MK at the base of the corona [e.g.
Mariska, 1986]. This anomalous temperature profile clearly indicates a source of
heating is driving the temperatures in solar atmosphere away from thermodynamic
equilibrium.
This high temperature corona was first hinted at during an August 7, 1869
solar eclipse. A green emission line at 530 nm originating from the solar corona was
observed independently by Charles Augustinus Young and William Harkness during
the lunar occultation. The emission line did not correspond to any known element
at the time, so a new element “Coronium” was hypothesized. Ultimately, Coronium
would never materialize; almost 60 years would pass before Walter Grotrian (1939)
and Bengt Edlén (1942) connected the green emission with the more terrestrial but
highly ionized Fe xiv. Lines of highly ionized nickel and calcium were also identified,
making it apparent that the corona must be very hot, as these high ionization states
could only exist at temperatures greater than 106K.
Under further scrutiny, the construct of layers tends to fall apart above the
photosphere. This is because tremendous variability in both temperature and
1The term “optically thin” is sometimes imprecisely (or ambiguously) used to described the
concept of transparent plasmas in the corona and transition region in the relevant literature.
3
density exists at any given radius in the solar atmosphere. As an example,
Figure 1.1 shows a collection of loops above the solar limb in three filter-bands of
the Atmospheric Imaging Assembly [AIA, Lemen et al., 2012] on board the Solar
Dynamics Observatory. In the AIA images, each filter band roughly corresponds to
an ionization temperature. At 211 Å, much of the emission is from Fe xiv at ∼2 MK.
In the 171 Å channel, emission is dominated by Fe ix at ∼0.7 MK, while in the 304 Å
channel He ii is the primary emitter at ∼0.5 MK [O’Dwyer et al., 2010]. Figure 1.1
shows that emission from the loops spans three different temperature regimes, and
that these three regimes co-exist in close proximity to each other. The loops also
highlight extreme variability in density, as these structures are surrounded by space
that is comparatively much less dense. Furthermore, because the plasma in this region
is attached, or “frozen-in,” [e.g. Priest, 1982] to the magnetic field, the observational
inference is that the emitting plasma in each of the three panels in Figure 1.1 traces
out loops in magnetic field lines. From this situation, combined with the extreme
disparities in temperatures and pressures in close proximity, a picture emerges of
each loop containing its own individual atmosphere. This distinct anisotropy and
inhomogeneity stands in stark contrast to the notion of a solar atmosphere that is
only a function of radius.
Emission from the transition region and corona is primarily from far ultraviolet
(FUV) and extreme ultraviolet (EUV) emission lines from highly ionized atoms,
formed between temperatures of 104 and 106 K [Vernazza and Reeves, 1978, Del
Zanna and Mason, 2018]. Shortward of ∼100 nm, blackbody emission quickly dies out
so that there is little continuum and the EUV solar spectrum is largely dominated
by individual emission lines. Assuming ionization equilibrium, these emission lines
are formed over relatively narrow temperature ranges and, in most cases, can be well
isolated with a spectral resolution of ∼0.3 nm [e.g. Vernazza and Reeves, 1978, noting
4
Figure 1.1: Loops over NOAA Active Region 12740. Emission from the loops is
seen in close proximity across three different AIA ionization temperature regimes,
AIA 211 Å (∼2 MK, left panel) AIA 171 Å (∼0.7 MK, center panel), and AIA 304 Å
(∼0.5 MK, right panel), showing that temperature is not strictly a function of height.
that there are of course closely spaced and blended lines].
Since optical depth effects and continuum are largely absent in many FUV
and EUV lines, spectroscopic interpretation of individual line profiles is relatively
straightforward. The ion velocity distribution (i.e. the profile of a particular line) is
due primarily to Doppler shifts caused by bulk flows of the plasma and microscopic
thermal motions of the ions in the transparent solar atmosphere. Further information
can be obtained by comparing emission line pairs. Emission by ions of the same
element formed in overlapping or close temperature regimes gives information about
temperature, while comparing lines of allowed and forbidden transitions of the same
ion yields density information [e.g. Feldman et al., 1978, Del Zanna and Mason, 2018].
For these reasons, spectroscopy is an ideal tool for diagnosing physical conditions in
5
the solar atmosphere. Imagers such as the Transition Region and Coronal Explorer
[TRACE, Handy et al., 1999] and AIA provide a complementary technology as
Figure 1.1 demonstrates. Multilayer vacuum ultraviolet (VUV) coatings make it
possible to image the sun in a relatively narrow band (λ/∆λ ∼ 10− 50, using normal
incidence mirrors [e.g. Underwood, 1981, Windt et al., 2004]). However, from a
spectroscopic point of view, these “narrow band” images contain contributions from
multiple emission lines [O’Dwyer et al., 2010]. Nevertheless, multilayer passbands that
are dominated by a single-peaked contribution function (i.e. lines formed at similar
temperatures) can be interpreted, with some care, as a single temperature regime.
Thus, this type of imagery not only provides sky-plane motions, but places the scene
in a particular temperature context. For example, from the three AIA images in
Figure 1.1 it is easy to discern the co-existence and spatial proximity of the loops
across three different temperature regimes in the solar atmosphere.
1.2 Stigmatic Solar Spectroscopy
In a stigmatic slit spectrograph, at a particular wavelength, each point along
the slit is mapped to a point at the focal plane. If the slit is placed at the focus
of a solar telescope, imaging and spectroscopy are combined so that spectra can be
correlated to specific physical structures on the Sun. The observation of Zeeman
splitting in sunspots by Hale [1908] is a classic example. In the right panel of
Figure 1.2, the splitting of the Fe 617.3 nm absorption line is clearly seen in Hale’s
1919 spectrum [Hale et al., 1919]. Comparing the Zeeman splitting of this stigmatic
spectrum with the co-pointed broadband white light imagery in the left panel of
Figure 1.2 clearly shows a strong magnetic field is correlated with the sunspot. Hale’s
observations led to the realization that sunspots mark locations where concentrations
of magnetic flux emerge from the photosphere into the solar atmosphere.
6
Figure 1.2: Sunspot (left) associated with concentrations of strong magnetic flux
emergence by Zeeman splitting of the Fe 617.3 nm line (right) from Hale et al. [1919].
The position of the spectrograph slit is marked by the dark vertical line in the left
image.
Observations in VUV wavelengths are key to understanding the structure and
dynamics of the solar atmosphere. This is because in these wavelengths the solar
atmosphere is bright while the photosphere is dark. In visible wavelengths, strong
emission from the photosphere dominates and “washes out” the much weaker contri-
bution from the more rarefied solar atmosphere. Hale’s Mount Wilson observations
were limited to visible wavelengths as the Earth’s atmosphere is effectively opaque
to VUV radiation. Since the late 1940s, research rockets have carried spectrographs,
7
imagers, and other instrumentation above the Earth’s atmosphere, enabling access
to solar VUV radiation [e.g. Baum et al., 1946, Tousey, 1986]. In more recent
years, satellites [e.g. Wilhelm et al., 2004, Del Zanna and Mason, 2018, and the
references therein] have enabled much longer and consistent solar VUV observation
than suborbital rockets. Rockets, however, continue to provide a low-cost and low-risk
platform to access space for novel and unconventional instrumentation [e.g. Tousey,
1986, Fox, 2011, Kobayashi et al., 2012, 2014, Brosius et al., 2014, Kubo et al., 2016,
Ishikawa et al., 2017].
Despite the decades of observation outlined above, our understanding of how
energy is transported from the relatively cool photosphere through the chromosphere
and TR to the ∼1 MK corona remains incomplete. It is generally agreed that the
source of energy is magnetic in nature; e.g. Pevtsov et al. [2003] showed a direct
correlation between photospheric magnetic flux and power radiated from the corona
in the form of X-rays. However, the exact heating mechanism(s) are yet to be
identified [e.g. Klimchuk, 2006, Schmelz and Winebarger, 2015, and the references
therein]. In the remainder of this section I describe two possible phenomena of
energy transport within the TR that have distinct spectroscopic signatures. Magnetic
reconnection may serve as a source of energy in the solar atmosphere by directly
converting magnetic energy to plasma kinetic energy. Magnetohydro dynamic (MHD)
waves provide a potential mechanism to move energy through the layers of the solar
atmosphere, depositing some energy in the TR and corona through dissipation, or
damping, of the wave amplitude. Through these two (or potentially, some other)
mechanisms, the strong magnetic fields first observed by Hale punctuating the
photosphere and emerging into the solar atmosphere may prove to be the source
of energy to the hot solar corona.
8
1.2.1 Magnetic Reconnection
Magnetic reconnection describes the process wherein pairs of differently directed
magnetic field lines in a plasma “break” and reconnect with each other, forming
a lower energy state [e.g. Parker, 1957, Petschek, 1964]. Reconnection allows the
magnetic field lines to relax by shortening, releasing kinetic energy in the process.
The electric field associated with this change in magnetic field can also cause particle
acceleration. Both kinetic energy (flows) and energetic particles can give rise to
heating so that, through the reconnection process, magnetic energy is converted
into thermal energy. The actual reconnection site is believed to be too small to be
resolved in the solar atmosphere. However, from the magnetic, kinetic, and thermal
signatures, reconnection can be implicated in many solar events, such as flares [Priest
and Forbes, 2002], macrospicules [Wang, 1998], and explosive events [EEs, Dere et al.,
1991]. Outside of the solar atmosphere, reconnection is observed during magnetic
“substorms” that release large amounts of solar wind energy stored in the Earth’s
magnetic field [Angelopoulos et al., 2008]. Although reconnection appears to be
ubiquitous in the solar atmosphere, the process (or processes) by which reconnection
proceeds is not well understood.
Explosive events (EEs) are an example of a reconnection-type process in the
TR. They are observed as exceptionally strong (∼100 km s−1) Doppler shifted (or
broadened) features in spectral line profiles [Brueckner and Bartoe, 1983, Dere et al.,
1984, 1991]. Figure 1.3 shows an example of such an EE observed by the Naval
Research Laboratory (NRL) High Resolution Telescope and Spectrograph [HRTS
Dere et al., 1991]; the strong Doppler shifts are apparent in the O iv and Si iv lines
near the center of the image. EEs are compact, numerous, and highly energetic, with
lifetimes on the order of 60−90 s [Brueckner and Bartoe, 1983, Dere et al., 1991, Fox
et al., 2010]. They are also relatively easily observed in multiple TR lines by numerous
9
Figure 1.3: Stigmatic spectra from the NRL Naval High Resolution Telescope and
Spectrograph (HRTS) showing an EE in lines of O iv (1399, 1401, and 1404 nm) and
Si iv (1402 nm) from Dere et al. [1991].
VUV spectrographs (e.g. C iv, Si iv, and He ii [Dere et al., 1989, Innes et al., 1997,
Rust, 2017, Innes et al., 2015]) and are so frequent that one can expect to observe
at least one EE with a slit spectrograph every ∼ 5 minutes [Dere, 1994, Innes et al.,
1997].
The fast, sometimes bi-directional, [e.g. Innes et al., 1997, Fox, 2011, Rust, 2017,
and the references therein], outflows from the core of an EE are a key signature of
impulsive energy release that implicates magnetic reconnection. This is because in
the TR and corona the plasma is essentially frozen into the magnetic field, able to
travel along but not across magnetic field lines [e.g. Priest, 1982, Rust, 2017]. Post-
10
reconnection, because the plasma is frozen-in, it is dragged along with the field lines,
and thus the motion is perpendicular to the magnetic field (e.g. the plasma motion
diagrammed schematically in Figure 1.4). This reconfiguration reduces the energy in
the field. Thus, magnetic energy is converted to plasma kinetic energy. The Alfvén
speed, va, is the characteristic velocity associated with this conversion of energy,
B
va = √4 , (1.1)πρ
where the plasma mass density can be approximated as ρ = nemp, the product of
electron density ne and the proton mass mp. Estimates of the Alfvén speed in the TR
are on the order of 100 km s−1 [e.g. Dere et al., 1991]. This is similar in magnitude
to the Doppler shifts produced by EEs, but much greater than the 25-30 km s−1 non-
thermal velocities observed from Si iv, O v and N v ions in TR quiet sun [e.g. Akiyama
et al., 2005].
The Petschek model of fast reconnection is an example of how reconnection might
proceed in a particular EE. Assuming and inflow velocity 1 to 110 100 of the Alfvén speed
(∼100 km s−1 in conditions associated with typical EE’s) and characteristic length
1000 km, the time for Petschek reconnection to convert magnetic energy to kinetic
energy is between 100−1000 s, comparable to the observed 60−90 s EE lifetime [Dere
et al., 1991]. MHD simulations by Innes and Tóth [1999] show high-velocity outflows
from the EE core resulting from Petschek reconnection. These simulations do not
show any associated emission from the core of the spectral line profile. A simplified
diagram and distinctly red and blue shifted spectral signature for the Petschek
reconnection scenario is presented in Figure 1.4 panels (a) and (b), respectively.
In another study, Innes et al. [2015] observed bi-directional outflows from an EE
in the Si iv line with the Interface Region Imaging Spectrograph, (IRIS) [De Pontieu
11
Figure 1.4: Diagrams of spectral signatures resulting from Petschek (panels a and b)
and Tearing mode (panels c and d) EE reconnection models from Innes and Tóth
[1999] and Innes et al. [2015] respectively. In (a) plasma is accelerated to the Alfvén
speed along the line of sight by retracting post-reconnection field lines; the moving
plasma appears as distinct red and blue shifts in the spectrum in (b). In (c) the
tearing mode of reconnection accelerates plasma at a series of locations to a significant
fraction of the Alfvén speed. However, the accelerated plasma is trapped in magnetic
islands so that its motion is slowed after a short time. Emission from this hot, dense,
and slow moving plasma creates the distinct core component in the spectrum shown
in (d).
et al., 2014]. However, in this case significant emission was also detected from the
core of the line profile. Similar EEs of this type showing brightening of the line
core have been reported elsewhere [e.g. Dere et al., 1991, Innes et al., 1997]. The
hypothesis of Innes et al. [2015] is that the core brightening observed after a short
time in this event is due to tearing-mode reconnection. First, the tearing mode of
reconnection accelerates plasma to high velocities at a series of locations along the
extended separatrix region. The accelerated plasma is trapped within a shrinking
12
magnetic island, so that its motion is soon damped (Figure 1.4 (c)). Emission from
this hot, dense, and slow moving plasma fills in the line core so that the resulting
tearing mode spectrum in Figure 1.4 panel (d) lacks the distinct double peaks as seen
in the Petschek mode of panel (b).
The above two examples show that the spectroscopic signature of an EE can
vary based on the type of reconnection that may be occurring. The example spectra
presented in Figure 1.4 are fundamentally different, and should be easily distinguished
by a spectrometer with sufficient spectral resolution. Thus, spectroscopy can serve
as a diagnosis of the type of magnetic reconnection that results in an EE if the event
can be captured by the spectrometer slit.
1.2.2 Alfvén Waves
MHD waves provide a source of energy transport into and through the solar
atmosphere. Alfvén waves (transverse mode MHD waves that travel along magnetic
field lines,[Alfvén, 1942]) are a particular example. These waves have been detected
in numerous regions of the solar atmosphere [e.g. Tomczyk et al., 2007, Jess et al.,
2009, Hahn et al., 2012, and the references cited therein]. Wave amplitudes on the
order of 10’s of km s−1 are sufficiently energetic to provide a means to heat the corona
and power the solar wind [De Pontieu et al., 2007, McIntosh et al., 2011, Hahn and
Savin, 2013].
The energy carried by an Alfvén wave can be converted to heat by damping
of the wave in different regions of the solar atmosphere. Since the amplitude of the
Alfvén wave contributes directly to emission linewidth [e.g. Hahn et al., 2012, Hahn
and Savin, 2013], dissipation of wave energy is observed directly as a decrease in the
non-thermal emission linewidth. In a particular example, Hahn et al. [2012] measured
non-thermal linewidth as a function of height for the Fe ix, x, xii, xiii and the Si x
13
ions using the Extreme Ultraviolet Imaging Spectrometer [EIS, Culhane et al., 2007]
on board Hinode [Kosugi et al., 2007]. In this work, one end of the EIS slit was placed
close to the limb and the length of the slit oriented radially outward from sun center
so as to encompass a large portion of the corona. In this configuration, a decrease in
the relative non-thermal linewidth as a function of height above the photosphere was
detected, beginning at approximately 1.1R [Hahn et al., 2012].
The examples given for magnetic reconnection and Alfvén waves show that stig-
matic spectroscopy allows the isolation of line profiles in particular solar structures;
these profiles directly measure plasma motions in the solar atmosphere. In the case
of magnetic reconnection, the line profile can be used to discriminate between rival
descriptions of energy release. In the case of Alfvén waves, the line profile traces
the flow and deposition of energy in the open parts of the lower corona. For both
waves and reconnection events, the imaging component provides crucial details on
morphology and the surrounding spatial context. For example, a spectrograph may
see a red shift and a broadening at a particular point on the slit. Only an image can
distinguish whether this spectrum originates from an isolated explosive event or from
a flare ribbon that crosses the slit. The insights described above cannot be obtained
through imaging alone or by spectroscopy alone.
1.2.3 The IRIS PSF
The state-of-the-art Interface Region Imaging Spectrograph, (IRIS) is a small
explorer spacecraft that provides simultaneous spectra and slit-jaw images of the
photosphere, chromosphere, transition region, and corona [De Pontieu et al., 2014].
IRIS is currently the highest spatial (0.33-0.4′′) and spectral (2653 mÅ) resolution
space-based solar observatory in operation. Instrumental effects, such as optical
aberration, diffraction, and stray light, can significantly alter the line profile observed
14
by IRIS and other imaging spectrometers. Thus, how the above plasma motions
described in the previous section are interpreted through line profiles can depend
significantly on how well the instrument is calibrated. In Chapter 3 of this thesis,
I derive on orbit point spread functions (PSFs) for the spatial axis of the IRIS
spectrograph. IRIS has undergone extensive calibration on the ground prior to
launch [De Pontieu et al., 2014]; the work described in Chapter 3 is part of an
ongoing effort to supplement and maintain this calibration for the instrument. To help
establish the importance of PSF characterization, here I describe how the instrument
PSF can contribute to the uncertainty in the examples of explosive events and Alfvén
waves discussed above.
For stigmatic spectrometers, instrumental resolution can be broadly classified
into two functions. The PSF describes the mapping of an infinitesimally small point
source to the spatial axis of the instrument, while the line spread function (LSF)
describes the mapping of spectral line source, i.e. monochromatic “line” illumination,
to the spectral axis. Optical aberration (and other effects) will cause the image of
the line and point sources to appear artificially broadened along their respective axes
when imaged at the detector plane. The result is that the image at the detector is
“blurred” by the convolution of the PSF and LSF (along their respective axes) with
the original scene.
The effect of the PSF and LSF on the spectra observed by the instrument
is detailed schematically in Figure 1.5. In panel (a) of Figure 1.5, convolution
of the signal with the PSF blurs intensity from spatially adjacent pixels. In the
example shown, this causes two spatially adjacent spectral signals with different center
wavelengths to appear as a spectrally broad signal with a single central peak that
spans multiple spatial pixels. Moreover, centroiding each of the resultant line profiles
would result in an underestimate of the velocities of these two features. In Figure 1.5
15
(b), convolution of the signal with the LSF causes a loss of spectral resolution by
blending two spectrally distinct peaks into a single, broad spectral signal.
Figure 1.5: Input and observed signals to scale; scale of PSF and LSF increased for
visualization; typically the PSF and LSF are normalized to unity. Convolution is
represented by the ⊗ operator. Panel (a): The PSF causes signals from spatially
adjacent signals to be blurred together. (b): The LSF causes blurring of spectrally
adjacent features of the input signal. Both functions impact spectral resolution
through different mechanisms.
In the study of magnetic reconnection in EEs, it is clear that the spectral
distribution of intensity in the line profile plays an important role in determining
the underlying reconnection mode at work. However, both the instrument PSF and
LSF can work to obfuscate the underlying reconnection mode(s). For example, panels
(a) and (b) of Figure 1.5 show that critical spectral features are lost to blurring by the
PSF and LSF. In the context of an EE, this results in a loss of distinction between
Petschek and tearing mode types of reconnection (e.g. the similarity in line profile
observed between both panels of Figure 1.5).
In the Alfvén wave study by Hahn et al. [2012], the contribution to linewidth
due to wave damping was about one-tenth of the EIS spectral pixel separation of
0.0022 nm/pixel; a fraction of the ∼0.006 nm full width at half max EIS line spread
function (LSF). To observe wave damping as a function of height, Hahn et al.
[2012] sampled linewidth at several positions along the EIS slit. This required the
16
characterization of the EIS LSF as a function of position along the slit by Hara et al.
[2011], so that wave broadening could be distinguished from the variation in the LSF
along the slit and stray light within the instrument [Moran, 2003, Dolla and Solomon,
2008].
These cases illustrate two specific roles that instrument spatial and spectral
resolution can play in stigmatic spectroscopy. In Chapter 3, I demonstrate how the
PSFs I obtained can alter the line profile of an EE. The spatially gradual effects
observed by Hahn et al. [2012] required a well characterized LSF at several points
along the EIS slit; in more general cases, where the characteristics of the line profile
are of interest, detailed characterization of the instrumental broadening (e.g. the LSF)
is needed to determine the amount of non-thermal broadening in the line profile [e.g.
Peter, 1999, Akiyama et al., 2005, Dud́ık et al., 2017]. These examples show that a
good understanding of instrumental effects is crucial to many aspects of solar spectral
observations.
1.3 Limitations of Slit-Spectrographs
Section 1.2 describes specific examples of what can be learned about the solar
atmosphere from a slit spectrograph. However, these works also help illustrate some
handicaps specific to slit spectrographs in VUV solar observations. Some of these
limitations are described in this section.
It is difficult, if not impossible, to directly capture the full spatial and temporal
variability of many solar events with the 1D FOV offered by a slit spectrograph. The
model of a solar flare by Kopp and Pneuman [1976] in Figure 1.6 is an intuitive
example. In this model, there will be plasma inflows and outflows associated
with the reconnection region, similar to the Petschek and tearing mode models
described earlier. In addition, chromospheric evaporation, or upflows due to the
17
gas pressure of heated chromospheric plasma [e.g. Shibata and Magara, 2011], will fill
the corona with hot plasma that rises along the magnetic loops from their footpoints
as indicated in Figure 1.6. After reconnection, plasma trapped by the loops cools
and condenses, falling back to the chromosphere. This model of a flare presents
plasma at a variety of temperatures and velocities, which can potentially be observed
with a slit spectrograph. However, imagining a straight line drawn through any
two points in Figure 1.6 to represent the spectrograph FOV, it is difficult (or perhaps
impossible) to capture both the reconnection flows and the chromospheric evaporation
or condensation from both sides of the flare arcade.
Similar to the above argument, the slit also enforces a particular geometry on
the Alfvén wave observations described earlier; Hahn et al. [2012] assumed that the
magnetic field is directed radially outward and parallel to the length of the EIS
slit. Imposing only a slightly more complicated magnetic field geometry would make
following the propagation of the Alfvén waves with a slit spectrograph difficult, if not
impossible.
From the flare loop and Alfvén examples it is clear that the situation could be
improved by increasing the FOV beyond what a 1D slit provides. Ultimately, what is
desired in both these situations is the ability to obtain a 3D datacube; a large FOV
2D “image” with a full spectrum available at each pixel. Such a data cube would
allow the full context of a flare or MHD wave event to be investigated without being
subject to the geometrical constraints of a spectrograph slit.
Stepping the spectrograph slit, or rastering, across the scene is one method to
build a 3D spatial/spectral data cube. A major drawback to the raster approach is
that the cadence is often slower than the evolutionary timescale of the solar features
under investigation. For example, in a post-flare loop study by Czaykowska et al.
[1999], CDS took ∼9 minutes to build a 160′′×160′′ raster covering the entire loop
18
Figure 1.6: Standard model of magnetic reconnection in a flaring region from Kopp
and Pneuman [1976]. Note the difficulty in choosing a pointing for a spectrograph
slit that captures all regions of interest such as the flare footpoints, outflows, and
reconnection regions.
area. A timescale for cooling of plasma suspended in the post-flare loops can be
estimated by taking the ratio of the internal energy of plasma in the corona (3nekT )
to the rate of radiative energy loss:
∆t = 3nekT/nenhQ(T ) , (1.2)
where ne and nh are electron and hydrogen number densities, respectively, k is the
Boltzmann constant, T is temperature, and Q(T ) is the radiative loss function. In
the corona, ne ≈ nh so that
∆t = 3kT/neQ(T ) . (1.3)
19
For the CDS observations, the maximum temperature observed corresponds
to the Fe xix emission line at T = 8.0 MK. At this temperature, assuming
ne = 1010 cm−3, Q(T ) = 3× 10−23 erg cm3/s from the CHIANTI database [Young
et al., 2019] using the coronal abundances profile. Under these assumptions, the
timescale for radiative cooling in the post-flare loops is about ∆t = 6 minutes, just
over half the time it took CDS to complete one raster across the loop region. This
means that the plasma suspended in a loop could have cooled significantly by the time
CDS completed a single raster, with all of the plasma in the loop having completely
cooled by the time the slit arrived at the same pointing for the second time. The
relevant timescales show that rastering can obfuscate the temporal evolution of a
post-flare loop arcade in this example.
The simplest technique available to slit spectroscopy is the sit-and-stare method.
The slit is held stationary so that temporal confusion is avoided. In this mode of
operation, clever (or more often fortuitous) positioning of the slit is used to capture
the time dependence of an event at a single location. An example is the study by
Brannon [2016] on the cooling and the subsequent draining of plasma in a flare loop
arcade. In this work, the IRIS slit was positioned so that it intersected multiple loops
across a flare arcade, with the slit spanning nearly from footpoint to footpoint. With
this positioning, Brannon [2016] was able to approximate a single loop from multiple
samples at different positions along the loops in the arcade.
The drawback to this approach by Brannon [2016] is that there is some ambiguity
as to what the compound loop represents due to the spatial sampling of the slit. For
example, it is impossible to tell from this slit positioning whether all of the loops in
the arcade are governed by the same space–time evolution or if independent temporal
and spatial variations in the emitting plasma exist within each individual loop. Some
ambiguity could be removed by rastering across a single loop in its entirety, or a larger
20
portion of the loop arcade, however, the same pitfalls will be encountered regarding
slit geometry and rastering as discussed earlier.
Another drawback of the sit-and-stare method is that the spatial context is
limited by the slit FOV. Take as an example a particular flare ribbon observed by
the IRIS spectrograph. Both Brosius and Daw [2015] and Brannon et al. [2015]
analyzed quasi-periodic intensity and velocity fluctuations in TR emission lines from
this event. However, in part due to the lack of context, the cause of these fluctuations
are difficult to interpret; Brosius and Daw [2015] hypothesize that quasi-periodic
magnetic reconnection or the periodic release of magnetic energy by an external
resonator is the source of the intensity fluctuation. An analysis by Brannon et al.
[2015] of this same region arrived at a different interpretation. Using the IRIS
slit jaw imager for additional context, Brannon et al. [2015] detected a “sawtooth”
substructure in the intensity of the flare ribbon. This substructure was found to
correlate with fluctuations of the Si iv, O iv, and C ii emission lines observed by the
IRIS spectrograph. This leads Brannon et al. [2015] to suggest that the observed
intensity variation is caused by a tearing mode or Kelvin-Helmholtz type instability,
a very different mechanism than that suggested by Brosius and Daw [2015]. Hence,
the limited FOV and lack of spectral context of this event leads to very different
interpretations of the underlying mechanism at work.
There are also solar features that are difficult to fully capture with the current
technology of slit spectrograph. EEs are a particular example. These features are
small enough to be well sampled spatially with only a handful of rasters, but are
difficult to fully observe because of their evolutionary timescales. In the study by
Innes et al. [1997], SUMER took upwards of 60 s to raster across an entire EE. This
timescale is on par with the average EE lifetime [Dere, 1994]. In this case, the
temporal confusion introduced by rastering makes it difficult to ascertain whether
21
the bi-directional jets emanating from an EE result from wholly spatial or temporal
variation. Sit-and stare observation is an alternative strategy, but this risks capturing
a non-representative portion of the EE, similar to the flare study by Brannon [2016].
In the sit-and-stare case, it is difficult to determine the reconnection process behind a
particular EE from only a small spatial sample of the whole event, e.g. imagine trying
to differentiate between Figure 1.4 (a) and (b) from only a small slice through each
diagram. For these reasons, EEs present a tricky target to observe with only a slit
spectrograph.
The examples presented here all serve to outline specific difficulties encountered
in solar observations with slit spectrographs. The limitations are summarized as
follows. The slit geometry is ill-suited to observe complex, extended, dynamic solar
structures. Rastering to build the necessary context introduces temporal and spatial
confusion, and the 1D sit-and-stare observing mode excludes critical nearby spectral
context. These limitations, derived from the examples described herein, suggest a
specific need for a different type of spectrograph.
1.4 Slitless Solar Spectroscopy
The limitations described in the previous section could be resolved by the ability
to quickly build a 3D data cube, or in other words, the ability to perform simultaneous
imaging and spectroscopy over a large 2D FOV. In visible wavelengths, a reasonable
approximation to this type of product is made available by fast-tuneable Fabry–Perot
etalons [e.g. Puschmann et al., 2012]. Unfortunately, materials that are transparent to
VUV wavelengths simply do not exist to extend this technology shortward of ∼150 nm
[e.g. Wuelser et al., 2000]. With this limitation in mind, I describe a different approach
that eliminates the slit from a stigmatic spectrograph.
One of the first VUV slitless spectrographs was flown by the Naval Research
22
Figure 1.7: Left image, EUV spectroheliogram from the NRL sounding rocket. Note
significant overlap exists even for widely spaced emission lines. Right image, grazing-
incidence spectrum that identifies the spectroheliogram images. Images from Tousey
[1986].
23
Laboratory (NRL) as a sounding rocket platform [Tousey, 1986] and later developed
into the SO82A instrument on the Skylab Apollo telescope mount [Tousey et al.,
1977]. An image from the NRL sounding rocket instrument is shown in the top panel
of Figure 1.7; here, the FOV is large enough to capture multiple spectral images of the
entire solar disc and portions of the corona in a single exposure. Each spectral image
corresponds to a different bright EUV emission line (or blended line) identified by
the grazing incidence slit spectrum in the lower panel of Figure 1.7 from a separate
instrument. While this type of instrument does not deliver a complete spectrum
at every pixel, the overall information content of a single image of this type is very
large. For example, from the SO82A spectroheliograms it is possible to derive electron
densities from several density-sensitive emission line ratios (e.g. Ca xvii [Doschek
et al., 1977], Fe ix, [Feldman et al., 1978], Mg vii and Si ix [Keenan et al., 1986]).
As the body of work that emerged from SO82A shows, the major obstacle faced
by slitless spectrographs is image overlap. In Figure 1.7 it is apparent that significant
confusion exists in and near areas where spectral images fall on top of one another;
in some cases, solar features are all but obscured by multiple images. Thus, the large
FOV afforded by a slitless spectrograph comes in trade for an exponential increase in
ambiguity caused by the mixing of spatial and spectral information.
The act of “inversion,” defined here as the recovery of a 3D spatial/spectral
data cube from a 2D projection, presents an ill-posed problem. One can imagine
the difficulty in what is analogous to a tomographic reconstruction problem [Kak
and Slaney, 1988]; i.e. recovering the shape and internal structure of a semi-opaque
3D object from its shadow projected onto a screen. In the case of SO82A, only one
projection of the 3D spatial/spectral solar scene is obtained by the single diffraction
order. In the tomographic analogy, knowledge of the 3D object is improved by
obtaining shadows from multiple different projection angles. Correspondingly, what is
24
sought in slitless spectroscopy is projections from multiple different diffraction orders.
Computed Tomographic Imaging Spectrometers [CTIS, Okamoto and Yamaguchi,
1991, Bulygin et al., 1991, Descour and Dereniak, 1995] leverage this concept
by obtaining multiple, simultaneous dispersed images from upwards of 25 grating
diffraction orders onto a single detector plane [Descour et al., 1997].
There is a practical limit to the maximum number of projections obtained by
a VUV solar slitless spectrograph. The spectral resolution of the CTIS instruments
mentioned earlier is only λ/∆λ ∼ 10, and the wavelength range covered is large
(e.g. all of the visible spectrum, a factor of ∼ 2 in wavelength). To attack the scientific
problems outlined above regarding the energization of the solar atmosphere, a different
approach is needed. Even a small wavelength range (a few percent) will typically have
several spectral lines, perhaps formed at multiple temperatures, and the spectral
resolution required to obtain line profiles is of order λ/∆λ ∼ 10, 000. This suggests a
different arrangement, with large dispersion and widely separated detectors dedicated
to each spectral order or channel. Moreover, a large detector area is needed to obtain a
sufficient FOV with enough spatial resolution to resolve solar features; one projection
per camera is appropriate. The number of cameras is limited by the spacecraft volume;
only a handful of cameras will fit in a typical sounding rocket payload (e.g. Chapter 4).
Thus, the approach of the Multi-Order Solar EUV Spectrograph [MOSES, Kankelborg
and Thomas, 2001, Fox et al., 2010], is to use a single diffraction grating to form
images at three cameras from the m = 0 and ±1 diffraction orders.
Inversion of MOSES data amounts to a limited look-angle tomography problem.
In lieu of additional projections, and in contrast to CTIS type instruments, the
inversion is improved by multilayer EUV mirror coatings that limit the instrument
spectral pass band. In this way, the MOSES inversion space is a priori confined to
the segment of wavelengths surrounding just a few bright emission lines.
25
In the context of VUV solar spectroscopy, what is gained by the addition of
more dispersed orders and the constraint on inversion space is access to higher order
line moments. For example, the bandpass of the first flight of MOSES in 2006 was
centered around the bright He ii emission line. From the MOSES m = +1 and m = 0
orders, Fox et al. [2010] performed a “parallax” analysis by hand-fitting gaussians
to the He ii spectral profile for an isolated event in the MOSES FOV. Changes in
position (line center) and linewidth of the profile between the two image orders are
interpreted as Doppler shifts and broadening of the He ii emission line. This enabled
Fox et al. [2010] to identify this event as an explosive event with a bright core and
distinct, anti-parallel but non-collinear jets. A more extensive investigation of several
EEs in the MOSES He ii data set was performed by Rust and Kankelborg [2019]
using a similar parallax analysis technique. In this work, Rust and Kankelborg [2019]
find at least 10 explosive events with bidirectional jets but a lack of core emission.
This suggests Petschek mode reconnection rather than a tearing mode, in contrast
to Innes et al. [2015]. Due to the large number of EEs identified, the observations
by Rust and Kankelborg [2019] also suggest that EEs may have a greater diversity of
morphology than previously observed by slit spectrographs and that a range of both
tearing mode and Petschek type reconnection modes may be present [e.g. Rust, 2017,
Rust and Kankelborg, 2019].
1.4.1 Challenges of Slitless Spectroscopy
As with any instrument, there is a unique set of difficulties associated with a
slitless spectrograph. MOSES, for example, has three disparate PSFs associated with
each image order [Rust, 2017] that simultaneously obfuscate the spatial and spectral
content of an individual pixel. As a result, any inversion that compares a pair of
MOSES image orders is subject to spectral artifacts caused by the differing image
26
PSFs. For example, spurious low velocity emission observed in the core of some
TR EEs could result from MOSES PSF artifacts [Rust and Kankelborg, 2019]. The
characterization of EEs with MOSES is therefore subject to limitations imposed by
the instrument spatial and spectral resolution, similar to the discussions given for
SUMER and IRIS in Section 1.2. Improving or avoiding such limitations is a major
theme of this dissertation.
In Chapter 2, I describe an alternative method for deriving only Doppler shifts
from a pair of MOSES dispersed images. Conceptually similar to the parallax
techniques described earlier, this method is based on local correlation tracking [LCT,
November and Simon, 1988] to quantify feature shifts along the dispersion axis in the
MOSES images. This work makes use of the PSF characterization by Rust [2017] and
is presented as an alternative method to obtain Doppler shifts from MOSES data.
An advantage of this method is that it is designed to be more robust when faced with
differing image PSFs.
Aside from disparate PSFs, inversion of MOSES data is complicated by other
aspects of the optical design. In Chapter 4, I describe the EUV Snapshot Imaging
Spectrograph (ESIS) instrument, which is a next generation slitless spectrograph
derived from the concept proven by MOSES. In Section 4.2, I give a detailed
comparison of the MOSES and ESIS designs, and the advantages of the new ESIS
concept gained through experience with MOSES.
To conclude this section, it is worth stating that the two spectrometer types
discussed in this chapter (slit- and slitless) are complementary rather than exclusive.
MOSES and ESIS target a small segment of the solar EUV spectrum, containing at
most a few emission lines. The intent of these instruments is to image and recover only
one or two line profiles over a large 2D FOV in this small slice of spectrum. For this
reason, a MOSES type instrument is not likely to discover or identify new spectral
27
lines, or, for example, estimate the density of H2 from relatively weak molecular
hydrogen lines [e.g. Jaeggli et al., 2018] in sunspots. Slit spectrographs that can
unambiguously isolate and resolve large numbers of individual lines, such as HRTS,
SUMER and IRIS, are much better suited to these tasks. Thus, MOSES and ESIS are
designed to uncover the dynamics and evolving morphology of a particular spectral
line spread over a large FOV, while SUMER and IRIS excel at the more classic task
of measuring a spectrum with many lines.
1.5 Summary of Dissertation Chapters
Each chapter that follows is a separate project within a body of work, organized
to reflect the progression of the discussion above. Here, I give a brief summary of the
content of each chapter.
In Chapter 2, I describe an efficient automated method for extracting Doppler
velocities from any pair of (co-temporal) MOSES images. In contrast to the work by
Fox et al. [2010] and Rust [2017], I obtain the Doppler shifted component of the line
profile for every pixel in a MOSES image rather than a limited region, however, this
is at the expense of recovering the higher order line moments. The method is also
insensitive to background, so that Doppler shifts can be diagnosed over the entire
MOSES FOV. This has the potential applications of identifying large-scale or widely
spread small-scale trends in mass and energy flow in MOSES (or ESIS) images.
Chapter 3 details my contributions to calibration/characterization and data
processing efforts of the IRIS observatory. In this work, I used a transit of Mercury
across the Sun to derive on-orbit point spread functions (PSFs) for the near (NUV)
and far ultraviolet (FUV) channels of the IRIS slit-jaw spectrograph. This is the first
on-orbit characterization of the spectrograph spatial resolution. I show that the PSF
in the NUV channel influences interpretation of small scale features (in this case, a
28
small explosive event); in the FUV channels, the instrument PSF does not significantly
influence the interpretation of this same feature. Also developed in this work is a PSF
deconvolution routine to correct the PSF contribution in the IRIS spectra. The PSFs
and a simple deconvolution routine are included in the SolarSoft [Freeland and Handy,
1998] library for public distribution to users of IRIS data.
In Chapter 4 I describe the EUV Snapshot Imaging Spectrograph (ESIS), in
which I had a major design role. ESIS is a sounding rocket based slitless imaging
spectrometer that is the logical continuation of MOSES. In this chapter, I compare
specifics of the ESIS and MOSES instruments, describe the scientific objectives for
the new instrument, and detail how ESIS is designed to meet these objectives. I have
tried to collect as much of the significant details of the ESIS as possible into this
chapter, so that Chapter 4 can serve as a definitive reference for this new instrument.
Finally, this dissertation concludes with Chapter 5, where I present the key
points, relevance and significance, and potential avenues of future study from each of
the three preceding chapters.
29
CHAPTER TWO
USING LOCAL CORRELATION TRACKING TO RECOVER SOLAR
SPECTRAL INFORMATION FROM A SLITLESS SPECTROGRAPH
Contribution of Authors and Co–Authors
Manuscript in Chapter 2
Author: Hans T. Courrier
Contributions: Conceived and implemented study design. Constructed code to
analyze and display data sets. Wrote first draft of the manuscript.
Co–Author: Charles C. Kankelborg
Contributions: Helped to conceive study. Provided guidance regarding analysis and
comments on drafts of the manuscript.
30
Manuscript Information
Hans T. Courrier, Charles C. Kankelborg
Journal of Astronomical Telescopes and Imaging Systems, SPIE
Status of Manuscript:
Prepared for submission to a peer–reviewed journal
Officially submitted to a peer–reviewed journal
Accepted by a peer–reviewed journal
x Published in a peer–reviewed journal
Published by SPIE the international society for optics and photonics
Published January, 2018, JATIS, 4(1), 018001
31
ABSTRACT
The Multi-Order Solar EUV Spectrograph (MOSES) is a sounding rocket
instrument that utilizes a concave spherical diffraction grating to form simultaneous
images in the diffraction orders m = 0, +1, and −1. MOSES is designed to capture
high-resolution co-temporal spectral and spatial information of solar features over a
large 2D field of view.
Our goal is to estimate the Doppler shift as a function of position for every
MOSES exposure. Since the instrument is designed to operate without an entrance
slit, this requires disentangling overlapping spectral and spatial information in the
m = ±1 images. Dispersion in these images leads to a field-dependent displacement
that is proportional to Doppler shift. We identify these Doppler shift induced
displacements for the single bright emission line in the instrument passband by
comparing images from each spectral order.
We demonstrate the use of local correlation tracking as a means to quantify
these differences between a pair of co-temporal image orders. The resulting vector
displacement field is interpreted as a measurement of the Doppler shift. Since three
image orders are available, we generate three Doppler maps from each exposure.
These may be compared to produce an error estimate.
32
2.1 Introduction
The transition region is the portion of the solar atmosphere between the
million degree corona and the much cooler chromosphere. In order to understand
the underlying physical mechanisms that result in this temperature disparity, it is
necessary to characterize the solar atmosphere in the spatial, temporal, and spectral
domains. Spectrographic observations point to a number of mechanisms by which
the corona may be heated. Large scale Alfvénic waves with amplitude ≈20 km s−1
and periods of 100 − 500s have been observed in the transition region and corona
by McIntosh et al. [2011] and are energetic enough to power the quiet corona and
fast solar winds. Magnetic reconnection may also play a part in heating the corona,
[Longcope and Tarr, 2015] and can be observed as spatially compact explosive events
(EEs) in the transition region and upper solar atmosphere [Dere, 1994, Dere et al.,
1991]. These events contrast Alfvén waves with much shorter lifetimes (≈75s) and
Doppler velocities on the order of 100 km s−1 (See Fox et al. [2010], and references
therein). Imaging either of these events with a slit style spectrograph can be
challenging, and is usually the result of a combination of fortuitous positioning of
the spectrograph slit, rastering, and exposure timing.
The Multi-Order Solar EUV Spectrograph (MOSES) [Kankelborg and Thomas,
2001, Fox et al., 2010] is a sounding rocket based snapshot imaging spectrograph.
MOSES obtains high cadence (≈10s) spectral and spatial information simultaneously
over a 20’ x 10’ field of view (FOV) by omitting the entrance slit usually associated
with rastering type spectrometers [Fox et al., 2010]. The high spatial resolution
(0.6” pixels) and large FOV of MOSES makes it possible to capture a multitude
33
of EEs and traveling wave phenomena within a single exposure. MOSES shares
this characteristic with other ground based instruments, such as the Computed
Tomography Imaging Spectrometer (CTIS) [Descour and Dereniak, 1995], and the
ground based observations made by DeForest et al. [2004] using the Advanced Stokes
Polarimeter (ASP) on the Dunn Solar Telescope at the National Solar Observatory.
Much like these two instruments, the increased field of view and temporal resolution
of MOSES comes at a cost. While MOSES can easily obtain co-temporal spectral
and spatial information over a large FOV, disentangling the overlapping spectral and
spatial information in the MOSES dispersed images presents an ill posed inversion
problem.
The MOSES instrument utilizes a concave spherical diffraction grating to form
images of m = 0, +1, and −1 diffraction orders on three 2048 x 1024 rear-illuminated
CCDs. A schematic of the grating and imaging detectors is shown in Fig. 2.1. The top,
center, and bottom detector planes in Fig. 2.1 image the m = +1, 0, and −1 spectral
orders respectively. The spatial axis is the same in all three spectral orders, however
the direction of the dispersion axis is reversed between the m = ±1 orders. The
images formed in these two orders are not redundant. When imaging an object that
has some spectral width, components that are redward of the instrument passband
center (the letter “A” in Fig. 2.1) are shifted away from the m = 0 order CCD in
the m = ±1 order images. Conversely, the blueward components of the object (“B”
in Fig. 2.1) are shifted towards the m = 0 order CCD. There is no dispersion in the
m = 0 order images; intensity in this order is simply a function of position integrated
over the instrument passband. Multilayer coatings and thin film filters limit the
instrument passband to a few spectral lines, the brightest of which is the Lyman
alpha transition of He II at 30.4 nm. More information about instrument specifics
can be found in Fox et al. [2010].
34
Any pair of MOSES spectral orders contains information about Doppler shifts
[Kankelborg and Thomas, 2001]. Fox et al. [2003] proposed a pair of inversion
techniques to solve the ill-posed problem of obtaining a spectrum for each pixel in
a MOSES image. We propose a solution to a better posed problem; estimating
just the Doppler shift from the strong He II line. Most of the solar emission
within the instrument passband comes from this emission line. Doppler shifts are
estimated by cross-correlating corresponding patches of two simultaneous images to
determine a local shift vector. The shift vector component parallel to the image
dispersion direction then corresponds to the Doppler shift. This method is based
on a stereoscopic inversion method described by DeForest et al. [2004] for ground
based magnetography. The Fourier Local Correlation Tracking (FLCT) [Fisher and
Welsch, 2008] routine is employed as a fast and efficient means of performing the cross-
correlation and generating subsequent per pixel vector displacement fields for image
pairs. There are two advantages to performing the inversion with local correlation
tracking; (1) correlation is not affected by differing background levels in image pairs
and (2) the method can track intensity in the dispersed and non-dispersed axis of the
images, allowing some compensation for differing aberration between image orders.
In Sec. 2.2, we prepare a synthetic data set that simulates MOSES flight data. We
use this synthetic data to characterize the spatial and spectral response of the FLCT
method in the context of a MOSES like data set, paying particular attention to
how differing point spread functions in the three spectral orders influence FLCT-
derived Doppler shifts. We then use the results of Sec. 2.2 and FLCT to generate
Dopplergrams of MOSES data collected during the Feb. 2006 flight [Fox et al., 2010]
in Sec. 2.3.
35
Figure 2.1: Schematic diagram of the MOSES instrument. Incident light on the right
forms an undispersed image on the central m = 0 CCD. Dispersed images are formed
on the outboard m = ±1 CCDs.
2.2 Methodology
In this section we demonstrate how we use FLCT to perform the stereoscopic
inversion between image pairs of the MOSES instrument. MOSES has three
diffraction orders that are imaged simultaneously. This results in three independent
image pairs for each exposure; m = 0,+1, m = 0,−1, and m = +1,−1.
The inversion process can be described by three high level operations: (1) FLCT
determines displacement vectors for each pixel in an image pair; (2) the displacement
vector array is converted into a line-of-sight (LOS) velocity array using the known
instrument dispersion; (3) ‘Dopplergrams’ are created by overlaying the color-coded
LOS velocities onto the m = 0 image. In Sec. 2.2.1 we determine the best FLCT
parameters to reconstruct the Doppler velocity from MOSES data, and in Sec. 2.2.2
we investigate artifacts that result from instrument aberration and the FLCT-based
inversion method.
36
2.2.1 FLCT Parameters
FLCT is a computationally efficient implementation of the local correlation
tracking (LCT) method developed by November and Simon [1988] to quantify proper
motion measurements of solar granulation. A variety of LCT techniques have been
developed to infer ‘optical flow’ from brightness patterns in a sequence of solar
images (e.g. Schuck [2006] and references therin). The optical flow is a 2-d field
that, when applied to the scalar field of an image, results in the best reproduction
of the next image in the sequence. In this context, the 2-d field can be used to
estimate velocities perpendicular to the line of sight (LOS). For MOSES, the optical
flow between image orders corresponds to spectral shifts, which we use to estimate
Doppler velocites. The fourier implementation [Fisher and Welsch, 2008] of LCT uses
a fast and straightforward approach that is easily adapted to finding displacements
between MOSES image orders.
Pursuant to its originally intended purpose, FLCT has five input arguments:
(1) amount of time between input images; (2) unit of length of a single pixel; (3)
optional threshold parameter to skip flow calculation for pixels based on input image
intensities; (4) optional low pass filtering parameter applied in the FFT domain;
(5) characteristic width, σ, of a Gaussian windowing function applied to the input
images. To output displacement vectors in pixels from FLCT, we set the ratio of the
first two input arguments equal to unity. The optional threshold and low pass filtering
parameters are not used. In this section we discuss how we threshold FLCT output
and choose the windowing parameter σ to provide the best stereoscopic inversion of
MOSES data.
We choose to threshold FLCT output based on the MOSES m = 0 order
image intensity for two reasons; (1) it places the FLCT-derived displacement vectors
(Doppler shifts) over the m = 0 order image, rather than the abstracted spectrally
37
‘smeared’ images produced by the m = ±1 orders, (2) As we explain below, FLCT
tends to shift the velocity field when comparing m = 0 to m = ±1; thresholding
using m = 0 intensity minimizes this effect. In general, LCT methods track features
by finding the maximum correlation between subsets of two images. Ideally, the
best correlation will be found where the subsets of each image overlap. Hence,
LCT will find a displacement field in between the initial and final locations of a
feature that appears in both images. Since we want to know the physical locations
of Doppler shifts, we require the FLCT-derived displacement field between MOSES
image orders to originate from the m = 0 order intensities. The shift in velocity field
is demonstrated in Fig. 2.2, where FLCT has generated displacement vectors between
two images of identical Gaussians (σ = 2 pixels) using a larger windowing function
with σ = 3. An exaggerated displacement field is created by shifting one image four
pixels horizontally with respect to the other. The dashed box centered over the left
Gaussian marks the nominal correlation window size of 2σ. While correlations are
possible outside of this box, the purpose of the windowing function is to discourage
correlations for comparatively large displacements. In Fig. 2.2 the displacement
vectors are shifted to the right side of this box, to a point in between the two images,
rather than over the left Gaussian. Thresholding Dopplergrams generated from the
two outboard order images based on the zero order intensity helps compensate for
this offset of the Doppler velocities.
The optimal value of σ is largely dependent on the size scales present in our
images [Fisher and Welsch, 2008, DeForest et al., 2004]. MOSES images the solar
transition region, which is highly dynamic. Small compact explosive events (spatial
size on the order of a few MOSES pixels) are associated with Doppler shifts of tens
to hundreds of km s−1 [Dere et al., 1989, Fox et al., 2010]. In general smaller values
of σ result in finer resolution in the displacement field, while larger values are better
38
Figure 2.2: FLCT-generated displacement vectors for a Gaussian that has been
shifted four pixels to the right. The black contour is drawn at half maximum intensity.
The gray contour marks the same and identifies the location of the shifted image. The
dashed box marks 2σ for the FLCT windowing function (σ = 3), centered over the
unshifted image; correlations outside of this box are considered unlikely. Displacement
vectors are scaled to fit within one pixel.
suited to reproducing larger shifts and reduce artifacts due to the differing size of the
PSF for each image order. One major limitation of FLCT (and all local correlation
techniques) is that spatial resolution of the extracted Doppler shift is affected by the
correlation window size [DeForest et al., 2004, Descour and Dereniak, 1995]. This
effect is illustrated by the dashed box in Fig. 2.2, which marks where the Gaussian
windowing function drops below four orders of magnitude for σ = 3. There must be
sufficient features contained within this box for FLCT to derive a displacement vector,
39
as the windowing function makes correlations increasingly unlikely for features that
are located further away. Fortunately the solar transition region is finely structured,
and acknowledging this limitation, we use knowledge of the MOSES instrument
aberration for each image order to set a lower limit for σ.
Figure 2.3: FLCT-generated vs. true displacement between the pair of symmetrically
displaced, identical Gaussian functions described in Fig. 2.2.
FLCT consistently recovers the displacement of correlated features that fall
within the window set by σ. This is shown in Fig. 2.3, where the displacement
between the pair of identical Gaussian functions described earlier is varied from
complete overlap (i.e. zero displacement) in half-pixel increments, then plotted against
the value recovered by FLCT. For all cases, σ = 3. In Figure 2.3, the distribution
of displacements recovered by FLCT is approximately linear between ±6 pixels,
although the magnitude of displacement is consistently undervalued, an artifact of the
40
method noted elsewhere (e.g. Freed et al. [2016], and the references therein). For this
reason, the displacement recovered by FLCT should be considered a lower limit on the
true displacement. For greater than six pixel displacements, the distribution of the
FLCT recovered values quickly becomes unstable, indicating that FLCT is having
difficulty finding the correct correlation when the magnitude of the displacement
exceeds 2σ. Thus, FLCT-derived Doppler shifts that correspond to values of greater
than 2σ pixel displacements should be considered unreliable.
The top row of Fig. 2.4 shows 2D estimates of the MOSES point spread functions
(PSFs) for each image order, estimated by Rust [2015]. A contour is drawn at half
maximum intensity that indicates the size and shape of each PSF. As seen in Fig. 2.4
the three PSFs extend differently over several pixels along the horizontal (dispersed)
and vertical (non-dispersed) axes. The bottom row of Fig. 2.4 shows line spread
functions (LSFs) for the dispersed axis of each image order, obtained by summing over
the vertical axis of the corresponding 2D PSF. The width of each LSF is estimated
by a least-squares Gaussian fit. Modulation Transfer Functions (MTFs) derived from
the LSFs of Fig. 2.4 are plotted in Fig. 2.5. MTFs for normalized Gaussian functions
of σ = 2 and 3 are overplotted in dashed lines. Both Fig. 2.4 and Fig. 2.5 highlight
the differences in imaging quality of the three MOSES image orders.
The disparity in aberration between image orders is a primary consideration in
our selection of two dimensional FLCT as an inversion method. The difference in
aberration between image orders causes intensity information, and thereby spectral
information, to be mapped differently into each of the MOSES image orders. Vertical
displacement between image pairs is wholly a result of instrument aberration, since
this axis is not dispersed. On the other hand, horizontal displacement is due to some
combination of the spectral content of the signal and instrument aberration. We
include the vertical component of displacement, so that signal that has moved in this
41
Figure 2.4: Estimates of the MOSES m = +1, 0, and −1, image order PSFs in
columns (a), (b), and (c), respectively. The contour is drawn at half maximum
intensity for each PSF image in the top row. In the bottom row, line spread functions
are formed by summing along the vertical axis of the PSF image directly above. A
Gaussian with characteristic width σ is fit to each LSF in the bottom panels, and
overplotted as dashed curves.
direction due to PSF differences can be identified and tracked. This is illustrated by
the FLCT-generated displacement vectors for two simplified cases in Fig. 2.6.
In Fig. 2.6(a)- 2.6(c), we estimate the instrument response to a monochromatic
point source with no Doppler shift. In this case the point source is not shifted in the
m = ±1 orders, so that the centroids of the PSF for each image order are co-located.
42
Figure 2.5: MTFs for each of the MOSES image orders, derived from the LSFs of
Fig. 2.4. Overplotted in dashed and dash-dot curves are MTFs of FLCT Gaussian
windowing functions with σ = 2 and 3.
In Fig. 2.6 panel (a) and (b) FLCT draws displacement vectors from the m = 0 to
the m = +1 and −1 image orders respectively, while the vectors are drawn from
the m = +1 to the m = −1 image order in panel (c). In these three panels the
horizontal displacement vectors are near zero where the PSFs overlap in each image
pair. Artificial displacement vectors appear where one PSF extends beyond the other
in each image pair; we investigate this in greater detail in Sec. 2.2.2. A window size of
σ = 3 was used to generate the displacement vectors in all panels, based on the MTFs
from Fig. 2.5. Since FLCT finds a corresponding point in the m = ±1 for every point
in the m = 0 PSF in Fig. 2.6, and similarly for for the m = +1 to m = −1 in panel
(c), we assert that σ = 3 is sufficiently large to resolve this case.
In Fig. 2.6(d)- 2.6(f), FLCT generates displacement vectors for a monochromatic
43
Figure 2.6: FLCT-generated displacement vectors for a point source based on the
PSF estimates of Fig. 2.4. Panels (a)-(c), the signal is monospectral. Panels (d) and
(e), dispersion is added by means of a two pixel redward shift in the m = ±1 orders.
This appears as a four pixel shift in (f) due to the symmetry of the instrument.
point source with a known Doppler shift. Each of these three panels are similar to
the one above, however a 58 km s−1 red shift has been simulated by translating the
m = +1 PSF leftward two pixels in Fig. 2.6 panel (d) and the m = −1 PSF rightward
by the same amount in panel (e). This appears as a four pixel displacement between
PSF centroids in Fig. 2.6 panel (f) due to the symmetry of the instrument. This two
pixel displacement is well reproduced over the whole of the m = 0 PSF in panels (d)
and (e) of Fig. 2.6, albeit with some errors in the non-overlapping portions resulting
from the differing PSF shapes noted earlier. The window size of σ = 3 remains
44
sufficient to resolve this case for the image pairs in these two panels. In Fig. 2.6 panel
(f), FLCT has failed to correlate the upper portion of the m = +1 to the m = −1
PSF. This is due in part to the elongated form and differing orientation of the PSFs
as well as the increased displacement for a given Doppler shift for this image pair.
Experimentation has shown that σ = 5 is a sufficiently large window size to map all
of the intensity of the m = +1 PSF into the m = −1 PSF.
From these two cases we conclude that setting the FLCT window parameter
σ = 3 for the m = 0,+1 and m = 0,−1 image pairs and σ = 5 for the m = +1,−1
provides the optimal resolution for our inversion method.
2.2.2 Inverting Synthetic Data
To investigate how the FLCT-based inversion method recovers Doppler informa-
tion from closely spaced sources, synthetic images that simulate the basic structure
of compact and dynamic events observed by MOSES were generated and analyzed.
Two test cases are considered in panels (a) of Fig. 2.7 and Fig. 2.8; an unresolved, and
marginally resolved case, respectively. For both cases, the synthetic images consist of
adjacent red, blue, and unshifted point sources. Point sources with Doppler shifts are
colored blue or red to indicate direction, while the magnitude of the shift is 29 km s−1
for either direction in accordance with the legends in Fig. 2.7 and Fig. 2.8. In panel
(a) of both Fig. 2.7 and Fig. 2.8 the point source located at (25,11) has zero spectral
linewidth, while the point source at (25,40) has a linewidth of 29 km s−1. These two
test cases help to visualize the combined resolution limits of the imaging system and
inversion method.
To mimic the MOSES instrument response for each image order, the synthetic
images are first convolved with the appropriate PSF estimate from Fig. 2.4. Poisson
noise is then added to each image, resulting in an approximation to compact, dim
45
Figure 2.7: Dopplergrams of synthetic images that mimic the MOSES instrument
response to spatially unresolved point sources. The color indicates line shift in km s−1
while color saturation shows intensity. Panel (a) is the original input image, (b)
is the expected instrument response. Panels (c), (d), and (e), are the inversion
results for each image pair. Horizontal and vertical cuts of each Dopplergram are
(indicated by dashed lines in panels (b)-(e)) plotted with error bars in panels (f) and
(g), respectively. Gray regions plots (f) and (g) indicate where Doppler velocities
have been thresholded out of the Dopplergrams. Inversion results are dominated by
systematic errors from instrument aberration (discussed in the previous section text)
in this case where the point sources are not sufficiently resolved.
46
events observed throughout the field of view of MOSES. The signal to background
for the m = 0 synthetic images is ∼2.9, set in a background with mean of 424 counts.
FLCT is then used to generate displacement vectors for each of the m = 0,+1,
m = 0,−1, and m = +1,−1 image order pairs.
Dopplergrams from each of the image pairs are shown in panels (c)-(e) of Figs. 2.7
and 2.8. The component of the FLCT-derived displacement vectors parallel to the
dispersion axis is converted to LOS velocity by multiplication with the instrument
dispersion. The magnitude of the MOSES dispersion is 29 km s−1 per pixel for the
m = 0,+1 and m = 0,−1 image pairs and 14.5 km s−1 per pixel for the m = +1,−1
image pair. The factor of two in difference in dispersion is due to the anti-symmetry
of dispersion of the m = ±1 image orders noted earlier. Dopplergrams are created
by overlaying color coded LOS velocities from each image pair on the m = 0 order
image. In Figs. 2.7 and 2.8 the Dopplergrams are thresholded by binning the m = 0
order image counts into halves and ignoring those velocities corresponding to the
dimmest half for clarity. Plots (f) and (g) of Figs. 2.7 and 2.8 show horizontal
and vertical cuts through Dopplergrams (b)-(e). The gray background in these two
plots indicate where Doppler velocity has been thresholded in the corresponding
Dopplergrams. Non-thresholded Doppler velocities are shown in these regions to
help characterize systematic errors in the inversion. Error bars indicate estimated
uncertainty in Doppler velocity due to random intensity errors in the data, derived
in Appendix A.
An additional Dopplergram is shown in panel (b) of Figs. 2.7 and 2.8. These
Dopplergrams present the expected distribution of Doppler velocity information of
the synthetic images after convolution with the m = 0 order PSF. The velocity field
displayed on the m = 0 order image, v′(x, y), is derived from the known velocity field,
47
v(x, y), of the synthetic images by
′( ) = I(x, y)v(x, y) ∗ κv x, y , (2.1)
I(x, y) ∗ κ
where I(x, y) is the intensity of the m = 0 order image in counts, κ is the m = 0
order PSF estimate, and ∗ is the convolution operator. Weighting v(x, y) by intensity
prevents the velocity signal from a point source from being ‘diffused’ when convolved
with κ, an unphysical situation since we measure Doppler velocity indirectly via
displacement of the dispersed intensity. This weighting maintains the magnitude
of the (artificial) velocity signal over an extended source, approximating the real
distribution of intensity when convolved with the MOSES PSFs. These ‘ideal’
Dopplergrams then illustrate how the Doppler information encoded into our synthetic
images is distributed in the m = 0 order images.
Contrasting Doppler shifts in sources separated by only one pixel will not be
resolved using FLCT with σ = 3 or σ = 5 window. This is illustrated in Fig. 2.7(c)-
2.7(e), where the inversion is dominated by spurious Doppler shifts resulting from
instrument aberration for all three image pairs. These artifacts appear as red shifts
near the top of the re-imaged point source, and blue shifts near the bottom, in panels
(c)-(e) of Fig. 2.7. For each of the three image pairs, the inversion returns similar
results for all point sources regardless of their spectral content. Comparing Fig. 2.7
(c),(d), and (e) to the ideal Dopplergram in panel (b), there is little correlation in
Doppler velocity except where the orientation of point sources in panel (a) tends to
match the orientation of the inversion artifacts. In Fig. 2.7 panel (f) there is some
correlation with true Doppler velocity near pixel 10, where systematic errors from
the PSFs align well with the Doppler shifted point sources in panel (a), however the
inversion returns spurious shifts for the other two features. This is most notable in
48
Figure 2.8: Dopplergrams with increased spatial separation between spectral point
sources. Panel layout is the same as Fig. 2.7; the original input image is shown in
panel (a). Artifacts contribute to the under- and over-estimation of Doppler velocity
in panels (c), (d), and (e), compared to (b), see text for details.
Fig. 2.7 panel (f), where the extracted Doppler shift is nearly identical for the features
located at pixels 10 and 40, despite the inverted Doppler velocities shown in panel
(a). For this case where the spectral point sources are not well separated, the true
Doppler shifts are overwhelmed by systematic error in the inversion.
49
The inversion method returns more favorable results when the separation
between spectral point sources is increased. This is illustrated in Fig. 2.8 (a) where the
horizontal separation between red and blue shifted point sources is increased to three
pixels horizontally and five pixels vertically. This is still below the spatial resolution
indicated by the MTFs in Fig. 2.5, however the additional spectral information allows
us to resolve the point sources in Fig. 2.8 (a) in most cases. Comparing each of
Fig. 2.8 (c), (d), and (e) to (a), the basic structure of panel (a) is well reproduced by
the inversion of each of the three image pairs. Comparing these same three panels to
Fig. 2.8 (b) shows that the inversion method reproduces the expected distribution
of Doppler velocities, but overestimates the magnitudes. This overestimation of
Doppler magnitude is attributed to the artifacts that result from differing instrument
aberration pointed out in Fig. 2.7.
In Fig. 2.8 panel (f) the Doppler field offset discussed in Sec. 2.2.1 is evident
near pixel 10. For the m = 0,+1 cut, the peak Doppler velocities occur near pixels 9
and 10, while lower peak velocities are reported by the m = 0,−1 cut at pixels 5 and
15. The Doppler field offset tends to smear the recovered Doppler signals together in
the m = 0,−1 cut near pixel 10, resulting in a softening of the transition from red
to blue shift. The inverse is true for the m = 0,+1 cut, as the recovered velocity
field is smeared away from the transition area. The m = −1,+1 cut has a smoother
response and the recovered signal tends to towards the average of the other two cuts
near pixel 10.
The m = 0,+1 image pair does not resolve the Doppler velocities for the feature
centered at pixel (40,11) in Fig. 2.8(a) and pixel 10 in panel (g). This is because the
orientation of the point sources in Fig. 2.8 leads to an unfavorable configuration in
the m = +1 image. In this case convolution with the m = −1 PSF causes the point
sources to nearly overlap in the y-axis in this order, causing this feature to look nearly
50
identical in the m = 0 and m = −1 orders. For this particular orientation of point
sources, the y-axis resolution of the PSFs are the limiting factor. We note that the
Doppler shifts of the opposite feature (pixel (40,40) in Dopplergrams and panel (f),
pixel 40) is well resolved, as the alignment of PSFs is more favorable for this feature.
Despite these shortcomings, Figure 2.8 shows that FLCT is able to at least
qualitatively reproduce Doppler shifts near the resolution limit for two images with
differing PSFs. Moreover, sources separated by three pixels are resolved even when
a σ = 5 FLCT window is used (e.g. Fig. 2.8). In most cases the inversion method
reproduces the general structure of the point sources (i.e. finding the correct sign
of Doppler shift), however systematic errors tend to under- or over-estimate the
magnitude of the Doppler shifts.
2.3 Inverting MOSES Data
In this section, we apply FLCT Doppler estimation to representative images and
features from solar observations obtained with MOSES. The MOSES instrument was
launched February 8, 2006 from White Sands Missile Range, New Mexico. Over the
course of approximately five minutes, 27 exposures were taken above 160 km. Data
from this flight have been dark subtracted, the m = ±1 order images co-aligned to the
m = 0 order, and optical distortion removed from all images. Intensities are in units of
data numbers (DN) per second. Exposures are normalized so that each image has the
same mean DN s−1 as the exposure with least atmospheric absorption, the fourteenth
exposure [Fox, 2011]. We generate Dopplergrams over the entire instrument FOV for
each set of exposures in this image set guided by the results of Sec. 2.2. A value of
σ = 3 is used for the the m = 0,+1 and m = 0,−1 image pairs while σ = 5 for the
m = +1,−1 image pair.
A Dopplergram generated from the m = −1 and 0 orders of the twenty-fourth
51
exposure is shown in Fig. 2.9. In this exposure, the orange boxed feature in Fig. 2.9
is fully developed and has also been analyzed in Fox et al. [2010], Fox [2011]. The
color map is scaled to ±150 km s−1 as the majority of Doppler velocities fall within
this range. Groups of white pixels in the FOV and the band of white pixels across
the left side and top of the image are a result of bad, missing, or saturated pixels in
one or more image orders. The image in Fig. 2.9 exemplifies the co-temporal spectral
and spatial data the MOSES instrument collects over a large field of view within a
single exposure. Several small, isolated features that show characteristics similar to
transition region explosive events [Fox et al., 2010, Dere et al., 1989] appear in these
exposures. Two of these features are shown in the orange and green boxed areas of
Fig. 2.9, and in greater detail in Fig. 2.10 and Fig. 2.11, respectively.
The feature depicted in Fig. 2.10 is the same explosive event analyzed by Fox
et al. [2010]. Our analysis produces similar structure, with the core of the feature
largely red shifted, becoming blue shifted in the lower wing and red shifted near the
tip of the upper wing. Unlike the analysis by Fox et al. [2010], we resolve the upper
wing as mostly blue shifted, only becoming red shifted towards the tip. We also
find the core of the feature to be red shifted. The differing offset of this red shift in
Fig. 2.10 panels (a) and (b) is due to the Doppler field shift, described in Sec. 2.2.1.
Based on our analysis in previous sections, the true position of this red shift is more
closely reproduced in panel (c). Blue shifts are also affected by the Doppler field
offset, leading to a softening of the transition from red to blue in the m = 0,−1 and
m = 0,+1 cuts of Fig. 2.10 panel (d) near pixel 32 and 19, respectively. Despite
these systematic errors, this event appears well resolved by the inversion method as
all three Dopplergrams report similar velocities and structure in Fig. 2.10 panel (d).
The feature depicted in Fig. 2.11 has some hidden complexity. This appears to
be an entirely blue shifted event in the m = −1,+1 Dopplergram, however a red shift
52
Figure 2.9: Top panel, FLCT-generated Dopplergram of a MOSES exposure from
the m = +1 and −1 order images. White pixels are bad or missing data. Orange
and green boxed areas shown in greater detail in Fig. 2.10 and Fig. 2.11 respectively.
Bottom panel, Doppler velocity and intensity legend for the Dopplergram above.
53
Figure 2.10: Dopplergrams of a compact bi-directional explosive event observed by
MOSES (a) +1 & 0, (b) −1 & 0, and (c) ±1 image orders. Diagonal cuts through the
Dopplergrams (panels (a)-(c), dashed lines) are plotted in panel (d). The differing
location in each panel of the red shifted core of this event is an artifact of the inversion
method, discussed in Sec. 2.2.
54
near the center of the feature is registered in both panels (a) and (b) of Fig. 2.11.
This indicates this feature is only partially resolved by our inversion method and
may be a compact version of the event in Fig. 2.10, with a red shifted core and blue
shifted wings extending to the north and south. The Doppler field offset spreads the
red and blue shifts away from the core of the event in Fig. 2.11 panels (a) and (b)
(similar to panels (a) and (b) of the Fig. 2.10), and PSF artifacts may contribute
to overestimation of the peak red and blue shifts. The red shift near center is not
resolved in Fig. 2.11 panel (c) from a combination of unfavorable PSF alignment and
the larger correlation window size in this Dopplergram. The m = 0,+1 and m = 0,−1
velocity cuts in Fig. 2.11 panel (d) show that the red shifts extend nearly to the core
of the feature in each case, also indicating that a red shift may be buried in the core
of this feature.
2.4 Discussion and Conclusions
The MOSES instrument is designed to provide simultaneous imaging and
spectroscopic information in a single snapshot over a wide field of view. To accomplish
this, MOSES collects simultaneous EUV images in three spectral orders of a concave
diffraction grating. Here we have demonstrated, on both synthetic and real data,
the derivation of Dopplergrams from image pairs using local correlation tracking.
Applications of FLCT to actual MOSES data in Sec. 2.3 show some promising
results. Strong events such as those shown in Fig. 2.10 and Fig. 2.11 look broadly
similar whether the Dopplergram is generated from the m = 0,+1, m = 0,−1, or
m = +1,−1 order image pairs. Comparing the features of Fig. 2.11 to the synthetic
images of Fig. 2.8, it is clear that resolving the Doppler shifts of adjacent features
located within one PSF radius (∼3 pixels) is near the limitations of our FLCT-based
method. However, for a σ = 3 and even σ = 5 window, the spatial resolution of our
55
Figure 2.11: Compact explosive event observed by MOSES; panel layout is the same
as Fig. 2.10. Offset red shifts in panels (a) and (b) may indicate this event has
a redshifted core. This red shift is not resolved in panel (c). See text for details.
Horizontal cuts through the Dopplergrams (panels (a)-(c), dashed lines) are plotted
in panel (d).
56
Doppler maps is only modestly degraded in comparison with the original intensity
maps (e.g. panel (d) of Fig. 2.8 in which Doppler shifts are resolved for sources three
and five pixels apart). DeForest et al. [2004] employed a difference of image intensity
integrals along the dispersion axis to capture the finest details. Before we can reach
that level of detail with MOSES data, we will need to apply explicit PSF correction
[Atwood and Kankelborg, 2018]. In Sec. 2.2, we show the origin of systematic errors
that mainly affect poorly resolved structures. Some of these systematic errors are due
to the differing PSFs of each image order. While the inversion method can compensate
for some degree of disparity between PSFs of the image orders, and the three available
Dopplergrams help identify these systematic errors, the method would be improved
treating PSF errors in the data prior to analysis. A procedure that equalizes PSFs
between image orders (e.g. the procedure by Atwood and Kankelborg [2018]) could
reduce or eliminate these systematic errors, and may be preferable to deconvolution
of the PSF estimates.
It is also apparent from Sec. 2.2 that FLCT systematically shifts the locations
of the Doppler shifts. This unfortunately hampers quantitative, pixel-by-pixel
comparison of the Dopplergrams derived from the m = 0,+1, and m = 0,−1 image
orders. It would be helpful to develop a similar algorithm that places the Doppler
shifts (displacement vectors) at the source locations in the m = 0 order image,
rather than between the m = ±1 and m = 0 order images. Once this shortcoming
is addressed, we expect to be able to better assess and improve our Doppler shift
estimates by comparing and perhaps combining results gained from different image
order pairs.
Moving forward, our strategy will be (1) Remove or reduce PSF contributions in
the MOSES data; (2) develop a local correlation tracking algorithm that minimizes
or eliminates the offset of the displacement field; (3) Apply this algorithm to both
57
synthetic and real MOSES data, as we have done in this study.
2.5 Acknowledgements
This work was supported by the NASA Heliophysics Sounding Rocket Program,
grant number NNX14AK71G.
58
CHAPTER THREE
AN ON ORBIT DETERMINATION OF POINT SPREAD FUNCTIONS FOR
THE INTERFACE REGION IMAGING SPECTROGRAPH
Contribution of Authors and Co–Authors
Manuscript in Chapter 3
Author: Hans T. Courrier
Contributions: Conceived and implemented study design. Helped to obtain data
sets. Constructed code to analyze data sets. Wrote first draft of the manuscript.
Co–Author: Charles C. Kankelborg
Contributions: Helped to conceive study. Provided guidance on analysis and
comments on drafts of the manuscript.
Co–Author: Bart De Pontieu
Contributions: Constructed code to obtain data sets. Provided feedback of analysis
and comments on drafts of the manuscript.
Co–Author: Jean-Pierre Wülser
Contributions: Constructed code to obtain data sets. Provided feedback of analysis
and comments on drafts of the manuscript.
59
Manuscript Information
Hans T. Courrier, Charles C. Kankelborg, Bart De Pontieu, Jean-Pierre Wülser
Solar Physics
Status of Manuscript:
Prepared for submission to a peer–reviewed journal
Officially submitted to a peer–reviewed journal
Accepted by a peer–reviewed journal
x Published in a peer–reviewed journal
Published September, 2018, Solar Physics, 293(125)
60
ABSTRACT
Using the 2016 Mercury transit of the Sun, we characterize on orbit spatial
point spread functions (PSFs) for the Near- (NUV) and Far- (FUV) Ultra-Violet
spectrograph channels of NASA’s Interface Region Imaging Spectrograph (IRIS). A
semi-blind Richardson–Lucy deconvolution method is used to estimate PSFs for each
channel. Corresponding estimates of Modulation Transfer Functions (MTFs) indicate
resolution of 2.47 cycles/arcsec in the NUV channel near 2796 Å and 2.55 cycles/arcsec
near 2814 Å. In the short (≈1336 Å) and long (≈1394 Å) wavelength FUV channels,
our MTFs show pixel-limited resolution (3.0 cycles/arcsec). The PSF estimates
perform well under deconvolution, removing or significantly reducing instrument
artifacts in the Mercury transit spectra. The usefulness of the PSFs is demonstrated
in a case study of an isolated explosive event. PSF estimates and deconvolution
routines are provided through a SolarSoft module.
61
3.1 Introduction
Images from a telescope are often well approximated as a convolution of the
real scene with the instrument point spread function [PSF, e.g. Hecht, 1987]. The
PSF describes the response of such an imaging system to a point source of light,
altering the perfect mapping of light from the observed object to the image plane
of the instrument. The PSF and its Fourier amplitude, the MTF, are widely used
for evaluating the performance of a telescope or optical system [e.g., Hecht, 1987,
Goodman, 2005, DeForest et al., 2009].
The Sun is an extended, high-contrast, and (often) finely structured source
in extreme-ultraviolet (EUV) wavelengths [Walker et al., 1988, Golub et al., 1990,
Antolin and Rouppe van der Voort, 2012]. Observations of such scenes may be subtly
smoothed (or blurred) by an instrument PSF, reducing contrast between adjacent
bright and dark features. This can affect many different types of measurements, in
particular those involving feature photometry [DeForest et al., 2009]. For example,
Shearer et al. [2012] found that the PSF scattering wings of the Extreme-UltraViolet
Imager (EUVI) instrument aboard STEREO-B could significantly alter the diag-
nostics of temperature and density in coronal holes on the solar disc. Instrument
artifacts in solar scenes may be significantly reduced through deconvolution when the
PSF is known [e.g., DeForest et al., 2009, Poduval et al., 2013] or by blind methods
where the scene and the PSF are estimated concurrently [Karovska et al., 1994, Golub
et al., 1999]. Therefore, a realistic estimate of the instrument PSF is desirable for
quantitative interpretation of solar observations.
The Interface Region Imaging Spectrograph [IRIS, De Pontieu et al., 2014] is
62
a dual channel solar spectrograph (SG) and slit-jaw imager (SJI) operating in Sun-
synchronous orbit since 27 June 2013. As IRIS is a space based observatory, it is not
subject to atmospheric distortion, or ‘seeing’ effects. Consequently, all contributions
to the IRIS PSFs are due to systematic effects within the observatory e.g., diffraction
from the instrument aperture, surface irregularities of the optics (roughness, scratches,
dust, figuring error), charge diffusion in the CCDs, and instrument pointing drift and
jitter. We infer PSFs along the spatial dimension of the IRIS SG from on orbit
observations. Instrumental blurring can then be significantly reduced or removed by
deconvolving the inferred PSFs from IRIS SG data.
Solar occultations due to planetary transits or solar eclipses provide a sharply
defined shadow that can often be used to characterize the PSF of a Sun-pointed
instrument. Weber et al. [2007] and Wedemeyer-Böhm [2008] fit PSFs to Mercury
transit data observed by the X-ray telescope (XRT), Broadband Filter Imager (BFI)
and the Solar Optical Telescope (SOT) onboard the Hinode spacecraft. DeForest
et al. [2009] constrained semi-empirical PSFs and measured the effect of stray
light in the Transition Region And Coronal Explorer (TRACE) extreme-ultraviolet
(EUV) telescope using Venus transit observations. More recently, Poduval et al.
[2013] characterized the diffuse component of the PSFs for the Atmospheric Imaging
Assembly (AIA) EUV telescopes on board the Solar Dynamics Observatory (SDO)
spacecraft using a lunar occultation of the Sun.
We use the May 2016 Mercury transit to characterize on orbit PSFs for the
IRIS SG. While Mercury’s limb (when occulting the Sun) provides a sharply defined
edge from which a spatial component of the SG PSF may be derived, the region in
Mercury’s shadow is devoid of any significant spectral information. Therefore, we
confine our attention to blurring in the spatial direction only (parallel to the SG
slit) and assume that the PSF is effectively invariant across the passband in each SG
63
channel. The structure of the paper is as follows: In Section 3.2 we describe IRIS, the
data, and processing required for our analysis. Section 3.3 describes model PSFs for
the far ultraviolet (FUV) and near ultraviolet (NUV) SG channels, and the semi-blind
deconvolution process we use to derive NUV PSF estimates. In Section 3.4 we present
these estimates and discuss their applications with representative deconvolved data.
We conclude by summarizing the characteristics of our PSF estimates and present
deconvolved spectra in Section 3.5.
The PSFs determined here are distributed via SolarSoft [SSW, Freeland and
Handy, 1998] with a deconvolution routine, iris sg deconvolve.pro, suitable for
direct application to IRIS SG Level 2 data.
3.2 Instrument and Data Selection
The IRIS instrument uses a Czerny–Turner style spectrograph and a slit-jaw
imager (SJI) to obtain solar images and spectral information over a range of ultraviolet
(UV) wavelengths. The SG and SJI instruments are fed by a single 19 cm Cassegrain
telescope [Podgorski et al., 2012]. A slit prism at the focus of the telescope separates
incoming light into three light paths: SG FUV (short, 1332 – 1358 Å, and long, 1389 –
1407 Å, channels), SG NUV (2783 – 2835 Å channel), and SJI channel. Spectra and
images are obtained by four 2061 × 1056 pixel CCDs. The field of view (FOV) of
the SG slit is 0.33′′ × 175′′. SG rasters are created by scanning the active secondary
mirror of the Cassegrain telescope, for a maximum raster FOV of 130′′ × 175′′. Each
13 µm pixel of the SG CCDs subtends 0.167′′ spatially and 12.8 mÅ (FUV) or 25.5 mÅ
(NUV) spectrally.
Level 2 IRIS data are available for download from the Lockheed Martin Solar
and Astrophysics Laboratory (LMSAL: https://iris.lmsal.com/data.html) and
are considered the standard science product. The Level 2 data are 32-bit floating
64
point numbers. Processing IRIS data to Level 2 includes removing overscan rows,
reorienting images to common axes, removing dark currents and pedestal, flat fielding,
applying geometric and wavelength calibrations, mapping images to a common plate
scale, subtracting FUV background, and recasting images into rasters (SG) and time
series (SJI) [De Pontieu et al., 2014]. The level 2 SG data may further be subdivided
into spectral regions, or “windows,” corresponding to a spectral line list that reads
out only a portion of the CCDs at the time of observation. The spectral regions are
denoted by the emission or photospheric reference line wavelength they encompass
[e.g. 1336, 1394, 1403, 2796 and 2814 Å; De Pontieu et al., 2014]. IRIS observed the
Mercury transit using a full readout for 15 s exposures and a small linelist otherwise
(see e.g. Table 3.1).
Figure 3.1: Panel (a), IRIS 2796 Å slit-jaw image of Mercury transit. Mercury is
the dark shadow near center, the dark vertical line through the center of the image
is the spectrograph slit. Panel (b), corresponding full NUV spectrograph readout.
Mercury’s shadow is the dark horizontal band across spatial pixels ≈490 to 570. Thin
horizontal dark lines near spatial pixels 240 and 775 are fiducial marks on the slit.
Solid white box outlines data analyzed for the 2796 Å window; dashed box is the same
for 2814 Å window. The vertical extent of both boxes is sized to exclude the fiducials.
65
On 09 May 2016, as seen from Earth, Mercury transited across the solar disc
from ≈10:50-19:00 UTC, moving from east to west. IRIS imaged the entire transit
in ≈50 minute increments, the length of time required for Mercury to travel across
the SJI FOV. Approximately 10 minutes of observing time was missed between each
increment, while the spacecraft changed pointing to keep Mercury in the SJI field of
view. The SG slit was oriented parallel to the solar north–south axis for the duration
of the transit, so that Mercury crossed the slit at least once during each pointing.
Figure 3.1 panel (a) shows a typical 2796 Å SJI image during the transit. The SG slit
is visible as a dark vertical line, passing through the shadow of Mercury near center
of Figure 3.1 (a).
Table 3.1: IRIS Mercury transit observations.
Data Set Obs. Period Exposure Max. Occultation Notes
UTC # of exps. len. (s) Index UTC
1 10:50:08–11:34:59 514 4 287 11:15:14 Sit & stare, SL
2 11:44:39–12:23:44 448 4 226 12:04:24 Sit & stare, Rot. track, SL
3 12:33:44–13:06:00 600 2 380 12:54:12 Sit & stare, Rot. track, SL
4 13:16:31–13:54:53 140 15 74 13:36:57 Sit & stare, Rot. track, FR
5 14:04:46–14:48:34 502 4 293 14:30:23 Sit & stare, Rot. track, SL
6 14:59:55–15:26:08 96 15 62 15:17:02 Raster, FR
7 15:36:23–16:20:57 512 4 264 15:59:24 Sit & stare, Rot. track, SL
8 16:31:03–17:10:31 144 15 72 16:50:55 Sit & stare, Rot. track, FR
9a 17:25:48–18:00:41 400 4 0 17:25:48 Raster, SL, †
9b 1 17:25:53
9c 2 17:25:58
9d 4 17:26:09
9e 6 17:26:19
9f 8 17:26:30
10 18:10:41–19:00:57 576 4 337 18:40:09 Sit & stare, W1
SL: Small line list: 1336 (C ii) and 1403 (Si iv), NUV: 2796 (Mg ii k), and 2814 Å.
FR: Full readout. To maintain consistency between data sets, we analyze only the portions
of the NUV spectra that overlap with the windows listed in SL from the full readouts.
† Raster motion closely matched that of Mercury at the start of data set 9, therefore
maximum occultation was imaged multiple times in this data set.
From the 10 sets of observations IRIS made during the transit, only a handful
of spectra were suitable for estimating the SG PSF. Spectra were selected in which
66
the signal-to-background ratio (SBR) was large enough so that both limbs on either
side of Mercury were sharp and well defined. The observing period, exposure length,
location of maximum occultation, and observing notes are listed in Table 3.1 for each
of the 10 SG data sets. To minimize the contribution of Mercury’s motion to the PSF,
we selected only the spectra from each data set where the occultation by Mercury’s
shadow was maximized over the slit. Except for data set 9, Mercury crossed the SG
slit once in each data set. In data set 9, the raster motion tracked Mercury for several
frames at the beginning of the observation, resulting in six occurrences of maximum
occultation.
The selection criteria were met by data sets 2 through 9 in the NUV channel.
Data sets 1 and 10 were ignored because the shadow of Mercury was partially off
the solar disc when imaged by the SG. For the off-disc portion of Mercury, SBR is
insufficient to present a well-defined limb in the NUV spectra. Figure 3.1 panel (b)
shows the full readout NUV CCD spectrum from data set 4; residual intensity from
the instrument PSF is clearly seen where Mercury’s shadow crosses the Mg ii doublet.
From the full NUV readouts (data sets 4, 6, and 8), we select only the spectral regions
that correspond to the 2814 Å and 2796 Å windows (see Section 3.2.1) to maintain
consistency across all data sets. Of the NUV windows, 14 suitable spectra were
obtained for both the 2814 Å and the 2796 Å windows.
For the FUV windows (1403, 1394, and 1336 Å), only the three 15 s exposures
(data sets 4, 6, and 8) from the 1394 Å and 1336 Å windows had sufficient SBR to
present well-defined limbs of the shadow of Mercury. Fewer data sets in FUV spectra
meet the selection criteria because quiet Sun and active region intensity in the FUV
[i.e., C ii, Si iv, and O iv, Vernazza and Reeves, 1978, Cook et al., 1995] is weaker
than that of the NUV [Mg ii and NUV continuum, Morrill and Korendyke, 2008,
Staath and Lemaire, 1995]. For this reason, and because SG throughput decreases
67
with wavelength [De Pontieu et al., 2014], SBR is sufficient only in the data sets with
the longest (15 s) integration times. We also note that in two of the three FUV data
sets, the north limb of Mercury is over a region of bright plage (see, e.g., Figure 3.3).
This results in significantly greater contrast at the north limb compared to the south
limb.
We modify the NUV and FUV spectra selected above for input to our semi-blind
deconvolution routine. Preparation of the data differs slightly between the NUV and
FUV cases, largely due to the lower SBR of the FUV data. In the following subsections
we first describe reduction of the NUV spectra, then we describe the differences in
this process for the FUV spectra.
3.2.1 NUV Data Reduction
IRIS SG images contain fiducial markings to aid in the geometric alignment of
the spectra. These markings are gaps in the slit, and appear as two dark horizontal
bands in the spectra (see, e.g., Figure 3.1 panel (b) near spatial Y pixels 240 and
775). Since the slit prism is placed after the telescope optics, the images of the
fiducial markings formed on the SG CCDs are not affected by aberrations inherent to
the telescope. The PSF in the region of the fiducial markings is therefore narrower. To
prevent biasing the PSF estimate, we cropped the fiducial markings from each transit
spectrum. A buffer region of several pixels adjacent to each fiducial is removed, the
size of which varies so that the shadow of Mercury is centered in the image frame.
We reduce the data to 1D by spectrally summing the transit images. There are
two advantages to performing this sum; (1) our task is reduced to finding a PSF in
one dimension instead of two, and (2) the signal-to-noise ratio (SNR) is improved
for the summed data set. In the NUV the presence of continuum in the spectrum
contributes to the overall signal level, so we include the entire window in the sum.
68
Figure 3.2: Reduced data from set 5. Vertical dashed lines mark Mercury limbs.
Data are summed over the 232 spectral pixels in this 2796 Å window, the horizontal
extent of the solid white box in Figure 3.1 panel (b). Fiducial markings are removed
by cropping data.
Data analyzed in the NUV windows is outlined by dashed (2814 Å) and solid (2796 Å)
boxes in Figure 3.1 spanning 103 and 232 spectral pixels, respectively. There are two
underlying assumptions in our choice to sum over wavelength. The range of reflection
angles across the spectral window is small, so we assume that any variation in the
PSF with respect to wavelength over the range of a spectral window is small enough
to be ignored. This assumption is supported by the nearly identical PSFs in each of
the two FUV and NUV windows, estimated independently by our Fourier model in
Section 3.3 and our results in Section 3.4. The second assumption is that dispersion
is oriented precisely along the pixel rows (i.e. the x-axis, or dispersion axis, of the
spectra). This applies only to IRIS Level 1.5 data and higher, in which the small
instrumental misalignment of the spectrum to the SG CCDs has been corrected for
69
[De Pontieu et al., 2014]. We have also verified by hand that the fiducial markings
are aligned precisely row-wise within each spectral window.
As part of the Level 1.5 processing, the IRIS spectra are warped by a second order
polynomial so that the spatial and spectral dimensions are rectilinear with respect
to the CCD pixel grid [Jaeggli, 2016]. The geometric correction varies in time and
space. A side effect of the image warping (i.e. geometric correction) is that sub-pixel
shifts result in varying attenuation of high spatial frequencies. Since the correction is
small, the offset from the original to the corrected grid of pixels varies slowly across
the CCD. For the worst case of a half-pixel shift, the Nyquist frequency is completely
lost. In the spatial dimension, the result is a periodic blurring. The phase of this
periodic blurring varies image-to-image due to temporal alignment variations in the
instrument. By summing along the spectral axis, we have averaged the best and
worse cases of this blurring in each image.
3.2.1.1 Estimation of Mercury’s limb The reduced version of the solid white box
in Figure 3.1 panel (b) is plotted in Figure 3.2; the vertical dashed lines mark the
locations of Mercury’s limbs. The limbs are located by finding the spatial locations
of maximum and minimum derivatives of the reduced spectra intensity in a region
that encompasses the entire shadow of Mercury. The derivative is computed using
centered differencing,
dI ∣∣∣∣∣ = I(yi+1)− I(yi−1) , (3.1)dy = yi+1 − yy y i−1i
where I(y) is the summed intensity at pixel y in the reduced data. Errors in limb
location of at least ±1 pixel are expected from discretization; noise in the data may
increase this uncertainty. Only approximate locations of the limbs are needed to
constrain the semi-blind deconvolution described in Section 3.3.2. Except data sets
5 and 7, we find the locations of the limbs to be consistent between the two NUV
70
windows using this method. For these two data sets, the north limb is displaced one
pixel northward in the 2796 Å window when compared to the 2814 Å window. From
the limb locations we find that Mercury’s shadow spans 72–73 pixels, or an angular
diameter of 12–12.2′′. For comparison, the angular diameter of Mercury, when viewed
from Earth, was estimated to subtend 12.1′′ during the time of the transit[U.S. G.P.O.,
2015].
3.2.2 FUV Data Reduction
The FUV data reduction proceeds in a similar fashion as the NUV, but with
notable modifications described below.
The continuum signal is absent in the FUV. The pixels between the bright
emission lines contain only background and readout noise. We therefore sum over
only the bright FUV spectral pixels outlined by the dashed boxes in Figure 3.3 panels
(b) and (c).
Contrast is insufficient to locate the limb using the derivative method. We select
the limb locations of the 2814 Å window as the reference for the FUV data sets. Using
the co-alignment performed between spectral windows during Level 2 processing, the
limb locations are transferred to the FUV windows.
We find the mean intensity in Mercury’s shadow is negative in several of the data
sets. This could be a result of small errors in the dark subtraction, which are amplified
by spectral summing. To correct this, we estimate the offset error by computing the
mean per-pixel intensity in no-signal regions of Mercury’s shadow in the FUV data
sets. These regions are outlined by solid black boxes in (b) and (c) of Figure 3.3.
We find offset error values that range from −0.03 to 0.06 DN (1394 Å) and −0.04 to
−0.18 DN (1336 Å). We correct these intensity errors by adding a DC offset to the
FUV data sets. The value of the DC offset is such that the mean per-pixel intensity
71
Figure 3.3: (a) 1330 Å SJI context image of Mercury transit. (b) and (c), full readout
of data set 4 in the two FUV channels 1394 Å and 1336 Å windows, respectively. Only
the spectral lines enclosed by the black dotted boxes are analyzed to maximize SBR.
Dark subtraction error is estimated by no-signal pixels in Mercury’s shadow, enclosed
by the black solid boxes. Intensity is logarithmically scaled in all panels; SG images
are displayed in inverse gray scale.
in the regions outlined in Figure 3.3 (b) and (c) is zeroed.
3.3 PSF Estimation
We estimate the IRIS SFG PSFs using a modified blind iterative deconvolution
(BID) technique, in contrast to the parameterized and semi-empirical methods
referenced in Section 3.1. BID typically refers to a technique first developed by
Ayers and Dainty [1988]; however, it can refer to any image restoration technique in
which both the un-degraded image and its degrading function (typically the PSF) are
unknown. BID techniques are most often used when a priori knowledge is limited
to only non-negativity of the images. For example, the Ayers and Dainty [1988]
method was subsequently used to derive PSFs and deconvolve images from Skylab
and Yohkoh data [Karovska et al., 1994], and to estimate the on orbit PSF for the
TRACE instrument [Golub et al., 1999].
72
Determining PSFs using BID techniques presents an ill-posed problem. Param-
eterizing the PSF may be considered a more robust approach [DeForest et al., 2009];
however, the BID method can be improved by incorporating a priori information
[Fish et al., 1995] resulting in the ‘semi-blind’ description of the modified BID
technique. We find that the IRIS Mercury transit data lends itself well to this
particular type of analysis. In much of our data, solar features immediately behind
Mercury’s limb are not uniformly illuminated (see, e.g., either side of Mercury’s
shadow in Figure 3.2). As a result, the data are not well approximated by a step
function precluding a similar analysis such as performed by Weber et al. [2007] and
Wedemeyer-Böhm [2008]. DeForest et al. [2009] and Poduval et al. [2013] used
scattered light in the interior shadows of occultations by Venus and the Moon to
semi-empirically constrain stray light PSFs for the TRACE and the AIA assembly
aboard SDO. This form of analysis is largely concerned with scattering wings so that
detailed information on the core structure of the PSFs is excluded. Since we have no
a priori knowledge of the IRIS PSF, we find BID is better suited to our purposes
since we can estimate the entire PSF from the same data set. Knowledge of the core
structure of the PSF allows us to investigate the resolution of the SG (Section 3.4)
and ultimately may influence the fine structure that we observe in the IRIS data.
A further advantage of a BID approach is that our PSF model is not constrained
by a small number of parameters. IRIS operates close to the diffraction limit so
that the core of the SG PSF may show significant structure, such as side lobes or
asymmetry (see, e.g., Figures 3.4 and 3.7). The parameterized models referenced
earlier cannot reproduce either of these structures, so by using BID we are free to
find features that we may not have guessed in advance. This allows us to derive a
PSF that is consistent with the data at hand.
For the above reasons, we feel that a BID method of estimating the IRIS PSFs is
73
advantageous over a parameterized model. We base our BID on the Richardson–Lucy
algorithm (see Equation 3.3), as this method has proven robust in the presence of noise
[Fish et al., 1995]. In the remainder of this section we describe initialization (and how
we include a priori information), the iterative routine, and stopping criterion for our
semi-blind deconvolution method.
3.3.1 Initial Guesses
Before we begin the process of deconvolution to determine the PSF, we must
prepare initial guesses both for the ideal deconvolved data and for the PSF. In
both cases, we will make use of prior information. For that reason, we describe
the deconvolution as semi-blind.
3.3.1.1 Mercury’s Shadow Since Mercury is opaque, Mercury’s shadow during
the solar transit will contain no UV radiation. Ideally, the limb of Mercury should
have a ‘hard’ edge in the SG spectra, where the signal drops abruptly to zero in the
shadow region. In the observed spectra, the SG PSF softens this edge and causes
residual intensity to appear in the shadow of Mercury (see, e.g., Figures 3.1, 3.2, and
3.5), indicating some level of scattered light is present in all spectral windows.
As an initial guess for the NUV deconvolved scene, we modify the reduced data
set by setting all pixels to zero between limb locations. The two pixels at the limbs
are not set to zero, to allow for subpixel location of the limb. Since the semi-blind
deconvolution is a multiplicative process of the initial guess (see, e.g., Equation 3.2
and 3.3), any pixel that is initially set to zero will remain unchanged after each
iteration. This initial guess therefore enforces the prior knowledge that the scene
should contain no light in the shadow of Mercury.
In the FUV, low SNR results in some negative intensity values. Convergence of
the Richardson–Lucy algorithm is neither desirable nor possible in this case [Lucy,
74
1974]. To counter this, we add a positive DC offset to the FUV reduced data. The
pixels in Mercury’s shadow are then forced to the value of the DC offset after each
iteration, rather than zero as in the NUV case discussed above. The magnitude of the
offset is arbitrary; it only needs to be large enough so that negative noise pixels are
not ‘clipped’ at zero. We choose a value of 103 DN, which is ample margin to prevent
clipping. The offset is subtracted after deconvolution to yield an unbiased estimate
of the deconvolved scene.
3.3.1.2 Model PSFs Using the theory of Fraunhofer diffraction [e.g. Goodman,
2005, pg. 74, or similar references], we calculate the diffraction pattern of the
Cassegrain telescope aperture at the emission line wavelength for each of the four
spectral windows. We reduce this 2D pattern to a 1D spatial PSF by summing
along the axis parallel to the dispersion direction of the instrument. Spatial PSFs
for the NUV and FUV windows are plotted in Figure 3.4. The diffraction caused
by Mercury’s limb has also been considered; appendix B demonstrates that this
diffraction pattern does not affect the PSFs estimated herein. The log plots of
Figure 3.4 clearly show side lobes in the wings of the model PSFs. The side lobes are
a result of the fringes of the diffraction pattern from the telescope entrance aperture,
including central obscuration and spiders. For the remainder of this report, we define
the core of the PSF as the radius extending to five pixels on either side of the individual
PSF peak value. The output of the semi-blind deconvolution depends on the initial
PSF choice, and in Section 3.4 we consider an alternate initialization.
Deconvolving the model PSFs from the reduced data gives an indication of the
SG performance compared to the diffraction-limited case. In Figure 3.5, model PSFs
are deconvolved from the reduced data and overplotted (solid curves) on the reduced
data (dashed curves). The iterative Richardson–Lucy algorithm is used to perform
75
Figure 3.4: Diffraction limit model PSFs for the IRIS Cassegrain telescope. Top
panels show the core (a) and wings (b, log scale plot) of the NUV 2814 Å PSF.
Remaining panels depict the same for the (c, d) NUV 2796 Å , (e, f) FUV 1394 Å ,
and (g, h) 1336 Å windows.
the deconvolution. This method of deconvolution corrects large deviations from the
true scene in relatively few iterations; further iterations result in small corrections
76
Figure 3.5: Model PSFs deconvolved from reduced data (solid curves), with original
overplotted (dashed curves). Panel (a) shows NUV 2814 Å window, (b) NUV 2796 Å
(c) FUV 1394 Å, and (d) FUV 1336 Å. Mean residual intensity in Mercury’s shadow
after deconvolution is plotted as the dotted curve in each panel.
77
that slowly tend to match the statistical fluctuations in the observed scene [i.e.,
noise, e.g. Lucy, 1974]. For this reason, a cost function is typically used to truncate
iterations. Often this takes the form of a χ2 goodness of fit between the observed
scene and a forward model consisting of the deconvolved scene re-convolved with
the PSF. For our purposes, we use a modified form of the Kullback–Leibler (KL)
divergence [Bertero et al., 2009] as the cost function, so that negative pixels may be
handled in the same way as Section 3.3.1.1. To prevent fitting to noise, we truncate
iterations when the derivative of the KL divergence is ≈ zero. Experimentally, we
find 50 iterations in NUV and 9–10 iterations in FUV windows are sufficient to meet
this criterion.
In the NUV channel, the effect of deconvolution is evident in panels (a) and (b)
of Figure 3.5. Residual intensity is clearly greater than zero in these panels, indicating
not enough energy is present in the wings of the NUV model PSFs. The core of the
NUV model PSFs also needs correction, as prominent ’shoulders’ are still evident at
Mercury’s limb after deconvolution. In panels (c) and (d) of Figure 3.5, deconvolution
of the diffraction-limited PSF results in little change for the two FUV spectra. Some
sharpening of the north limb is evident (e.g. near pixel 560 in panels (c) and (d) in
Figure 3.5); however, residual intensity (dotted line, refer to Section 3.3.2) remains
slightly greater than zero in the shadow of Mercury. Mercury’s limb is sharpened,
and scattered light is reduced in both SG channels by deconvolving the model PSFs;
however, Figure 3.5 clearly shows that the model PSFs are inadequate at describing
the SG performance in the NUV channel. The effectiveness of the FUV model PSFs
are more difficult to discern due to lower SBR in this channel.
78
3.3.2 Semi-blind Deconvolution
PSFs were estimated using an iterative blind deconvolution routine to simultane-
ously estimate the PSF and the deconvolved image. We consider our implementation
to be a semi-blind method, since a priori knowledge of both the diffraction-limited
form of the instrument PSF and the complete opacity of Mercury are incorporated
into the first iteration of the routine by the initial guesses described previously.
The deconvolution routine consists of alternating applications of Richardson–Lucy
deconvolutions [Richardson, 1972, Lucy, 1974], expressed as
[( ′ ) ]
i+1( ) = c (y)g y ( ) ( ) ∗ f
i(−y) · gi(y) , (3.2)
gi y ∗ f i y
[( ′ ) ]
f i+1(y) = c (y) i+1 i
f i( ∗ g (−y) · f (y) , (3.3)y) ∗ gi+1(y)
where g(y) is the PSF, f(y) is the deconvolved image, c′(y) is the original (detrended)
degraded image, y is spatial position in IRIS pixels, i is iteration number, and ∗ is
the convolution operator [Fish et al., 1995]. One iteration consists of one evaluation
of Equation 3.2 to find the next PSF estimate, gi+1(y), followed by one evaluation of
Equation 3.3 to find the next deconvolved image, f i+1(y) [Holmes, 1992]. Integration
of Equation 3.3 shows that the total flux is conserved. Conservation of flux is enforced
in Equation 3.2 by re-normalizing gi(y) after each iteration. Iterations are started with
the guesses from Section 3.3.1.1 and Section 3.3.1.2 for f 0(y) and g0(y), respectively.
The convolution operations in Equations 3.2 and 3.3 are performed in Fourier
space for computational efficiency. To reduce contamination from edge effects, we
79
detrend the reduced data. For the left edge of c(y), we write this as
 [ ] [ ]2 πy 2 πy
c′  µ cos 2 + c(y) sin , 0 ≤ y ≤ a( ) =  a 2ay , (3.4)c(y) , y > a
where µ is the mean of the two endpoints of c(y) and a is the number of pixels the
smoothing extends from the edge of the data. A similar treatment is applied to the
right edge (see, e.g., Figure 3.2). We set a = 30, the geometric mean of the PSF half
width (five pixels) and the length of data from the left edge to Mercury’s limb (≈ 175
pixels). To prevent a symmetric bias in the data, we pad c′(y) to twice its original
length with the value of µ and zero pad gi(y) to match.
3.3.3 Stopping Criterion
Figure 3.6: Log plot of cost functions for the (a) NUV 2814 Å, (b) NUV 2796 Å, and
(c) FUV 1336 (solid) and 1394 Å (dashed) windows. The cost function is a measure
of residual intensity in Mercury’s shadow. Iterations are truncated when the cost
function reaches zero.
Since the Richardson–Lucy process is an iterative approximation to decon-
volution [Lucy, 1974], iterations are truncated when a stopping criterion is met.
The stopping criterion is typically derived from a cost function that quantifies
80
the difference between the observed data and a forward model formed from the
deconvolved function and the PSF. This function may take different forms depending
on the application [e.g., Richichi, 1989, Fish et al., 1995, Bertero et al., 2009, and
the references therein]. For our cost function we choose the mean value of residual
intensity in the shadow of Mercury, since a priori it is known that this value is zero
in the ideal case. We write this function as
∑ [ ]N
Ci = 1[ + 1] F
−1 F [c(yk)]
N − n k=n F [gi(yk)]
, (3.5)
where F (F−1) is the (inverse) Fourier transform, c(yk) is the original degraded data,
and k runs only over those pixels between the south (n) and north (N) limbs of
Mercury’s shadow. The deconvolution is performed as division in Fourier space, so
that non-negativity is not inherently enforced. This results in an unbiased estimate
of the mean shadow intensity. Iteration of the semi-blind deconvolution is truncated
when Ci < 0 so that the previous PSF, gi−1(yk), is the best estimate that does not
over-deconvolve the data. In Figure 3.6 we plot cost functions for all data sets. In
every case the cost function reaches a zero-crossing, so that the moment of convergence
is well defined.
3.4 Results and Discussion
Figure 3.7 displays normalized PSFs for the selected data sets (light gray curves
in plots) of the NUV and FUV spectral windows. In each panel of Figure 3.7, the
black curve is the mean of PSFs in that spectral window. We take the mean as
the best PSF estimate for the two NUV windows, since it preserves normalization
while reducing the noise in the wings of the PSFs. We note that the two NUV
PSF estimates show similar core (panels (a) and (c), Figure 3.7) and wing structures
81
Figure 3.7: PSF estimates from the semi-blind Richardson–Lucy routine for the (a,
b) 2814 Å, (c, d) 2796 Å, (e, f) 1394 Å, and (g, h) 1336 Å observation windows. Gray
curves represent the estimate(s) from data sets 2–9 for the NUV and 4, 6, and 8 for
the FUV windows. The mean value PSF is overplotted as a black curve in each panel.
Variation in the left wing of (f) and (h) results from low contrast in quiet Sun area
south of Mercury, see text for details.
82
(panels (b) and (d), Figure 3.7) despite being derived from different spectral windows.
The similarities between the NUV PSF estimates conforms to our expectation that
the PSF should not change significantly over a short wavelength range. We assume
that any differences between the two NUV PSFs are due to random error.
For the FUV 1394 Å and 1336 Å windows (panels (e) and (g) of Figure 3.7,
respectively), the mean PSFs also display similar core structure. In data sets 4 and
6, the southern limb of Mercury is positioned over a region of quiet Sun. Lower
solar emission in this region reduces the contrast of this limb in these two data sets.
In Figures 3.7 (f) and (h), this manifests as significant variation in the left wing
of the FUV PSFs. To remove the uncertainty, we assume the FUV PSF wings are
symmetric. We replace the left wing of the mean PSF in both FUV spectral windows
(pixels < −5, panels (f) and (h) Figure 3.7) with a mirrored version of its right wing
(pixels > 5), then renormalize the result to unity (e.g., (f) and (h) in Figure 3.14).
Comparing (a–d) of Figure 3.7 to the same panels in Figure 3.4, we find
that our NUV PSF estimates have more distinct, asymmetric side lobes than the
diffraction-limited case. The wings of the NUV PSF estimates are also flatter, which
indicates more light is scattered in the NUV channel than the diffraction-limited case.
Comparing panels (e–h) of Figure 3.7 and Figure 3.4 we do not find side lobes in the
FUV PSF cores; however, wing structure is very similar in both cases.
Table 3.2: PSF energy distribution.
Window Diff. Model PSF Estimate
(Å) Core Wings Core Wings PLSR
2814 0.898 0.102 0.815±0.003 0.185 0.725±0.003
2796 0.899 0.101 0.789±0.010 0.211 0.652+0.008−0.010
1394 0.954 0.046 0.951+0.003−0 078 0.049 0.975+0.025. −0.098
1336 0.957 0.043 0.939+0.015 +0.066−0.041 0.061 0.928−0.052
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Figure 3.8: Cumulative total energy for the NUV (a) 2814 Å, (b) 2796 Å, FUV (c)
1394 Å, and (d) 1336 Å windows. Total energy is calculated between horizontal line
pairs, solid for diffraction limit PSFs and dashed for PSF estimates. NUV plots (a
and b) show similar asymmetric energy distributions.
84
Table 3.2 lists the wing and core energies for the diffraction limit and PSF
estimates. The error ranges reported in Table 3.2 reflect uncertainties in dark
subtraction. If the dark signal is overestimated, then after subtraction the signal
will be low, and the method will underestimate the core width of the PSF. Low signal
also reduces the residual intensity in Mercury’s shadow, causing the cost function to
truncate iterations early. In general, as the iterations proceed, flux migrates from
the PSF core to the tails. Consequently, an overestimate in dark signal results
in an underestimate in scattered light. The inverse is true if the dark signal is
underestimated. In the NUV channel, dark subtraction uncertainty is ±0.1 DN per
pixel [Wülser et al., 2018]. For the FUV channels, lower SBR means that the offset
error must be asymmetrically bounded so that residual intensity in Mercury’s shadow
is not reduced below zero (clearly an unphysical situation). For an underestimate of
dark subtraction, we use the greater of the maximum magnitude of offset error noted
in Section 3.2.2 or the per-pixel residual intensity in Mercury’s shadow in each FUV
channel. There is no bound for overestimating dark subtraction, so we may use the
maximum magnitude of offset error from Section 3.2.2.
We estimate total dark subtraction uncertainty as a simple DC offset to the SG
spectra. PSFs are recomputed for the extrema of dark subtraction offset to arrive
at the uncertainties listed in Table 3.2. The asymmetry in FUV offset error carries
through to the listed FUV uncertainty. The last column of Table 3.2 is computed by
direct analogy to Strehl ratio. We call this pixel-limited Strehl ratio (PLSR), since
integration of the peak intensity over the central pixel reduces the peak value of each
PSF. Uncertainty in PLSR is estimated in a similar fashion to the core energy. We
note that for an underestimate of dark subtraction error, PLSR is reduced and vice
versa for an overestimate.
As another measure of how energy is distributed between the scattering wings
85
and core, we calculate the cumulative total energy of the NUV PSF estimates.
Dash (diffraction-limited) and dash-dot (PSF estimate) horizontal lines demarcate
the energy contained in the core of the PSF for each panel in Figure 3.8. Figure 3.8
also shows that the asymmetry of the NUV PSF estimates is similar, and largely
constrained to the core of these PSFs.
Table 3.2 and Figure 3.8 show that the PSF estimates have more energy in the
wings than the diffraction-limited PSFs in both the NUV and FUV channels. This
indicates the instrument scatters more light than the diffraction-limited case. All
else being equal, scattered light should be more prevalent at shorter wavelengths.
However, our results show that scattering is less prevalent in the FUV than NUV,
and scattering is a contributing factor to the reduction in PLSR in the NUV channel.
We caution that the FUV transit data are of lesser quantity and quality than the
NUV data. In particular, the FUV signal in the shadow of Mercury, which is critical
to the estimation of scattered light, is comparatively weak and dominated by noise.
Nevertheless, the result holds over the full range of our estimated uncertainties.
To check the plausibility of the PSF estimates, we deconvolve them from the
reduced data. By using Fourier deconvolution, we obtain an unbiased estimate of the
residual intensity in Mercury’s shadow. Since we are using the best estimate (average)
PSF on all the individual data sets, this is not merely a recapitulation of the cost
function that was used as a stopping criterion in Section 3.3.3. Table 3.3 lists residual
intensity in the shadow of Mercury after Fourier deconvolution. For the NUV and
both FUV channels, we find that residual intensity after deconvolution is reduced
to a fraction of a DN (mean, per pixel) in all but one case. The outlier in NUV
data set 4 may result from small dark subtraction errors similar to those noted in
Section 3.2.2. Figure 3.9 plots the results of Fourier deconvolution in solid curves for
select reduced data sets. For comparison, the observed data is overplotted in dashed
86
Figure 3.9: Deconvolution of reduced data using PSF estimates. Direct FFT
deconvolution is used so that an unbiased estimate is obtained for the mean intensity
in Mercury’s shadow (dotted lines). NUV 2814 Å (a) and 2796 Å (b) PSF estimates
perform well, greatly sharpening the limb of Mercury (compare (a) and (b) in
Figure 3.5) and reducing residual intensity to near zero. FUV 1394 Å (c) and 1336 Å
(d) PSF estimates remove more residual intensity when compared to (c) and (d) of
Figure 3.5.
87
Table 3.3: Residual intensity in the shadow of Mercury after PSF deconvolution.
Data Set 1336 Å 1394 Å 2796 Å∗ 2814 Å∗
[DN]? [%]† [DN]? [%]† [DN]? [%]† [DN]? [%]†
2 0.13 7.9 0.21 5.3
3 0.07 9.0 0.04 1.8
4 0.32 20.1 0.64 49.2 -1.84 -22.1 -1.49 -7.6
5 -0.06 -2.7 -0.37 -6.2
6 0.13 30.2 0.12 48.3 0.73 9.9 -0.65 -3.0
7 0.05 3.1 -0.13 -2.4
8 0.44 58.1 0.22 57.0 0.19 3.0 0.35 2.0
9a -0.06 -3.6 -0.07 -1.6
9b -0.05 -2.8 0.03 0.7
9c -0.01 -0.6 0.04 0.9
9d 0.08 4.5 0.18 4.2
9e 0.05 2.8 0.19 4.3
9f -0.11 -5.9 0.18 3.9
∗ Negative indicates residual intensity is less than zero after deconvolution.
? DN is the mean per-pixel value in the shadow of Mercury.
† Residual intensity given as percentage of original value before deconvolution.
curves in each panel. The PSF estimates perform well in all data sets compared to
the diffraction limit models in Figure 3.5; panels (a)–(d) in Figure 3.9 show that the
limbs of Mercury are sharp and steep in the NUV and FUV channels, while residual
intensity is reduced to near zero after deconvolution.
The instrument resolution is estimated by the modulation transfer functions
(MTFs) in Figure 3.10 panel (a) for NUV and (b) for FUV. In both panels of
Figure 3.10 the diffraction-limited MTF is overplotted as a solid black curve. Aliasing
(shown by the dashed curves in the figure) causes the MTF to be overestimated
by double-counting at the Nyquist frequency. A compensation has been applied to
reduce the effect of aliasing on each MTF (solid curves represent aliasing compensated
results in Figure 3.10). The aliasing compensation is computed as follows. First a
‘non-aliased’ diffraction-limited PSF is modeled on a higher resolution grid, so that
88
Figure 3.10: MTFs for the SG (a) NUV and (b) the FUV channels. Diffraction-
limited performance (solid black curve) and resolution criterion (dashed black curve)
are overplotted in both panels. A compensation has been applied to all MTFs to
reduce the effects of aliasing (see text for details). Aliased curves are plotted in
dashed lines for all MTFs.
aliasing is negligible at the IRIS SG Nyquist frequency (refer to Section 3.3.1.2). We
find that using 1024 pixels is sufficient to suppress aliasing, rather than the 420 pixel
length of the reduced data sets. An aliased PSF is then created by applying a boxcar
filter the width of an IRIS pixel to the non-aliased PSF. MTFs are then computed
from both the aliased and non-aliased PSFs. We define the compensation curve as the
ratio of the non-aliased to the aliased diffraction-limited MTFs. The compensation
curve is re-sampled to match the length of the reduced data set, then multiplied by
the MTF estimates for each spectral window. The resulting compensated MTFs are
reduced to half the value of the aliased versions at the Nyquist frequency.
We may estimate the spatial resolution of the IRIS SG by analogy to the Rayleigh
criterion [Lord Rayleigh F.R.S., 1879]. We choose a resolution criterion of 9%, as this
is the value of the MTF of the classic Airy pattern at the resolution attributed to it by
Rayleigh. NUV MTFs are plotted in Figure 3.10 (a), showing a significant degradation
in MTF, dropping to almost a third of the diffraction limit at the Nyquist frequency.
Despite the reduction in resolution, the 2796 Å MTF satisfies the resolution criteria
out to 0.41 cycles/pixel (2.47 cycles/arcsec) and the 2814 Å MTF does slightly better
89
at 0.42 cycles/pixel (2.55 cycles/arcsec). Panel (b) of Figure 3.10 shows that the MTFs
for both FUV channels are reduced by ≈ 10% compared to the diffraction limit, but
still double the resolution criterion at the Nyquist frequency. This shows that the
FUV channels are essentially pixel-limited in resolution.
Our PSF estimates include subtle contributions from the blur induced geometric
correction, as described in Section 3.3.1. As the geometric blurring varies in
time and space, a PSF estimate and deconvolution that accounts in detail for the
geometric correction would be prohibitively complicated. This complication could be
sidestepped by deriving the PSF for Level 1 data, but that would be of limited value,
since geometrical correction is desirable for nearly all scientific use. We have therefore
worked from Level 2 IRIS spectra, which are the standard for scientific work. Since
our method averages over the geometric blurring, we consider the resulting PSFs as
the best average estimates that can be applied to any geometrically corrected IRIS
spectra. However, we note that for the same reason, we underestimate the intrinsic
imaging capabilities of the instrument.
In Figure 3.11, we present the results of deconvolution using our PSF estimates
for the NUV 2814 Å (a, b) and 2796 Å (c, d). Figure 3.12 follows the same format
for the FUV 1394 Å (a, b) and 1336 Å (c, d) spectral windows. The Mercury spectra
from data sets 3 (FUV) and 4 (NUV) are used to illustrate the effect of PSF artifacts
in Figures 3.11, 3.12, and 3.13. As the PSFs are one dimensional, deconvolution
is performed only along the spatial axis. The deconvolved spectra are calculated
by the Richardson–Lucy algorithm, using the same method and criteria described in
Section 3.3.1.2. In both NUV spectra, contrast is enhanced throughout the images by
deconvolution, evident in the narrower and more peaked spectrum of the deconvolved
data in (a) and (b) of Figure 3.13. The limbs of Mercury are also sharpened to a
steep cutoff (panels (a) and (b) in Figure 3.13). Scattered light, the ‘haze’ in the
90
Figure 3.11: Comparison of original (a) and deconvolved (b) images for the IRIS FUV
2814 Å window. Remaining panels follow the same format: (c, d) 2796 Å. Spectra
are square root scaled.
91
Figure 3.12: Comparison of original (a) and deconvolved (b) images for the IRIS FUV
1394 Å window. Remaining panels follow the same format: (c, d) 1336 Å. Intensity
is displayed in inverse gray scale and logarithmically scaled.
NUV spectra (a) and (c) of Figure 3.11, is eliminated in Mercury’s shadow in the
corresponding deconvolved spectra (b) and (d).
The FUV channels show only modest improvement, since our FUV PSF
estimates are essentially pixel limited. Scattered light is not apparent in either (a) or
(c) of Figure 3.12 so that deconvolution in (b) and (d) has little to improve upon in
this regard. Some sharpening of Mercury’s limbs is evident in panels (c) and (d) of
92
Figure 3.13.
Figure 3.13: (a) Depicts intensity variations along a single spectral cut indicated by
the black triangle on the wavelength axis in Figure 3.11 (a) and (b). Panels (b),
(c), and (d) show the same for Figure 3.11 (c, d), and Figure 3.12 (e, f), and (g, h),
respectively.
93
Figure 3.14: Comparison of results from an alternate Voigt PSF initialization (gray
curve) to diffraction-limited (black curve) for the four spectral windows. Both
initializations result in prominent side lobes in the core of the (a) 2814 and (c) 2796 Å
PSFs. For all PSFs derived from the Voigt initialization, the wings of the PSF are
smoother; however, a distinct discontinuity appears at ≈ ±65 pixels in panels (b),
(d), and (f) and ≈ ±120 pixels in panel (h).
94
3.4.1 Effect of the Initial Guess on the PSF
Our initial guess was a diffraction-limited PSF (Figure 3.4). To find how
much this initial guess influences our results, we substituted a Voigt profile, fit
to the diffraction-limited PSF, as the initializing PSF. A complete exploration of
the initializing parameter space is beyond the scope of this document; we choose
Voigt profiles as an alternate initialization since it is fundamentally different from the
Fourier model PSFs. The initial Voigt profiles are smoother and lack the side lobes
and undulating structure of the Fourier models.
PSF estimates from both initializations are compared in Figure 3.14; similar
core structures and distinct, asymmetric side lobes result from either initialization
(i.e. Figure 3.14 (a) and (c)) for the NUV PSFs. We note that the side lobes
and asymmetry appear in the NUV Voigt PSFs estimates, despite the absence of
these traits in the initializing PSF. For all channels, the PSFs developed from the
Voigt initialization have wings that are less noisy, and lack the undulations due to
diffraction. This shows that our blind deconvolution method does not resolve fine
structure far from the core of the PSF. Yet, the wings still fall off at similar rate
compared to the diffraction-limited initialization. Subtle steps are visible in the wings
in each NUV channel for the Voigt initialization (±65 pixels panels (b) and (d) of
Figure 3.14). Since these features appear in both NUV PSFs for this initialization,
their presence may be genuine. They may also appear in the diffraction-initialized
PSFs; however, their existence is somewhat obscured by undulations in the wing.
As a further diagnostic of initial conditions, we perform the deconvolutions in
Section 3.4.2 using both the Fourier model and the Voigt initialized PSF. Side by
side results from either initialization can then be compared. Hereafter we refer to the
spectra obtained from the Voigt initialized PSF estimates as the alternate deconvolved
spectra.
95
3.4.2 PSF Effect on Data
To demonstrate the effect of the SG PSFs on IRIS observations, we consider a
simple example of an explosive event (EE). Explosive events are ubiquitous, compact
events characterized by large, non-thermal Doppler broadenings [≈ 100 km s−1 to
the red or blue; Dere et al., 1989, Dere, 1994] and may exhibit a bi-directional jet
structure [Innes et al., 1997]. Typically EEs were observed in the FUV [e.g., Si iv
1393 Å, and C iv 1548 and 1550 Å, Dere et al., 1989, Innes et al., 1997], but are also
detected at EUV and NUV wavelengths [e.g., He ii 304 Å and Mg ii 2796 Å, Fox et al.,
2010, Huang et al., 2014]. Observations of bright, compact, and often isolated EEs
are particularly sensitive to any PSF-induced blurring, and can serve as a diagnostic
of the IRIS SG PSFs. For our example, we select a typical EE observed by IRIS
close to disc center, shown in the boxed region of Figure 3.15 (a). This event is
well isolated from nearby bright features and is captured in only one frame in both
the NUV and the FUV channels. Its Doppler signature is clearly visible in Mg ii
(pixel 89 of panel (b), Figure 3.15) and particularly obvious in Si iv emission (panel
(c), Figure 3.15). We use the 2796 Å and 1396 Å PSF estimates to deconvolve the
spectra in Figure 3.15 (b) and (c), respectively. Deconvolution is performed using the
same method described in Section 3.3.1.2, again truncating after 50 iterations for the
2796 Å and 10 iterations for the 1403 Å window.
The observed and deconvolved EE Mg ii k wing spectra are plotted in Fig-
ure 3.16. Labeling of the Mg ii profile follows convention, with features blueward of
the line core (k3) denoted by v and redward by r. Leenaarts et al. [2013b] describe
diagnostics of the upper chromosphere using the Mg ii h & k features, based on the
formation properties discussed in detail in Leenaarts et al. [2013a]. In Table 3.4 we
re-list the Mg ii k spectral observables from Pereira et al. [2013], with the addition
of the values observed from the NUV EE spectra for reference. The IDL routine
96
iris get mg features.pro [Pereira et al., 2013] was used to derive the spectral
observables for the EE in Table 3.4. If we were observing quiet Sun, the derived
numerical values in Table 3.4 could be directly interpreted. However, we note that
EEs are very dynamic and likely differ significantly from the plasma conditions in
the quiescent Bifrost [Gudiksen et al., 2011] simulations on which the results from
Leenaarts et al. [2013a] and Leenaarts et al. [2013b] are based. We only use Table 3.4
to illustrate the quantitative impact of the deconvolution, and we do not mean to
imply that the derived numerical values are necessarily correlated with the physical
variables identified in Leenaarts et al. [2013b] and Pereira et al. [2013]. Interpreted
in this manner, Table 3.4 shows that deconvolution has significant impact on the
diagnostic parameters of the Mg ii line profile.
Analysis of the Si iv EE spectra plotted in Figure 3.17 is more straightforward.
The spectra are first background subtracted using the mean spectral value of the
region bordered by the white horizontal lines in Figure 3.15 (c) (the background is
computed after deconvolution for the deconvolved spectra). The equivalent width is
calculated between the vertical dashed lines in Figure 3.17, the approximate locations
of where the shoulder of the spectral line goes to zero. This provides a direct measure
of the spectral extent of the EE in each case. Since the FUV PSFs are very nearly
diffraction-limited, the effects of deconvolution are very subtle. In the example shown
in Figure 3.17, equivalent width is only slightly reduced in the deconvolved spectra.
We attribute the decrease in width to a combination of slightly increased fidelity in
the deconvolved spectra and the introduction of noise from the deconvolution process.
Figures 3.16 and 3.17 and Table 3.4 all show that the Voigt and Fourier PSF
initializations return identical results under deconvolution. We therefore conclude
that the differences in the two PSF estimates in Figure 3.14 are below the level of
accuracy that the underlying data can provide. We choose to provide the diffraction-
97
limited PSF estimates in the associated SSW routine since these estimates are based
on the physical properties of the instrument.
Table 3.4: Correlation between Mg ii Features and Atmospheric Properties.
Spectral Observable Atmospheric Property Obs. Deconv. Alt. Dcv.
∆v∗k3 Upper chromospheric velocity 7.0 6.2 6.2
∆v∗k2 Mid chromospheric velocity 19.0 24.4 24.4
∆vk3 −∆v∗h3 Upper chromospheric velocity gradient -1.1 -4.9 -4.9
k peak separation∗ Mid chromospheric velocity gradient 39.4 50.0 50.0
k2 peak intensity† Chromospheric temperature 586.7 601.8 601.8
(Ik2v − Ik2r)/(Ik2v + I †k2r) Sign of velocity above z(τ = 1) of k2 0.3 0.4 0.4
∗ [km s−1]
† [DN ]
3.5 Concluding Remarks
The PSF of the IRIS spectrograph results in non-zero intensity in the occulted
area during a Mercury transit. From the Mercury transit spectra, we estimated
instrument spatial PSFs for four spectral windows (2814 Å, 2796 Å, 1394 Å, and
1336 Å) of the NUV and FUV SG channels using a semi-blind Richardson–Lucy
method.
In the NUV channel, we find similar PSFs in both the 2814 Å and the 2796 Å
windows over multiple data sets. The NUV PSFs have broader cores and asymmetric
side lobes, as well as broadened wings when compared to the diffraction-limited case
(see, e.g., Figures 3.4, 3.7, and 3.8). The pixel-limited Strehl ratio (PLSR) is 0.73
and 0.65 for the 2814 Å and 2796 Å windows, respectively. The PLSR is affected by
increased energy in the side lobes and scattering wings of our PSF estimates. MTFs
show that the NUV SG has a resolution (defined by MTF > 0.9) of 0.42 cycles/pixel
(2.55 cycles/arcsec) and 0.41 cycles/pixel (2.47 cycles/arcsec) in the 2814 Å and 2796 Å
windows, respectively.
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Figure 3.15: (a) IRIS SJI 1330 Å image of the explosive event used as a diagnostic of
the SG PSFs. Boxed region outlines the approximate location of the EE (note that
the SJI image was taken 17 s after the SG images). The EE results in a broadening
of the spectra near Y pixel 89 in Mg ii (b) and Si iv (c) emission. White horizontal
lines in (c) denote the region used for the FUV background subtraction.
For the FUV 1394 Å and 1336 Å windows, we estimate PSFs with 0.98 and 0.93
PLSR, respectively. The FUV MTFs are within 10% of their ideal values in both
windows. The SG achieves Nyquist-limited resolution in both FUV channels.
We find that the IRIS SG PSFs contain more energy in the wings than the
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Figure 3.16: Mg ii k wing EE spectra.
Figure 3.17: Si iv EE spectra. Equivalent width is calculated between dashed vertical
lines.
diffraction-limited PSFs in both the NUV and the FUV channels. We attribute this
excess to scattering. Contrary to our expectations, scattering is apparently more
prevalent in the NUV PSFs than in FUV.
Our results are derived from IRIS Level 2 SG data, which is blurred slightly
by geometrical correction. We cannot reliably separate this contribution to our PSF
estimates from intrinsic instrument effects. Therefore, we underestimate the true
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instrument performance.
Deconvolution of the PSF estimates improves the spectra in both FUV and NUV
channels. Applied to the Mercury spectral data, we find that deconvolution reduces
the residual intensity in Mercury’s shadow to a fraction of a DN in all channels,
indicating that scattered light is reduced to near zero. NUV PSF artifacts, such as
the blurring of Mercury’s limb, are also greatly reduced while contrast is enhanced,
with no adverse effects noted. When applied to the spectra of an isolated EE, we find
that deconvolution reveals significant differences in intensity and sometimes velocities
derived from the Mg ii (NUV) line profiles. Deconvolution of the FUV EE spectra
produces more subtle results, reducing the equivalent width of the line profile by
0.02 Å. In addition, the deconvolution can improve assessment of the physical size of
detected features in both FUV and NUV channels.
The PSFs estimated here are distributed through SolarSoft (SSW) IDL, along
with a program, iris sg deconvolve.pro, for direct application to IRIS level 2 data.
PSFs for the 2814, 2796, 1394, and 1336 Å spectral windows are contained in the
module, corresponding to the NUV and both FUV channels. The module performs
a Richardson–Lucy deconvolution using the corresponding PSF estimate for each
spectral window. The provided software will allow the community to perform more
extensive testing of deconvolution of different types of solar scenes.
3.6 Acknowledgements
Funding for this work was supplied through subcontract 8100002702 from Lock-
heed Martin, in support of phases C/D/E of the NASA Interface Region Imaging
Spectrograph (IRIS) mission. B.D.P. and J.P.W. were supported by NASA contract
NNG09FA40C (IRIS).
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Disclosure of Potential Conflicts of Interest The authors declare that they have
no conflicts of interest.
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CHAPTER FOUR
THE EUV SNAPSHOT IMAGING SPECTROGRAPH (ESIS)
Contribution of Authors and Co–Authors
Manuscript in Chapter 4
Author: Hans T. Courrier
Contributions: Responsible for optical design and optimization. Contributed to
design and construction of instrumentation. Drafted manuscript and managed
contributions from co-authors.
Co–Author: Charles C. Kankelborg
Contributions: Principal investigator; conceived and designed instrumentation.
Contributed research and content to introduction. Provided feedback of analysis
and comments on drafts of the manuscript.
Co–Author: Amy Winebarger
Contributions: Co-investigator; contributed research and content to introduction.
Contributed to development of Camera assembly.
Co–Author: Ken Kobayashi
Contributions: Co-investigator; Contributed to development of Camera assembly.
Co–Author: Brent Beabout
Contributions: Designed camera assembly electronics and interface hardware.
Co–Author: Dyana Beabout
Contributions: Designed camera and ground support equipment software.
Co–Author: Ben Carroll
Contributions: Designed field stop mount and camera baffles.
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Co–Author: Jonathan Cirtain
Contributions: Co-investigator; Led collaborative effort between MSU and Marshall
Space Flight Center (MSFC.)
Co–Author: James A. Duffy
Contributions: Designed camera assembly mount and hardware.
Co–Author: Carlos Gomez
Contributions: Provided thermal analysis of camera assembly.
Co–Author: Eric Gullikson
Contributions: Developed and applied EUV multi-layer coatings to optics.
Co–Author: Micah Johnson
Contributions: Designed and constructed alignment transfer apparatus.
Co–Author: Jake Parker
Contributions: Assembled and aligned instrument optics.
Co–Author: Laurel Rachmeler
Contributions: Provided analysis and characterization of cameras.
Co–Author: Roy T. Smart
Contributions: Developed and implemented software for instrument computer control
systems.
Co–Author: Larry Springer
Contributions: Managed MSU resources and interface between MSU and MSFC.
Co–Author: David L. Windt
Contributions: Designed and developed EUV multi-layer for ESIS optics.
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Manuscript Information
Hans T. Courrier, Charles C. Kankelborg, Amy R. Winebarger, Ken Kobayashi, Brent
Beabout, Dyana Beabout, Ben Carroll, Jonathan W. Cirtain, James A. Duffy, Carlos
Gomez, Eric M. Gullikson, Micah Johnson, Jacob D. Parker, Laurel A. Rachmeler,
Roy T. Smart, Larry Springer, David L. Windt
Status of Manuscript:
x In preparation for submission to a peer–reviewed journal pending co-author
contribution
Officially submitted to a peer–reviewed journal
Accepted by a peer–reviewed journal
Published in a peer–reviewed journal
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ABSTRACT
The Extreme ultraviolet Snapshot Imaging Spectrograph (ESIS) is a next
generation rocket borne instrument that will investigate magnetic reconnection and
energy transport in the solar atmosphere using the transition region O v 62.9 nm and
coronal Mg x 62.5 nm emission lines. The instrument is a pseudo Gregorian telescope;
from prime focus, an array of spherical diffraction gratings re-image with differing
dispersion angles. The slitless multi-projection design will obtain co-temporal spatial
(0.76 ′′/pixel) and spectral (37 mÅ/pixel) images at high cadence (<4 s). A single
exposure will enable us to reconstruct line profile information at high spatial and
spectral resolution over a large (11.3′) field of view. The instrument is currently in
the build up phase prior to spacecraft integration, testing, and launch.
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4.1 Introduction
The solar atmosphere, as viewed from space in its characteristic short wave-
lengths (FUV, EUV, and soft X-ray), is a three dimensional scene evolving in
time: I[x, y, λ, t]. Here the solar sky plane spatial coordinates, x and y, and the
wavelength axis, λ, comprise the three dimensions of the scene, while t represents
the temporal axis. An ideal instrument would capture a spatial/spectral data cube
(I[x, y, λ]) at a rapid temporal cadence (t), however, practical limitations lead us
to accept various compromises of these four observables. Approaching this ideal is
the fast tunable filtergraph (i.e. fast tunable Fabry–Pérot etalons, e.g. The GREGOR
Fabry–Pérot Interferometer, Puschmann et al. [2012]), but the materials do not exist
to extend this technology to extreme ultraviolet wavelengths (EUV) shortward of
∼150 nm [Wuelser et al., 2000]. Imagers like the Transition Region and Coronal
Explorer (TRACE) [Handy et al., 1999] and the Atmospheric Imaging Assembly
(AIA) [Lemen et al., 2012] collect high cadence 2D EUV spatial scenes, but they
collect spectrally integrated intensity over a fixed passband that is not narrow
enough to isolate a single emission line. In principle, filter ratios that make use
of spectrally adjacent multilayer EUV passbands could detect Doppler shifts [Sakao
et al., 1999]. However, the passbands of the multilayer coatings are still wide enough
that the presence of weaker contaminant lines limits resolution of Doppler shifts to
∼1000 km s−1 [Kobayashi et al., 2000]. Slit spectrographs (e.g. The Interface Region
Imaging Spectrograph, IRIS [De Pontieu et al., 2014]) obtain fast, high resolution
spatial and spectral observations, but are limited by the narrow field of view (FOV)
of the spectrograph slit. The I[x, y, λ] data cube can be built up by rastering the
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slit pointing, but it cannot be co-temporal along the raster axis. Moreover, extended
and dynamic scenes can change significantly in the time required to raster over their
extant.
A different approach is to forego the entrance slit employed by traditional
spectrographs entirely. The Naval Research Laboratory’s (NRL) SO82A [Tousey
et al., 1973, 1977] was one of the first instruments to pioneer this method. The
‘overlappograms’ obtained by SO82A identified several spectral line transitions [Feld-
man et al., 1985], and have more recently been used to determine line ratios in solar
flares [Keenan et al., 2006]. Unfortunately, for closely spaced EUV lines, the dispersed
images from the single diffraction order suffer from considerable overlap confusion.
Image overlap is all but unavoidable with this configuration, however, overlappograms
can be disentangled, or inverted, under the right circumstances.
In analogy to a tomographic imaging problem [Kak and Slaney, 1988], inversion
of an overlapping spatial/spectral scene can be facilitated by increasing the number
of independent spectral projections, or ‘look angles,’ through the 3D (x, y, λ)
scene [DeForest et al., 2004]. For example, DeForest et al. [2004] demonstrated
recovery of Doppler shifts in magnetograms from two dispersed orders of a grating at
the output of the Michelson Doppler Imager (MDI [Scherrer et al., 1995]). The
quality of the inversion (e.g. recovery of higher order spectral line moments) can
also be improved by additional projections [Kak and Slaney, 1988, Descour et al.,
1997], generally at the cost of computational complexity [Hagen and Dereniak, 2008].
Computed Tomographic Imaging Spectrographs (CTIS) [Okamoto and Yamaguchi,
1991, Bulygin et al., 1991, Descour and Dereniak, 1995] leverage this concept by
obtaining multiple, simultaneous dispersed images of an object or scene; upwards of 25
grating diffraction orders may be projected onto a single detector plane [Descour et al.,
1997]. Through post processing of these images, CTIS can recover a 3D data cube
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from a (spectrally) smooth and continuous scene over a large bandpass (e.g. Hagen
and Dereniak [2008]).
The Multi-Order Solar EUV Spectrograph (MOSES Fox et al. [2010], Fox [2011])
is our first effort aimed at developing the unique capability of simultaneous imaging
and spectroscopy for solar EUV scenes. MOSES is a three-order slitless spectrograph
that seeks to combine the simplicity of the SO82A concept with the advantages of
a CTIS instrument. A single diffraction grating (in conjunction with a fold mirror)
projects the m = ±1 and the un-dispersed m = 0 order onto three different detectors.
Through a combination of dispersion and multi-layer coatings, the passband of the
m = ±1 orders encompasses only a few solar EUV emission lines. Thus, MOSES
overlappograms consist of only a handful of spectral images. This constraint on
the volume of the 3D data cube helps make inversion of MOSES data better-
posed despite the discontinuous nature of the solar EUV spectrum. This working
concept enabled by MOSES has been proven over the course of two previous rocket
flights. Through inversion of MOSES overlappograms, Fox et al. [2010] obtained
unprecedented measurements of Doppler shifts (i.e. line widths) of TR explosive
events as a function of time and space while Rust [2017] recovered splitting and
distinct moments of compact TR bright point line profiles.
Building on the working concept demonstrated by MOSES, here we describe a
new instrument, the EUV Snapshot Imaging Spectrograph (ESIS), that will improve
on past efforts to produce a solar EUV spectral map. ESIS will fly alongside MOSES
and will observe the transition region (TR) and corona of the solar atmosphere in the
O v 63.0 nm and Mg x 62.5 nm and 61.0 nm spectral lines. In Section 4.2 we detail
how our experience with the MOSES instrument has shaped the design of ESIS.
Section 4.3 describes the narrow scientific objectives and the requirements placed
on the new instrument. Section 4.4 describes the technical approach to meet our
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scientific objectives, followed by a brief description of the expected mission profile
in Section 4.5. The current status and progress toward launch is summarized in
Section 4.6.
4.2 The ESIS Concept
A primary goal of the ESIS instrument is to improve the implementation of
EUV snapshot imaging spectroscopy demonstrated by MOSES. Therefore, the design
of the new instrument draws heavily from experiences and lessons learned through two
flights of the MOSES instrument. ESIS and MOSES are both slitless, multi-projection
spectrographs. As such, both produce dispersed images of a narrow portion of the
solar spectrum, with the goal of enabling the reconstruction of a spectral line profile
at every point in the field of view. The similarities end there, however, as the optical
layout of ESIS differs significantly from that of MOSES. In this section, we detail
some difficulties and limitations encountered with MOSES, then describe how the
new design of ESIS addresses these issues.
4.2.1 Limitations of the MOSES Design
The MOSES design features a single concave diffraction grating forming images
on three CCD detectors [Fox et al., 2010] (Fig. 4.1). The optical path is folded
in half by a single flat secondary mirror (omitted in Fig. 4.1). Provided that the
three cameras are positioned correctly, this arragement allows the entire telescope to
be brought into focus using only the central (undispersed) order and a visible light
source. Unfortunately this design uses volume inefficiently for two reasons. First, the
lack of magnification by the secondary mirror limits the folded length of the entire
telescope to be no less than half the 5 m focal length of the grating [Fox et al., 2010,
Fox, 2011]. Second, the dispersion of the instrument is controlled by the placement of
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Figure 4.1: Schematic diagram of the MOSES instrument. Incident light on the right
forms an undispersed image on the central m = 0 CCD. Dispersed images are formed
on the outboard m = ±1 CCDs.
the cameras. To achieve the maximum dispersion of 29 km s−1 [Fox et al., 2010], the
outboard orders are imaged as far apart as possible in the ∼ 22′′ diameter cross section
of the rocket payload. The resulting planar dispersion poorly fills the cylindrical
volume of the payload, leaving much unused space along the orthogonal planes.
Furthermore, the monolithic secondary, though it confers the focus advantage
noted above, does not allow efficient placement of the dispersed image order cameras.
For all practical purposes, the diameter of the payload (0.56 m) can only accommodate
three diffraction orders (m = −1, 0,+1). Therefore, MOSES can only collect, at most,
three pieces of information at each point in the field of view. From this, it is not
reasonable to expect the reconstruction of more than three degrees of freedom in this
spectrum, except in the case very compact, isolated features such as those described
by Fox et al. [2010] and Rust [2017]. Consequently, it is a reasonable approximation to
say that MOSES is sensitive primarily to spectral line intensities, shifts, and widths
[Kankelborg and Thomas, 2001]. With any tomographic apparatus, the degree of
detail that can be resolved in the object depends critically on the number of viewing
angles [Kak and Slaney, 1988, Descour et al., 1997, Hagen and Dereniak, 2008]. So
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it is with the spectrum we observe with MOSES: more dispersed images are required
to confer sensitivity to finer spectral details such additional lines in the passband or
higher moments of the spectral line shape.
A related issue stems from the use of a single grating, with a single plane of
dispersion. Since the solar corona and transition region are structured by magnetic
fields, the scene tends to be dominated by field aligned structures such as loops [Rosner
et al., 1978, Bonnet et al., 1980]. When the MOSES dispersion direction happens to
be aligned nearly perpendicular to the magnetic field, filamentary structures on the
transition region serve almost as spectrograph slits unto themselves. The estimation
of Doppler shifts then becomes a simple act of triangulation, and broadenings are
also readily diagnosed [Fox et al., 2010, Courrier and Kankelborg, 2018]. A double-
peaked profile can also be observed with sufficiently isolated features [Rust, 2017].
Unfortunately, solar magnetic fields in the transition region are quite complex and
do not have a global preferred direction. In cases where the field is nearly parallel to
the instrument dispersion, spectral shifts and broadenings are not readily apparent.
The single diffraction grating also leads to a compromise in the optical
performance of the instrument. Since the MOSES grating forms images in three orders
simultaneously, aberration cannot be simultaneously optimized for all three of those
spectral orders. A result of this design is that the orientations (i.e. the central axis) of
the PSFs vary order to order [Rust, 2017]. During the first mission, MOSES was flown
with a small amount of defocus [Rust, 2017], which exacerbated the inter-order PSF
variation and caused the individual PSFs to span several pixels [Rust, 2017, Atwood
and Kankelborg, 2018]. The combination of these two effects results in spurious
spectral features that require additional consideration [Atwood and Kankelborg, 2018]
and further increase the complexity of the inversion process [Rust, 2017, Courrier and
Kankelborg, 2018].
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Another complication is that the spatial and spectral content differs slightly
between the three MOSES image orders. This is because the MOSES FOV is defined
by a combination of the aperture of the grating (i.e. the entrance aperture of the
telescope) and the spatial extent of the CCDs. The FOV in the m = ±1 orders is
shifted along the dispersion axis as a function of wavelength, dependant upon where
the dispersed spectral images intercept the m = ±1 CCDs. Spatially, this effect is
limited to only a handful of pixel columns at the edges of each image order. Of
higher concern is the ‘spectral contamination’ allowed by this layout; Parker and
Kankelborg [2016] found that bright spectral lines and continuum far outside the
wavelength passband and nominal m = 0 FOV could be diffracted onto the outboard
order CCDs. This off-band contamination is detected as systematic intensity variation
that lacks an anti-symmetric pairing in the opposite dispersed image order. Analysis
of the spectral contamination is ongoing.
Finally, the exposure cadence of MOSES is hindered by an ∼6 s readout time for
the CCDs [Fox, 2011]. The observing interval for a solar sounding rocket flight is very
short, typically about five minutes. Consequently, every second of observing time is
precious, both to achieve adequate exposure time and to catch the full development of
dynamical phenomena. The MOSES observing duty cycle is ∼50 % since it is limited
by the readout time of the CCDs. Thus, valuable observing time is lost. The readout
data gap impelled us to develop a MOSES exposure sequence with exposures ranging
from 0.25-24 s, a careful trade-off between deep and fast exposures.
In summary, our experience leads us to conclude that the MOSES design has
the following primary limitations:
1. inefficient use of volume
2. dispersion constrained by payload dimensions
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primary mirror
diffraction gratings
field stop
ESIS Optical Layout  (not to scale) detectors
Figure 4.2: The ESIS instrument is a pseudo-Gregorian design. The secondary mirror
is replaced by a segmented array of concave diffraction gratings. The field stop at
prime focus defines instrument spatial/spectral FOV. CCDs are arrayed around the
primary mirror, each associated with a particular grating. Eight grating positions
appear in this schematic; only six fit within the volume of the rocket payload. Four
channels are populated for the first flight.
3. too few dispersed images (orders)
4. single plane dispersion
5. lack of aberration control
6. insufficiently defined FOV
7. sub-optimal exposure cadence
In designing ESIS, we have sought to improve upon each of these points.
4.2.2 ESIS Features
The layout of ESIS (Fig. 4.2) is a modified form of Gregorian telescope. Incoming
light is brought to focus at an octagonal field stop by a parabolic primary mirror. In
the ESIS layout, the secondary mirror of a typical Gregorian telescope is replaced by
a segmented, octagonal array of diffraction gratings. From the field stop, the gratings
re-image to CCD detectors arranged radially around the primary mirror. The gratings
are blazed for first order, so that each CCD is fed by a single corresponding grating,
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and all the gratings are identical in design. The features of this new layout address
all of the limitations described in Sect. 4.2.1, and are summarized here.
Replacing the secondary mirror with an array of concave diffraction gratings
confers several advantages to ESIS over MOSES. First, the magnification of the ESIS
gratings results in a shorter axial length than MOSES, without sacrificing spatial
or spectral resolution. Second, the magnification and tilt of an individual grating
controls the position of the dispersed image with respect to the optical axis, so that
the spectral resolution is not as constrained by the payload dimensions. Third, the
radial symmetry of the design places the cameras closer together, resulting in a more
compact instrument. Furthermore, by arranging the detectors around the optical
axis, more dispersed grating orders can be populated; up to eight gratings can be
arrayed around the ESIS primary mirror (up to six with the current optical table).
This contrasts the three image orders available in the planar symmetry of MOSES.
Taken together, these three design features make ESIS more compact than MOSES
(§ 4.2.1 item 1), improve spectral resolution (§ 4.2.1 item 2) and allow the collection
of more projections to better constrain the interpretation of the data (§ 4.2.1 item 3).
The ESIS gratings are arranged in a segmented array, clocked in 45◦ increments,
so that there are four distinct dispersion planes. This will greatly aid in reconstructing
spectral line profiles since the dispersion space of ESIS occupies a 3D volume rather
than a 2D plane as with MOSES. For ESIS, there will always be a dispersion plane
within 22.5◦ of the normal to any loop-like feature in the solar atmosphere. As
discussed in § 4.2.1, a nearly perpendicular dispersion plane allows a filamentary
structure to serve like a spectrographic slit, resulting in a clear presentation of the
spectrum. This feature addresses § 4.2.1 item 4.
Rather than forming images at three spectral orders from a single grating,
each ESIS imaging channel has a dedicated grating. Aberrations are controlled by
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optimizing the grating design to form images in first order, over a narrow range of ray
deviation angles. This design controls aberration well enough to allow pixel-limited
imaging, avoiding the PSF mismatch problems inherent to the MOSES design (§ 4.2.1
item 5). A disadvantage of this arrangement is that ESIS lacks a zero order focus.
In its flight configuration with gratings optimized around a 63 nm wavelength, the
instrument cannot be aligned and focused in visible light like MOSES. Visible gratings
and a special alignment transfer apparatus (§ 4.4.5) must be used for alignment and
focus of ESIS.
The ESIS design also includes an octagonal field stop placed at prime focus.
This confers two advantages. First, the field stop fully defines the instrument FOV,
so that ESIS is not susceptible to the spectral contamination observed in MOSES data
(§ 4.2.1 limitation 6). Second, each spectral image observed by ESIS will be bordered
by the outline of the field stop (e.g. § 4.4.1). This aids the inversion process since
outside of this sharp edge the intensity is zero for any look angle through an ESIS
data cube. Additionally, the symmetry of the field stop gives multiple checkpoints
where the edge inversion is duplicated in the dispersed images produced by adjacent
orders. The size and octagonal shape of the field stop are defined by the requirement
that all CCDs must see the entire FOV from edge to edge, while leaving a small
margin for alignment.
Lastly, in contrast to MOSES, ESIS employs frame transfer CCDs to make
optimum use of our five minutes of observing time. The ESIS design is shutterless,
so that each detector is always integrating. The result is a 100 % duty cycle. The
lack of downtime for readout also allows ESIS to operate at a fixed, rapid cadence of
∼3 s. Longer integration times can be achieved for faint features by exposure stacking
(§ 4.2.1 item 7).
In summary, the ESIS concept addresses all the limitations of the MOSES design
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enumerated in § 4.2.1. The volume of the ESIS optical layout is smaller than MOSES
by almost a factor of two, yet with a smaller PSF, improved spectral resolution,
and faster exposure cadence. ESIS offers several features to improve the recovery of
spectral information, including more channels, crossed dispersion planes, and a field
stop.
4.3 Science Objectives
The previous section discussed the qualitative design aspects of ESIS learned
from experience with the MOSES instrument. MOSES, in turn, demonstrated a
working concept of simultaneous EUV imaging and spectroscopy. This concept adds
a unique capability to the science that we can obtain from the EUV solar atmosphere.
ESIS, sharing the same payload volume as MOSES, is manifested to fly in 2019. In
this section, we set forth specific scientific objectives for the combined ESIS/MOSES
mission. From these objectives, and with an eye toward synergistic operation of
MOSES and ESIS, in § 4.3.3 we derive the quantitative science requirements that
drive the ESIS design.
The combined ESIS/MOSES mission will address the following two overarching
science goals: (1) observe magnetic reconnection in the TR, and (2) map the transfer
of energy through the TR with emphasis on magnetohydrodynamic (MHD) waves.
These objectives have significant overlap with the missions of IRIS [De Pontieu et al.,
2014], the EUV Imaging Spectrometer (EIS, Culhane et al. [2007]) aboard Hinode,
the EUV Normal-Incidence Spectrometer (EUNIS, Brosius et al. [2007, 2014]), and
a long history of FUV and EUV slit spectrographs. The ESIS instrument, however,
can obtain both spatial and spectral information co-temporally. This will allow us to
resolve complicated morphologies of compact TR reconnection events (as was done
with MOSES [Fox, 2011, Rust, 2017, Courrier and Kankelborg, 2018]) and observe
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signatures of MHD waves over a large portion of the solar disk. Therefore, in support
of goal 1, we will use ESIS and MOSES to map flows as a function of time and
space in multiple TR reconnection events. To achieve goal 2, we will cross-correlate
the evolution at multiple temperatures in the TR to map the vertical transport of
energy over a wide FOV. In the latest configuration, the MOSES optics are optimized
around Ne vii (0.5 MK). To achieve our goals, ESIS should have a complementary
wavelength choice such that we can observe a reasonably isolated emission line formed
in the lower TR.
4.3.1 Magnetic Reconnection Events
Magnetic reconnection describes the re-arrangement of the magnetic topology
wherein magnetic energy is converted to kinetic energy resulting in the acceleration
of plasma particles. Reconnection is implicated in many dynamic, high energy solar
events. Solar flares are a well studied example (e.g. Priest and Forbes [2002] and
the references therein), however we have little hope of pointing in the right place
at the right time to observe a significant flare event in a rocket flight lasting only
five minutes. Instead, we will search for signatures of magnetic reconnection in TR
spectral lines. A particular signature of reconnection in the TR is the explosive
energy release by ubiquitous, small scale events. These explosive events (EEs) are
characterized as spatially compact (≈1.5 Mm length [Dere, 1994]) line broadenings
on the order of 100 km s−1 [Dere et al., 1991]. They are observed across a range of TR
emission lines that span temperatures of 20.000–250.000 K (C ii–O v) [Moses et al.,
1994]. The typical lifetime of an EE is 60-90 s [Moses et al., 1994, Dere, 1994, Dere
et al., 1991]. Due to their location near quiet sun magnetic network elements, and the
presence of supersonic flows near the Alfvèn speed, Dere et al. [1991] first suggested
that EEs may result from fast Petschek [Petschek, 1964] reconnection.
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The spectral line profile of EEs may indicate the type of reconnection that
is occurring in the TR (e.g. Rust [2017]). For example, the Petschek model of
reconnection predicts a ‘bi-directional jet’ line profile with highly Doppler shifted
wings, but little emission from the line core [Innes and Tóth, 1999]. Innes et al. [2015]
developed a reconnection model resulting from a plasmoid instability [Bhattacharjee
et al., 2009]. In contrast to the bi-directional jet, this modeled line profile has bright
core emission and broad wings. Both types of profile are seen in slit spectrograph data
(e.g., Innes et al. [1997, 2015], and the references therein), however MOSES observed
EEs with more complicated morphologies than either of these two models suggest [Fox
et al., 2010, Rust, 2017]. It is unclear whether the differing observations are a function
of wavelength and temperature, a result of a limited number of observations, or
because the morphology of the event is difficult to ascertain from slit spectrograph
data.
ESIS will observe magnetic reconnection in the context of EEs, by extending
the technique pioneered by MOSES to additional TR lines. Explosive events are
well suited to sounding rocket observations; a significant portion of their temporal
evolution can be captured in >150 s (e.g. the analysis by Rust [2017]) and they are
sufficiently common to provide a statistically meaningful sample in a 5-minute rocket
flight (e.g., Dere et al. [1989, 1991]). In similarity with MOSES, we seek a TR line
for ESIS that is bright and well enough isolated from neighboring emission lines so
as to be easily distinguished.
4.3.2 Energy Transfer
Tracking the mass and energy flow through the solar atmosphere is a long-
standing goal in solar physics. Bulk mass flow is evidenced by Doppler shifts
or skewness in spectral lines. However, the observed non-thermal broadening of
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TR spectral lines may result from a variety of physical processes, including MHD
waves [De Pontieu et al., 2015, 2007], high-speed evaporative up-flows (e.g. nanoflares,
Patsourakos and Klimchuk [2006]), turbulence, and other sources (e.g. Mariska
[1992]). This is a broad topic which ESIS can address in many ways. Here we
will focus on a single application; ESIS will search for sources of Alfvén waves in the
solar atmosphere by observing line broadening as the spectroscopic signature of these
waves.
Alfvén waves in coronal holes are observed to carry an energy flux of
7× 105 erg/cm2/s, enough to energize the fast solar wind [Hahn et al., 2012, Hahn
and Savin, 2013]. The source and frequency spectrum of these waves is unknown.
Here, we hypothesize that MHD waves are similarly ubiquitous in quiet Sun and
active regions, and play an important role in the energization of the quiescent corona.
The magnitude of non-thermal broadening of optically thin spectral lines is a
direct measure of the wave amplitude [Banerjee et al., 2009, Hahn et al., 2012, Hahn
and Savin, 2013]. We may estimate a lower limit on the non-thermal velocity to
be observed as follows. We assume that the magnetic field is constant for small
changes in scale height in the TR and that line of sight effects are negligible
for observations sufficiently far from disk center. Since the solar wind is not
accelerated to an appreciable fraction of the Alfvén wave velocity at altitudes below
R ≤ 1.15R [Cranmer and van Ballegooijen, 2005], the wave amplitude, vnt, depends
only weakly on electron density, n , so that v ∝ n−1/4e nt e [Hahn and Savin, 2013, Moran,
2001]. Assuming pressure balance between the low corona and transition zone, we may
infer non-thermal velocities in the TR by scaling according to the temperature drop,
vnt ∝ T 1/4. The measured non-thermal velocity of 24 km s−1 for Si viii [Doyle et al.,
1998] (0.8 MK [Moran, 2003]) near the limb should, neglecting damping, correspond
to velocities of at least 21 km s−1 in mid TR Ne vii, and 18 km s−1 in the lower O v
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(0.25 MK) line. The above non-thermal velocities are arrived at assuming both O v
and Ne vii are formed near their ionization equilibrium temperatures. For O v, the
thermal width is ∼11 km s−1 at 0.25 MK which means the total linewidth is primarily
due to the non-thermal component.
More recently, Srivastava et al. [2017] observed torsional Alfvén waves with
amplitude ∼20 km s−1 and period ∼30 s in the chromosphere. Modeling shows that
these torsional waves can transfer a significant amount of energy to the corona [Kudoh
and Shibata, 1999]. The torsional motion will be observed as Doppler shifts when
viewed from the side. The oscillation period is long enough to be well resolved but
short enough to see ∼10 cycles in a single rocket flight. An ESIS-like instrument
is therefore well suited to observations of torsional Alfvén wave propagation over
multiple heights in the TR.
By mapping Doppler velocities over a wide field of view in the TR, ESIS
can address questions about both the origin of waves and whether they are able
to propagate upward into the corona. Independent of the two propagation modes
discussed above, there is a range of possible sources for Alfvén (and other MHD)
waves in the solar atmosphere. Three potential scenarios are: (1) Waves originate
in the chromosphere or below and propagate through the TR at a spatially uniform
intensity ; (2) Intense sources are localized in the TR, but fill only a fraction of
the surface; and (3) Weak sources are localized in the TR, but cover the surface
densely enough to appear like the first case. The resulting non-thermal widths
for localized sources will be significantly higher than the ∼20 km s−1 mean derived
above. The concentration of non-thermal energy observed by ESIS will serve as an
indicator of source density. Comparison of Doppler maps from ESIS and MOSES will
indicate whether a uniform source density originates in the chromosphere or below
(scenario 1) or is associated with spatially distributed TR phenomena (scenario 3)
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such as explosive events, or macrospicules. Comparison with a wider selection of
ground and space based imagery will allow us to determine whether intense, localized
sources (scenario 2) are associated with converging or emerging magnetic bipoles, type
ii spicules, spicule bushes, or other sources beneath the TR. For these comparisons,
we need only to localize, rather than resolve, wave sources. A spatial resolution of
∼2 Mm will be sufficient to localize sources associated with magnetic flux tubes that
are rooted in photospheric inter-granular network lanes (e.g. Berger et al. [1995]).
4.3.3 Science Requirements
ESIS will investigate two science targets; reconnection in explosive events, and
the transport of mass and energy through the transition region. The latter may
take many forms, from MHD waves of various modes to EUV jets or macro-spicules.
To fulfill these goals, ESIS will obtain simultaneous intensity, Doppler shift and line
width images of the O v 63 nm line in the solar transition region at rapid cadence.
This is a lower TR line (0.25 MK) that complements the MOSES Ne vii. The bright,
optically thin O v emission line is well isolated except for the two coronal Mg x lines.
These coronal lines can be viewed as contamination or as a bonus; we expect that
with the four ESIS projections it will be possible to separate the O v emission from
that of Mg x. From the important temporal, spatial, and velocity scales referenced
Sections 4.3.1 and 4.3.2 we define the instrument requirements in Table 4.1 that are
needed to meet our science goals.
4.4 The ESIS Instrument
ESIS is a multiple projection slitless spectrograph that obtains line intensities,
Doppler shifts, and widths in a single snapshot over a 2D FOV. Starting from the
notional instrument described in Sec. 4.2, ESIS has been designed to ensure all of the
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Table 4.1: ESIS instrument requirements. AR is active region, QS quiet sun, and CH
coronal hole.
Parameter Requirement Science Driver Capabilities
Spectral line O v Explosive events O v, Mg x, & He i, Table 4.2
Spectral res. 18 km s−1 broadening MHD waves 18 km/s/ pixel, Table 4.2
Spatial res. 2 ′′ (1.5 Mm) Explosive events 1.52′′, Table 4.2
Desired SNR 17.3 in CH MHD waves in CH >17.7 w/20×10 s exp., § 4.4.4
Cadence 15 s Torsional waves 10 s eff., § 4.4.4
Obs. time > 150 s Explosive events >270 s, § 4.5
FOV 10′ diam. Span QS, AR, limb 11.3′, Table 4.2
science requirements set forth in Table 4.1 are met. The final design parameters are
summarized in Table 4.2.
A schematic diagram of a single ESIS channel is presented in Fig. 4.3 [A], while
the mechanical features of the primary mirror and gratings are detailed in Figs. 4.3
[B] and [C], respectively.
4.4.1 Optics
Figure 4.3 [A] shows the relative layout of the optics and detectors for a single
ESIS channel. Here we give specific details of the primary mirror and gratings (Fig. 4.3
[B] and [C], respectively). The features of the field stop have been described previously
in Sec. 4.2.2, while the CCD and cameras are covered in Sec. 4.4.7.
The primary mirror is octagonal in shape. A triangular aperture mask in front
of the primary mirror defines the clear aperture of each channel, imaged by a single
grating. Figure 4.3 [B] shows one such aperture mask superimposed upon the primary
mirror. The octagonal shape of the primary also allows dynamic clearance for filter
tubes that are arranged radially around the mirror (§ 4.4.3). The mirror is attached
to a backing plate by three “bipods”; thin titanium structures that are flexible in
the radial dimension, perpendicular to the mirror edge, but rigid in the other two
dimensions. The bipods form a kinematic mount, isolating the primary mirror figure
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Table 4.2: ESIS Design Parameters.
Primary Parabolic
Octagonal Aperture, D=144 mm
Focal length 1.0 m
SiC single layer coating optimized for λ63 nm
Transparent vis/IR
Field Stop 11.3′, projected on sky plane
Octagonal
Gratings (4) Spherical varied line space
(Individual master gratings)
Trapezoidal Aperture, Height: 16.9 mm,
Long Base: 18.0 mm, Short Base: 3.8 mm
Groove spacing d0=0.3866 µm
Magnification M=3.9
Mg/Al/SiC multilayer, λ63 nm
Efficiency 14 % (Uncoated 39 %)
Filters (4) 30 mm clear aperture
Thin film, 100 nm Al
82 % open Ni mesh
Detectors (4) E2V CCD230-42
Active area 2048× 1024
Pixel size 15 µm
QE 33 %, λ63 nm
Max readout time or min cadence here for ver. table 1?
Back Focal Length 127 mm
Plate scale 0.76 ′′/pixel
37 mÅ (18 km s−1) per pixel
Resolution 1.52′′ (Nyquist limited)
from mounting stress.
The mirror will have to maintain its figure under direct solar illumination, so
low expansion (Corning ULE) substrates were used. The transparency of ULE,
in conjunction with the transparency of the mirror coating in visible and near IR
wavelengths (e.g., Table 4.2 and § 4.4.3), helps minimize the heating of the mirror.
Surface figure specifications for the ESIS optics are described in Sec. 4.4.2.
The spherical gratings (Fig. 4.3 [C]) re-image light from the field stop to form
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Figure 4.3: [A] Schematic diagram of the ESIS optical train. Dimensions and clear
aperture of the ESIS [B] primary mirror and [C] diffraction gratings.
dispersed images at the CCDs. Each grating is individually mounted to a backing
plate in a similar fashion as the primary mirror. For these much smaller optics,
lightweight bipods were wire EDM cut from thin titanium sheet. The bipods are
bonded to both the grating and backing plate along the three long edges of each
grating. The individual mounts allow each grating to be adjusted in tip and tilt to
center the image on the CCD.
The gratings have a varied line space ruling pattern optimized to provide, in
principle, pixel limited imaging from the field stop to the CCDs. The pitch at the
center of the grating is d0 =0.3866 µm resulting in a dispersion of 17.5 km s−1 at the
center of the O v FOV. The groove profile is optimized for the m = 1 order, so that
each grating serves only a single CCD. The modeled grating groove efficiency in this
125
Field stop image height = 890 pixels
1000
97
9 8
800 . 2.
4 .9
2 4
3
 6  6
0 .
  
6 58
V g
X gX eI
 
O M M H
600
400
200
0
0 500 1000 1500 2000
detector x (pixels)
Figure 4.4: Areas occupied by strong spectral lines on the ESIS detectors. The plot
axes are sized exactly to the CCD active area. The ESIS passband is defined by a
combination of the field stop and grating dispersion.
order is 36 % at 63 nm.
Figure specification and groove profile are not well controlled near the edges of
the gratings. Therefore, a baffle is placed at each grating to restrict illumination to
the clear aperture marked in Fig. 4.3 [C].
The ESIS passband is defined through a combination of the field stop, the grating
dispersion, and the CCD size. The passband includes the He i (58.43 nm) spectral line
through Mg x (60.98 and 62.49 nm) to O v (62.97 nm). Figure 4.4 shows where images
of each of the strong spectral lines will fall on the CCD. The instrument dispersion
satisfies the spectral resolution requirement in Table 4.1 and ensures that the spectral
images are well separated; Figure 4.4 shows that He i will be completely separated
detector y (pixels)
126
from the target O v line.
4.4.2 Optimization and Tolerancing
The science resolution requirement of 2.0′′ (Table 4.1) was flowed down to
specifications for the ESIS optics. To ensure that ESIS meets this requirement, an
imaging error budget was developed to track parameters that significantly influence
instrument resolution. The budget is roughly divided into two categories; the first
includes ‘variable’ parameters that can be directly controlled (e.g., the figure and
finish of the optics, grating radius and ruling, placement of the elements in the system,
and the accuracy to which the instrument is focused). The second category consists
of ‘fixed’ contributions (e.g., CCD charge diffusion, pointing stability, and diffraction
from the entrance aperture). In this sub-section we describe the optimization of the
first category to balance the contributions of the second.
Figure and surface roughness specifications for the primary mirror and gratings
were developed first by a rule of thumb and then validated through a Fourier optics
based model and MonteCarlo simulations. Surface figure errors were randomly
generated, using a power law distribution in frequency. The model explored a range of
power spectral distributions for the surface figure errors, with power laws ranging from
0.1 to 4.0. For each randomly generated array of optical figure errors, the amplitude
was adjusted to yield a target MTF degradation factor, as compared to the diffraction
limited MTF. For the primary mirror, the figure of merit was a MTF degradation
of 0.7 at 2.0′′ resolution. Though the grating is smaller and closer to the focal
plane, it was allocated somewhat more significant MTF degradation of 0.6 based on
manufacturing capabilities. The derived requirements are described in table 4.3. Note
that this modeling exercise was undertaken before the baffle designs were finalized.
The estimated diffraction MTF and aberrations were therefore modeled for a rough
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estimate of the ESIS single sector aperture.
Table 4.3: Figure and surface roughness requirements compared to metrology for the
ESIS optics. Slope error (both the numerical estimates and the measurements) is
worked out with integration length and sample length defined per ISO 10110.
Element Parameter Requirement Measured
Primary RMS Slope error (µrad) < 1.0
integration length (mm) 4.0
sample length (mm) 2.0
Primary RMS roughness (nm) < 2.5
Periods (mm) 0.1-6
Grating RMS slope error (µrad) < 3.0
integration length (mm) 2
sample length (mm) 1
Grating RMS roughness (nm) < 2.3
Periods (mm) 0.02-2
The initial grating radius of curvature, Rg, and ruling pattern of the ESIS
gratings were derived from the analytical equations developed by Poletto and Thomas
[2004] for stigmatic spectrometers. A second order polynomial describes the ruling
pattern,
d = d + d r + d r20 1 2 , (4.1)
where r runs radially outward from the optical axis with its origin at the center of the
grating (Fig. 4.3 [C]). The parameters of Equation 4.1 and Rg were chosen so that
the spatial and spectral focal curves intersect at the center of the O v image on the
CCD.
Starting from the analytically derived optical prescription, a model of the system
was developed in ray-trace software. Since the instrument is radially symmetric, only
one grating and its associated lightpath was analyzed. In the ray trace model, Rg,
d1, d2, grating cant angle, CCD cant angle, and focus position were then optimized
to minimize the RMS spot at select positions in the O v FOV, illustrated in Fig. 4.5.
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Figure 4.5: (Left:) Ray traced spot diagrams for ESIS, illustrated at the center and
vertices of the O v FOV on the CCD. The grid spacing is 1 µm and the diffraction
limit airy disk (overplotted on each spot) radius is 2 µm. Imaging performance will
be limited by the 15 µm pixel size. (Right:) RMS spot radius through focus for the
three centered spots; top of FOV (purple curve), center (maroon), and bottom (red).
The optical prescription derived from the ray trace is listed in Table 4.2 and 4.3.
The ray trace model was also used to quantify how mirror and positional
tolerances affect the instrument’s spatial resolution. Each element of the model was
individually perturbed, then a compensation applied to adjust the image on the CCD.
The compensation optimized grating tip/tilt angle and CCD focus position, so that
the image was re-centered and RMS spot size minimized at the positions in Fig. 4.5.
We then computed the maximum change in RMS spot size over all spot positions
between the optimized and perturbed models. The computed positional tolerances
for each element in the ESIS optical system are listed in Table 4.4
The imaging error budget is displayed in Table 4.4. For the primary mirror and
grating surface figure contributions, we choose the MTF figures of merit from the
surface roughness specifications described earlier. To quantify the remaining entries,
we assume that each term can be represented by a gaussian function of width σ2 that
“blurs” the final image. The value of σ then corresponds to the maximum change
in RMS spot size for each term as it is perturbed in the tolerance analysis described
above. The value of the modulation transfer function (MTF) in the right-most column
129
of Table 4.4 is computed from each of the gaussian blur terms at the Nyquist frequency
(0.5 cycles/arcsecond). From Table 4.4, we estimate the total MTF of ESIS to be
0.109 at the Nyquist frequency. Compared to, for example, the Rayleigh criterion of
0.09 cycles/arcsecond [Lord Rayleigh F.R.S., 1879] we estimate the resolution of ESIS
to be essentially pixel limited. Since ESIS pixels span 0.76′′, the resolution target in
Table 4.1 is obtained by this design.
Table 4.4: Imaging error budget and tolerance analysis results. MTF is given at
0.5 cycles/arcsecond.
Element Tolerance σ2 [µm] MTF
Primary M. Surface figure (Ref. Table 4.3) 0.700
Decenter 1 mm 1.700 0.881
Grating Surface figure (Ref. Table 4.3) 0.600
Radius 2.5 mm 1.410 0.916
Decenter 1 mm 0.001 1.000
Defocus 0.015 mm 0.801 0.972
Clocking 13 mrad 1.300 0.929
CCD Decenter 1 mm 0.310 0.996
Defocus 0.229 mm 0.706 0.978
Max RMS spot radius (modeled) 1.720 0.878
CCD charge diffusion (est.) 2.000 0.839
Thermal drift 0.192 0.998
SPARCS drift 1.920 0.998
Pointing jitter 3.430 0.597
Diff. Limit 0.833
Total MTF 0.109
4.4.3 Coatings and Filters
The diffraction gratings are coated with a multilayer optimized for a center
wavelength of 63.0 nm, developed by a collaboration between Reflective X-Ray
Optics LLC and Lawrence Berkeley National Laboratory (LBNL). In Fig. 4.6 (A),
characterization of a single, randomly selected multilayer coated grating at LBNL
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Figure 4.6: (A) Measured efficiency of a single grating as a function of reflection
angle. Note flat response in first order over instrument FOV and suppression of zero
order. (B) Schematic of the Al/SiC/Mg multilayer with N = 4 layers. (C) Measured
reflectance for several multilayer coated witness samples. Dashed lines mark He i
(left, 58.4 nm) and O v (right, 63.0 nm) emission line wavelengths, with additional
vertical line showing suppression of He ii emission (far left dashed line, 30.4 nm) (D)
Measured multilayer coated grating efficiency as a function of wavelength. Dashed
lines mark the same emission lines as in (C)..
shows that the grating reflectivity is constant over the instrument FOV in the m = 1
order while the m = 0 order is almost completely suppressed. Figure 4.6 (B) shows a
schematic of the coating that achieves peak reflectivity and selectivity in the m = 0
order using four layer pairs of silicon carbide (SiC) and magnesium (Mg). The
Aluminum (Al) layers are deposited adjacent to each Mg layer to mitigate corrosion.
131
The maximum reflectance for the coating alone in the nominal instrument
passband is ∼35 % in Fig. 4.6 (C), measured from witness samples coated at the
same time as the diffraction gratings. Combined with the predicted groove efficiency
from § 4.4.1 and, given the relatively shallow groove profile and near normal incidence
angle, the total reflectivity in first order is ∼13 % at 63 nm. This is confirmed by the
first order efficiency measured from a single ESIS grating in Fig. 4.6 (D).
Unlike EUV imagers (e.g., TRACE [Handy et al., 1999], AIA [Lemen et al.,
2012], and Hi-C [Kobayashi et al., 2014]) the ESIS passband is defined by a
combination of the field stop and grating (§ 4.4.1, Fig. 4.4) rather than multi-layer
coatings. The coating selectivity is therefore not critical in this respect, allowing the
multi-layer to be manipulated to suppress out-of-band bright, nearby emission lines.
Figure 4.6 (D) shows the peak reflectance of the grating multilayer is shifted slightly
towards longer wavelengths to attenuate the He i emission line, reducing the likelihood
of detector saturation. A similar issue arises with the bright He ii (30.4 nm) line.
Through careful design of the grating multilayer, the reflectivity at this wavelength is
∼2 % of that at 63 nm (Fig. 4.6 (D)). In combination with the primary mirror coating
(described below) the rejection ratio at 30.4 nm is ∼32 dB. Thus, He ii emission will
be completely attenuated at the CCD.
The flight and spare primary mirrors were coated with the same Al/SiC/Mg
multilayer. Corrosion of this multilayer rendered both mirrors unusable. The failed
coating was stripped from primary mirror SN001. The mirror was then re-coated
with a 5 nm thick layer of chromium (Cr) to improve adhesion followed by a 25 nm
thick layer of SiC. The reflectance of this coating deposited on a silicon (Si) wafer
witness sample appears in Fig. 4.7. The spare primary mirror (SN002) retains the
corroded Al/SiC/Mg multilayer.
The Si CCDs are sensitive to visible light as well as EUV. Visible solar radiation
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Figure 4.7: Measured reflectivity of the ESIS primary mirror 25 nm thick SiC coating
deposited on a Si witness sample. Dashed lines mark He I (left, 58.4 nm) and O V
(right, 63.0 nm) emission line wavelengths.
is much stronger than EUV, and visible stray light can survive multiple scatterings
while retaining enough intensity to contaminate the EUV images. Luxél [Powell et al.,
1990] Al filters 100 nm thick will be used to shield each CCD from visible light. The
Al film is supported by a 70 line per inch (lpi) Ni mesh, with 82% transmission. The
theoretical filter transmission curve, modeled from CXRO data [Henke et al., 1993],
is displayed in Fig. 4.8. We conservatively estimate filter oxidation at the time of
launch as a 4nm thick layer of Al2O3.
An Al filter is positioned in front of the focal plane of each CCD by a filter
tube, creating a light tight box with a labyrinthine evacuation vent (e.g., Fig. 4.11).
The placement of the filter relative to the CCD is optimized so that the filter mesh
shadow is not visible. By modeling the filter mesh shadow, we find that a position
far from the CCD (>200 mm) and mesh grid clocking of 45◦ to the detector array
reduces the shadow amplitude well below photon statistics. The MOSES instrument
utilizes a similar design; no detectable signature of the filter mesh is found in data
and inversion residuals from the 2006 MOSES flight.
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Al2O3/Al/Al2O3 Ni Mesh filter
0.4
0.3
0.2
0.1
0.0
40 50 60 70 80 90
Wavelength [nm]
Figure 4.8: Model of ESIS filter transmissivity, including filter mesh and 4 nm thick
oxidation layers on either side of the 100 nm Al film.
To prevent oxidation, and to minimize the risk of tears, pinholes, and breakage
from handling, the filters will be stored in a nitrogen purged environment until after
payload vibration testing.
4.4.4 Sensitivity and Cadence
Count rates for ESIS are estimated using the expected component throughput
from Section 4.4.3 and the CCD quantum efficiency (QE) listed in Table 4.2.
Line intensities are derived from Vernazza and Reeves [1978] (V&R) and the
SOHO/Coronal Diagnostic Spectrometer (CDS) [Harrison et al., 1995] data. The
100 % duty cycle of ESIS (§ 4.4.7) gives us the flexibility to use the shortest exposures
that are scientifically useful. So long as the shot noise dominates over read noise
(which is true even for our coronal hole estimates at 10 s exposure length), we can
stack exposures without a significant SNR penalty. Table 4.5 shows that ESIS is
effectively shot noise limited with a 10 s exposure. The signal requirement in Table 4.1
is met by stacking exposures. Good quality images (∼ 300 counts) in active regions
can be obtained by stacking 30 s worth of exposures. This cadence is sufficient to
observe explosive events, but will not resolve torsional Alfvén waves described in
§ 4.3. However, by stacking multiple 10 s exposures, sufficient SNR and temporal
Transmission
134
resolution of torsional Alfvén wave oscillations can be obtained. The count rates
given here are for an unvignetted system as described in § 4.4.6.
Table 4.5: Estimated signal statistics per channel (in photon counts) for ESIS lines
in coronal hole (CH), quiet Sun (QS), and active region (AR).
Source V&R V&R V&R CDS
Solar Context QS CH AR AR
10 s Exp.
Mg x (62.5 nm) 3 0 26 16
O V (62.9 nm) 22 19 66 34
Total Counts 25 19 92 50
Shot Noise 5.0 4.3 9.6 7.0
Read Noise (est.) – 1.9 –
SNR 4.7 4.0 9.4 6.8
3×10 s Exp. Stack
Total Counts 75 56 276 148
SNR 8.1 6.8 16.3 11.7
4.4.5 Alignment and Focus
In the conceptual phase of ESIS, the decision was made to perform focus and
alignment in visible light with a HeNe source. Certain difficulties are introduced by
this choice, however, the benefits outweigh the operational complexity and equipment
that would be required for focus in EUV. Moreover, a sounding rocket instrument
requires robust, adjustment-free mounts to survive the launch environment. Such a
design is not amenable to iterative adjustment in vacuum. The choice of alignment
wavelength is arbitrary for most components; CCD response and multilayer coating
reflectively is sufficient across a wide band a visible wavelengths. The exceptions are
the thin film filters (which will not be installed until just before launch and have no
affect on telescope alignment and focus) and the diffraction gratings. Visible light
gratings have been manufactured specifically for alignment and focus. These gratings
135
are identical to the EUV flight version, but with a ruling pattern scaled to a 632.8 nm
wavelength.
Figure 4.9: ESIS alignment transfer device, consisting of three miniature confocal
microscopes that translate along the optical axis. Trapezoidal grating, bipods, and
mounting plate are installed on the tuffet in front of the apparatus (left of center).
After alignment and focus has been obtained with the HeNe source, the
instrument will be prepared for flight by replacing the visible gratings by the EUV
flight versions. Each grating (EUV and alignment) is individually mounted to a
backing plate using a bipod system similar to that of the primary mirror. The array
of gratings on their backing plates are in turn mounted to a single part which we call
the ‘tuffet.’ The backing plate is attached to the tuffet by bolts through spherical
washers. With this mounting scheme, the gratings can be individually aligned in
136
tip/tilt. The tuffet is attached to the secondary mirror mount structure (Fig. 4.9).
This enables the entire grating array to be replaced simply by removing/installing
the tuffet, such as when switching between alignment and EUV gratings.
Properly positioning the gratings will be the most difficult aspect of final
telescope assembly. Table 4.4 shows that the telescope is very sensitive to defocus.
The depth of field is an order of magnitude smaller in EUV than in visible light.
Moreover, the sensitivity to defocus at the gratings is M2 + 1 = 17 times greater
than at the detectors. Another sensitive aspect of the telescope is grating tip/tilt. A
tolerance of ∼ ±0.5 mrad will be needed to insure that the entire image lands on the
active area of the CCD.
Once the visible gratings are aligned and focused, the challenge is to transfer
this alignment to the UV gratings. Johnson et al. [2018] describes a procedure and
the apparatus constructed to accurately transfer the position of an alignment grating
radius to an EUV flight grating. This device, displayed in Fig. 4.9, consists of an array
of three miniature confocal microscopes that record the position of the alignment
grating radius. The alignment grating is replaced by an EUV grating, which is then
measured into position by the same apparatus. This device (and procedure) is capable
of obtaining position measurements of the diffraction gratings to a repeatability of
≈14 µm in the three confocal channels. This alignment transfer apparatus will ensure
that the EUV flight gratings are positioned to within the tolerances described in
Table 4.4.
4.4.6 Apertures and Baffles
Each channel of ESIS has two apertures: one at the surface of the grating and
another in front of the primary mirror. The purpose of the aperture at the grating
is to mask the out-of-figure margins at the edges of these optics. This provides a
137
Figure 4.10: Model view of ESIS baffle placement and cutouts.
well defined edge to the clear aperture of each grating while also keeping unwanted
rays from being reflected from the grating margins and back onto the CCDs. The
dimensions of the grating aperture match those of the grating clear aperture shown
in Figure 4.3 [C].
The aperture placed at the primary mirror is the stop for each individual channel.
The area of the stop has been maximized under the constraint that no rays be
vignetted anywhere else in the system. The gratings and their clear apertures were
the most significant areas of concern for potential vignetting. Thus, the shape of
stop at the primary is largely influenced by the shape of the grating clear aperture.
The inner extent of the primary stop (the “tip” of the triangle in Figure 4.3 [B])
is defined by the occultation of the primary by the shadow cast from the gratings
and their mounts. This presented an intricate geometry problem, as the occultation
is a function of the incoming field angle, the radial extent of the grating mount,
and the distance of the mount to the primary mirror along the optical axis. Hence,
the inner extent of the primary stop was solved for iteratively with the optimization
described in Section 4.4.2, which affected the placement of the gratings relative to the
138
primary mirror. The resulting optimized and non-vignetting stop geometry is shown
in Figure 4.3 [B].
After final optimization, the stop geometry was analyzed to check for vignetting
at the grating with the optical model. A footprint diagram was generated at the
grating from of multiple grids of rays. The incidence angle of each grid of rays
corresponded to the extremes of FOV defined by the positions of the eight points of
the octagonal field stop. The footprint diagram showed that, with the stop completely
filled, no ray landed outside of the grating clear aperture in Figure 4.3 [C], and no
ray was intercepted by the central obscuration.
From Figure 4.3 [C] it is apparent that considerable surface area of the primary
mirror is unused by the non-vignetting stop design. The primary apertures could be
enlarged considerably if the vignetting constraint were to be relaxed.
The ESIS baffles are designed to block direct light paths between the front
aperture plate and the CCDs for any ray <1.4◦ from the optical axis. This angle is
purposefully larger than the angular diameter of the sun (∼0.5◦) so that any direct
paths are excluded from bright sources in the solar corona. All baffles are bead-
blasted, anodized Al sheet metal oriented perpendicular to the optical axis. The
size and shape of the cutouts were determined using a combination of the ray trace
from Section 4.4.2 and 3D modeling. The light path from the primary mirror to the
field stop is defined as the volume that connects each vertex of the primary mirror
aperture mask (e.g., Fig. 4.3) to every vertex of the octagonal field stop. This is
a conservative definition that ensures no rays within the FOV are excluded, and
therefore unintentionally vignetted by the baffles. Light paths from the field stop to
the grating, and from the grating to the image formed on the CCD, are defined in a
similar manner. The cutouts in the baffles are sized using the projection of these light
paths onto the baffle surface. A conservative 1 mm margin is added to each cutout
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to prevent unintentional vignetting. A model of the six baffles, showing cutouts and
position on the optical bench, is displayed in Fig. 4.10.
4.4.7 Cameras
Figure 4.11: ESIS camera assembly as built by MSFC. Thin film filters and filter
tubes are not installed in this image.
The ESIS CCD cameras were designed and constructed by Marshall Space Flight
Center (MSFC), and are the latest in a series of camera systems developed specifically
for use on solar space flight instruments. The ESIS camera heritage includes those
flown on both the Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) [Kano
et al., 2012, Kobayashi et al., 2012] and the High-Resolution Coronal Imager (Hi-
C)[Kobayashi et al., 2014].
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The ESIS detectors are CCD230-42 astro-process CCDs from E2V. For each
camera, the CCD is operated in a split frame transfer mode with each of the four
ports read out by a 16-bit A/D converter. The central 2048 × 1024 pixels of the
2k× 2k device are used for imaging, while the outer two regions are used for storage.
Two overscan columns on either side of the imaging area and eight extra rows in each
storage region will monitor read noise and dark current. When the camera receives
the trigger signal, it transfers the image from the imaging region to the storage regions
and starts image readout. The digitized data are sent to the Data Acquisition and
Control System (DACS) through a SpaceWire interface immediately, one line at a
time. The frame transfer takes <60 ms, and readout takes 1.1 s. The cadence is
adjustable from 2-600 s in increments of 100 ms, to satisfy the requirement listed in
Table 4.1. Because the imaging region is continuously illuminated, the action of frame
transfer (transferring the image from the imaging region to the storage regions) also
starts the next exposure without delay. Thus the exposure time is controlled by the
time period between triggers. Camera 1 (Fig. 4.11) generates the sync trigger, which
is fed back into Camera 1’s trigger input and provides independently buffered triggers
to the remaining three cameras. The trigger signals are synchronized to better than
±1 ms. Shutterless operation allows ESIS to observe with a 100 % duty cycle. The
cadence is limited only by the 1.1 s readout time.
MSFC custom designed the camera board, enclosure, and mounting structure
for ESIS to fit the unique packaging requirements of this experiment (Fig 4.11). The
front part of the camera is a metal block which equalizes the temperature across
the CCD while fastening it in place. The carriers of all cameras are connected to a
central two-piece copper (3 kg) and aluminum (1 kg) thermal reservoir (cold block)
by flexible copper cold straps. The flexible cold straps allow individual cameras to be
translated parallel to the optical axis (by means of shims) up to ∼13 mm to adjust
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focus in each channel prior to launch. The centrally located cold block will be cooled
by LN2 flow from outside the payload until just before launch. The LN2 flow will be
controlled automatically by a Ground Support Equipment (GSE) computer so that all
cameras are maintained above survival temperature but below the target temperature
of −55 ◦C to insure a negligible dark current level.
The gain, read noise, and dark current of the four cameras were measured at
MSFC using an 55Fe radioactive source. Cameras are labeled 1, 2, 3, and 4 with
associated serial numbers SN6, SN7, SN9, and SN10 respectively in Fig. 4.11. Gain
ranges from 2.5-2.6 e−/DN in each quadrant of all four cameras. Table 4.6 lists gain,
read noise, and dark current by quadrant for each camera.
The Quantum Efficiency (QE) of the ESIS CCDs will not be measured before
flight. Similar astro-process CCDs with no AR coating are used in the Solar X-ray
Imager (SXI) aboard the Geosynchronous Orbiting Environmental Satellites (GOES)
N and O. A QE range of 43% at 583Å to 33% at 630Å is expected for the ESIS CCDs,
based on QE measurements by Stern et al. [2004] for GOES SXI instruments.
4.4.8 Avionics
The ESIS DACS are based on the designs used for both CLASP [Kano et al.,
2012, Kobayashi et al., 2012] and Hi-C [Kobayashi et al., 2014]. The electronics
are a combination of Military Off-The-Shelf (MOTS) hardware and custom designed
components. The DACS is a 6-slot, 3U, open VPX PCIe architecture conduction
cooled system using an AiTech C873 single board computer. The data system also
include a MOTS PCIe switch card, MSFC parallel interface card, and two MOTS
Spacewire cards. A slot for an additional Spacewire card is included to accommodate
two more cameras for the next ESIS flight. The C873 has a 2.4 GHz Intel i7 processor
with 16 Gb of memory. The operating temperature range for the data system is -40
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Table 4.6: ESIS Camera properties.
Camera Quad Gain Read Noise Dark Current
[e−/DN ] [DN] [e−/ms]
1 (SN6) 1 2.57 3.9 1.37e−4
2 2.50 4.0 9.66e−5
3 2.52 4.1 6.85e−5
4 2.53 3.7 9.80e−5
2 (SN7) 1 2.55 3.9 6.77e−5
2 2.58 4.0 5.89e−5
3 2.57 4.0 8.98e−5
4 2.63 4.0 1.01e−4
3 (SN9) 1 2.57 4.1 3.14e−5
2 2.53 4.1 2.68e−5
3 2.52 4.1 3.18e−5
4 2.59 4.3 3.72e−5
4 (SN10) 1 2.60 3.9 6.39e−4
2 2.60 3.9 5.07e−5
3 2.54 4.2 6.63e−5
4 2.58 4.1 8.24e−5
to +85 C. The operating system for the flight data system is Linux Fedora 23.
The DACS is responsible for several functions; it controls the ESIS experiment,
responds to timers and uplinks, acquires and stores image data from the cameras,
downlinks a subset of images through telemetry, and provides experiment health
and status. The DACS is housed with the rest of the avionics (power supply,
analog signal conditioning system) in a 0.56-0.43 m transition section outside of the
experiment section. This relaxes the thermal and cleanliness constraints placed on the
avionics. Custom DC/DC converters are used for secondary voltages required by other
electronic components. The use of custom designed converters allowed additional
ripple filtering for low noise.
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4.4.9 Pointing System
The imaging target will be selected prior to launch, the morning of the day
of flight. During flight, pointing will be maintained by the Solar Pointing Attitude
Rocket Control System (SPARCS) [Lockheed Missiles and Space Co. Report]. Images
from Camera 1 will be downlinked and displayed in real time on the SPARCS control
system console at intervals of ∼16 s to verify pointing is maintained during flight.
4.4.10 Mechanical
ESIS and MOSES are mounted on opposite sides of a composite optical table
structure originally developed for the Solar Plasma Diagnostics Experiment rocket
mission (SPDE, Bruner [1995]). The layered carbon fiber structure features a
convenient, precisely coplanar array of threaded inserts with precision counterbores.
The carbon fiber layup is designed to minimize the longitudinal coefficient of thermal
expansion. The optical table is housed in two 0.56 m diameter skin sections, with a
total length of 3 m. A ball joint and spindle assembly on one end and flexible metal
aperture plate on the other hold the optical table in position inside the skin sections.
The kinematic mounting system isolates the optical table from bending or twisting
strain of the skins.
4.5 Mission Profile
ESIS will be launched aboard a sub-orbital Terrier Black Brant sounding rocket
from White Sands Missile Range. The experiment is currently scheduled for launch
in August, 2019. Trajectory will follow a roughly parabolic path, with >270 s solar
observing time above 160 km. ESIS will begin continuously taking exposures at a
fixed cadence immediately after launch, terminating just before the payload impacts
the upper atmosphere. Exposure length will be determined by the target selected
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for launch day. Exposures taken while the payload shutter door is closed (< 160 km)
will be used for dark calibration. Data will be stored on board and downloaded
after recovery, however a limited amount of data will be transmitted to the ground
station via high speed telemetry as a safeguard against payload loss or destruction.
A parachute will slow the descent of the payload after it enters the atmosphere, and
recovery will be accomplished by helicopter after the payload is located on the ground.
4.5.1 ESIS Mission Update
Since the time of writing ESIS launched and was recovered successfully from
White Sands Missile Range on September 30, 2019. Unfortunately, due to failure
of the mechanical shutter, no MOSES data was obtained during this flight. A
paper is forthcoming that will document the ESIS instrument in its as-flown
configuration [Courrier et al., 2020]. A companion paper will describe ESIS first
results [Parker et al., 2020]. Two significant changes, one to the ESIS instrument
and one to our alignment procedures, were made prior to launch and are summarized
below.
The transfer from visible to EUV grating alignment was completed by an
alternative means. The apparatus described by Johnson et al. [2018] was not able to
maintain sufficient repeatability during test runs on diffraction grating surfaces. To
maintain the launch schedule, a phase shifting interferometer was used to transfer the
alignment of the visible gratings to the EUV flight gratings.
A trade study was conducted, and it was decided to remove the primary aperture
stop. The advantage was an increase in sensitivity. The disadvantage was to
sacrifice the unvignetted design described in section 4.4.6. The effective aperture
is increased by a factor of 1.7 to 2.7 as a function of FOV in the radial dimension.
The corresponding signal gradient is oriented along the dispersion direction of each
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channel; vignetting increases (and signal decreases) when moving towards blue
wavelengths (i.e. moving to the left in Figure 4.4). This gradient is due almost entirely
to vignetting by the central obscuration, and is linear across the entire FOV. The
principal challenge is that the images cannot be corrected directly; rather, since the
gradient is repeated for each of the overlapping spectral line images, the vignetting
can only be accounted for by forward modeling. Since forward modeling is required
for all of the inversion procedures under consideration for ESIS data analysis, the
vignetting was deemed low risk to the mission science.
4.6 Conclusion and Outlook
ESIS is a next generation slitless spectrograph, designed to obtain co-temporal
spectral and spatial images of the solar transition region and corona. In this report, we
present details of the scientific objectives, instrument, image and spectral resolution,
data acquisition, and flight profile.
ESIS follows on the proven MOSES design, incorporating several design changes
to improve the utility of the instrument. The symmetrical arrangement of CCDs and
diffraction gratings results in a compact instrument while increasing the number of
dispersed images and dispersion planes. This aids the inversion process, while also
allowing access to higher order spectral line profile moments. Individual gratings
improve resolution by controlling aberration in each channel. The addition of a field
stop eliminates spectral contamination and provides an easily recognizable edge for
data inversion. The ESIS design also demonstrates that all this can be accomplished
in a volume small enough to serve as a prototype for a future orbital instrument.
For the first flight, four of the six available ESIS channels will be populated
with optics optimized around the O v emission line. The large (11.3′), high resolution
FOV (1.52′′, 74 mÅ) can simultaneously observe the evolution of small scale EUV
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flows and large scale MHD waves in high temporal cadence. ESIS also enables the
study of transport of mass and energy in the transition region and corona during the
∼ 5 minute data collection portion of rocket flight.
ESIS was recovered after a successful first launch on September 30, 2019, with
analysis of collected data currently in-process. Subsequent flights will be proposed
and the instrument refined with an eye toward orbital opportunities. Suborbital
flights will allow us to expand the instrument to its full complement of six channels
and refine our data analysis methods, but do not provide access to major flares and
eruptive events that drive space weather. The long term prospect is that an ESIS-
like instrument on an orbital platform could provide high cadence maps of spectral
line profiles in solar flares, allowing unique and comprehensive observations of the
dynamics in solar eruptive events, flare ribbons, and the flare reconnection region.
4.7 Acknowledgements
We gratefully acknowledge the support of the NASA Heliophysics Low-Cost
Access to Space program, grant number NNX14AK71G.
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CHAPTER FIVE
CONCLUSION
The solar atmosphere above the temperature minimum (chromosphere, transi-
tion region and corona) is characterized by a positive temperature gradient (∂T > 0,
∂r
on average) and marked departure from the local thermodynamic equilibrium (LTE)
of the solar interior and photosphere. A long standing goal in solar physics is to
understand the non-thermal mechanisms by which mass and energy are transported
from the relatively cool photosphere to the million degree solar corona. Dissipation
of magnetic energy, through some combination of magnetohydrodynamic (MHD)
waves and/or magnetic reconnection events may power the hot corona and solar
wind [e.g. De Moortel and Browning, 2015, and references therein]. Emission from
the solar atmosphere spans many VUV spectral lines that are observable only from
space. Short-ward of 150 nm there is little continuum and the spectrum comprises
well separated emission lines (well separated in the sense that the stronger lines can
be isolated in ∼1–3 Å [Vernazza and Reeves, 1978]). Much of our knowledge of the
TR in the past two decades has been gained from spectroscopic observations [e.g.,
Wilhelm et al., 2004, Tian, 2017]. The review paper by Tian [2017] cites observations
by SOHO/SUMER and IRIS as key in uncovering the role the transition region (TR)
may play in transporting mass and energy to the corona and solar wind. These
observations also show that rather than a stratified layer, the TR is tenuous, finely
textured, and highly dynamic.
Investigations of the TR and surrounding atmosphere are limited by our
observational capabilities. The TR phenomena of interest have complex structure
and are extensive in two dimensions (or more accurately three dimensions considering
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the line of sight). Spectroscopy allows direct access to the mechanics of the TR
through analysis of spectral line shifts, or better yet, resolving the entire line profile.
Diffraction gratings are the only technology available to resolve VUV spectral lines;
the materials do not exist to create a Fabry-Pèrot etalon shortward of ≈100 nm [e.g.,
Wuelser et al., 2000], and Multi-layer mirror coatings cannot achieve a narrow enough
pass band to isolate a single emission line (e.g. Fig. 4.6). Therefore, the usual design
for VUV solar spectroscopy is a slit spectrograph. However, the 1D field of view of
these instruments makes it difficult to capture the spatial and temporal variability of
the TR.
In chapters 2, 3 and 4 of this thesis, I presented three investigations that
advance the state of the art in imaging spectroscopy of the solar atmosphere in VUV
wavelengths. This advancement is achieved through slitless, multi-order spectroscopy
in Chapters 2 and 4 as a new technology to image the TR. Chapter 3 focuses on
improving IRIS observations through characterization of the instrument PSF. In this
chapter, I summarize the objectives of each project, and assesses its value to the
scientific community. I will also describe how each study leads to further questions,
and suggest how those questions may be answered in the future.
5.1 MOSES Doppler Inversion
In Chapter 2 [Courrier and Kankelborg, 2018] I presented a method to infer
Doppler shifts from MOSES data. MOSES is a slitless spectrograph, imaging with
three detectors placed at the m = −1, 0, and +1 orders of a diffraction grating,
allowing it to overcome the spatial and temporal limitations associated with slit
spectroscopy. The data MOSES collects are co-temporal over a large FOV. The
disadvantage of this configuration is that the data obtained are an overlapping series
of images from the bright emission lines in the instrument passband (He ii 304Å and
149
Si xi 303Å). Disentangling this overlapping information is ill posed [Kankelborg and
Thomas, 2001]. A full “inversion” of MOSES data is analogous to a tomographic
three-projection inversion. Fox [2011] and Rust [2017] have performed separate
inversions of select features in MOSES He ii data using variations of the multiplicative
algebraic reconstruction technique (MART) developed by Gordon et al. [1970].
Rather than perform a full inversion of select features, I sought to obtain only
Doppler shifts over the entire MOSES dataset. The automated method I developed
measures the perceived displacement of individual features between pairs of MOSES
image orders using local correlation tracking (LCT). The displacements directly
correspond to He ii line shifts in the 2006 February MOSES data. This is not an
optically thin line, so radiative transfer effects may broaden the profile [e.g. Jordan,
1975]. Nevertheless, I assume that the LCT derived displacements correspond to
bulk flows along the line-of-sight (LOS). These flows may indicate energy release, as
in explosive events [Fox et al., 2010, Rust, 2017], mass supply to the corona [Tian
et al., 2008, Brannon et al., 2015], or cooling material in flare loops [Brannon, 2016].
The LCT based method is sensitive to Doppler shifts of the He ii line profile,
but not higher order line moments (e.g. line width). The trade-off in recovering
only a subset of the available spectral information is the problem becomes better
posed compared to the full inversions mentioned previously. This may make the
LCT based method more robust when faced with a crowded and/or complicated
field. For example, LCT is insensitive to image background, which must be carefully
treated in MART based inversions [Fox, 2011, Rust, 2017]. Also, the 2D nature of
the correlation provides a degree of freedom orthogonal to the dispersion axis, so that
the LCT method can accommodate differing PSFs in each of the three image orders.
Since the transition region is finely structured, it is desirable to resolve Doppler
shifts at the smallest spatial scales possible. For the method developed in Chapter 2,
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the Doppler map spatial resolution is limited by correlation window size. Tests with
synthetic data showed that the minimum useful window is of the same scale as the
instrument PSF (≈ 3 pixels). This makes the resolution of the derived Doppler maps
similar to that of the original intensity images.
The LCT based method yields similar results for Doppler shifts compared to
inversion for the full spectrum. Fox et al. [2010] identified and analyzed a single
explosive event (EE) in MOSES He ii 304 Å data. In that study, the EE was
background subtracted by hand, then fitted with Gaussian profiles row-by-row, with
human supervision of the fitting process. The automated LCT method is more
efficient; Doppler shift estimates for each pixel in the entire MOSES He ii data set
(30 exposures, 2048x 1024 pixels each) were obtained in only a few minutes.
5.1.1 Future Directions for LCT Doppler Maps
While I was successful in deriving Doppler shifts from MOSES data, analysis
of both this and synthetic data identified areas that could be improved with future
work. The two critical concerns are PSF effects and LCT displacement offset.
Systematic errors arise from the differing PSFs of each image order. Compact,
isolated features in MOSES data are dominated by the instrument PSF, the shape of
which varies in each image order. The regions where these PSFs do not overlap, or are
not “well-aligned” between image orders are falsely interpreted by the LCT method as
displacements. The result is underestimation if the mis-alignment is opposed to the
true Doppler shift direction, and overestimation if it is directed along the true shift.
The false Doppler signatures can have magnitudes of tens of km s−1 and often appear
as bi-polar jet structures in features where the true Doppler signal is weak [Fox, 2011,
Rust, 2017].
Deconvolution offers one possible method of removing the PSF artifacts. Like
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inversion, deconvolution of a known PSF is an ill-posed problem, the outcome of
which may vary greatly depending on the form of the PSF chosen. In Chapter 2
the PSF estimates I used were sufficient to illustrate the expected error that arises
from their differing shapes. A more refined estimate of the MOSES PSFs was
made by Rust [2017]. The new versions were inferred from unresolved features in
the 08 February 2006 data, that were isolated by a partial wavelet reconstruction
technique. Deconvolution of these PSFs from the MOSES data could greatly reduce
the appearance of spatial PSF effects in the LCT inversion. Note, however, that Rust
showed the MOSES PSFs tend to change with time during flight.
An alternate form of correction is PSF equalization. A recent study, completed
just after the publication of Chapter 2, filters images from each of the three MOSES
orders so that they all share one “equalized” PSF [Atwood and Kankelborg, 2018].
Unlike known PSF deconvolution, the filtering does not sharpen (or for that matter,
smooth) the images. However, a filter to equalize the PSFs is a better posed problem
than deconvolution. Atwood and Kankelborg [2018] showed that false bi-polar PSF
artifacts were significantly reduced in MOSES images, while features larger than the
equalized image PSF retained their spectral characteristics. Applying this filtering
before the the LCT inversion could potentially eliminate dissimilar PSF shape as a
source of error without affecting the spatial resolution of the Doppler maps.
Another systematic error arises from “displacement offset” inherent to the LCT
technique used to perform the inversions. LCT correlates sub-regions of two images
to find a local displacement between the pair [November and Simon, 1988]. The
Fourier method I employed defines the sub-regions of each image with a Gaussian
windowing function, centered at the same pixel location in each image [Fisher and
Welsch, 2008]. Correlations can therefore only be drawn for the portions of features
that are contained in both sub-regions. Since the correlation is best when the window
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straddles the corresponding copies of the feature in both images, this results in an
offset of the perceived position of the derived displacement vectors. The magnitude of
the offset equals one-half the magnitude of displacement between the two images. This
formulation of LCT makes sense for its originally intended purpose, but is problematic
for inversion of MOSES data. Fortunately, the symmetric positioning of the two
outboard image orders avoided this effect, so that the offset displacement vectors
tended to fall over the correct positions on the Sun. This form of correction is not
possible for the first flight of ESIS, as none of the four dispersion orders will be
oppositely positioned. To reduce this systematic error in ESIS inversions, it may be
desirable to develop a more suitable algorithm for comparing asymmetric pairs of
diffraction orders.
5.2 PSFs for IRIS
In Chapter 3 [Courrier et al., in press], I determined on-orbit spatial PSFs for
the NUV and FUV channels of the IRIS spectrograph from a Mercury transit of the
Sun. This is the first PSF characterization of the IRIS spectrograph since its launch
in 2014. I found that the NUV channel PSF estimates contain more energy in the
scattering wings, and wider cores when compared to models that include only pixel
size and diffraction. In the FUV channels, the PSF estimates are comparable to the
models. Modulation transfer functions derived from the PSF estimates show that
the spectrograph can achieve a spatial resolution of 2.47 cycles/arcsec in the NUV
channel near 2796 Å and 2.55 cycles/arcsec near 2814 Å. In the short (≈1336 Å) and
long (≈1394 Å) wavelength FUV channels, the MTFs show pixel limited resolution
(3.0 cycles/arcsec)
Deconvolution of the estimated PSFs improves some aspects the observed
spectra. PSF effects are more obvious in the NUV channel than the FUV channel.
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This is because the broad core of the NUV PSF estimates reduces fine scale resolution,
especially noticeable in compact bright (relative to background) isolated features.
Doppler shifts and other line profile metrics are also attenuated because adjacent
spectra are blurred together. When comparing spectra, deconvolution increased the
observed peak intensity by 3% and velocity by 22% when derived from Mg ii (NUV)
line profiles of a single isolated explosive event (EE). The core of the FUV PSFs
estimates are not broadened, so deconvolution of the FUV EE spectra produces more
subtle results. In this channel, the equivalent width of the EE line profile is reduced
by only 0.02 Å.
Deconvolution also reduces scattered light in the NUV spectra, improving
contrast at all scales. In the Mercury transit data, scattered light is visible as non-zero
intensity deep within Mercury’s shadow. After deconvolution this ‘residual’ intensity
is reduced to a small fraction of a DN in the NUV channel.
In summary, the accuracy of spectral observables (e.g., Doppler shifts, line
widths, and line ratios) depends on resolving the structure(s) in which they occur.
Deconvolution using the PSF estimates derived in Chapter 3 will allow the scientific
community to perform these measurements at the best possible resolution for IRIS.
The results of Chapter 3 are made available through a SolarSoft module [Freeland
and Handy, 1998]. The routine iris sg deconvolve.pro implements either a
Richardson-Lucy or FFT deconvolution of IRIS spectra along the spatial axis. It also
includes a pointer to the file that contains the PSF estimates in the IRIS SolarSoft
distribution.
5.2.1 Future Directions for IRIS PSF Characterization
In the comparison of the NUV and FUV PSF estimates in Chapter 3, I cautioned
that the FUV transit data is of lesser quality and quantity than the NUV. An
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exposure-to-exposure fluctuation in camera pedestal was observed in both FUV
channels that influenced the results of the PSF analysis. Signal in the FUV channels
was also comparatively lower than that in the NUV. Both of these issues were
exacerbated by the short exposure lengths required to minimize motion blur (up
to approximately a half pixel of blurring can be expected over 15 s), so that the FUV
PSF estimates are considerably noisier than their NUV counterparts. Since the IRIS
resolution is effectively limited by the noise floor of the instrument, noise gating the
Mercury spectra could lead to an improvement in the quality of both the FUV and
NUV PSF estimates.
Finally, the PSF characterization focused only on the spectrograph spatial
resolution. IRIS also observed the Mercury transit in all slit-jaw imager channels.
The method I developed could be generalized to two dimensions, so that 2D spatial
PSFs could be estimated for the slit-jaw imager from the Mercury transit.
5.3 ESIS
Chapter 4 [Courrier et al., 2020] describes a new instrument, the EUV Snapshot
Imaging Spectrograph (ESIS). Since the time of writing in Chapter 4, ESIS has been
recovered from a successful launch on September 30, 2019. Unfortunately, due to
failure of the mechanical shutter, no MOSES data was obtained during this flight.
Like MOSES, ESIS is a slitless spectrograph, combining imaging and spectroscopy
to address the observational challenges of the finely structured and highly dynamic
solar transition region. The ESIS and MOSES instruments fly together on the same
payload, each observing distinct temperature regions in the TR. The passband of
each instrument is narrow enough to encompass only a few bright spectral lines
(MOSES: Ne vii, ESIS: O v and Mg x). Both instruments collect co-temporal spatial
and spectral information over a large FOV (MOSES: 20′ × 10′, ESIS: 11′ octagonal)
155
at high-cadence (minimum ≈4 s) observing distinct temperature regions in the TR.
While the instruments share similar objectives, the design of ESIS is significantly
different. This is a direct result of experience gained from MOSES. The new design
reduces (and in some cases, removes altogether) many of the instrumental artifacts
and limitations that affect MOSES inversions. The ESIS optics are based on a
Gregorian telescope layout, with the multiple projections rotationally symmetric
about the optical axis (e.g. Fig. 4.2). A field stop is placed at the intermediate
focus of the parabolic primary mirror. This eliminates contamination of the spectra
from sources outside the FOV, such as that observed by Parker and Kankelborg
[2016] in MOSES data. The secondary mirror is replaced by a segmented array of
identical spherical variable line space (SVLS) gratings. Each grating produces only
one projection, compared to three projections by the single MOSES grating. This
allows optimization of the SVLS grating for a single spectral order. The modeled
PSF of an ESIS image projection is not rotationally invariant, but is small enough
to be mostly contained in a single pixel. This significantly reduces systematic errors
due to PSF shape in the inversion method described in Chapter 2. The design of
ESIS is also more compact than MOSES, so that more projections and projection
planes can be accommodated. MOSES has three projections arrayed along a single
plane. The initial flight of ESIS was populated with four projections (of a maximum
of six), each of which occupies a different projection plane. The placement of the ESIS
projections not only increases the number of “look angles” available for tomographic
reconstruction, but also expands the space occupied by the projections to three
dimensions instead of the two dimensional plane occupied by MOSES. The additional
dimension reduces the extent of the null space (spatial-spectral structures to which the
instrument has zero response, e.g. [Kankelborg and Thomas, 2001]) of ESIS compared
to MOSES. This in turn results in less inherent ambiguity in the inversion problem
156
posed by ESIS than that of MOSES.
5.3.1 ESIS Objectives
A primary science objective of ESIS is to study magnetic reconnection in the
TR by observing multiple explosive events (EEs). These extremely common events
appear to be closely associated with magnetic reconnection in the solar atmosphere,
however, their exact nature and morphology remains elusive. The MOSES instrument
analyzed previously unobserved structure and morphology in He ii transition region
explosive events [Fox et al., 2003, Rust, 2017]. ESIS also observed multiple EEs and
ongoing analysis will map line profiles over the full extent of each event, improving
upon and extending the characterization of TR EEs first begun by MOSES.
ESIS data will also allow investigation of energy transport in the TR and corona.
Alfvén waves can carry sufficient energy to power the fast solar wind [De Pontieu et al.,
2007, McIntosh et al., 2011], presenting a mechanism by which mass and energy may
be transported to the hot solar corona. The motions of these waves are detectable
to ESIS through the non-thermal broadening of optically thin spectral lines in the
instrument passband. The concentration of non-thermal energy observed by ESIS
serves as an indicator of Alfvén wave source density in the sky-plane. In a similar
manner, comparison of Doppler maps from ESIS and MOSES can indicate whether
Alfvén waves originate in the chromosphere or below (i.e. along the line-of-sight).
Thus, ESIS (and MOSES) can detect and localize MHD waves and their origins in
the three spatial dimensions of the solar atmosphere.
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APPENDICES
175
APPENDIX A
ERROR ESTIMATION
176
In this section we estimate error in correlation between two images due to random
intensity errors in the data. We begin by assuming we have two different 1D Gaussian
intensity distributions, F (x) and G(x), centered at the origin,
−x2
( ) = ( )± = 2σ2F x f x  ff f0e + Ef (x) , (A.1)
−x2
2
G(x) = g(x)± g = g 2σ0e g + Eg(x) , (A.2)
where x is position in pixels, fo is intensity at x = 0, σf is the characteristic
width of the distribution, Ef (x) is per pixel Gaussian distributed noise with mean
zero and standard deviation f , and similarly for Eq. A.2. The correlation function
is then written,
√ −x2
H(x) = F (x)⊗G( ) ≈ √2πf0g0σfσg 2(σ2 +σ2)x e f g +[f(x)⊗Eg(x)]+[g(x)⊗Ef (x)] , (A.3)
σ2f + σ2g
where ⊗ is the cross-correlation operator. Assuming the real intensity distribu-
tions contain sufficient background so that Ef (x) and Eg(x) vary only weakly with
x, we write √∫ ∞
f(x)⊗ E (x) ≈  f 2 √ 1g g (x)dx = f0g σfπ 4 , (A.4)
√∫−∞∞
g(x)⊗ E (x) ≈  g2 √ 1f f (x)dx = g0f σgπ 4 . (A.5)
−∞
The uncertainty in H(x)√is therefore:√ √
σ⊗ = πσf (f0 )2g + πσg(g0 2f ) , (A.6)
where Eq. A.6 results from adding Eq. A.4 and Eq. A.5 in quadrature. For small
displacements of x (not accounting for errors in intensity), we Taylor expand the first
term of Eq. A.3 so that
√√ ( )2πf0g σ 20 fσg −xh(x) ≈ 1 + . (A.7)
σ2 + σ2 2(σ2 + σ2)c g f g
To find how the position of the maximum correlation, h(0), varies with intensity
fluctuations we solve
h(0)− h(x) = σ⊗ , (A.8)
for x. The error in doppler velocity from random intensity fluctuations, σd, is
177
then x multiplied by the M −1√OSES pixel dispersion (29 km s ) so that√√√√ [ ] 12(σ2f + σ2 3 2 2 4= 29× g) σf (√f0g) + σg(√g0f )σd . (A.9)
f0g0σfσg π π
Values of σf and σg are estimated for each MOSES image order by the Gaussian
fits in Fig. 2.4. For convenience we list the characteristic width, σm, together with
gain (j) and read noise (σ2r) determined by Ref. 134 in Table A.1 for each of the
MOSES CCDs. The value of f is then
2f = jf 20 + σr , (A.10)
for each image order, and similarly for g.
Table A.1: Error model parameters at 30.4 nm.
CCD σm [Pixel] j [DN/photon] σ2r [DN]
m = −1 2.33 1.79 4.4
m = 0 2.15 1.73 4.3
m+ 1 1.84 1.76 5.1
178
APPENDIX B
DIFFRACTION FROM MERCURY’S LIMB
179
In some cases, diffraction at the Moon’s limb is a measurable effect at the Earth’s
surface; e.g. diffraction effects from Lunar occultations has been used to determine
the angular diameters of distant stars [e.g. Nather and Evans, 1970, and references
therein]. The question is then raised, in the case of the IRIS Mercury transit
observations, does diffraction from Mercury’s limb have a measurable contribution
to the PSF estimates derived in chapter 3? Here, diffraction from Mercury’s limb
is modeled (conservatively) using Fresnel (near field) diffraction. The results of the
model described herein shows that diffraction from Mercury’s limb is negligible at
IRIS resolution.
B.1 Mercury Diffraction Model
Similar to the occultation of distant stars by celestial bodies, the occlusion
caused by Mercury can be approximated by an opaque, semi-infinite knife-edge.
A schematic diagram of the Sun-Mercury-Earth geometry is shown in Figure B.1.
The resulting intensity pattern at the Earth is modeled by the Fresnel (near field)
diffraction equation since the aperture created by the knife-edge extends to infinity
in one direction. For distant stars, the diffraction pattern created under these
circumstances consists of alternating bright and dark bands in the starlight that
extends beyond the edge of the geometric shadow. The characteristic length between
these shadow bands is much larger than a typical telescope aperture. Hence, the
diffraction effect is detected as a modulation in intensity with time as the shadow
bands sweep across the telescope aperture in concert with the sky-plane motion of
the diffracting object. These intensity fluctuations can be detected by large telescopes
with millisecond exposure lengths (e.g. Peterson et al. [1989]).
To estimate the diffraction of sunlight from the limb of Mercury, an infinitesi-
mally small portion of the solar surface can be treated as a point source similar to
the stellar diffraction case outlined above. Following the stellar diffraction model,
the Fresnel diffraction equation for illumination by a single point source located far
behind Mercury’s limb can then be obtained. To model the Sun as an extended source,
the diffraction pattern created at the location of IRIS can then be approximated by
the contribution from a collection of mutually incoherent point sources that fill the
angular width of an IRIS pixel. The relevant Sun-Mercury-Earth (IRIS) geometry
shown in Figure B.1.
B.1.1 IRIS -Specific Assumptions
To help simplify the model, the following assumptions are made: First, as
mentioned earlier, the occultation caused by Mercury is well approximated as a semi-
infinite, 1D knife edge. This treatment is valid (as will be shown below) because, at
IRIS resolution, the extent of the limb diffraction effects are small and well contained
within a single pixel as compared to the ∼70 pixel extent of Mercury along the
IRIS slit found in chapter 3. Thus, diffraction from only one edge of Mercury’s limb
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need be considered as it crosses the IRIS spectrograph slit. Second, since IRIS is
a slit spectrograph, the Sun can be approximated as a monochromatic source. This
is a conservative approach that disregards any smoothing of the diffraction pattern
(e.g. Nather and Evans [1970]) over the optical bandwidth of a single IRIS pixel (the
IRIS spectral scale is 12.8 mÅ FUV and 25.6 mÅ NUV per pixel, respectively, De
Pontieu et al. [2014]). Under this assumption, the diffraction pattern can then be
investigated anywhere in the IRIS spectral range by choosing a column of constant
wavelength, λ.
B.1.2 Fresnel Diffraction Model
Similar to the case of stellar occultations, here we consider a point source located
far behind Mercury, so that the distribution of complex field, U(ξ), directly behind
Mercury’s limb (the IRIS or earthward side) is approximated by a plane wave. Once
the plane wave encounters Mercury’s limb, it takes the form of the Heaviside function
so that U(ξ) = U0H(ξ), where the point of the knife edge is located at ξ = 0 and the
amplitude of the field is U0. The geometric shadow cast by the knife-edge lands at
x = 0 after traveling a distance L to Earth, as illustrated schematically in Figure B.1.
Figure B.1: Schematic diagram (not drawn to scale) representing the complex field
immediately behind Mercury’s limb. The incoming solar radiation is incident from
the left in this diagram. L is the Earth-Mercury distance, while ξ and x are the
coordinates parallel to the IRIS slit at Mercury and Earth, respectively. The dashed
line indicates the geometric shadow cast by Mercury’s limb, which lands at x = 0 at
the Earth.
Under the aforementioned assumptions the complex field at the location of the
Earth can be found from the convolution form of the Fresnel diffraction equation
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(e.g. Goodman [2005]). Here the convolution kernel, h(x), is
( ) = iπx
2
h x e Lλ (B.1)
where x is the spatial coordinate (parallel to the IRIS slit) of the shadow landing at
Earth, and L is the distance from IRIS (Earth) to Mercury. The complex field at
IRIS is then ∫ ∞ ∫ ∞ ∫ x ′2
U(x) = U0 H(ξ)h(x− ξ)dξ = U0 h(x− ξ)dξ =
iπx
U e dx′0 Lλ , (B.2)
−∞ 0 −∞
where the variable substitution x′ = x− ξ is made in the last step. The intensity at
IRIS (along the slit) is I(x) = |U(x)|2 s∣o that∣∣∣∫ x iπx′2I(x) = I0 e ′Lλ dx ∣∣∣∣2 , (B.3)
−∞
with I0 = |U 20| . Re-writing Equation B.3 as the sum of two real integrals,[∫ ′2 ]2 [∫ ′2 ]x 2
( ) = πx
x πx 
I x I0 cos( )dx′ + sin( )dx′−∞ Lλ −∞ Lλ  . (B.4)
Equation B.4 can be re-written in terms of the Fresnel integrals [e.g. Subrah-
manya, 1980, Goodman, 2005]. Since both cos(πt2 ) and sin(πt2 )√are even about 0,∫ ∫ ∫ Lλ Lλ0 πx′2 0 ′2 ∞ ′2cos( )dx′ = sin(πx ) ′ = cos(πx ) ′ = Lλdx dx 8 . (B.5)−∞ Lλ −∞ Lλ 0 Lλ
Equation B.4 is t[hen∫ ′2 ∫ ′2 ]0 2πx x πx
I(x) = I0[ cos( )dx
′ + cos( )dx′
∫−∞ Lλ ∫ 0 Lλ0 ′2 x ′2 ]2
+ πxI0  sin( )dx
′ + sin(πx )dx′ ,
−√∞ Lλ √ 0 L√λ √   (B.6) 2 2Lλ 2 Lλ 2 
I(x) = I0 + C  x +  + S  x8 Lλ 8 Lλ  ,
using the Fresnel integrals given by
∫ (u πu′2)
C(u) = cos ′
0 2
du , (B.7)
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Figure B.2: Solar point source diffraction pattern from Mercury’s limb at the position
of IRIS .
∫ ( )u
( ) = sin πu
′2
S u ′2 du , (B.8)0
Here, Equations B.7 and B.8 [are e(valuated u1− 1 + √ )
sing the (error functi)on], erf(u),√
C(u) = i4 erf
i + erf 1− i2 πu i 2 πu , (B.9)
1 + [ ( ) (i 1 + i√ √ )]
S(u) = 4 erf 2 πu − i erf
1− i
2 πu . (B.10)
B.2 Mercury Limb Diffraction at IRIS
In Figure B.2, the point source diffraction pattern described by Equation B.6 is
plotted for λ = 134 nm and λ = 281 nm. These values correspond to the shortest and
longest nominal wavelengths in the IRIS spectrograph passband, respectively. Since
only the modulation in intensity due to diffraction is of interest, the total amplitude
is normalized so that I0Lλ = 1. Figure B.2 shows that the spacing between fringes is
orders of magnitude greater than the 19 cm IRIS telescope aperture [De Pontieu et al.,
2014]. Therefore, in this approximation of the Sun as a point source, it is clear that
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no spatial modulation of intensity would be detected along the IRIS slit. However,
a temporal modulation of intensity would be detected as the shadow bands from
Mercury sweep across the IRIS telescope aperture. In this case, assuming Mercury
has a velocity of ∼20 km s−1 relative to Earth (e.g. U.S. G.P.O. [2015]), an exposure
length of less than 2.5 ms would be needed to temporally resolve the bright and dark
fringes.
Figure B.3: Schematic diagram showing geometry for diffraction patterns from
multiple sources. The Sun is approximated as a collection of point sources that
span the IRISangular FOV. The IRIS aperture is centered at the geometric shadow
at x = 0. The intensity pattern that IRIS sees from a point source located along the
blue line (field angle θ) is centered around the intersection of the red line (angle γ)
and the plane located at the Earth.
The Sun, however, is an extended source. To evaluate this case we assume,
for simplicity, that the solar surface intensity is constant. Figure B.3 shows a
representative source, off-axis at field angle θ. As indicated by the red line, the
edge of the geometric shadow cast by Mercury’s limb from this source projects to the
point x = −γL, where γ = θ1− L . The intensity incident at IRIS, located at x = 0,1AU
from the extended, constant intensity source is then expressed in terms of θ using the
I(x) function in Equation B.6, ( )
IIRIS(
−θL
θ) = I(−γL) = I L . (B.11)1− 1AU
IIRIS(θ) is plotted in red in Figure B.4. This represents the idealized intensity
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Figure B.4: Solar diffraction pattern from Mercury’s limb as seen at the location of
IRIS. The red curve is the (impossible to observe) diffraction pattern created by an
extended, constant intensity source located at the position of the sun as a function of
field angle θ. The black dash-dot curve is the red curve convolved with a 1/6′′ boxcar,
modeling IRIS pixel limited resolution. The gray dotted lines indicate the angular
width of an IRIS pixel.
observed by an impossible instrument with infinite spatial resolution despite a
finite (i.e. diffraction limited) aperture. The details of IIRIS(θ) are on the order of
milliarcsecond scale, and cannot be resolved in practice. If, for example, we imagine
that IRIS is pixel limited, then the red intensity curve in Figure B.4 would be
convolved with a boxcar of 1/6′′ width [De Pontieu et al., 2014], as illustrated by
the black dash-dot curve in the same figure. However, the black dash-dot curve
shows no hint of modulation due to diffraction, and so it is indistinguishable from
the intensity that would be observed from a geometrically perfect shadow. Therefore,
diffraction from Mercury’s limb can have no measurable contribution to the point
spread functions derived in chapter 3.