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Item Stigmatic spectroscopy of the solar atmosphere in the vacuum-ultraviolet(Montana State University - Bozeman, College of Letters & Science, 2020) Courrier, Hans Thomas; Chairperson, Graduate Committee: Charles C. Kankelborg; Charles C. Kankelborg was a co-author of the article, 'Using local correlation tracking to recover solar spectral information from a slitless spectrograph' in the journal 'Journal of astronomical telescopes and imaging systems, SPIE' which is contained within this dissertation.; Charles C. Kankelborg, Bart De Pontieu and Jean-Pierre Wulser were co-authors of the article, 'An on orbit determination of point spread functions for the interface region imaging spectrograph' in the journal 'Solar physics' which is contained within this dissertation.; 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 and David L. Windt were co-authors of the article, 'The EUV snapshot imaging spectrograph (ESIS)' which is contained within this dissertation.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.