Chairperson, Graduate Committee: Charles C. KankelborgLastufka, Erica Anne2014-06-042014-06-042014https://scholarworks.montana.edu/handle/1/3287Modern telescopes are beginning to resolve structure in the Sun's photosphere at scales near and below 100 km, the length of the typical photon mean free path. In this thesis we discuss how LTE and non-LTE conditions affect the polarized spectral signatures of very small solar magnetic structures. Emergent spectra produced by atmospheres in LTE conditions are dominated by the integral along the entire line of sight, while under non-LTE conditions they originate from volumes on scales of the mean free photon path or longer. On scales approaching the mean free path, we expect non-LTE effects to result in a 'smearing' of the spectroscopic data. We examined magnetic and atmospheric features from numerical sunspot models created by Rempel (2012), which simulate the photosphere with spatial resolutions down to 12 km horizontally and 8 km vertically (Rempel et al., 2009a,b). Using a multi-dimensional non-LTE radiative transfer code and a multi-level iron atom, we generated polarization profiles of small magnetic structures in both 2- and 3D. The common diagnostic Fe I line pair at 630 nm allowed us to investigate the implications for our ability to accurately measure small-scale kilogauss magnetic elements. We searched a Hinode/SOT 2006 observation of a sunspot for matches to the simulated polarimetric data and examined the results of the MERLIN Milne-Eddington inversion code in light of our findings.enSolar photosphereMagnetic structureAstrophysical spectropolarimetryThermodynamicsThesisCopyright 2014 by Erica Anne Lastufka