Strong correlations have been found in the polarization of light transmitted through a polycrystalline material and the grain sizes and orientations of that material. Experiments and supporting simulations with irregularly shaped single quartz crystals show that linear polarization is lost more rapidly as grain sizes decrease and the angular spread of the crystal orientations increase. A quantitative method using Stokes matrices to predict such changes is described and experimentally verified using an apparatus to vary the orientation of irregular quartz crystals. Grain sizes are varied between 1mm and 4mm, and the angular spreads in the crystal orientation are varied between 9° and 27°. This technique has applications to identify changes in crystal structure of transparent uniaxial polycrystalline materials, especially in the nondestructive characterization of glacial ice.