Abstract: In this article we derive the complete set of formulas needed to generate physically plausible images of uniaxial crystals. So far no computer graphics publication contains all the formulas one needs to compute the interaction of light with such crystals in a form that is useable by a graphics application, especially if a polarization-aware rendering system is being used.

This paper contains the complete derivation of the Fresnel coefficients for birefringent transparent materials, as well as for the direction cosines of the extraordinary ray and the Mueller matrices necessary to describe polarization effects. The formulas we derive can be directly used in a ray based renderer, and we demonstrate these capabilities in test scenes.