On the Bertin surfaces of photoelastic crystals

Conoscopic analysis of interference fringes is one of the most useful tools for investigating the mechanical properties of a crystal. These fringes are generated by a surface of constant phase difference, called the Bertin surface, whose shape depends on the piezo-optic properties of the material and on the applied stress. Here we investigate systematically for the first time, to the best of our knowledge, these surfaces as algebraic surfaces. We also describe their dependence on the stress when these are "small" and give a detailed analysis for all crystallographic classes.