Isochromate fringes simulation by Cassini-like curves for photoelastic analysis of birefringent crystals

In optically birefringent uniaxial and biaxial crystals, analyzed by plane polariscope, isochromate interference fringes can be observed. By means of the classical electromagnetic theory a Cassini-like analytical equation of the isochromate fringes, depending on the refraction indexes, has been obtained. The proposed analytical equation is a useful tool to evaluate the internal stress state, as it is related to the isochromate shapes owing to the induced variation of the refraction indexes. Uniaxial crystals can assume complex biaxial behaviour due to particular stress configurations. PbWO4 (PWO) uniaxial scintillating crystals have been studied. The Cassini-like curves fit well experimental measurements in the case of uniaxial stress. In this research work, a simple model has been proved in the case of strong isochromate fringes distortion due to a stress gradient induced by the bending load. The model fits well the interference pattern, acquired experimentally. This study can pave the way for the quality control on scintillating crystals, used in the fields of high-energy detectors, security and biomedical applications, with complex internal stress state.