Fringe modelling and Photoelastic stress Measurement method in tetragonal PWO observed in the plane normal to a crystallographic a-axis

Scintillator crystals like the tetragonal PbWO${}_4$ (PWO) are largely used in calorimeters, for instance the CMS at CERN and in the PANDA calorimeter project. The performances of those calorimeters are directly linked to crystals homogeneity and quality, which can be assessed using indicators such as residual stress state condition. Since it is fundamental to develop and refine new mathematical models for the structural characterization and stress analysis of the crystalline materials, in this paper we present a novel approach aimed at the evaluation of stress or defect distribution and inhomogeneity, by analysing images obtained with photoelastic conoscopic system. A new model is proposed for the correct mathematical interpretation of the fringe pattern obtained by investigating the crystal in direction orthogonal to the uniaxial optical axis and parallel to the crystallographic a-axis. The model will be validated against experimentally acquired fringe patterns. A comparison with a simplified procedure, which operatively, reduces the computational effort, will be detailed. After a complete description of the fringe pattern, a linearized model is proposed in such a way that we obtain a simple stress intensity evaluation via experimentally easy measurable parameters, thus realizing a model based measurement of stress state. The results make the proposed procedure reliable, and useful also for other crystals symmetries.