Factorization of the polarization transformation matrix in integrated photoelasticity

In integrated photoelasticity, assessment of stresses in a three-dimensional specimen is based on the measurement of the change of polarization on many light rays that pass the specimen. Since the medium is optically anisotropic and inhomogeneous, the optical phenomena are nonlinear and solution of the inverse problem is complicated. Several methods of solving the inverse problem demand an efficient algorithm for solving the direct problem, i.e., for the calculation of the polarization transformation matrix on the basis of the stress field in the medium. We propose for this use factorization of the transformation matrix. We show that if the transformation of polarization is described by characteristic parameters, the three characteristic parameters can be determined by solving a single third-order differential equation. Since characteristic parameters can be measured experimentally, this approach can be used in practical three-dimensional stress analysis with integrated photoelasticity.