The linearized problem of magneto-photoelasticity

The equations of magneto-photoelasticity are derived for a nonhomogeneous background isotropic medium and for a variable gyration vector. They coincide with Aben's equations in the case of a homogeneous background medium and of a constant gyration vector. We obtain an explicit linearized formula for the fundamental solution under the assumption that variable coefficients of equations are sufficiently small. Then we consider the inverse problem of recovering the variable coefficients from the results of polarization measurements known for several values of the gyration vector. We demonstrate that the data can be easily transformed to a family of Fourier coefficients of the unknown function if the modulus of the gyration vector is agreed with the ray length.