On the optical theory of photoelastic tomography

In recent years many authors have considered the possibility of using tomography for nondestructive determination of three-dimensional stress fields. A natural starting point for this is integrated photoelasticity. The problem is complicated since the stress field is a tensor field, and in the general case in integrated photoelasticity the relationships between the measurement data and the parameters of the stress field are non-linear. To elucidate these relationships, we have systematically studied the propagation of polarized light in an inhomogeneous birefringent medium. The inverse problem of integrated photoelasticity is formulated in the general form, and particular cases in which the polarization transformation matrix is exactly determined by integrals of the stress tensor components are considered. The possibility of using the Radon inversion for approximate determination of the normal stress field in an arbitrary section of the test object is outlined.