Stress state of a hale-space of inhomogeneous depth

Kaliningrad Technical Institute of the Fish Industry and Economy. Translated from Prikladnaya Mekhanika, Vol. 24, No. 11, pp. 3–9, November, 1988.     

Tomography in Optically Axisymmetric Media

A generalization of the Cormac algorithm for the inversion of the Radon transformation in an optical medium with an axisymmetric index of refraction has been proposed. The distribution of rays is such that only one ray passes through any two points in the circle. A “parallel scanning scheme” of tomography has been considered: a cylindrical object is illuminated by a parallel beam of light, the rays of which are deflected into the cylinder. There is no refraction on the surface of the cylinder. The algorithm assumes the possibility of attenuation on a ray, which also has an axisymmetric character. Such a type of ray deflection occurs in problematic issues of the tomography of GRADANs, light guides, and plasma.

     

Tensor tomography of residual stresses of hexagonal single crystals

A method for determining residual stresses in elongated transparent blanks of hexagonal single crystals the optical axis of which is directed along the crystal is proposed. It is assumed that the residual deformation tensor is of thermal character and is characterized by a fictitious temperature. Characteristic parameters of polarized light have been measured by the tomographic method in the plane orthogonal to the single crystal axis.     

Ray integrals of integrated photoelasticity at weak optical anisotropy

As initial data, optical polarization tomography of tensor and vector fields uses ray integrals the values of which are determined from polarization measurements. Most algorithms of integrated photoelasticity are based on the linear approximation of the solution of the birefringence equations. In this work, the approximation of smooth rotation of quasi-principal axes of the polarization tensor is proposed for use in approximating values of ray integrals.     

Polarization tomography of the tokamak plasma magnetic field

Optical polarization tomography of the tokamak plasma magnetic field is considered in the context accepted for large magnetic fields. Two models of the interaction between the magnetic field and radiation are studied: (1) the Faraday rotation (FR) of the polarization plane is imposed on birefringence caused by the toroidal component and (2) the Cotton-Mouton effect (CME) is imposed on the FR. Previously, these problems were solved with allowance for only one of the optical effects. New integrals caused by the amplification of the magnetic field are added to ray integrals used earlier. The retrieval of the magnetic field is based on the vector Radon transform (VRT) of imaginary absorption. Formulas of the inverse VRT are derived using generalized conditions from R. Novikov on the Radon transform with absorption.