Reconstruction of spatially inhomogeneous dielectric tensors via optical tomography

Abstract

A method to reconstruct weakly anisotropic inhomogeneous dielectric tensors inside a transparent medium is proposed. The mathematical theory of Integral Geometry is cast into a workable framework which allows the full determination of dielectric tensor fields by scalar Radon inversions of the polarization transformation data obtained from six planar tomographic scanning cycles. Furthermore, a careful derivation of the usual equations of integrated photoelasticity in terms of heuristic length scales of the material inhomogeneity and anisotropy is provided, making the paper a self-contained account about the reconstruction of arbitrary three-dimensional, weakly anisotropic dielectric tensor fields.