Polarimetric Tomography for Anisotropic Samples

Abstract

Injection-molded lenses exhibit inhomogeneous stress-induced birefringence, which degrades optical performance. Conventional measurement techniques, such as the photoelastic method, have been used to analyze 3D birefringence distributions, but typically rely on predefined material constants, limiting their applicability. This dissertation introduces a framework for 3D characterization of birefringence in inhomogeneous anisotropic materials using tomographic polarimetry, where the birefringence distribution is represented by spatially varying 3D index ellipsoids describing the local anisotropic refractive index. A linear forward model links these ellipsoids to tomographic polarimetric observations, enabling a tensor-valued backprojection algorithm for reconstructing the full 3D distribution. A key feature of this framework is a novel algorithm capable of reconstructing the 3D index ellipsoid distribution from sinograms composed solely of cross-sectional ellipses orthogonal to each projection direction. Using this approach, both reconstructions from optical path lengths, which serve as an intermediate step, and reconstructions based directly on tomographic polarimetric observations achieve errors below 10%. While the current model excludes refraction to establish a clear theoretical foundation, future work will incorporate refraction to further improve accuracy and broaden applicability.