Reconstructing Inhomogeneous Birefringence Using a Tensor-Valued Backprojection

Injection-molded optical components often exhibit inhomogeneous stress-induced birefringence, which degrades optical performance. Conventional measurement techniques, such as the photoelastic method, can reconstruct 3D birefringence distributions by combining stress–optic relations with tomography, but their applicability is limited by the requirement for predefined photoelastic constants. This work presents a tensor-valued backprojection framework that reconstructs 3D birefringence distribution, formulated as spatially varying index ellipsoids, directly from tomographic views. Simulations demonstrate that six ellipsoid parameters can be reconstructed from 90 tomographic views with a relative reconstruction error below 10%. Furthermore, unobservable sinograms - containing a projection parallel to the view direction - are successfully derived from observable ones using pseudoinverse formulations. For this system to be full rank, a new constraint is derived: the spatial sampling must be limited to one-third the number of tomographic views. This approach establishes the feasibility of recovering the full index ellipsoid distribution from experimentally accessible measurements alone. By eliminating reliance on photoelastic constants, this framework provides a rigorous foundation for tomographic polarimetric imaging and non-destructive evaluation of anisotropic optical materials.