Polarization-optical tomography of mechanical stresses in dielectric cylindrical structures of hexagonal single crystal

An Integrated Photoelasticity-Based Approach for the Reconstruction of Stress Profiles and Optical Anisotropy of GRIN Lenses

“…That is, the length of the periodicity L0 depends on the 𝑔R constant: As shown in [24][25][26], in the case of weakly and moderately gradient axisymmetric objects, the polarization of a probing beam is influenced by axial stresses σ z (r) in transverse translucence and by the difference of tangential and radial stresses ∆σ(r) = ∆σ θr (r) = σ θ (r) − σ r (r) in longitudinal translucence. RS difference distributions ∆σ θr (r) can be used to solve the direct problem of longitudinal translucence, that is, finding the radial distribution of the IPD and birefringence for GRIN segments of various lengths.…”

“…For the direct problem, we also take into account the contribution to the IPD from the component ∆ L 1 , which was neglected when considering the inverse problem for longitudinal translucency (i.e., the reconstruction of the RS from the corresponding experiments) [24][25][26].…”

“…When determining the stresses with this method, it is common to perform translucency on separate cross-sections of the object. As shown in [24,25], the integral equation for the phase difference (1) is reduced to the Abel integral equation for the case of transverse translucency of GRIN lenses with gR ≤ 0.3:…”

“…where x m -is the translucency parameter corresponding to the IPD minimum near the cylinder surface; ∆ T min -IPD value at point x m , u (r) = du/dr. Taking these into account, a regularized algorithm based on the spline approximation of ∆ T (x) and optimization of boundary conditions for ensuring the stability of the solution near the boundaries of the interval (0, R) was developed in [24][25][26].…”

“…Such a generalization of the relations in the inverse and direct problems of integral photoelasticity for the cases of transverse, longitudinal, and sagittal translucency GRIN lenses, taking into account the curvature of the trajectories of the rays propagating in them, was made in [24,25]. The analysis for the first two cases was also published in [26].…”