Quantifying Stress States of Theoretically Modelled Polarimetric Measurements on Dielectric Media

TL;DR

This paper presents a theoretical model for reconstructing surface stress states of dielectric materials using polarimetric measurements, achieving an accuracy of a few MPa in stress magnitude estimation.

Contribution

The work introduces a novel approach to determine surface stress states from reflected polarization signals by modeling and fitting the Stokes vector dependencies.

Findings

The model accurately estimates surface stress magnitude within a few MPa.

A database of reflected Stokes vectors was created to relate polarization signals to stress states.

The approach enables reconstruction of principal stress axes and their orientations.

Abstract

This work introduces and characterizes a theoretical model of a reflective polarimetric measurement technique determining the surface stress of a dielectric material, e.g. glass. We have developed a procedure to reconstruct the actual stress state, which is the orientation and value of the principal axes of stress, from the calculated Stokes vector components that would appear as polarization signals in a measurement. We consider a special geometry of the principle stress axis, where we chose one of them to be perpendicular to the surface and relaxed to a zero value. Our new approach of reconstructing surface stress states from reflected polarization states embraces the determination of the reflection M\"uller matrix. With that and an initial Stokes vector, the resulting reflected Stokes vector is calculated to create a database. The database represents the dependence of the resulting Stokes vector on the initial Stokes vector and the stress states included in the reflection matrix, which is iteratively calculated for several stress components and its orientations. Introducing a model for the dependency of the reflected Stokes vector components on the stress states and fitting it to the database results in a system of equations of those dependencies which are solved for the stress state components and orientation. Finally, we found a theoretical determination accuracy of the model for surface stress magnitude to be of the order of a few MPa.