# Photoelastic model measurement with rotated principal axes by scattered-light photoelasticity

## Authors

- Received:
- Revised:

DOI: 10.1007/BF02427956

- Cite this article as:
- Kihara, T. Experimental Mechanics (2004) 44: 455. doi:10.1007/BF02427956

- 3 Citations
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## Abstract

The method of measurement of a three-dimensional photoelastic model with rotated principal axes has not yet been fully experimentally established. It is known that a three-dimensional photoelastic model can be reduced to an optically equivalent model. In this paper, the optically equivalent model is realized from a stratified model consisting of two layers of the frozen stress model. The secondary principal stress direction and the relative phase retardation of the frozen disk model in the stratified frozen stress model are determined for the entire field from Stokes parameters obtained by scattered-light photoelasticity using unpolarized light. The accuracy of these values is confirmed by a comparison with results only from the frozen stress disk model.

### Key Words

Scattered-light photoelasticitythree-dimensional photoelasticitydigital photoelasticityrotated principal axesunpolarized light### Nomenclature

*M*_{j}Mueller matrix of linear retarder between points

*y*_{j}and*y*_{j−1}- ρ
_{j} relative phase retardation between points

*y*_{j}and*y*_{j−1}- ψ
_{j} angle of one of the principal stress directions between points

*y*_{j}and*y*_{j−1}*M*_{j−1,0}Mueller matrix of linear retarder of the equivalent model between points

*y*_{j−1}and*y*_{0}- ρ
_{j−1,0} characteristic phase retardation between points

*y*_{j−1}and*y*_{0}- ψ
_{j−1,0} primary characteristic direction between points

*y*_{j−1}and*y*_{0}*R*(2ω_{j}−1,0)Mueller matrix of pure rotator of the equivalent model between points

*y*_{j−1}and*y*_{0}**E**_{yj};θ)incident unpolarized light along θ deg with the

*x*-axis in the*x−z*plane at point*y*_{j}(**S***y*_{j}; θ)Stokes vector of resultant scattered light of

**E**_{yj;θ}observed from the*y*-axis, which is the linearly polarized light of azimuth θ measured from the*z*-axis in the*x−z*plane(**S***y*_{j}, y_{0};θ)Stokes vector of the light emerged through the medium between the points

*y*_{j}and*y*_{0}from the scattered light(**S***y*_{j};θ) at point*y*_{j}**s**(*y*_{j}, y_{0};θ)normalized Stokes vector of

(**S***y*_{j}, y_{0};θ)*I*_{j}(θ_{2},α_{2})light intensity through analyzing system from the scattered light at point

*y*_{j}- θ
azimuth of the linearly polarized light of the scattered light, as measured from the

*z*-axis- β
_{2}and α_{2} azimuth of the fast axis of

*Q*_{2}and aximuth of the transmission axis of*P*_{2}of analyzing system, as measured from the*z*-axis, respectively- Δρ
phase difference error of

*Q*_{2}to light wavelength used*V*Jones matrix of the photoelastic model which allows the rotation of the principal axes

*S(A)*rotation matrix with rotary power

*A**G*(γ)matrix of the retardation plate with retardation 2γ and fast axis at 0°

*J*_{1}Jones matrix of a linear retarder with the principal stress direction ψ

_{2}and the relative retardation ρ_{1}*J*(y_{2}, y_{0})Jones matrix of the stratified photoelastic model constructed from two linear retarders

*J*_{1}and*J*_{2}