Experimental Mechanics

, Volume 37, Issue 1, pp 39–44

A measurement method of scattered light photoelasticity using unpolarized light

  • T. Kihara
Article

DOI: 10.1007/BF02328748

Cite this article as:
Kihara, T. Experimental Mechanics (1997) 37: 39. doi:10.1007/BF02328748

Abstract

This paper describes an automatic measurement method for the stress analysis of a three-dirnensional photoelastic model having the rotation of the principal stress by scattered-light photoelasticity using unpolarized light. The relative phase retardation and the principal stress directions of a linear retarder for a distance in the solid model are expressed in terms of measurable Stokes parameters. The method was used for measurements on a frozen stress sphere under diametral compression.

List of Symbols

ρ

relative phase retardation

PiEmphasis>/j

relative phase retardation at λi between the pointsyjandyj−1 in the model

λi

light wavelength

ψ

angle of one of the principal stress directions

ψj

angle of one of the principal stress directions between the pointsyjandyj−1 in the model

Eλiyj

incident unpolarized light at λi along θ deg with thex-axis in thexz plane at the pointyj

S(yj;θ)λi

Stokes vector of resultant scattered light ofEλiyj observed from they-axis, which is the linearly polarized light of azimuth θ measured from thez-axis in thexz plane

Mλij

Mueller matrix of linear retarder between pointsyj andyj−1at λi

U(yj,y0)λi

Mueller matrix of the photoelastic model between pointsyjandy0

Mλij−1,1

Mueller matrix of linear retarder with retardation pij-1,1, principal axes of azimuths ψj-1,1 and ψj-1,1 + σ/2 of optically equivalent model between pointsyj−1 andy0

R(ωj-1,1)

Mueller matrix of pure rottor with rotatory power ωj-1,1, of optically equivalent model between pointsyj−1 andy0

S(yj,y0;θ)λi

Stokes vector of the light emerged through the medium between pointsyjandy0 from the scattered lightS(yj;θ)λi at pointyj

s(yj,y0;θ)λi

normalized Stokes vector ofS(yj;y0;θ)λi

S0(yj;θ)λi

intensity of the scattered lightS(yj;θ)λi

N

integer

T(θ,β22)

light intensity emergin from analyzing system

β22

azimuth of the fast axis ofQ2 and azimuth of the transmission axis ofP2 of analyzing system, as measured fromz-axis, respectively

Δρi

phase difference error ofQ2 to λi

Copyright information

© Society for Experimental Mechanics, Inc. 1997

Authors and Affiliations

  • T. Kihara
    • 1
  1. 1.Department of Industrial Engineering, Faculty of Science and TechnologyKinki University, KowakaeHigashi-OsakaJapan