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Experimental Mechanics

, Volume 9, Issue 1, pp 9–16 | Cite as

The optical-rotation effect in photoelastic shell analysis

Paper shows how modern descriptions of polarized light can be advantageously used to predict the influence of the rotation effect on optical observations
  • J. D. Riera
  • R. Mark
Article

Abstract

A difficulty commonly encountered in the three-dimensional photoelastic analysis of thin-shell structures1–9 is the so-called optical rotation effect4,8–10 which, in spite of some noteworthy efforts, has not yet been fully elucidated. The objective of this paper is to show how modern descriptions of polarized light can be advantageously used to predict the influence of the rotation effect on optical observations. Use will be made of the Poincaré sphere representation of polarized light and of the associated Mueller calculus. Because these subjects may be unfamiliar, the fundamental concepts involved are briefly discussed in each case and readily available supplementary references are given.

Keywords

Mechanical Engineer Fluid Dynamics Optical Rotation Fundamental Concept Optical Observation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols

a

amplitude

d

semiaxis diameter of polarization ellipse

D, E, F, G

functions defined by eq (16)

D

Jones vector

E

electric vector

Ex,Ey

electric-vector components

f

normal stress-fringe constant in monochromatic light

H

magnetic vector

h

retarder thickness

M

Mueller matrix

Mx

moment

m

matrix elements

N

number of linear retarder elements

n

retardation

n

retardation with zero rotation

O

origin

P

point on Poincaré sphere representing polarization state

R

point on Poincaré sphere representing retarder fast-axis azimuth

r

dimensionless ratio of rotation to retardation

\(\bar r\)

average rotation to retardation ratio

r

position vector=r(x, y, z)

S0,S1,S2,S3

Stokes parameters

s

unit vector in a fixed direction

t

time

V

Stokes vector

ν

velocity of propagation

x, y, z

rectangular coordinates

α

angle between model reference axis and algebraically largest principal stress direction

α′

angle between model reference axis and largest in-plane stress direction

δ

relative phase retardation; Poincaré sphere rotation

λ

angle between reference axis and polarization-ellipse major axis

Σ

Poincaré sphere

\(\sigma _1 , \sigma _2 \)

principal stress normal to the axis of light propagation

τ

variable part of the phase factor=Ω[t(r·s)/ν]

ω

ellipticity defined by eq (8)

Ω

angular velocity

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References

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Copyright information

© Society for Experimental Mechanics, Inc. 1969

Authors and Affiliations

  • J. D. Riera
    • 1
  • R. Mark
    • 1
  1. 1.Civil EngineeringPrinceton UniversityPrinceton

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