Experimental Mechanics

, Volume 11, Issue 4, pp 161–166

Interpretation of fringes in stress-holo-interferometry

Detailed analysis of the light-intensity equations corrects errors in earlier interpretations of the interference-fringe patterns
  • R. J. Sanford
  • A. J. Durelli
Article

DOI: 10.1007/BF02324907

Cite this article as:
Sanford, R.J. & Durelli, A.J. Experimental Mechanics (1971) 11: 161. doi:10.1007/BF02324907

Abstract

Previous studies had concluded that stressholo-interferometry patterns consist of the independent superposition of the isopachic family (with half-order fringe shifts) and the isochromatic family. It is shown here that this interpretation is not always valid and can result in serious errors in some cases. In particular, it is demonstrated that the position, and even the existence of the fringes, are affected by the interaction of the isopachics and isochromatics. This effect is most pronounced when the two families of fringes are nearly parallel and of approximately the same spatial frequency. The independent superposition interpretation is most accurate when the two families of fringes are orthogonal, whatever the ratio of spatial frequencies might be. These properties are illustrated using computer-generated holographic interference patterns.

Nomenclature

Iv

normalized intensity of the virtual image

t

thickness of the unstressed model

E

modulus of elasticity

ν

Poisson's ratio

no

index of refraction of unstressed model

n

index of refraction of surrounding media

A, B

Maxwell-Neumann stress-optic constants

λ

wavelength of the light employed

\(\sigma _1 ,\sigma _2 \)

principal stresses in the plane of the wavefront

t1,t2

exposure times of the unstressed and stressed model, respectively

Ω

ratio of spatial frequencies of the isopachic to the isochromatic fringes

ξ

dimensionless distance between isochromatic fringes

Φ

phase angle of the isopachic function at an isochromatic fringe

np

isopachic-fringe order

nc

isochromatic-fringe order

A

\(A\prime - \frac{v}{E}(n_0 - n)\)

B

\(B\prime = A - \frac{v}{E}(n_0 - n)\)

C

A−B

Copyright information

© Society for Experimental Mechanics, Inc. 1971

Authors and Affiliations

  • R. J. Sanford
    • 1
  • A. J. Durelli
    • 2
  1. 1.Naval Research LaboratoryWashington, D. C.
  2. 2.Catholic University of AmericaWashington, D. C.