# Interpretation of fringes in stress-holo-interferometry

DOI: 10.1007/BF02324907

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

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## 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

*I*_{v}′normalized intensity of the virtual image

*t*thickness of the unstressed model

*E*modulus of elasticity

- ν
Poisson's ratio

*n*_{o}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

*t*_{1},*t*_{2}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

*n*_{p}isopachic-fringe order

*n*_{c}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*