## Abstract

Digital speckle-pattern interferometry systems for automatic measurement of deformations of a diffuse object are presented, which are based on a fringe scanning method with phase-shifted speckle interferograms. A digital speckle pattern before deformation of an object is recorded in the mass storage device of a computer facility. After deformation, four digital speckle patterns are recorded as changing the phase of reference light such as 0, *π*/2, *π*, and 3*π*/2, respectively. Four speckle interferograms, whose phases are shifted by 0, *π*/2, *π*, and 3*π*/2, are generated by calculating the square of the differences between speckle patterns before and after deformation. These interferograms are low-pass filtered to reduce speckle noise. The calculation of the arctangent with four phase-shifted speckle interferograms gives the optical path difference which is proportional to the deformation. A correction of the discontinuity of the calculated phase gives the numerical data of the deformation in the whole object area. Some experimental results for the measurement of out-of-plane, in-plane, and 3-D deformations are presented.

© 1985 Optical Society of America

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### Equations (9)

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(1)
$$\mathrm{\Phi}={tan}^{-1}\phantom{\rule{0.2em}{0ex}}\left[\frac{{I}_{4}-{I}_{2}}{{I}_{1}-{I}_{3}}\right]\phantom{\rule{0.3em}{0ex}}.$$
(2)
$${d}_{z}=\frac{\theta}{2\pi}\cdot \frac{\mathrm{\lambda}}{2}\cdot $$
(3)
$${d}_{x}=\frac{\mathrm{\lambda}}{2\phantom{\rule{0.2em}{0ex}}sin\phantom{\rule{0em}{0ex}}\theta}\cdot \frac{\varphi}{2\pi},$$
(4)
$${\mathrm{\Theta}}_{i}=\frac{2\pi}{{\mathrm{\lambda}}_{i}}[{l}_{i}\cdot \delta u+{m}_{i}\cdot \delta \upsilon +(1+{n}_{i})\cdot \delta w]\phantom{\rule{0.1em}{0ex}},$$
(5)
$${\mathrm{\Delta}}_{i}=\frac{2\pi}{{\mathrm{\lambda}}_{i}}[{l}_{i}\cdot \delta u+{m}_{i}\cdot \upsilon +(1+{n}_{i})\cdot w]\phantom{\rule{0.1em}{0ex}}.$$
(6)
$$\mathrm{\Delta}=\mathrm{A}\mathbf{\text{d}},$$
(7)
$$\begin{array}{cc}\mathrm{\Delta}=\frac{1}{2\pi}\phantom{\rule{0.2em}{0ex}}\left[\begin{array}{c}{\mathrm{\Delta}}_{1}\cdot {\mathrm{\lambda}}_{1}\\ {\mathrm{\Delta}}_{2}\cdot {\mathrm{\lambda}}_{2}\\ {\mathrm{\Delta}}_{3}\cdot {\mathrm{\lambda}}_{3}\end{array}\right],& \mathbf{\text{d}}=\phantom{\rule{0.2em}{0ex}}\left[\begin{array}{l}u\\ \upsilon \\ w\end{array}\right]\phantom{\rule{0.2em}{0ex}},\end{array}$$
(8)
$$\text{A}=\left[\phantom{\rule{0.1em}{0ex}}\begin{array}{ccc}{l}_{1}& {m}_{1}& 1+{n}_{1}\\ {l}_{2}& {m}_{2}& 1+{n}_{2}\\ {l}_{3}& {m}_{3}& 1+{n}_{3}\end{array}\phantom{\rule{0.1em}{0ex}}\right]\cdot $$
(9)
$$\mathbf{\text{d}}{=\text{A}}^{-1}\mathrm{\Delta},$$