## Abstract

The compensation of large in-plane motions in digital
speckle-pattern interferometry (DSPI) with the use of digital
speckle photography (DSP) is demonstrated. Ordinary recordings
of DSPI are recombined and analyzed with DSP. The DSP result is
used to compensate for the bulk speckle motion prior to calculation of
the phase map. This results in a high fringe contrast even for
deformations of several speckle diameters. In addition, for the
case of an in-plane deformation, it is shown that the absolute phase
change in each pixel may be unwrapped by use of the DSP result as an
initial guess. The principles of this method and experiments
showing the in-plane rotation of a plate and the encounter of two
rounded plates are presented.

© 1999 Optical Society of America

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### Equations (13)

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(1)
$${I}_{n}\left({x}_{1},{y}_{1}\right)={I}_{0}\left({x}_{1},{y}_{1}\right)+{I}_{m}\left({x}_{1},{y}_{1}\right)cos\left[\mathrm{\varphi}\left({x}_{1},{y}_{1}\right)+n\mathrm{\pi}/2\right],n=0,1,2,3,$$
(2)
$${I}_{n}\left({x}_{2},{y}_{2}\right)={I}_{0}\left({x}_{2},{y}_{2}\right)+{I}_{m}\left({x}_{2},{y}_{2}\right)cos\left[\mathrm{\varphi}\left({x}_{2},{y}_{2}\right)+n\mathrm{\pi}/2+\mathrm{\Omega}\left({x}_{2},{y}_{2}\right)\right],n=0,1,2,3,$$
(3)
$${C}_{1}={I}_{0}\left({x}_{1},{y}_{1}\right)-{I}_{2}\left({x}_{1},{y}_{1}\right)=2{I}_{m}\left({x}_{1},{y}_{1}\right)cos\left[\mathrm{\varphi}\left({x}_{1},{y}_{1}\right)\right],$$
(4)
$${S}_{1}={I}_{3}\left({x}_{1},{y}_{1}\right)-{I}_{1}\left({x}_{1},{y}_{1}\right)=2{I}_{m}\left({x}_{1},{y}_{1}\right)sin\left[\mathrm{\varphi}\left({x}_{1},{y}_{1}\right)\right],$$
(5)
$${C}_{2}={I}_{0}\left({x}_{2},{y}_{2}\right)-{I}_{2}\left({x}_{2},{y}_{2}\right)=2{I}_{m}\left({x}_{2},{y}_{2}\right)cos\left[\mathrm{\varphi}\left({x}_{2},{y}_{2}\right)+\mathrm{\Omega}\left({x}_{2},{y}_{2}\right)\right],$$
(6)
$${S}_{2}={I}_{3}\left({x}_{2},{y}_{2}\right)-{I}_{1}\left({x}_{2},{y}_{2}\right)=2{I}_{m}\left({x}_{2},{y}_{2}\right)sin\left[\mathrm{\varphi}\left({x}_{2},{y}_{2}\right)+\mathrm{\Omega}\left({x}_{2},{y}_{2}\right)\right].$$
(7)
$$2{I}_{m}\left({x}_{1},{y}_{1}\right)={\left(C_{1}{}^{2}+S_{1}{}^{2}\right)}^{1/2},$$
(8)
$$2{I}_{m}\left({x}_{2},{y}_{2}\right)={\left(C_{2}{}^{2}+S_{2}{}^{2}\right)}^{1/2}.$$
(9)
$$\mathrm{\Omega}\left(x,y\right)=\left(4\mathrm{\pi}/\mathrm{\lambda}\right)u\left(x,y\right)sin\mathrm{\theta},$$
(10)
$${\mathrm{\Omega}}_{w}\left(x,y\right)=\mathrm{arctan}\left(\frac{{C}_{1}{S}_{2}-{C}_{2}{S}_{1}}{{C}_{1}{C}_{2}+{S}_{1}{S}_{2}}\right),$$
(11)
$$\stackrel{\u02c6}{\mathrm{\Omega}}\left(x,y\right)=\left(4\mathrm{\pi}/\mathrm{\lambda}\right){u}_{\mathrm{DSP}}\left(x,y\right)sin\mathrm{\theta},$$
(12)
$$\mathrm{\Omega}\left(x,y\right)=2\mathrm{\pi}m+{\mathrm{\Omega}}_{w}\left(x,y\right),$$
(13)
$$m=\mathrm{INT}\left[\frac{\stackrel{\u02c6}{\mathrm{\Omega}}\left({x}_{1},{y}_{1}\right)-{\mathrm{\Omega}}_{w}\left({x}_{1},{y}_{1}\right)}{2\mathrm{\pi}}\right],$$