## Abstract

We outline a novel method for determining the shape of an object by
use of temporal Fourier-transform analysis in dual-beam illumination
speckle interferometry. The object whose shape is to be determined
is rotated about an axis, and a number of frames of the image of the
object motion are acquired. Temporal in-plane displacement that is
due to the object rotation is related to the shape of the object and is
retrieved from this large set of data by Fourier
transformation. With this method one can determine the absolute
height of the object with variable resolution, thereby allowing shapes
of objects with large and small slopes to be determined. The theory
of the method along with experimental results is presented.

© 1998 Optical Society of America

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### Equations (6)

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(1)
$$I\left(x,y,t\right)={I}_{0}\left(x,y\right)\left(1+Vcos\left\{{\mathrm{\Phi}}_{0}\left(x,y\right)+\frac{2\mathrm{\pi}}{\mathrm{\lambda}}\left[2U\left(x,y,t\right)sin{\mathrm{\theta}}_{1}\right]\right\}\right).$$
(2)
$$f\left(\mathrm{med}\right)\left[x,y,t\right]=\frac{2U\left(x,y,t\right)sin\mathrm{\theta}}{\mathrm{\lambda}t}.$$
(3)
$$\mathrm{\Phi}\left(x,y\right)=\frac{4\mathrm{\pi}U\left(x,y\right)sin\mathrm{\theta}}{\mathrm{\lambda}}.$$
(4)
$$U\left(x,y\right)=\frac{2h\left(x,y\right)sin\left(\mathrm{\omega}/2\right)cos\left[\mathrm{\alpha}\left(x,y\right)+\mathrm{\omega}/2\right]}{cos\left[\mathrm{\alpha}\left(x,y\right)\right]}.$$
(5)
$$h\left(x,y\right)\approx \frac{\mathrm{\Phi}\left(x,y\right)\mathrm{\lambda}}{8\mathrm{\pi}sin\left(\mathrm{\omega}/2\right)sin\mathrm{\theta}}.$$
(6)
$${N}_{max}=\frac{2\mathrm{\sigma}sin\mathrm{\theta}}{\mathrm{\lambda}}.$$