## Abstract

Micrometer-scale rigid-body translations are determined from
electronic speckle interferometric fringe patterns. An iterative
minimum error procedure employs the relative fringe order of picked
positions of fringe maxima and minima within a single interferogram to
calculate the displacement field directly. The method does not
calculate the displacement at a single point but relies on the
assumption that the character, but not the magnitudes or directions, of
the displacements over the viewing area of the interferogram is
known. That is, a model of the displacements exists. On
perfect, noise-free forward modeled fringe patterns calculated for an
8.0-μm displacement, the phase error is less than 2 ×
10^{-6} fringe orders (1.3 × 10^{-5} rad)
and probably results only from numerical noise in the inversion. On
real fringe patterns obtained in electronic speckle interferometric
experiments, mean phase errors are generally less than 5 ×
10^{-5} fringe orders (3.2 × 10^{-4}
rad), suggesting that the technique is robust despite errors
resulting from speckle noise, lack of accuracy in positioning of
experimental components, and image-distortion corrections.

© 1998 Optical Society of America

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