Model-based inversion of speckle interferometer fringe patterns

Abstract

Micrometer-scale rigid-body translations are determined fromelectronic speckle interferometric fringe patterns. An iterativeminimum error procedure employs the relative fringe order of pickedpositions of fringe maxima and minima within a single interferogram tocalculate the displacement field directly. The method does notcalculate the displacement at a single point but relies on theassumption that the character, but not the magnitudes or directions, ofthe displacements over the viewing area of the interferogram isknown. That is, a model of the displacements exists. Onperfect, noise-free forward modeled fringe patterns calculated for an 8.0-mum displacement, the phase error is less than 2 x10(-6) fringe orders (1.3 x 10(-5) rad)and probably results only from numerical noise in the inversion. Onreal fringe patterns obtained in electronic speckle interferometricexperiments, mean phase errors are generally less than 5 x10(-5) fringe orders (3.2 x 10(-4)rad), suggesting that the technique is robust despite errorsresulting from speckle noise, lack of accuracy in positioning ofexperimental components, and image-distortion corrections.