Enhanced-displacement measurement using a generalized formulation for double-aperture specklegrams

A generalized form for the intensity distribution at the observation plane of a spatially filtered double-aperture specklegram is derived using classical Fresnel diffraction theory. The simplified formulas obtained by previous authors are found to be a special case of the general formula. In addition, both analytical and experimental results show that a variation in sensitivity of the double-aperture method exists within any given halo in the filter plane, even in the central D.C. halo. Also, in the D.C. halo, analytical and experimental work has shown that displacements can be measured parallel to the embedded grid present on the image, thereby demonstrating that a moiré analogy is inadequate to fully describe the phenomena. Finally, a comparison of experimental data to theoretical results based on the generalized formulation demonstrates (a) that the limits proposed by the authors for measuring displacements by use of the double-aperture method are valid, and (b) that the double-aperture method can be extended to measure displacements beyond those predicted by a moiré interpretation.