Maximum-likelihood analysis of speckle photography fringe patterns

A new method for analyzing the Young's fringe patterns from a double-exposure speckle photograph is proposed based on maximum-likelihood estimation. Unlike previous linear algorithms, which rely on Fourier spectral analysis, the method permits knowledge of the speckle-noise statistics (in particular, that the noise is multiplicative rather than additive) to be incorporated in a systematic way. As a result, random errors in the measured displacement components are reduced, in the case of good visibility fringe patterns by a factor of up to 6. The proposed method is also applicable to the general problem of measuring the spatial frequency components of a two-dimensional sinusoid in the presence of signaldependent noise.