Range and accuracy of speckle displacement measurement in double-exposure speckle photography

Abstract

A theoretical analysis is made of the possible range and accuracy of speckle displacement measurement in double-exposure speckle photography. It is shown that the condition of marginally possible fringe reading and the accuracy of the measurement of speckle displacement in pointwise reading of a doubly recorded specklegram are determined by the degree of correlation between the two recorded speckle patterns and the number of speckles illuminated by the reading beam. Specifically, the fringe reading is possible only if γ>2/N, and the statistical error δd of the measured speckle displacement is ηωx{(1/N)|7 + 4[(1 − γ2)/γ2]|}1/4, where γ is the degree of similarity between the two correlated speckle patterns, N is the number of speckle grains probed by the reading laser beam, and ηωx is the mean radius of curvature of a speckle grain at its peak. Also, it is shown that strain on the object surface introduces an additional systematic error ∊0 · d0/2, where ∊0 is the surface strain and d0 is the measured displacement vector of the speckles.