Finding small displacements of recorded speckle patterns: revisited

Abstract

? Copyright 2015 SPIE.An analytical expression for the bias effect in digital speckle correlation is derived based on a Gaussian approximation of the spatial pixel size and array extent. The evaluation is carried out having assumed an incident speckle field. The analysis is focused on speckle displacements in the order of one pixel, thus having no speckle decorrelation. Furthermore, sensitivity is a main issue wherefore we need speckles close to the pixel size, which means that speckle averaging becomes important, and that Nyquist's criteria may not be fulfilled. Based on these observations, a new correlation method is introduced, which alleviates the need to know the expected shape of the crosscovariance between the original and the off-set recorded speckle pattern. This concept calls for correlating the crosscovariance with the auto covariance, which essentially carries information on the expected shape of the crosscovariance.