Fringe positions in double-exposure speckle photography

Double-exposure records in speckle photography or particle image velocimetry are often evaluated by analysis of the system of Young's diffraction fringes. Fringe spacing, necessary to calculate the displacement, is determined from the positions of fringe maxima or minima. These, however, are influenced by the diffraction halo function and by fringe visibility. A generalized theory of the effects is presented, including position dependent visibility and fringe phase. Evaluations are given for disk-shaped particle images in particle image velocimetry, and for coherent and incoherent speckle photography. Fringe shifts are determined numerically for commonly encountered values of fringe density and visibility thus presenting a basis for rapid assessment of accuracy in metrological experiments.