Localization of fringes in speckle photography that are due to axial motion of the diffuse object

Speckle photographic techniques have been employed for the measurement of axial displacement of a diffuse object. In this method a double exposure is made on a photographic plate (specklegram) with the object axially translated between exposures. The specklegram is kept in a collimated beam for filtering. A set of circular fringes is formed when a circular aperture is placed a distance behind the specklegram on axis. The plane of localization shifts when an uncollimated beam is used for filtering. It is shown that the fringes never localize at the specklegram plane. It is also shown that there is an optimum aperture size for obtaining high-contrast fringes. The optimum aperture size and localization plane depend on the degree of collimation during filtering. Both theory and experimental results are presented in this paper.