Contrast of time-averaged speckle patterns at a defocused image plane

Abstract

An expression for the contrast of time-averaged speckle patterns formed at a defocused image plane by an out-of-plane vibrating diffuse object is derived with the assumptions that circular Gaussian statistics hold for the formation of speckles and the object surface is approximated by the deep phase screen. The theoretical result shows that the contrast degradation occurs at all the positions of the observation plane and increasingly proceeds with the increase of both the vibration slope of the object and the aperture width of pupil used. It is also found that the contrast variation due to the object vibrations becomes particularly noticeable at a defocused plane taken close to the focal plane.