<title>Enhanced backscatter and turbulence effects on pupil-plane speckle imaging system</title>

Abstract

We investigate the effects of turbulence on pupil-plane speckle imaging system that has been proposed to provide highresolution images of a low Earth orbit (LEO) satellite using laser illumination. We present a theory and numerical results for the normalized speckle covariance for one-dimensional object in the turbulent atmosphere and demonstrate that turbulenceinduced anisoplanatism and scintillation degrades this characteristic. The effect of anisoplanatism is associated with the finite size of a satellite. Due to a finite satellite dimension, optical waves arrive at the receiver from different directions determined by the angular size of the satellite and sample different turbulence. The resulting phase difference degrades the normalized speckle covariance. This effect is similar to the degradation of the performance of adaptive optics system caused by turbulence-induced anisoplanatism when a reference beacon is separated from the target at some distance. Scintillation on the downlink path also degrades the normalized speckle covariance. It causes the dc-and ac-components of the speckle correlation to exceed their values in a free space when the separation between the observation points is smaller than the spatial correlation scale of the scintillation. At the same time, both components are decreased for large separations when scintillation is uncorrelated. This reduces the normalized speckle covariance and can degrade the performance of a pupilplane speckle imaging system. The effect of scintillation on the dc-and ac-components of the speckle correlation is similar to the enhanced backscatter phenomenon, in which the average power of the laser return in the strictly backward direction in the turbulent atmosphere exceeds its value in free space. For a small object, the effect of scintillation on the speckle covariance predominates. The speckle statistics for the space-to-ground scenario differ from that for the horizontal path.