Abstract

An optical system that incorporates active coherent illumination of a distant, optically rough surface will suffer speckle effects in the receiver plane. The statistics of optical energy detection with integrated speckle and additive Gaussian noise are shown to be characterized by a parabolic cylinder probability density. Expressions are obtained for the moments of the density, signal-to-noise ratio, and probability of detection. Receiver performance is shown to be highly dependent on the parameter M, which describes the number of independent spatial and temporal correlation cells included within the observation. An example calculation is performed for a laser radar system, illustrating that extra illuminator power is required to compensate for speckle. Together with earlier work by Goodman [ Proc. IEEE 53, 1688 ( 1965)] that defines detection of integrated speckle with Poisson counting statistics, the limiting performance bounds are established for optical energy detection with integrated speckle.

© 1984 Optical Society of America

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