A lidar model for a rough-surface target: Method of partial coherence

Renewed interest in the propagation characteristics of a partially coherent beam has led to several recent studies that have extended theoretical developments started in the 1970s and 1980s. In this paper we use a model developed by the authors for single-pass propagation of a partially coherent beam and extend it to the case of a Gaussian-beam wave reflected from a finite rough-surface reflecting target. This model can be modeled as a random phase screen (or diffuser) in front of a smooth finite reflector. The target acts like a deep random phase screen for the case of a fully diffuse surface and becomes a continually weakening phase screen as the target surface become smoother. We present mathematical models for the mutual coherence function (MCF) and the scintillation index of the reflected Gaussian-beam wave in the presence of atmospheric turbulence. This analysis includes partial and fully developed speckle from the target. From the normalized MCF, estimates are given for the speckle size in the pupil plane and image plane as a function of transmitted beam wave characteristics, size and roughness of the target, and size of the receiver-collecting lens. Expressions for the scintillation index are valid under weak-to-strong fluctuation conditions and are shown to agree with well-known results in limiting cases of a fully diffuse target and a smooth reflector.