Folded-path weighting function for a high-frequency spherical wave

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Abstract
Analysis of signal characteristics observed in the receiving plane of an optical beam has yielded information about the turbulence characteristics and cross winds over the propagation path. The measurements are generally made over relatively short paths, near the ground, with a laser at one end and one or more detectors situated at the opposite end of the propagation path. In some cases it may be desirable to have the laser and detectors at the same location. This can be accomplished by use of a reflector at the far end of the path to direct the transmitted energy back to the detectors. In a previous publication, the characteristics were developed for the optical filter function appropriate to a high-frequency plane wave propagating over a folded path. The purpose of this communication is to extend the previous analysis to the case of a spherical wave propagating over a folded path. In particular, an expression is developed showing the dependence of the observed amplitude covariance on the spectral density of the turbulence and the path geometry.

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