Effects of receiver optics contamination on the performance of laser velocimeter systems

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Abstract
Comprehensive, general expressions are derived for various statistical functions that characterize the performance of paraxial ABCD optical systems illuminated by partially coherent light in the presence of a collecting aperture that is contaminated by absorbing and/or scattering inhomogeneities. The contaminants are modeled here as consisting of thin random absorbing and/or phase (i.e., scattering) screens. In particular, a novel expression is derived for the autocorrelation function of a random screen consisting of both absorbing and scattering patches that partially cover an aperture. Expressions for the resulting mean irradiance distribution expected in an image plane of laser velocimeter systems are derived and discussed. The effects of contamination on the performance of both laser time-of-flight velocimeters (LTV’s) and laser Doppler velocimeter (LDV) systems are considered. In general, the effects of contamination result in a reduction in magnitude of the time-lagged covariance of the photocurrent compared with the corresponding covariance function in the absence of contamination. It is also shown that contamination effects may lead to bias errors in the estimated mean velocity for LTV systems and an increased variance of the estimated velocity for both LTV and LDV systems.