Abstract

In this paper, we investigate the range of validity of a certain class of nonperturbation methods for predicting the statistical properties of a scalar wave in a random medium. These methods are called “dishonest” by Keller, since they rely on unjustified statistical assumptions to close the relevant equations after averaging. We show that such methods can correctly predict the first moment of the wave field for long-distance propagation in a weakly inhomogeneous medium or, in the short-wavelength limit, for propagation in a strongly inhomogeneous medium. We demonstrate that such methods can never give correct results for the second moment.

© 1968 Optical Society of America

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