The Influence of Random Wavefront Errors on the Imaging Characteristics of an Optical System

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Abstract
The influence of random wavefront errors on the transfer function and point spread function of an optical system is studied theoretically. The stochastic part of the aberration function is assumed to be Gaussian and spatially stationary (although the requirement of stationarity is relaxed in § 5). The stochastic transformation from wavefront to transfer function is non-linear. The consequences of this non-linear transformation are two-fold: first, the statistics of the transfer function are non-Gaussian, second, the transfer function is non-stationary. (The same statements hold for the point spread function.) Therefore the characterization of these processes requires an infinite number of averaged products (moments), not just the first two if the processes were Gaussian. These averaged products are obtained in the form of multiple integrals involving the characteristic function of the wavefront and are suitable for calculation on a high speed computer. Some numerical results for the mean of both processes are presented.

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