A method for optimizing optical systems which process information-carrying signals is presented. The method consists of deriving the transcorrelation function for a general optical system and then maximizing it with respect to the variable parameters of the system. The transcorrelation function is a space- and time-averaged statistic relating the desired object, or “signal” field, and the system output, or image field. The suggested procedure not only minimizes aberrations in the system itself, but also discriminates against noise in both the object and image regions. It can be shown that the maximization of the transcorrelation coefficient also maximizes the useful information content at the output relative to the desired input. For this reason, the criterion is particularly appropriate to optical systems which are used for transmitting and processing information.
An example of the application of transcorrelation theory to lens design is carried out at the end of the paper. A meniscus lens is chosen for optimization, where the variable parameters are the radii of curvature of the lens surfaces, which are constrained to be circular in cross section. The transcorrelation function for this lens is determined, and the optimum radii are found by maximizing this function.
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