How Well Can A Lens System Transmit Information?

Abstract

A lens system may be judged by its ability to relay information from object to image. A pertinent criterion of optical quality is h, the change in entropy between corresponding sampling points in the object and image planes. Since h is a unique function of the optical pupil, for a given bandpass 20 of the object, through the proper choice of a pupil function it is possible to maximize h at a given Q. Physically, the optimum pupil function is an absorption coating applied to a diffraction - limited lens system. A numerical procedure is established for determining, with arbitrary accuracy, the optimum absorption coating, the resulting transfer function, and the maximum h, all at a given 0. These quantities are determined, both for the one -dimensional pupil and the circular pupil, in the approximation that the optimum pupil function may be represented as a Fourier - ( Bessel) series of five terms. The computed values of hmax, at a sequence of 52 values, are estimated to be correct to 0.2% for the 1 -D pupil, and to 0.5% for the circular pupil. The optimum pupil functions are apodizers at small S2 and superresolvers at large 0. Finally, we use the computed curve of hmax to relate the concept of "information transfer" to that of "classical resolving power ": we show that a binary object (as defined) cannot radiate information to the image when the spacing between object sampling points is less than 0.87 times the Rayleigh resolution length.