The sampling theorem is applied to optical diffraction theory as a computational tool. Formulas are developed in terms of sampled values of the point spread function for the transfer function, total illuminance, line spread function and cumulative line spread function. Typical numerical examples are presented. The theory is presented for general point spread functions for slit and square apertures, but only for rotationally symmetric point spread functions for circular apertures. In the case of the slit aperture, the following question is answered: Given the real part of the incoherent transfer function, determine its imaginary part and vice versa. The theory of conjugate Fourier series and finite Hilbert transforms is introduced in order to answer this question.
RICHARD BARAKAT, "Application of the Sampling Theorem to Optical Diffraction Theory," J. Opt. Soc. Am. 54, 920-929 (1964)