An Axial Form of the Sampling Theorem and its Application to Optical Diffraction

The sampling theorem is used to obtain expressions for the diffracted amplitude G(y, z) at any point in space, once the distribution along the axis G(y, 0) is known at the sampling points. In the case of a circular symmetrical pupil, G(y, 0) is simply the Fourier transform of the pupil function. The real or imaginary parts of G(y, z) may be obtained either from the real or from the imaginary part of G(y, 0). By suitable oversampling, the real part of G(y, z) may be found from its imaginary part, and vice versa. A technique for the synthesis of antenna patterns is suggested.