Synthesis of linear-aperture distributions by pattern sampling

The classical Woodward method for synthetising linear-aperture distributions by pattern sampling is shown here to give a hybrid form of edge behaviour, in which the aperture distribution for the even part terminates in a pedestal (edge exponent ¿ = 0), while that for the odd part approaches zero linearly (¿ = 1). Hence the Woodward sampling functions are not the proper functions to use for representing an arbitrary aperture-limited function of either the order ¿ = 0 or ¿ = 1. Instead, a new set of sampling functions is constructed, for each order ¿ = 0 and 1 separately, that is capable of representing exactly an arbitrary pattern space factor of that particular order.