An algorithm to find two-dimensional signals with specified zero crossings

We present an iterative method for finding two-dimensional band-limited functions with predetermined zero crossings. This problem arises when we want to generate a prescribed binary image at the output of a diffraction-limited imaging system with high-contract recording. An important application of this image generation problem is in the design of masks for microlithography. After describing the algorithm, a proof of its convergence, based on the properties of nonexpansive mappings, is given. The relevance of this algorithm to the image construction problem is then discussed, and we conclude by illustrating two patterns generated by our proposed method.