A Class of near-Perfect Coded Apertures

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Abstract
Coded aperture imaging of gamma ray sources has long promised an improvement in the sensitivity of various detector systems. The promise has remained largely unfulfilled, however, for either one of two reasons. First, the encoding/decoding method produces artifacts, which even in the absence of quantum noise, restrict the quality of the reconstructed image. This is true of most correlation-type methods. Second, if the decoding procedure is of the deconvolution variety, small terms in the transfer function of the aperture can lead to excessive noise in the reconstructed image. We propose to circumvent both of these problems by use of a uniformly redundant array (URA) as the coded aperture in conjunction with a special correlation decoding method. The correlation of the decoding array with the aperture results in a delta function with deterministically zero sidelobes. The properties of the encoding/decoding method are similar to those of the nonredundant pinhole array (NRA), however, the URA can be composed of thousands of holes whereas the NRA contains less than 40. In short, the URA offers the transmission advantage of the random array or Fresnel zone plate without introducing the artifacts typically seen when those apertures and others are used. It is shown that the reconstructed image in the URA system contains virtually uniform noise regardless of the structure in the original source. Therefore, the improvement over a single pinhole camera will be relatively larger for the brighter points in the source than for the low intensity points.

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