Coded aperture imaging: predicted performance of uniformly redundant arrays

Uniformly redundant arrays (URA) have autocorrelation functions with perfectly flat sidelobes. The URA combines the high-transmission characteristics of the random array with the flat sidelobe advantage of the nonredundant pinhole arrays. A general expression for the signal-to-noise ratio (SNR) has been developed for the URA as a function of the type of object being imaged and the design parameters of the aperture. The SNR expression is used to obtain an expression for the optimum aperture transmission. Currently, the only 2-D URAs known have a transmission of (1/2). This, however, is not a severe limitation because the use of the nonoptimum transmission of (1/2) never causes a reduction in the SNR of more than 30%. The predicted performance of the URA system is compared to the image obtainable from a single pinhole camera. Because the reconstructed image of the URA contains virtually uniform noise regardless of the original object's structure, the improvement over the single pinhole camera is much larger for the bright points than it is for the low intensity points. For a detector with high background noise, the URA will always give a much better image than the single pinhole camera regardless of the structure of the object. In the case of a detector with low background noise, the improvement of the URA relative to the single pinhole camera will have a lower limit of ~(2f)(-(1/2)), where f is the fraction of the field of view that is uniformly filled by the object.