Coded aperture imaging: the modulation transfer function for uniformly redundant arrays

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Abstract
Coded aperture imaging uses many pinholes to increase the SNR for intrinsically weak sources when the radiation can be neither reflected nor refracted. Effectively, the signal is multiplexed onto an image and then decoded, often by computer, to form a reconstructed image. We derive the modulation transfer function (MTF) of such a system employing uniformly redundant arrays (URA). We show that the MTF of a URA system is virtually the same as the MTF of an individual pinhole regardless of the shape or size of the pinhole. Thus, only the location of the pinholes is important for optimum multiplexing and decoding. The shape and size of the pinholes can then be selected based on other criteria. For example, one can generate self-supporting patterns, useful for energies typically encountered in the imaging of laser-driven compressions or in soft x-ray astronomy. Such patterns contain holes that are all the same size, easing the etching or plating fabrication efforts for the apertures. A new reconstruction method is introduced called δ decoding. It improves the resolution capabilities of a coded aperture system by mitigating a blur often introduced during the reconstruction step.