We present a new technique—photon folding—for imaging in nonfocusing telescopes. Inspired by the epoch-folding method in timing analysis, the photon-folding technique directly provides the statistical significance of signals in images, by use of projection matrices. The technique is robust against common imaging problems such as aspect errors and a nonuniform background. The technique provides a deterministic recursive algorithm for improving images, which can be implemented on line. The higher-order photon-folding technique allows a systematic correction for coding noises, which is suitable for studying weak sources in the presence of highly variable strong sources. The technique can be applied to various types of nonfocusing telescopes such as coded-aperture optics, rotational collimators, or Fourier grid telescopes.
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