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Characteristic Count Rate Profiles for a Rotating Modulator Gamma-Ray Imager

Rotating modulation is a technique for indirect imaging in the hard x-ray and soft gamma-ray energy bands, which may offer an advantage over coded aperture imaging at high energies. A rotating modulator (RM) consists of a single mask of co-planar parallel slats typically spaced equidistance apart, suspended above an array of circular non-imaging detectors. The mask rotates, temporally modulating the transmitted image of the object scene. The measured count rate profiles of each detector are folded modulo the mask rotational period, and the object scene is reconstructed using pre-determined characteristic modulation profiles. The use of Monte Carlo simulation to derive the characteristic count rate profiles is accurate but computationally expensive; an analytic approach is preferred for its speed of computation. We present both the standard and a new advanced characteristic formula describing the modulation pattern of the RM; the latter is a more robust description of the instrument response developed as part of the design of a wide-field high-resolution telescope for gamma-ray astronomy. We examine an approximation to the advanced formula to simplify reconstruction software and increase computational speed, and comment on both the inherent limitations and usefulness of the approach. Finally, we show comparisons to the standard formula and demonstrate image reconstructions from Monte Carlo simulations.