Statistical Limits of Fourier Transform Imaging in the Gamma-ray Energy Range

Recent advances in imaging techniques and position-sensitive gamma-ray detectors have made feasible hard x-ray and gamma-ray telescopes with arc-second resolution [ 1]. Above an energy of 100 keV, past instrumentation has been limited to a typical angular resolution of a few degrees. A gamma-ray imaging device with 1 arc-second resolution would be a dramatic improvement over conventional, non-imaging instrumentation and have substantial new capabilities for observation of astrophysical gamma-ray sources. The arc-second gamma-ray imager is based on the Fourier transform imaging technique [2]. We briefly describe Fourier transform imaging and its application to hard x-ray and gamma-ray imaging. This description is followed by an analysis of Fourier transform imaging in the statistics limited regime. Computer simulations and laboratory demonstrations of practical gamma-ray imaging systems are presented.