INVERSE PROBLEMS IN X-RAY AND GAMMA-RAY ASTRONOMICAL IMAGING

Imaging with mirrors is difficult at high photon energies, and this ha s led to the development by x- and gamma-ray astronomers of a variety of alternative approaches to forming images. Most of these involve 'co ding' the sky brightness distribution, such that a single bright point source at a given position produces a complex but characteristic sign ature on the detector. The mathematical description of the imaging pro cess, and the advantages and disadvantages of focusing and non-focusin g approaches are discussed. The problem of image reconstruction in the focusing case is similar to that in familiar optical imaging applicat ions, though complicated by variations in point spread function with p osition and energy. We therefore concentrate on the inversion of coded images, which are more characteristic of high-energy astronomy. The d esign of the coding process, which is crucial to achieving good imagin g performance, is discussed, as are techniques for image reconstructio n in the case of 'perfect coding', and a variety of remedies for makin g the best use of imperfectly coded data.