Aberration calculation and image reconstruction in Laue lenses made of bent crystals for future gamma-ray astrophysics telescopes

Forthcoming hard X-ray (50-700 keV) telescopes designed for high-energy astrophysics will rely on concentrating radiation through diffractive systems utilizing crystals and solid-state detectors at focal plane. Our current focus involves exploring the feasibility of employing Laue lenses, made from Germanium and Silicon crystals curved to fit the lens curvature. In this study, we estimate the aberration of an X-ray Laue lens made of bent crystals arranged in concentric rings on a disk of 2.5 m in diameter when incident X-rays arrive on- and off-axis on the lens. In each ring the crystals are pre-oriented in order to diffract an X-ray beam to a focus plane positioned at 20 m from the lens. Each crystal is a tile 3x1 cm2, with the longer edge oriented toward the center of the lens. Due to the 40 m curvature each crystal produces a spot 1.5x10 mm2 in size at the focus plane. While an on-axis X-ray source is focused with a 40 arcsecond point spread function, off-axis sources produce rings of diffraction on the focal plane, confirming the poor imaging performance of the Laue lens. We report a mathematical approach performing an X-ray image reconstruction with increased angular resolution.