The optics of a number of future X-ray telescopes will have very long focal lengths (10 - 20 m), and will consist of a number of nested/stacked thin, grazing-incidence mirrors. The optical quality characterization of a real mirror can be obtained via profile metrology, and the Point Spread Function of the mirror can be derived via one of the standard computation methods. However, in practical cases it can be difficult to access the optical surfaces of densely stacked mirror shells, after they have been assembled, using the widespread metrological tools. For this reason, the assessment of the imaging resolution of a system of mirrors is better obtained via a direct, full-illumination test in X-rays. If the focus cannot be reached, an intra-focus test can be performed, and the image can be compared with the simulation results based on the metrology, if available. However, until today no quantitative information was extracted from a full-illumination, intra-focal exposure. In this work we show that, if the detector is located at an optimal distance from the mirror, the intensity variations of the intra-focal, full-illumination image in single reflection can be used to reconstruct the profile of the mirror surface, without the need of a wavefront sensor. The Point Spread Function can be subsequently computed from the reconstructed mirror shape. We show the application of this method to an intra-focal (8 m distance from mirror) test performed at PANTER on an optical module prototype made of hot-slumped glass foils with a 20 m focal length, from which we could derive an expected imaging quality near 16 arcsec HEW.
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