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6 October 2011 Point spread function of real Wolter-I X-ray mirrors: computation by means of the Huygens-Fresnel principle
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Abstract
The Point Spread Function (PSF) of an imaging X-ray telescope is mostly determined by the defects of its grazing reflection optics. In terms of Fourier components of the mirrors' profile, figure errors comprise long spatial wavelengths, whilst short spatial wavelengths are identified as microroughness. The former contribution is in general treated by means of geometrical optics, while the contribution of the latter - strongly dependent on the X-ray energy - is usually derived from the first order scattering theory. This approach, however, requires setting a sudden transition between these two treatments, whereas in the general case the change is expectedly more gradual. In order to compute the PSF expected from a mirror profile, we need a general method that does not need to classify surface defects as roughness or profile errors. In this work we show how to compute the PSF of real X-ray mirror shells in a typical Wolter-I configuration, at any X-ray energy. The suggested method is an application of the Huygens-Fresnel principle to grazing incidence Wolter-I profiles, and is an extension of the single-reflection formalism we presented in a previous paper. A few integral equations, applied from UV to hard X-rays, return the expected PSFs from measured or simulated profiles, accounting for the surface roughness along with its PSD (Power Spectral Density). The results are consistent with the ray-tracing results whenever geometric optic can be applied, and they merge with the results of the first order X-ray scattering theory when the roughness is within the smooth-surface limit. Finally, the PSF computed from the profile and the roughness of a real mirror is in very good agreement with the one experimentally measured in hard X-rays.
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L. Raimondi and D. Spiga "Point spread function of real Wolter-I X-ray mirrors: computation by means of the Huygens-Fresnel principle", Proc. SPIE 8147, Optics for EUV, X-Ray, and Gamma-Ray Astronomy V, 81470Z (6 October 2011); https://doi.org/10.1117/12.895321
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