Analytical evaluation of the X-ray scattering contribution to imaging degradation in grazing-incidence X-ray telescopes
INAF/Osservatorio Astronomico di Brera, via E. Bianchi 46, 23807 Merate (LC), Italy e-mail: firstname.lastname@example.org
Accepted: 27 March 2007
Aims.The focusing performance of X-ray optics (conveniently expressed in terms of HEW, Half Energy Width) strongly depend on both mirrors deformations and photon scattering caused by the microroughness of reflecting surfaces. In particular, the contribution of X-ray Scattering (XRS) to the HEW of the optic is usually an increasing function of the photon energy E. Therefore, in future hard X-ray imaging telescopes of the future (SIMBOL-X, NeXT, Constellation-X, XEUS), the X-ray scattering could be the dominant problem since they will operate also in the hard X-ray band (i.e. beyond 10 keV). In order to ensure the imaging quality at all energies, clear requirements have to be established in terms of reflecting surfaces microroughness.
Methods.Several methods were proposed in the past years to estimate the scattering contribution to the HEW, dealing with the surface microroughness expressed in terms of its Power Spectral Density (PSD), on the basis of the well-established theory of X-ray scattering from rough surfaces. We faced that problem on the basis on the same theory, but we tried a new approach: the direct, analytical translation of a given surface roughness PSD into a trend, and – vice versa – the direct translation of a requirement into a surface PSD. This PSD represents the maximum tolerable microroughness level in order to meet the requirement in the energy band of a given X-ray telescope.
Results.We have thereby found a new, analytical and widely applicable formalism to compute the XRS contribution to the HEW from the surface PSD, provided that the PSD had been measured in a wide range of spatial frequencies. The inverse problem was also solved, allowing the immediate evaluation of the mirror surface PSD from a measured function . The same formalism allows establishing the maximum allowed PSD of the mirror in order to fulfill a given requirement. Practical equations are firstly developed for the case of a single-reflection optic with a single-layer reflective coating, and then extended to an optical system with N identical reflections. The results are approximately valid also for multilayer-coated mirrors to be adopted in hard X-rays. These results will be extremely useful in order to establish the surface finishing requirements for the optics of future X-ray telescopes.
Key words: telescopes / methods: analytical / instrumentation: high angular resolution / X-rays: general
© ESO, 2007