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8 September 2005 Boundary between geometric and wave optical treatment of x-ray mirrors
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The brightness distribution of specularly reflected and diffusely scattered rays off an X-ray mirror illuminated under grazing incidence is determined by the mirror surface topography. An attempt is made to cover the full range of random surface roughness which runs from microscopic to macroscopic imperfections, for which currently available scattering theories cannot be used. In a new attempt the size of geometric slope errors and diffraction angles of a 1-D profile are compared, spatial frequency component by spatial frequency component of the Fourier decomposed profile. By this approach the well known expression of the Rayleigh scattering factor could be derived though, for each component separately. Because of the different dependence of the relevant angles on spatial frequency a critical spatial frequency is found at which geometric optics and the diffraction regime separate. Furthermore, for frequencies greater than the intersection frequency the total microroughness is shown to be as low as to allow the application of the existing scattering theories in the smooth surface limit. At lower spatial frequencies geometric slope errors dominate.
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B. Aschenbach "Boundary between geometric and wave optical treatment of x-ray mirrors", Proc. SPIE 5900, Optics for EUV, X-Ray, and Gamma-Ray Astronomy II, 59000D (8 September 2005);

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