Abstract
Like all short-wavelength optics, whispering-gallery mirrors that are intended for use with soft x rays require a high-quality surface finish. A coupled-mode description of scatter in whispering-gallery mirrors provides a convenient way of understanding the effects of surface imperfections and of establishing fabrication tolerances. Different kinds of imperfection have different effects on mirror performance and can be tolerated to different degrees. Figure errors, for example, are not critical, but periodic toolmarks are potentially disastrous. The acceptable amounts of random waviness and microscopic roughness depend on the correlation lengths involved. Overall, the tolerances are strict but less severe than those for normal-incidence optics.
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