Optical EngineeringNear origin divergent brightness behavior of grazing incidence images
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Grazing incidence systems, such as extreme ultraviolet and x-ray telescopes, produce images that differ qualitatively from those of conventional normal incidence systems. Among the more well known effects are increased scatter due to the short radiation wavelengths, and pronounced pupil diffraction patterns due to the high obscuration ratios. However, a much less well known effect is the rapidly increasing intensity very near the center of the image. Within a substantial part of the image core, the intensity can be shown to increase inversely with the image radius ("l/r" behavior). This behavior applies to both pupil diffraction and scatter effects. One of the important implications is that the full-width-half-maximum (FWHM) for the image is inherently and misleadingly small and is thus not a suitable image descriptor for grazing incidence systems. In this paper, we first review the well-known scatter and diffraction effects. We then give some intuitive explanations for the less well known behavior of the intensity, derive the mathematics to define the effect quantitatively, and give some examples.