Abstract

Pupil diffraction usually defines the achievable resolution in conventional optical systems. However, since diffraction-limited resolution is proportional to radiation wavelength (for a given aperture size), diffraction is usually ignored for x-ray systems with wavelengths in the angstrom regime. Nonetheless, high-resolution x-ray systems are arising which use very narrow annular apertures, relatively long x-ray wavelengths, or both. In a surprising number of these systems, pupil diffraction can have a non-negligible effect on resolution. There is excellent work in the literature describing the diffraction pattern from such apertures in terms of Airy rings and ring groups. It can be shown that this approach is equivalent in a wide range of conditions to considering an infinite 1-D slit with a width equal to the actual annular width. It can be shown that the energy enclosed in the focal plane dimension transverse to the slit is very close to the energy encircled in the true annular system focal plane. In short, the system designer can make an excellent first approximation of pupil diffraction effects in an x-ray system by applying standard single-slit diffraction formulas to the annular aperture width and x-ray wavelength.

© 1987 Optical Society of America