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When one performs a coherent small-angle X-ray scattering experiment, the incident beam must be spatially filtered by slits on a length scale smaller than the transverse coherence length of the source which is typically around 10 µm. The Fraunhofer diffraction pattern of the slit is one of the important sources of background in these experiments. New slits which minimize this parasitic background have been designed and tested. The slit configuration apodizes the beam by the use of partially transmitting inclined slit jaws. A model is presented which predicts that the high wavevector tails of the diffraction pattern fall as the inverse fourth power of the wavevector instead of the inverse second power that is observed for standard slits. Using cleaved GaAs single-crystal edges, Fraunhofer diffraction patterns from 3 and 5.5 keV X-rays were measured, in agreement with the theoretical model proposed. A novel phase-peak diffraction pattern associated with phase variations of the transmitted electric field was also observed. The model proposed adequately accounts for this phenomenon.

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