The total reflection of x-rays is applied to focusing the rays issuing from a fine slit. A method of computing the geometrical optics of surfaces of bent beams is given; it is shown that under certain conditions lateral aberrations for practical apertures are of the order of one micron or less. These results are confirmed by experiment.
W. EHRENBERG, "X-Ray Optics: The Production of Converging Beams by Total Reflection," J. Opt. Soc. Am. 39, 741-742 (1949)