Line focus of an elliptic cone for an x-ray crystal spectrograph

Abstract

The crystal in any flat crystal x-ray spectrograph with the film plane at any angle and any position may be bent sagittally into an elliptic conical shape such that a perfect line focus is formed on the film plane for a point source at a fixed location. However, for high spectral resolution, only a narrow strip along the cone can be utilized. This strip will be near the plane formed by the axis of the cone and the source point. The elliptic cone has mirror symmetry in this plane. The equation of this cone is determined and its properties are discussed. Any conical surface has zero intrinsic curvature since one of the two principal radii of curvature is zero, so it is no more difficult to bend a crystal to this shape than to a concave circular cylinder with the same principal radius of curvature.