The use of elastic bending to form the shapes of high-power x-ray mirrors for synchrotron radiation beamlines is considered. An approach in which the bending mechanism and the mirror are cut from the same monolithic block by electric-discharge-machining techniques is especially advocated. A discussion of the theory and practical design philosophies is given that includes circular and elliptical cylinder mirrors. The influence of gravity on the mirror shape is studied with emphasis on the optimum positions for the mirror supports that, for a uniform mirror, turn out to be at a spacing equal to the mirror length divided by root three.
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Malcolm R. Howells (1993) studied this question.
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