Optical Effect of Flexure in Vertically Mounted Precision Mirrors

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Abstract
Under their own weight, large concave mirrors, such as used in telescopes and various research equipment, may elastically bend beyond tolerable limits. The problem of preventing harmful mirror deformations arises in full severity when gravity has a substantial component in the direction of the optical axis. The less serious case of gravity acting perpendicular to the optical axis has been dismissed by one author as harmless for mirror sizes up to 120 inches. However, disfigurations observed on much smaller vertically mounted mirrors are definitely traceable to elastic flexure by gravity. This paper briefly discusses the elastic deformation of an upright solid disk with a concave front surface and a plane back, supported along its edge by a distribution of radial forces which originate in the contact areas between disk and mount. The loss of image definition through flexure is related to the Fourier coefficients of the edge-pressure distribution in an explicit form simple enough as to permit the analysis of various types of mounts, as well as the synthesis of optimum mounting conditions. Numerical values and graphs are presented from which the optical effect can be appraised for different mirror shapes. The results are compared with observations made in practical tests.

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