Calculation of the Optical Telescope Mirror

Abstract

This work considers the problem of bending a thick annular plate of variable thickness on point supports under the action of its own weight. The problem describes the stress-strain state of the primary mirrors of large optical telescopes when the mirror axis is directed to the zenith. The main feature of this problem is the transverse displacements of the plate reference surface, which coincides with the rear flat base of the plate where the supports are located, and the front surface from which the incident light is reflected. Errors of the wavefront of the reflected light, including the standard deviation and the magnitude of the wavefront, are associated with the transverse displacement. The problem is solved with the use of two nonclassical theories of plates, the Timoshenko-Reissner theory of plates and the Palii-Spiro theory of mean thickness shells. The case of the optimal location of the supports corresponds to the smallest values of the deviation of the wavefront magnitude and the standard deviation. Calculations according to the Timoshenko-Reissner and the Palii-Spiro theories gave the same optimal location of the supports. The Palii-Spiro theory, which takes into account the variation of the transverse displacement along the thickness of the plate, is preferable for calculating the distortion of the reflecting surface of the primary mirrors of optical telescopes.