Calculating of the optical telescope mirror

Abstract

The problem of bending of a thick annular plate of variable thickness based on point supports under its weight is considered. The stress-strain state of primary mirrors of large optical telescopes, when the mirror axes point to the Zenith, is analyzed. The main specific feature of the problem is the transverse displacement of the plate reference surface and the front surface of the plate. The flat base is assumed as the reference surface, where all supports are fixed. The front surface is surface, where the incident light is reflected. The wave front errors of the reflected light are associated with the transverse displacement: the standard deviation and the span of wave front. For the solution the Timoshenko - Reissner theory of plates and Palii - Spiro shells theory of the middle thickness are used. The case of the optimal supports location corresponds to the smallest magnitude of the wave front. Both Timoshenko - Reissner theory and Palii - Spiro theory provide same result for the optimal supports location. In order to make the calculation of the distortion of the reflecting surface of the mirror of an optical telescope more accurate it is recommended to use the Palii - Spiro theory, which takes into account the variableness of the transverse displacement along the plate thickness.