Shape control apparatus for reflecting mirrors

摘要

The control of a mirror's shape, such as for use in large reflecting telescopes, is associated with discrete points so as to avoid incurring constraints and exerting undesirable stress on the reflecting mirror through control unrelated to the mechanical characteristics. Thus, a reflecting mirror (1) is approximated by a non-constrained circular plate having a similar mechanical structure, and an eigenfunction value arithmetic unit (9) calculates values of Bessel-Fourier functions which are eigenfunctions of free vibrations of the circular plate. Using these function values, a mode displacement identification unit (10) approximates a required mirror displacement (12), which is necessary to correct for wavefront distortion, with a linear combination up to a prescribed mode of vibration of the eigenfunction. A support mechanism command unit (11) controls an actuator (6) so that the value of the linear combination function equals the amount of mirror displacement at a position supported by a reflecting mirror support mechanism (2).