Flexible adaptive mirror in the form of a thin plate with a free edge and ball-and-socket joints along a circular contour

An analytic model is proposed for a deformable adaptive mirror in the form of a thin plate with a free edge, supported by a finite number of elastic actuators and linked by ball-and-socket joints to the base that sets the position of the mirror in space; a finite number of support contours, generally of arbitrary shape, is assumed. The results are given of optimization calculations for an adaptive mirror with ball-and-socket joints along a circular contour with a ring configuration of discrete actuators. The results are reported of an experimental investigation, carried out by the method of two-exposure holographic interferometry, of the formation of surfaces of different shapes of a prototype adaptive mirror of this kind.