要約

We propose the new method of control of geometry of the axis-symmetrically deformed mirror of the space telescope on the basis of solving the inverse problem of the theory of thin shells. Recovering of the shape of the adaptive mirror is realized by normal forces. We state the problem of the inverse problem and show its uniqueness. Algorithm peculiarities of the numerical solution of the inverse problem, which are caused by loss of accuracy on numerical differentiation, are ascertained. We present numerical results of solving of agreed problems according to the scheme "direct problem — inverse problem — direct problem" and give their analysis. We discover high sensitivity of the solution of the inverse problem relative to adequacy of the mathematical model of the mirror, smoothness of input data and neglect of tangent displacements. It was shown that in the case of deformation of the thin mirror by gravity forces neglect of geometric nonlinearity results in overcompensation of deflection by significant from point of view of optics value.