  Optical designs for astronomy involve implementation of active optics and
adaptive optics from X-ray to the infrared. Developments and results of active
optics methods for telescopes, spectrographs and coronagraph planet finders are
presented. The high accuracy and remarkable smoothness of surfaces generated by
active optics methods also allow elaborating new optical design types with high
aspheric and/or non-axisymmetric surfaces. Depending on the goal and
performance requested for a deformable optical surface analytical
investigations are carried out with one of the various facets of elasticity
theory: small deformation thin plate theory, large deformation thin plate
theory, shallow spherical shell theory, weakly conical shell theory. The
resulting thickness distribution and associated bending force boundaries can be
refined further with finite element analysis. Keywords: active optics, optical
design, elasticity theory, astronomical optics, diffractive optics, X-ray
optics
