Review of active optics methods in astronomy from x-rays to the infrared

This review on Active Optics Methods presents various concepts of deformable uv, visible and ir telescope optics which have been mainly developed at the Marseille Observatory - for now 40 years - and other institutes. An optical surface generated by active optics and spherical figuring is free from high spatial frequency errors i.e. ripple errors. Active Optics allows applications of new concepts as: stress figuring aspherization processes, variable curvature mirrors, in situ stressing aspherization processes, under stress replications to generate corrected diffraction gratings, multimode deformable compensators, and situ control of large telescope optics. X-ray telescope mirrors could also benefit soon from the enhanced imaging performances of active optics. The 0.5- 1 arcsec spatial resolution of Chandra should be followed up by increased resolution space telescopes. This requires constructing new grazing-incidence telescopes which will strictly satisfy Abbe's sine condition, i.e. a Chase-VanSpeybroeck design for the two-mirror case. The recent elaboration of an elasticity theory of weakly conical shells allows reviewing some potential innovative concepts for the active figuring and in situ control of either monolithic or segmented telescope mirrors for x-ray astronomy.