For more than 40 years in Marseille Provence observatories active optics concepts have found many fruitful
developments in uv, visible and ir telescope optics. For these wavelength ranges, active optics methods are now
widely extended by current use of variable curvature mirrors, in situ aspherization processes, stress figuring
apsherization processes, replications of stressed diffraction gratings, and in situ control of large telescope optics.
X-ray telescope mirrors will also benefit soon from the enhanced performances of active optics. For instance, the
0.5-1 arcsec spatial resolution of Chandra will be followed up by increased resolution space telescopes which will
require the effective construction of more strictly aplanatic grazing-incidence two-mirror systems.
In view to achieve a high-resolution imaging with two-mirror grazing-incidence telescope, say, 0.1 arcsec,
this article briefly reviews the alternative optical concepts. Next, active optics analysis is investigated with the
elasticity theory of shells for the active aspherization and in situ control of monolithic and segmented telescope
mirrors for x-ray astronomy. An elasticity theory of weakly conical shells is developed for a first approach which
uses a monotonic extension (or retraction) of the shell.