On-orbit adjustment calculation for the Generation-X x-ray mirror figure

Generation-X will be an X-ray observatory with 50 m2 collecting area at 1 keV and 0.1" angular resolution. A key concept to enable such a dramatic improvement in angular resolution is that the mirror figure will be adjusted on-orbit; e.g., via piezo-electric actuators deposited on the back side of very thin glass and imparting strains in a bi-morph configuration. To make local adjustments to the individual mirror shells we must employ an imaging detector far forward of the focal surface, so that rays from the individual shells can be measured as distinct rings. We simulate this process on a few representative shells via ray-traces of perfect optics, perturbed axially by low order Legendre polynomial terms. This elucidates some of the requirements for the on-orbit measurements, and on possible algorithms to perform the on-orbit adjustment with acceptably rapid convergence.