The next generation of large X-ray telescopes with sub-arcsecond resolution will require very thin, highly nested grazing incidence optics. To correct the low order figure errors resulting from initial manufacture, the mounting process, and the effects of going from 1 g during ground alignment to zero g on-orbit, we plan to adjust the
shapes via piezoelectric “cells” deposited on the backs of the reflecting surfaces. This presentation investigates how well the corrections might be made. We take a benchmark conical glass element, 410×205 mm, with a 20×20 array of piezoelectric cells 19×9 mm in size. We use finite element analysis to calculate the influence function of
each cell. We then simulate the correction via pseudo matrix inversion to calculate the stress to be applied by each cell, considering distortion due to gravity as calculated by finite element analysis, and by putative low order manufacturing distortions described by Legendre polynomials. We describe our algorithm and its performance,
and the implications for the sensitivity of the resulting slope errors to the optimization strategy.