Alignment estimation and control of the James Webb Space Telescope mirrors using decomposition of an influence matrix

Abstract

The James Webb Space Telescope (JWST) is a three-mirror anastigmatic telescope. For a "blind" telescope alignment estimation and control study at the Goddard Space Flight Center (GSFC), influence functions for each of the primary mirror's 18 segments (6 degrees of freedom each) and for the secondary mirror (5 degrees of freedom) were used to construct a 113-element influence matrix. The singular value vector obtained from pseudoinverse of this influence matrix indicates that the most dominant modes in the control of the telescope are rotation, piston, clocking and translation, in order of significance. The application of an iterative-control algorithm to ten cases of random misalignments, involving both the primary segmented mirror and secondary mirror, shows strong convergence after 5 iterations in most of the cases.