Wavefront sensing of x-ray telescopes

Phase Retrieval analysis of off-axis or defocused focal-plane data from telescope optics has been proven effective in understanding misalignments and optical aberrations in normal incidence telescopes. The approach is used, e. g., in commissioning of the James Webb Space Telescope (JWST) segmented primary mirror. There is a similar need for evaluating low-order figure errors of grazing incidence mirrors and nested telescope assemblies. When implemented in these systems, phase retrieval does not depend on normal incidence access to each mirror (shell) surface and, therefore, provides an effective means for evaluating nested x-ray telescopes during integration and test. We have applied a well-known phase retrieval algorithm to grazing incidence telescopes. The algorithm uses the Levenberg-Marquardt optimization procedure to perform a non-linear least-squares fit of the telescope Point Spread Function (PSF). The algorithm can also retrieve low order figure errors at visible wavelengths where optical diffraction is the dominant defect in the PSF. In this paper we will present the analytical approach and its implementation for grazing incidence mirrors of the International X-Ray Observatory (IXO). We analyze the effects of low order axial surface errors individually, and in combination on the system PSF at 633 nanometers. We demonstrate via modeling that the wavefront sensing algorithm can recover axial errors (of the grazing incidence mirrors) to a small fraction of the known axial figure errors using simulated PSFs as input data to the algorithm.