Mirrors for Xray telescopes: Fresnel diffractionbased computation of point spread functions from metrology
Abstract
Context. The imaging sharpness of an Xray telescope is chiefly determined by the optical quality of its focusing optics, which in turn mostly depends on the shape accuracy and the surface finishing of the grazingincidence Xray mirrors that compose the optical modules. To ensure the imaging performance during the mirror manufacturing, a fundamental step is predicting the mirror point spread function (PSF) from the metrology of its surface. Traditionally, the PSF computation in Xrays is assumed to be different depending on whether the surface defects are classified as figure errors or roughness. This classical approach, however, requires setting a boundary between these two asymptotic regimes, which is not known a priori.
Aims: The aim of this work is to overcome this limit by providing analytical formulae that are valid at any light wavelength, for computing the PSF of an Xray mirror shell from the measured longitudinal profiles and the roughness power spectral density, without distinguishing spectral ranges with different treatments.
Methods: The method we adopted is based on the HuygensFresnel principle for computing the diffracted intensity from measured or modeled profiles. In particular, we have simplified the computation of the surface integral to only one dimension, owing to the grazing incidence that reduces the influence of the azimuthal errors by orders of magnitude. The method can be extended to optical systems with an arbitrary number of reflections  in particular the WolterI, which is frequently used in Xray astronomy  and can be used in both near and farfield approximation. Finally, it accounts simultaneously for profile, roughness, and aperture diffraction.
Results: We describe the formalism with which one can selfconsistently compute the PSF of grazingincidence mirrors, and we show some PSF simulations including the UV band, where the aperture diffraction dominates the PSF, and hard Xrays where the Xray scattering has a major impact on the PSF degradation. The results are validated with raytracing simulations, or by comparison with the analytical computation of the halfenergy width based on the known scattering theory, where these approaches are applicable. Finally, we validate this by comparing the simulated PSF of a real WolterI mirror shell with the measured PSF in hard Xrays.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 January 2015
 DOI:
 10.1051/00046361/201424907
 arXiv:
 arXiv:1409.1750
 Bibcode:
 2015A&A...573A..22R
 Keywords:

 telescopes;
 methods: analytical;
 instrumentation: high angular resolution;
 Xrays: general;
 Astrophysics  Instrumentation and Methods for Astrophysics
 EPrint:
 Final version with typos corrected