Global PSD tolerance for the VERT-X Wolter-I mirror

Abstract

In this brief note, in the context of developing the Wolter-I mirror for the VERT-X project, we describe the global tolerances, accounting for longitudinal errors, sagittal errors and, finally, errors of the curvature radii in the longitudinal and sagittal direction. The document summarizes some preliminary formulation for the fabrication tolerances for the VERT-X Wolter-I collimator. PSDs for the longitudinal and sagittal polishing and figuring are provided in order to keep the HEW < 1.2 arcsec below 3.5 keV (not including the X-ray source size, that is assumed to be well characterized and removable by deconvolution). Fabrication tolerances for the sagittal radii (< 50 μm and coincident within 20 μm) are designed in order to make their effect negligible provided that the focal length can be corrected. The error in the sagittal radii can even vanish, if the longitudinal curvature error can be corrected to match the actual value of the sagittal radius according the pseudo-Rowland condition and correcting the focal length by the requested amount.