Open AccessAnalytic descriptions of parabolic X‐ray mirrors
Author(s) -
Goldberg Kenneth A.
Publication year - 2022
Publication title -
journal of synchrotron radiation
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.172
H-Index - 99
ISSN - 1600-5775
DOI - 10.1107/s1600577522004593
Subject(s) - parabolic reflector , optics , focus (optics) , collimated light , coordinate system , tangent , physics , metrology , ray , plane (geometry) , polynomial , mathematical analysis , mathematics , geometry , laser
On X‐ray beamlines and telescopes, glancing‐incidence mirrors with parabolic profiles are used to collimate, focus, and collect light. Here, analytic descriptions for paraboloidal, plane‐parabolic, and parabolic cylindrical mirrors in several congruent geometries that are commonly used in fabrication, metrology, and modeling are provided. The exact expressions are derived directly from Fermat's principle, without coordinate transformations, in several mirror‐centered coordinate systems, including one with the surface tangent to the central point of intersection. Coefficients for a sixth‐order polynomial series approximation are calculated for that coordinate system.