Goldberg KA. Analytic descriptions of parabolic X-ray mirrors.
JOURNAL OF SYNCHROTRON RADIATION 2022;
29:985-990. [PMID:
35787564 PMCID:
PMC9255577 DOI:
10.1107/s1600577522004593]
[Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2021] [Accepted: 05/01/2022] [Indexed: 05/22/2023]
Abstract
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.
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