Open AccessDiaboloidal mirrors: algebraic solution and surface shape approximations
Author(s) -
Yashchuk Valeriy V.,
Goldberg Kenneth A.,
Lacey Ian,
McKinney Wayne R.,
Sanchez del Rio Manuel,
Padmore Howard A.
Publication year - 2021
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/s1600577521004860
Subject(s) - optics , monochromator , physics , focus (optics) , collimated light , bent molecular geometry , cylinder , toroid , coordinate system , point (geometry) , geometry , mathematics , materials science , laser , wavelength , plasma , quantum mechanics , composite material
A new type of optical element that can focus a cylindrical wave to a point focus (or vice versa) is analytically described. Such waves are, for example, produced in a beamline where light is collimated in one direction and then doubly focused by a single optic. A classical example in X‐ray optics is the collimated two‐crystal monochromator, with toroidal mirror refocusing. The element here replaces the toroid, and in such a system provides completely aberration free, point‐to‐point imaging of rays from the on‐axis source point. We present an analytic solution for the mirror shape in its laboratory coordinate system with zero slope at the centre, and approximate solutions, based on bending an oblique circular cone and a bent right circular cylinder, that may facilitate fabrication and metrology.