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Updated: Oct 30, 2025

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
Published on: August 12, 2013
Diaboloidal mirrors: algebraic solution and surface shape approximations
Valeriy V Yashchuk1, Kenneth A Goldberg1, Ian Lacey1
1Advanced Light Source, Lawrence Berkeley National Laboratory, 1 Cyclotron Rd, Berkeley, CA 94720, USA.
Abstract:
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.
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