Analytical expressions of the surface shape of ‘diaboloid’ mirrors

Valeriy V. Yashchuk; Ian Lacey; Manuel Sanchez del Rio

doi:10.1117/12.2568332

21 August 2020 Analytical expressions of the surface shape of ‘diaboloid’ mirrors

Valeriy V. Yashchuk, Ian Lacey, Manuel Sanchez del Rio

Author Affiliations +

Proceedings Volume 11493, Advances in Computational Methods for X-Ray Optics V; 114930N (2020) https://doi.org/10.1117/12.2568332
Event: SPIE Optical Engineering + Applications, 2020, Online Only

Abstract

Modern deterministic polishing processes allow fabrication of x-ray optics with almost any arbitrary aspherical surface shape. Among these optics, the so called “diaboloid” mirror is of special interest. The diaboloid mirror that converts a cylindrical wave to a spherical wave would improve focusing in x-ray beamlines implementing a diffraction element between a parabolic cylinder and a toroidal mirror. The replacement of the toroidal mirror in existing beamlines by the diaboloid mirror would mitigate aberrations. The shape of the diaboloid mirror is usually calculated numerically based on a truncated polynomial solution of the optical path problem. Here, we present an exact analytical solution for the shape of a diaboloid mirror as a function of the conjugate parameters of the mirror placed in a beamline. The derived analytical expressions for the diaboloid mirror in both the canonical and mirror-based coordinate systems are implemented in ray-tracing simulations to verify the beamline performances.

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Valeriy V. Yashchuk, Ian Lacey, and Manuel Sanchez del Rio "Analytical expressions of the surface shape of ‘diaboloid’ mirrors", Proc. SPIE 11493, Advances in Computational Methods for X-Ray Optics V, 114930N (21 August 2020); https://doi.org/10.1117/12.2568332

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