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

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.

Citation Download Citation

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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