Analytical expressions of the surface shape of ‘diaboloid’ mirrors

Conference · Fri Aug 21 04:00:00 EDT 2020 · Advances in Computational Methods for X-Ray Optics V

DOI:https://doi.org/10.1117/12.2568332· OSTI ID:1963421

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

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.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
• DOE Contract Number: AC02-05CH11231
• OSTI ID: 1963421
• Conference Information: Journal Name: Advances in Computational Methods for X-Ray Optics V
• Country of Publication: United States
• Language: English