XXIX Symposium "Nanophysics and Nanoelectronics" in Nizhny Novgorod, March 10-14, 2025
Photonics

A computer algebra application for the solution of the ray tracing problem

V. Pauls, A. A. Chertovskikh

Institute for Physics of Microstructures, Russian Academy of Sciences, Nizhnii Novgorod

Abstract: For X-ray optical schemes with mirrors described by second-order surfaces, ray tracing can be performed explicitly. In this article we have considered two variants of the Schwarzschild scheme: a heterocentric spherical mirror arrangement and an arrangement where the first mirror is an ellipsoid of revolution. The obtained exact solutions were analyzed using symbolic algebra systems, which, in some cases, enables us to calculate higher order aberrations, such as all fifth-order aberrations. For the Schwarzschild scheme with spherical mirrors, it was shown that the approximating solutions converge well to the exact ones. For the scheme with one elliptical mirror, we caclulated the third-order aberrations and analyzed the conditions for the aplanaticity.

Keywords: X-ray optics, Schwarzschild optic, elliptical mirror, ray tracing, aberrations, symbolic algebra.

Received: 28.05.2025
Revised: 28.05.2025
Accepted: 28.05.2025

DOI: 10.61011/JTF.2025.10.61340.113-25

Bibliographic databases:

•