A computer algebra application for the solution of the ray tracing problem
W. Pauls 1, A.A. Chertovskikh1
1Institute for Physics of Microstructures, Russian Academy of Sciences, Afonino village, Kstovsky District, Nizhny Novgorod Region, Russia
Email: walter.pauls@gmail.com

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For X-ray optics with mirrors described by second-order surfaces, raytracing can be performed explicitly. Two types of the Schwarzschild configuration are considered - a configuration with nonconcentric spherical mirrors and a configuration where the first mirror is a spheroid. 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 aplanaticity. Keywords: X-ray optics, Schwarzschild configuration, elliptical mirror, ray tracing, aberrations, symbolic algebra.
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