Derivation of aberration coefficients for single-element plane-symmetric reflecting systems using Mathematica

Wayne R. McKinney; Christopher A. Palmer

doi:10.1117/12.292730

3 November 1997 Derivation of aberration coefficients for single-element plane-symmetric reflecting systems using Mathematica

Wayne R. McKinney, Christopher A. Palmer

Author Affiliations +

Proceedings Volume 3150, Gratings and Grating Monochromators for Synchrotron Radiation; (1997) https://doi.org/10.1117/12.292730
Event: Optical Science, Engineering and Instrumentation '97, 1997, San Diego, CA, United States

Abstract

The definition of the generalized optical path function for a grating or mirror with a single plane of symmetry is reviewed. The generalized optical path function is then expanded in a series of wavefront aberration terms using only a few lines of code in the MathematicaTM scientific programming environment. The use of the algebraic capabilities of the MathematicaTM environment allows straightforward calculation of aberration coefficients that would normally require considerable effort if undertaken by paper and pencil. In addition, the derivation can be carried out to higher order aberration terms, limited only by the capabilities of the computer platform used.

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Wayne R. McKinney and Christopher A. Palmer "Derivation of aberration coefficients for single-element plane-symmetric reflecting systems using Mathematica", Proc. SPIE 3150, Gratings and Grating Monochromators for Synchrotron Radiation, (3 November 1997); https://doi.org/10.1117/12.292730

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KEYWORDS

Mirrors

Wavefront aberrations

Computing systems

Diffraction gratings

Imaging systems

Optical design

Scientific programming

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