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Proceedings Paper

Describing freeform surfaces with orthogonal functions
Author(s): D. Ochse; K. Uhlendorf; L. Reichmann
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Paper Abstract

In optical design with freeform surfaces descriptions of the surfaces are needed that use only few parameters and are suitable for optimisation. Depending on the merit function – spot size or wavefront error – and the position of the surface in the system, different surface types can yield different optimisation performance. It has been demonstrated by G. Forbes that slope orthogonal polynomials are an advantageous freeform description. From literature on Gaussian moments it is known that this can be achieved using differences of Zernike polynomials, which are easy to compute and implement with recent algorithms. We will demonstrate the benefits of Zernike polynomials with optimisation examples. Furthermore we present an orthogonal surface representation on a rectangular aperture based on Chebyshev polynomials. This description is very convenient when the aperture has a very high aspect ratio, or when designing a system with a rectangular pupil.

Paper Details

Date Published: 23 September 2015
PDF: 8 pages
Proc. SPIE 9626, Optical Systems Design 2015: Optical Design and Engineering VI, 962612 (23 September 2015); doi: 10.1117/12.2191421
Show Author Affiliations
D. Ochse, JENOPTIK Optical Systems GmbH (Germany)
K. Uhlendorf, JENOPTIK Optical Systems GmbH (Germany)
L. Reichmann, JENOPTIK Optical Systems GmbH (Germany)

Published in SPIE Proceedings Vol. 9626:
Optical Systems Design 2015: Optical Design and Engineering VI
Laurent Mazuray; Rolf Wartmann; Andrew P. Wood, Editor(s)

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