Title

Comparative assessment of freeform polynomials as optical surface descriptions

Authors

Authors

I. Kaya; K. P. Thompson;J. P. Rolland

Comments

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Abbreviated Journal Title

Opt. Express

Keywords

SHAPE-DESCRIPTION; ROBUST; FORM; Optics

Abstract

Slow-servo single-point diamond turning as well as advances in computer controlled small lap polishing enables the fabrication of freeform optics, or more specifically, optical surfaces for imaging applications that are not rotationally symmetric. Various forms of polynomials for describing freeform optical surfaces exist in optical design and to support fabrication. A popular method is to add orthogonal polynomials onto a conic section. In this paper, recently introduced gradient-orthogonal polynomials are investigated in a comparative manner with the widely known Zernike polynomials. In order to achieve numerical robustness when higher-order polynomials are required to describe freeform surfaces, recurrence relations are a key enabler. Results in this paper establish the equivalence of both polynomial sets in accurately describing freeform surfaces under stringent conditions. Quantifying the accuracy of these two freeform surface descriptions is a critical step in the future application of these tools in both advanced optical system design and optical fabrication. (C)2012 Optical Society of America

Journal Title

Optics Express

Volume

20

Issue/Number

20

Publication Date

1-1-2012

Document Type

Article

Language

English

First Page

22683

Last Page

22691

WOS Identifier

WOS:000309522400086

ISSN

1094-4087

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