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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 50, Iss. 6 — Feb. 20, 2011
  • pp: 822–828

B-spline representation of optical surfaces and its accuracy in a ray trace algorithm

Philipp Jester, Christoph Menke, and Karsten Urban  »View Author Affiliations

Applied Optics, Vol. 50, Issue 6, pp. 822-828 (2011)

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We introduce a representation of aspheric surfaces that is based on a B-spline quasi-interpolation scheme. The scheme is implemented in a ray trace algorithm, and bounds on the approximation error are established. Examples for the reproduction of aspheric surfaces in polynomial description and the ray tracing accuracy are presented. The proposed approach allows the specification of local and global structures and the efficient treatment of measured surface data. The representation gives access to a wavelet analysis, offering extended possibilities for the tolerance analysis of optical systems containing aspheric elements.

© 2011 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(080.0080) Geometric optics : Geometric optics
(220.1250) Optical design and fabrication : Aspherics
(240.6700) Optics at surfaces : Surfaces
(080.1753) Geometric optics : Computation methods

Original Manuscript: September 16, 2010
Revised Manuscript: January 6, 2011
Manuscript Accepted: January 6, 2011
Published: February 11, 2011

Philipp Jester, Christoph Menke, and Karsten Urban, "B-spline representation of optical surfaces and its accuracy in a ray trace algorithm," Appl. Opt. 50, 822-828 (2011)

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