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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 49, Iss. 18 — Jun. 20, 2010
  • pp: 3442–3451

Ray-tracing simulation method using piecewise quadratic interpolant for aspheric optical systems

Shin-ya Morita, Yohei Nishidate, Takashi Nagata, Yutaka Yamagata, and Cristian Teodosiu  »View Author Affiliations

Applied Optics, Vol. 49, Issue 18, pp. 3442-3451 (2010)

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We present a new method for precise ray-tracing simulation considering form errors in the fabrication process of aspheric lenses. The Nagata patch, a quadratic interpolant for surface meshes using normal vectors, is adopted for representing the lens geometry with mid-spectral frequencies of surface profile errors. Several improvements in the ray–patch intersection calculation and its acceleration technique are also proposed. The developed algorithm is applied to ray-tracing simulation of optical disk pick-up aspheric objectives, and this technique requires 10 5 to 10 9 times fewer patches than a polygonal approximation. The simulation takes only several seconds on a standard PC.

© 2010 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
(220.2740) Optical design and fabrication : Geometric optical design
(240.0240) Optics at surfaces : Optics at surfaces
(080.1753) Geometric optics : Computation methods

Original Manuscript: March 18, 2010
Manuscript Accepted: May 3, 2010
Published: June 10, 2010

Shin-ya Morita, Yohei Nishidate, Takashi Nagata, Yutaka Yamagata, and Cristian Teodosiu, "Ray-tracing simulation method using piecewise quadratic interpolant for aspheric optical systems," Appl. Opt. 49, 3442-3451 (2010)

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  1. A. K. Rigler and T. P. Vogl, “Spline functions: an alternative representation of aspheric surfaces,” Appl. Opt. 10, 1648–1651 (1971). [CrossRef] [PubMed]
  2. J. L. Rayces and X. Cheng, “Numerical integration of an aspheric surface profile,” Proc. SPIE 6342, 634224 (2007). [CrossRef]
  3. T. P. Vogl, A. K. Rigler, and B. R. Canty, “Asymmetric lens design using bicubic splines: application to the color TV lighthouse,” Appl. Opt. 10, 2513–2516 (1971). [CrossRef] [PubMed]
  4. J. E. Stacy, “Asymmetric spline surfaces: characteristics and applications,” Appl. Opt. 23, 2710–2714 (1984). [CrossRef] [PubMed]
  5. G. G. Gregory, E. R. Freniere, and L. R. Gardner, “Using spline surfaces in optical software,” Proc. SPIE 4769, 75–83(2002). [CrossRef]
  6. A. Glassner, An Introduction to Ray Tracing (Academic, 1989).
  7. T. Nishita, T. W. Sederberg, and M. Kakimoto, “Ray tracing trimmed rational surface patches,” Comput. Graph. 24, 337–345 (1990). [CrossRef]
  8. S. H. M. Roth, P. Diezi, and M. H. Gross, “Ray tracing triangular Bézier patches,” Comput. Graph. Forum 20, 422–430(2001). [CrossRef]
  9. H. Chase, “Optical design with rotationally symmetric NURBS,” Proc. SPIE 4832, 10–24 (2002). [CrossRef]
  10. T. Nagata, “Simple local interpolation of surfaces using normal vectors,” Comput. Aided Geom. Des. 22, 327–347(2005). [CrossRef]
  11. T. Hama, T. Nagata, C. Teodosiu, A. Makinouchi, and H. Takuda, “Finite-element simulation of spring back in sheet metal forming using local interpolation for tool surfaces,” Int. J. Mech. Sci. 50, 175–192 (2008). [CrossRef]
  12. T. Hama, M. Takamura, A. Makinouchi, C. Teodosiu, and H. Takuda, “Formulation of contact problems in sheet metal forming simulation using local interpolation for tool surfaces,” J. Comput. Sci. Technol. 2, 68–80 (2008). [CrossRef]
  13. E. W. Weisstein, “Quartic equation,” from Wolfram MathWorld, http://mathworld.wolfram.com/QuarticEquation.html.
  14. M. S. Petković, C. Carstensen, and M. Trajkovíc, “Weierstrass formula and zero-finding methods,” Numer. Math. 69, 353–372 (1995). [CrossRef]

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