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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 9 — Apr. 23, 2012
  • pp: 9692–9697

Application and evaluation of quasi-Monte Carlo method in illumination optical systems

Shuhei Yoshida, Shuma Horiuchi, Zenta Ushiyama, and Manabu Yamamoto  »View Author Affiliations


Optics Express, Vol. 20, Issue 9, pp. 9692-9697 (2012)
http://dx.doi.org/10.1364/OE.20.009692


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Abstract

In this article, we evaluate a quasi-Monte Carlo (QMC) method with various low-discrepancy sequences (LDS) in illumination optical systems which are adopted in some commercial products, and clarify the method’s effectiveness quantitatively. We assumed the evaluated systems were an illumination optical system with a perfectly diffusing surface, and we compared them against the theoretical irradiance distribution. The evaluation results indicate that the QMC method delivers higher asymptotic convergence rate than the MC method does, and there is little difference between each LDS. In evaluation of simple optical systems that can be boiled down to low-dimensional numerical integration problems, the QMC method was found to be extremely effective.

© 2012 OSA

OCIS Codes
(080.1753) Geometric optics : Computation methods
(220.2945) Optical design and fabrication : Illumination design

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: March 1, 2012
Revised Manuscript: April 5, 2012
Manuscript Accepted: April 9, 2012
Published: April 12, 2012

Citation
Shuhei Yoshida, Shuma Horiuchi, Zenta Ushiyama, and Manabu Yamamoto, "Application and evaluation of quasi-Monte Carlo method in illumination optical systems," Opt. Express 20, 9692-9697 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-9-9692


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References

  1. H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods (Society for Industrial and Applied Mathematics, 1992).
  2. M. Drmota and F. Robert, Tichy, Sequences, Discrepancies and Applications (Springer, 1997).
  3. J. Dick and F. Pillichshammer, Digital Nets and Sequences (Cambridge University Press, 2010).
  4. S. Ninomiya and S. Tezuka, “Toward real-time pricing of complex financial derivatives,” Appl. Math. Finance3, 1–20 (1996).
  5. A. Keller, “Instant radiosity,” in Proceedings of the 24th annual conference on Computer graphics and interactive techniques, G. S. Owen, T. Whitted and B. Mones-Hattal ed. (ACM Press, 1997).
  6. T. Kollig and A. Keller, “Efficient multidimensional sampling,” Comput. Graph. Forum21, 557–563 (2002).
  7. I. M. Sobol', “On the distribution of points in a cube and the approximate evaluation of integrals,” USSR Comput. Math. Math. Phys.7, 86–112 (1967).
  8. R. D. Richtmyer, “The evaluation of definite integrals, and a quasi-Monte-Carlo method based on the properties of algebraic numbers,” LA-1342, Los Alamos Scientific Laboratories, (1951).
  9. J. H. Halton, “On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals,” Numer. Math.2, 84–90 (1960).
  10. J. M. Hammersley, “Monte Carlo methods for solving multivariable problems,” Ann. N. Y. Acad. Sci.86, 844–874 (1960).
  11. H. Faure, “On the star-discrepancy of generalized Hammersley sequences in two dimensions,” Monatsh. Math.101, 291–300 (1986).
  12. M. Matsumoto and T. Nishimura, “Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator,” ACM Trans. Model. Comput. Simul.8, 3–30 (1998).

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