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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 53, Iss. 21 — Jul. 20, 2014
  • pp: 4784–4790

Simplifying numerical ray tracing for characterization of optical systems

Yakir Luc Gagnon, Daniel I. Speiser, and Sönke Johnsen  »View Author Affiliations

Applied Optics, Vol. 53, Issue 21, pp. 4784-4790 (2014)

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Ray tracing, a computational method for tracing the trajectories of rays of light through matter, is often used to characterize mechanical or biological visual systems with aberrations that are larger than the effect of diffraction inherent in the system. For example, ray tracing may be used to calculate geometric point spread functions (PSFs), which describe the image of a point source after it passes through an optical system. Calculating a geometric PSF is useful because it gives an estimate of the detail and quality of the image formed by a given optical system. However, when using ray tracing to calculate a PSF, the accuracy of the estimated PSF directly depends on the number of discrete rays used in the calculation; higher accuracies may require more computational power. Furthermore, adding optical components to a modeled system will increase its complexity and require critical modifications so that the model will describe the system correctly, sometimes necessitating a completely new model. Here, we address these challenges by developing a method that represents rays of light as a continuous function that depends on the light’s initial direction. By utilizing Chebyshev approximations (via the chebfun toolbox in MATLAB) for the implementation of this method, we greatly simplified the calculations for the location and direction of the rays. This method provides high precision and fast calculation speeds that allow the characterization of any symmetrical optical system (with a centered point source) in an analytical-like manner. Next, we demonstrate our methods by showing how they can easily calculate PSFs for complicated optical systems that contain multiple refractive and/or reflective interfaces.

© 2014 Optical Society of America

OCIS Codes
(080.0080) Geometric optics : Geometric optics
(080.1510) Geometric optics : Propagation methods
(080.1753) Geometric optics : Computation methods
(080.4225) Geometric optics : Nonspherical lens design
(080.4228) Geometric optics : Nonspherical mirror surfaces

ToC Category:
Geometric Optics

Original Manuscript: March 20, 2014
Revised Manuscript: June 11, 2014
Manuscript Accepted: June 13, 2014
Published: July 18, 2014

Yakir Luc Gagnon, Daniel I. Speiser, and Sönke Johnsen, "Simplifying numerical ray tracing for characterization of optical systems," Appl. Opt. 53, 4784-4790 (2014)

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  1. Y. L. Gagnon, R. H. H. Kröger, and B. Söderberg, “Adjusting a light dispersion model to fit measurements from vertebrate ocular media as well as ray-tracing in fish lenses,” Vis. Res. 50, 850–853 (2010). [CrossRef]
  2. L. F. Garner, G. Smith, S. Yao, and R. C. Augusteyn, “Gradient refractive index of the crystalline lens of the Black Oreo Dory (Allocyttus niger): comparison of magnetic resonance imaging (MRI) and laser ray-trace methods,” Vis. Res. 41, 973–979 (2001). [CrossRef]
  3. A. Sharma, D. V. Kumar, and A. K. Ghatak, “Tracing rays through graded-index media: a new method,” Appl. Opt. 21, 984–987 (1982). [CrossRef]
  4. W. S. Jagger, “The optics of the spherical fish lens,” Vis. Res. 32, 1271–1284 (1992). [CrossRef]
  5. Y. L. Gagnon, T. T. Sutton, and S. Johnsen, “Visual acuity in pelagic fishes and mollusks,” Vis. Res. 92, 1–9 (2013). [CrossRef]
  6. D. Y. C. Chan, “Determination and modeling of the 3-D gradient refractive-indexes in crystalline lenses,” Appl. Opt. 27, 926–931 (1988). [CrossRef]
  7. P. L. Chu, “Nondestructive measurement of index profile of an optical-fibre preform,” Electron. Lett. 13, 736–738 (1977). [CrossRef]
  8. Y. L. Gagnon and R. H. H. Kröger, “Gradient index models of monofocal and multifocal spherical fish lenses,” Investig. Ophthalmol. Vis. Sci. 47, 1211 (2006).
  9. Y. L. Gagnon, B. Söderberg, and R. H. H. Kröger, “Optical advantages and function of multifocal spherical fish lenses,” J. Opt. Soc. Am. A 29, 1786–1793 (2012). [CrossRef]
  10. Y. L. Gagnon, B. Söderberg, and R. H. H. Kröger, “Effects of the peripheral layers on the optical properties of spherical fish lenses,” J. Opt. Soc. Am. A 25, 2468–2475 (2008). [CrossRef]
  11. R. H. H. Kröger, M. C. W. Campbell, R. D. Fernald, and H. J. Wagner, “Multifocal lenses compensate for chromatic defocus in vertebrate eyes,” J. Comp. Physiol. A 184, 361–369 (1999). [CrossRef]
  12. R. H. H. Kröger, M. C. W. Campbell, R. Munger, and R. D. Fernald, “Refractive index distribution and spherical aberration in the crystalline lens of the African cichlid fish Haplochromis burtoni,” Vis. Res. 34, 1815–1822 (1994). [CrossRef]
  13. O. E. Lind, A. Kelber, and R. H. H. Kröger, “Multifocal optical systems and pupil dynamics in birds,” J. Exp. Biol. 211, 2752–2758 (2008). [CrossRef]
  14. L. Matthiessen, “Ueber die beziehungen, welche zwischen dem brechungsindex des kerncentrums der krystalllinse und den dimensionen des auges bestehen,” Pflüger’s Archiv 27, 510–523 (1882).
  15. J. M. Schartau, B. Sjögreen, Y. L. Gagnon, and R. H. H. Kröger, “Optical plasticity in the crystalline lenses of the cichlid fish Aequidens pulcher,” Curr. Biol. 19, 122–126 (2009). [CrossRef]
  16. J. G. Sivak and R. O. Kreuzer, “Spherical aberration of the crystalline lens,” Vis. Res. 23, 59–70 (1983). [CrossRef]
  17. P. Mouroulis and J. Macdonald, Geometrical Optics and Optical Design (Oxford University, 1997).
  18. E. Hecht, Optics (Addison-Wesley, 2002).
  19. J. Arasa and J. Alda, Real Ray Tracing (Marcel Dekker, 2004).
  20. J. Portilla and S. Barbero, “Accuracy of geometric point spread function estimation using the ray-counting method,” Proc. SPIE 8550, 855003 (2012). [CrossRef]
  21. O. N. Stavroudis and D. P. Feder, “Automatic computation of spot diagrams,” J. Opt. Soc. Am. 44, 163–164 (1954). [CrossRef]
  22. C.-S. Liu and P. D. Lin, “Computational method for deriving the geometric point spread function of an optical system,” Appl. Opt. 49, 126–136 (2010). [CrossRef]
  23. L. N. Trefethen, “Chebfun Version 4.2,” The Chebfun Development Team (2011), http://www.chebfun.org/ .
  24. Y. L. Gagnon, “chebRay,” (2014), https://github.com/yakir12/chebRay .
  25. M. F. Land, “Activity in the optic nerve of Pecten maximus in response to changes in light intensity, and to pattern and movement in the optical environment,” J. Exp. Biol. 45, 83–99 (1966).

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