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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: James C. Wyant
  • Vol. 47, Iss. 2 — Jan. 10, 2008
  • pp: 195–205

ABCD matrix of the human lens gradient-index profile: applicability of the calculation methods

José Antonio Díaz  »View Author Affiliations


Applied Optics, Vol. 47, Issue 2, pp. 195-205 (2008)
http://dx.doi.org/10.1364/AO.47.000195


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Abstract

The applicability of different approximate methods proposed to determine the paraxial properties of the gradient-index (GRIN) distribution resembling that of the human lens, by means of the system ABCD matrix, is tested. Thus, the parabolic-ray-path approximation has been extended to provide the ABCD matrix of a slab lens comprised of a rotationally GRIN medium. The results show that this method has good numerical stability, and it is also the easiest one in determining the Gaussian constants of the human lens GRIN profile.

© 2008 Optical Society of America

OCIS Codes
(080.2710) Geometric optics : Inhomogeneous optical media
(080.2730) Geometric optics : Matrix methods in paraxial optics
(330.4460) Vision, color, and visual optics : Ophthalmic optics and devices
(330.5370) Vision, color, and visual optics : Physiological optics

ToC Category:
Vision, Color, and Visual Optics

History
Original Manuscript: September 24, 2007
Revised Manuscript: November 20, 2007
Manuscript Accepted: November 25, 2007
Published: January 8, 2008

Virtual Issues
Vol. 3, Iss. 2 Virtual Journal for Biomedical Optics

Citation
José Antonio Díaz, "ABCD matrix of the human lens gradient-index profile: applicability of the calculation methods," Appl. Opt. 47, 195-205 (2008)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-47-2-195


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References

  1. M. Born and E. Wolf, Principles of Optics, 8th ed. (Cambridge U. Press, 2002).
  2. E. W. Marchand, Gradient Index Optics (Academic, 1978).
  3. E. W. Marchand, "Ray tracing in gradient-index media," J. Opt. Soc. Am. 60, 1-8 (1970). [CrossRef]
  4. S. Doric and N. Renaud, "Analytical expressions for the paraxial parameters of a single lens with a spherical distribution of refractive index," Appl. Opt. 131, 5197-5200 (1992). [CrossRef]
  5. D. T. Moore, "Design of singlets with continuously varying indices of refraction," J. Opt. Soc. Am. 61, 886-894 (1971). [CrossRef]
  6. S. Doric, "Paraxial raytrace for rotationally symmetric homogeneous and inhomogeneous media," J. Opt. Soc. Am. A 1, 818-821 (1984). [CrossRef]
  7. 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] [PubMed]
  8. R. K. Luneburg, Mathematical Theory of Optics (Univ. of California Press, 1964).
  9. P. J. Sands, "Inhomogeneous lens, III. Paraxial optics," J. Opt. Soc. Am. 61, 879-885 (1971). [CrossRef]
  10. D. A. Atchison and G. Smith, "Continuous gradient index and shell models of the human lens," Vision Res. 35, 2529-2538 (1995). [CrossRef] [PubMed]
  11. G. Smith and D. A. Atchison, "Equivalent power of the crystalline lens of the human eye: comparison of methods of calculation," J. Opt. Soc. Am. A 14, 2537-2546 (1997). [CrossRef]
  12. L. Matthiessen, "Untersuchungen über den aplanatismus und die periscopie der krystalllinsen in den augen der fische," Pfluegers Arch. Gesamte Physiol. Menschen Tiere 231, 287-307 (1880). [CrossRef]
  13. L. Matthiessen, "Untersuchungen über den Aplanatismus und die Periscopie der Krystalllinsen in den Augen der Fische," Pfluegers Arch. Gesamte Physiol. Menschen Tiere 27, 510-523 (1882). [CrossRef]
  14. A. Gullstrand, Hemholtz's Handbuch der Physiologischen Optik, 3rd ed., Vol. 1, Appendix II, pp. 301-358 (English translation edited by J. P. Southall, Optical Society of America, 1924).
  15. J. W. Blaker, "Toward an adptative model of the human eye," J. Opt. Soc. Am. 70, 220-283 (1980). [CrossRef] [PubMed]
  16. H. Liou and N. A. Brennan, "Anatomically accurate, finite model eye for optical modeling," J. Opt. Soc. Am. A 14, 1684-1695 (1997). [CrossRef] [PubMed]
  17. Y. Huang and D. T. Moore, "Human eye modeling using a single equation of gradient index crystalline lens for relaxed and accommodated states," Proc. SPIE 6342, 63420D (2006). [CrossRef]
  18. J. A. Díaz, C. Pizarro, and J. Arasa, "A single dispersive GRIN profile for the aging human eye," J. Opt. Soc. Am. A 25, 250-261 (2008). [CrossRef] [PubMed]
  19. M. Dublemann and G. van der Heijde, "The shape of the human lens: curvature, equivalent refractive index and the lens paradox," Vision Res. 41, 1867-1877 (2001). [CrossRef]
  20. M. Dublemann, G. van der Heijde, and H. A. Weeber, "Change in the shape of the aging human crystalline lens with accommodation," Vision Res. 45, 117-132 (2005). [CrossRef] [PubMed]
  21. C. Jones, D. Atchison, R. Meder, and J. Pope, "Refractive index distribution and optical properties of the isolated human lens measured using magnetic resonance imaging (MRI)," Vision Res. 45, 2352-2366 (2005). [CrossRef] [PubMed]
  22. G. Smith, "Paraxial raytracing in gradient-index media: problems of convergence," J. Opt. Soc. Am. A 9, 331-333 (1992). [CrossRef] [PubMed]
  23. K. Halbach, "Matrix representation of Gaussian optics," Am. J. Phys. 3, 90-108 (1964). [CrossRef] [PubMed]
  24. A. Gerrard and J. Burch, Introduction to Matrix Methods in Optics (Dover, 1975). [PubMed]
  25. H. Arsenault, "Generalization of the principal plane concept in matrix optics," Am. J. Phys. 66, 397-399 (1980). [CrossRef] [PubMed]
  26. H. Arsenault and B. Macukow, "Factorization of the transfer matrix for symmetrical optical systems," J. Opt. Soc. Am. 73, 1350-1359 (1983). [CrossRef]
  27. W. M. Rosenblum, J. W. Blaker, and M. G. Block, "Matrix methods for the evaluation of lens systems with radial gradient-index elements," Am. J. Optom. Physiol. Opt. 65, 661-665 (1988). [PubMed]
  28. D. S. Goodman, "Geometrical Optics" in Handbook of Optics, Vol. I (Optical Society of America, 1995), pp. 1.1-1.80.
  29. W. T. Weltford, Aberrations of Optical Systems (Hilger, 1986).
  30. M. V. Pérez, C. Bao, M. T. Flores-Arias, M. A. Rama, and C. Gómez-Reino, "Description of gradient-index crystalline lens by a first order optical system," J. Opt. A, Pure Appl. Opt. 7, 103-110 (2005). [CrossRef]
  31. M. V. Pérez, C. Bao, M. T. Flores-Arias, M. Rama, and C. Gómez-Reino, "Gradient parameter and axial and field rays in the gradient-index crystalline lens model," J. Opt. A, Pure Appl. Opt. 5, S293-S297 (2003). [CrossRef] [PubMed]
  32. V. Lakshminarayanan and M. Calvo, "The optical transmission function and point spread function of the human eye treated as a cascade linear system in the Fresnel regime," in Selected Topics in Mathematical Physics, K.S. R. R.Sridhar and V.Lakshminarayanan, eds. (Allied, 1995). [PubMed]
  33. M. T. Flores-Arias, M. V. Pérez, C. Bao, A. Castelo, and C. Gómez-Reino, "Gradient-index human lens as a quadratic phase transformer," J. Mod. Opt. 4, 495-506 (2006). [CrossRef] [PubMed]
  34. P. J. Sands, "Third-order aberrations of inhomogeneous lenses," J. Opt. Soc. Am. 60, 1436-1443 (1970). [CrossRef]
  35. H. A. Buchdahl, Optical Aberrations Coefficients (Dover, 1968). [PubMed]
  36. K. Tanaka, "Paraxial theory of rotationally distributed-index media by means of Gaussian constants," Appl. Opt. 23, 1700-1706 (1984). [CrossRef] [PubMed]
  37. W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems (Wiley, 2001). [PubMed]
  38. E. D. Rainville, Intermediate Differential Equations, 2nd ed. (Macmillan, 1964).
  39. C. Gomez-Reino, M. V. Pérez, and C. Bao, Gradient-Index Optics (Springer-Verlag, 2002).
  40. C. Palma and V. Bagini, "Extension of the fresnel transform to ABCD systems," J. Opt. Soc. Am. A 14, 1774-1779 (1997). [CrossRef]
  41. S. Wolfram, The Mathematica Book, 5th ed. (Wolfram Media, 2003).
  42. G. Smith, D. A. Atchison, and B. K. Pierscionek, "Modeling the power of the aging human eye," J. Opt. Soc. Am. A 9, 2111-2117 (1992). [CrossRef] [PubMed]
  43. B. A. Moffat, D. A. Atchison, and J. Pope, "Explanation of the lens paradox," Optom. Vision Sci. 79, 148-150 (2002). [CrossRef]

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