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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 10 — Oct. 1, 2006
  • pp: 2551–2565

Tomographic method for measurement of the gradient refractive index of the crystalline lens. II. The rotationally symmetrical lens

Daniel Vazquez, Eva Acosta, George Smith, and Leon Garner  »View Author Affiliations


JOSA A, Vol. 23, Issue 10, pp. 2551-2565 (2006)
http://dx.doi.org/10.1364/JOSAA.23.002551


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Abstract

In the first part of this paper we presented a tomographic method to reconstruct the refractive index profile of spherically symmetrical lenses. Here we perform the generalization to lenses that are rotationally symmetrical around the optical axis, as is the ideal human lens. Analysis of the accuracy and versatility of this method is carried out by performing numerical simulations in which different magnitudes of experimental errors and two extreme case scenarios for the likely shape of the refractive index distribution of the human lens are considered. Finally, experimental results for a porcine lens are shown. Conceptually simple and computationally swift, this method could prove to be a valuable tool for the accurate retrieval of the gradient index of a broad spectrum of rotationally symmetrical crystalline lenses.

© 2006 Optical Society of America

OCIS Codes
(080.2710) Geometric optics : Inhomogeneous optical media
(110.2760) Imaging systems : Gradient-index lenses
(170.6960) Medical optics and biotechnology : Tomography
(290.3030) Scattering : Index measurements
(330.4300) Vision, color, and visual optics : Vision system - noninvasive assessment

ToC Category:
Scattering

History
Original Manuscript: February 3, 2006
Revised Manuscript: April 6, 2006
Manuscript Accepted: April 27, 2006

Virtual Issues
Vol. 1, Iss. 11 Virtual Journal for Biomedical Optics

Citation
Daniel Vazquez, Eva Acosta, George Smith, and Leon Garner, "Tomographic method for measurement of the gradient refractive index of the crystalline lens. II. The rotationally symmetrical lens," J. Opt. Soc. Am. A 23, 2551-2565 (2006)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-10-2551


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References

  1. P. L. Chu, "Nondestructive measurements of index profile of an optical fibre preform," Electron. Lett. 13, 736-738 (1977).
  2. D. Marcuse, "Refractive index determination by the focusing method," Appl. Opt. 18, 9-13 (1979).
  3. V. I. Vlad and N. Ionescu-Pallas, "New treatment of the focusing method and tomography of the refractive index distribution of inhomogeneous optical components," Opt. Eng. (Bellingham) 35, 1305-1310 (1996).
  4. D. Y. C. Chan, J. P. Ennis, B. K. Pierscionek, and G. Smith, "Determination of the 3-D gradient refractive indices in crystalline lenses," Appl. Opt. 27, 926-931 (1988).
  5. B. K. Pierscionek and D. Y. C. Chan, "Refractive index gradient of human lenses," Optom. Vision Sci. 66, 822-829 (1989).
  6. 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," Vision Res.41, 973-979 (2001).
  7. E. Acosta, R. Flores, D. Vazquez, S. Rios, L. F. Garner, and G. Smith, "Tomographic method for measurement of the refractive index profile of optical fibre preforms and rod GRIN lenses," Jpn. J. Appl. Phys., Part 1 41, 4821-4824 (2002).
  8. E. Acosta, D. Vazquez, L. Garner, and G. Smith, "Tomographic method for measurement of the gradient refractive index of the crystalline lens. I. The spherical fish lens," J. Opt. Soc. Am. A 22, 424-433 (2005).
  9. R. D. Fernald, "The optical system of the fish" in The Visual System of Fish, R.H.Douglas and M.B. A.Djamgoz, eds. (Chapman & Hall, 1990), pp. 50-52.
  10. W. S. Jagger, "The optics of the spherical fish lens," Vision Res. 32, 1271-1284 (1992).
  11. J. G. Sivak, "Optical variability of the fish lens," in Ref. , pp. 63-74.
  12. M. C. W. Campbell, "Measurement of refractive index in an intact crystalline lens," Vision Res. 24, 409-415 (1984).
  13. K. F. Barrell and C. Pask, "Nondestructive index profile measurements of noncircular optical fibre preforms," Opt. Commun. 27, 230-234 (1978).
  14. G. Beliakov and D. Y. C. Chan, "Analysis of inhomogeneous optical systems by the use of ray tracing. II. Three-dimensional systems with symmetry," Appl. Opt. 37, 5106-5111 (1998).
  15. J. R. Kuszak, K. L. Peterson, and H. G. Brown, "Electron microscopy observations of the crystalline lens," Microsc. Res. Tech. 33, 441-479 (1996).
  16. D. T. Moore, "Design of singlets with continuously varying indices of refraction," J. Opt. Soc. Am. 61, 886-894 (1971).
  17. J. W. Blaker, "Toward an adaptive model of the human eye," J. Opt. Soc. Am. 70, 220-223 (1980).
  18. G. Smith, B. K. Pierscionek, and D. A. Atchison, "The optical modelling of the human lens," Ophthalmic Physiol. Opt. 11, 359-369 (1991).
  19. E. W. Marchand, Gradient Index Optics (Academic Press, 1978), Chap. 9, p. 99.
  20. B. A. Moffat, D. A. Atchison, and J. M. Pope, "Age-related changes in refractive index distribution and power of the human lens as measured by magnetic resonance micro-imaging in vitro," Vision Res. 42, 1683-1693 (2002).
  21. A. Gullstrand, Appendix II in Helmholtz'sHandbuch der Physiologischen Optik, Vol. 1, 3rd ed. (English translation edited by J.P.Southall, Optical Society of America, Dover, 1962), pp. 351-352.
  22. L. Montagnino, "Ray tracing in homogeneous media," J. Opt. Soc. Am. 58, 1667-1668 (1968).
  23. A. Sharma, D. V. Kumar, and A. K. Ghatak, "Tracing rays through graded-index media: a new method," Appl. Opt. 21, 984-987 (1982).
  24. P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, 1992), Chap. 11, pp. 205-209.
  25. H. L. Liou and N. A. Brennan, "Anatomically accurate, finite model eye for optical modeling," J. Opt. Soc. Am. A 14, 1684-1695 (1997).
  26. J. F. Koretz, C. A. Cook, and P. L. Kaufman, "Aging of the human lens: changes in lens shape upon accommodation and with accommodative loss," J. Opt. Soc. Am. A 19, 144-151 (2002).
  27. R. C. Gonzalez and R. E. Woods, Digital Image Processing (Addison-Wesley, 1993), Chap. 7, pp. 416-423.
  28. R. Halír and J. Flusser, "Numerically stable direct least squares fitting of ellipses," in Proceedings of the Sixth International Conference in Central Europe on Computer Graphics and Visualization (WSCG'98), V.Skala, ed. (Vydavatelstvi Zapadoceske Univerzity, , 1998), Vol. 1, pp. 125-132.
  29. W. S. Jagger, "The refractive structure and optical properties of the isolated crystalline lens of the cat," Vision Res. 30, 723-738 (1990).
  30. C. E. Jones and J. M. Pope, "Measuring optical properties of an eye lens using magnetic resonance imaging," Magn. Reson. Imaging 22, 211-220 (2004).
  31. S. Barbero, A. Glasser, C. Clark, and S. Marcos, "Accuracy and possibilities for evaluating the lens gradient-index using a ray tracing tomography global optimization strategy," Invest. Ophthalmol. Visual Sci. 45 Suppl. 1, U706 1723 (2004).

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