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Biomedical Optics Express

Biomedical Optics Express

  • Editor: Joseph A. Izatt
  • Vol. 5, Iss. 1 — Jan. 1, 2014
  • pp: 31–39

Age-dependence of the average and equivalent refractive indices of the crystalline lens

W. Neil Charman and David A. Atchison  »View Author Affiliations

Biomedical Optics Express, Vol. 5, Issue 1, pp. 31-39 (2014)

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Lens average and equivalent refractive indices are required for purposes such as lens thickness estimation and optical modeling. We modeled the refractive index gradient as a power function of the normalized distance from lens center. Average index along the lens axis was estimated by integration. Equivalent index was estimated by raytracing through a model eye to establish ocular refraction, and then backward raytracing to determine the constant refractive index yielding the same refraction. Assuming center and edge indices remained constant with age, at 1.415 and 1.37 respectively, average axial refractive index increased (1.408 to 1.411) and equivalent index decreased (1.425 to 1.420) with age increase from 20 to 70 years. These values agree well with experimental estimates based on different techniques, although the latter show considerable scatter. The simple model of index gradient gives reasonable estimates of average and equivalent lens indices, although refinements in modeling and measurements are required.

© 2013 Optical Society of America

OCIS Codes
(330.4460) Vision, color, and visual optics : Ophthalmic optics and devices
(330.7326) Vision, color, and visual optics : Visual optics, modeling

ToC Category:
Ophthalmology Applications

Original Manuscript: September 20, 2013
Revised Manuscript: November 17, 2013
Manuscript Accepted: November 22, 2013
Published: December 2, 2013

W. Neil Charman and David A. Atchison, "Age-dependence of the average and equivalent refractive indices of the crystalline lens," Biomed. Opt. Express 5, 31-39 (2014)

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  1. W. Drexler, O. Findl, L. Schmetterer, C. K. Hitzenberger, and A. F. Fercher, “Eye elongation during accommodation in humans: differences between emmetropes and myopes,” Invest. Ophthalmol. Vis. Sci.39(11), 2140–2147 (1998). [PubMed]
  2. E. A. H. Mallen, P. Kashyap, and K. M. Hampson, “Transient axial length change during the accommodation response in young adults,” Invest. Ophthalmol. Vis. Sci.47(3), 1251–1254 (2006). [CrossRef] [PubMed]
  3. S. A. Read, M. J. Collins, E. C. Woodman, and S. H. Cheong, “Axial length changes during accommodation in myopes and emmetropes,” Optom. Vis. Sci.87(9), 656–662 (2010). [CrossRef] [PubMed]
  4. D. A. Atchison and G. Smith, “Possible errors in determining axial length changes during accommodation with the IOLMaster,” Optom. Vis. Sci.81(4), 283–286 (2004). [CrossRef] [PubMed]
  5. D. A. Atchison and G. Smith, Optics of the Human Eye (Butterworth-Heinemann, Oxford 2000), pp.250–258.
  6. M. Dubbelman, G. L. van der Heijde, and H. A. Weeber, “The thickness of the aging human lens obtained from corrected Scheimpflug images,” Optom. Vis. Sci.78(6), 411–416 (2001). [CrossRef] [PubMed]
  7. M. Dubbelman and G. L. Van der Heijde, “The shape of the aging human lens: curvature, equivalent refractive index and the lens paradox,” Vision Res.41(14), 1867–1877 (2001). [CrossRef] [PubMed]
  8. N. G. M. Wiemer, M. Dubbelman, P. J. Kostense, P. J. Ringens, and B. C. P. Polak, “The influence of diabetes mellitus type 1 and 2 on the thickness, shape, and equivalent refractive index of the human crystalline lens,” Ophthalmology115(10), 1679–1686 (2008). [CrossRef] [PubMed]
  9. A. Glasser and M. C. W. Campbell, “Biometric, optical and physical changes in the isolated human crystalline lens with age in relation to presbyopia,” Vision Res.39(11), 1991–2015 (1999). [CrossRef] [PubMed]
  10. D. Borja, F. Manns, A. Ho, N. Ziebarth, A. M. Rosen, R. Jain, A. Amelinckx, E. Arrieta, R. C. Augusteyn, and J. M. Parel, “Optical power of the isolated human crystalline lens,” Invest. Ophthalmol. Vis. Sci.49(6), 2541–2548 (2008). [CrossRef] [PubMed]
  11. M. Bahrami and A. V. Goncharov, “Geometry-invariant gradient refractive index lens: analytical ray tracing,” J. Biomed. Opt.17(5), 055001 (2012). [CrossRef] [PubMed]
  12. R. Navarro, F. Palos, and L. González, “Adaptive model of the gradient index of the human lens. I. Formulation and model of aging ex vivo lenses,” J. Opt. Soc. Am. A24(8), 2175–2185 (2007). [CrossRef] [PubMed]
  13. R. Navarro, F. Palos, and L. M. González, “Adaptive model of the gradient index of the human lens. II. Optics of the accommodating aging lens,” J. Opt. Soc. Am. A24(9), 2911–2920 (2007). [CrossRef] [PubMed]
  14. G. Smith, D. A. Atchison, and B. K. Pierscionek, “Modeling the power of the aging human eye,” J. Opt. Soc. Am. A9(12), 2111–2117 (1992). [CrossRef] [PubMed]
  15. S. Kasthurirangan, E. L. Markwell, D. A. Atchison, and J. M. Pope, “In vivo study of changes in refractive index distribution in the human crystalline lens with age and accommodation,” Invest. Ophthalmol. Vis. Sci.49(6), 2531–2540 (2008). [CrossRef] [PubMed]
  16. C. E. Jones, D. A. Atchison, R. Meder, and J. M. Pope, “Refractive index distribution and optical properties of the isolated human lens measured using magnetic resonance imaging (MRI),” Vision Res.45(18), 2352–2366 (2005). [CrossRef] [PubMed]
  17. Y. Le Grand and S. G. El Hage, Physiological Optics (Springer Verlag, Berlin, 1980 ) pp. 65–67.
  18. H. von Helmholtz, Treatise on Physiological Optics, Vol. 1, translated from the 3rd German edition by J. P. C. Southall, Optical Society of America, Rochester, p.100. (1924).
  19. D. A. Atchison, “Age-related paraxial schematic emmetropic eyes,” Ophthalmic Physiol. Opt.29(1), 58–64 (2009). [CrossRef] [PubMed]
  20. W. N. Charman, Adnan, and D. A. Atchison, “Gradients of refractive index in the crystalline lens and transient changes in refraction among patients with diabetes,” Biomed. Opt. Express3(12), 3033–3042 (2012). [PubMed]
  21. S. R. Uhlhorn, D. Borja, F. Manns, and J.-M. Parel, “Refractive index measurement of the isolated crystalline lens using optical coherence tomography,” Vision Res.48(27), 2732–2738 (2008). [CrossRef] [PubMed]
  22. A. de Castro, D. Siedlecki, D. Borja, S. Uhlhorn, J.-M. Parel, F. Manns, and S. Marcos, “Age-dependent variation of the gradient index profile in human crystalline lenses,” J. Mod. Opt.58(19-20), 1781–1787 (2011). [CrossRef] [PubMed]
  23. C. E. Jones, D. A. Atchison, and J. M. Pope, “Changes in lens dimensions and refractive index with age and accommodation,” Optom. Vis. Sci.84(10), 990–995 (2007). [CrossRef] [PubMed]
  24. R. P. Hemenger, L. F. Garner, and C. S. Ooi, “Change with age of the refractive index gradient of the human ocular lens,” Invest. Ophthalmol. Vis. Sci.36(3), 703–707 (1995). [PubMed]
  25. A. de Castro, J. Birkenfeld, B. Maceo, F. Manns, E. Arrieta, J.-M. Parel, and S. Marcos, “Influence of shape and gradient refractive index in the accommodative changes of spherical aberration in nonhuman primate crystalline lenses,” Invest. Ophthalmol. Vis. Sci.54(9), 6197–6207 (2013). [CrossRef] [PubMed]
  26. C. de Freitas, M. Ruggeri, F. Manns, A. Ho, and J.-M. Parel, “In vivo measurement of the average refractive index of the human crystalline lens using optical coherence tomography,” Opt. Lett.38(2), 85–87 (2013). [CrossRef] [PubMed]
  27. M. Dubbelman, G. L. Van der Heijde, H. A. Weeber, and G. F. Vrensen, “Changes in the internal structure of the human crystalline lens with age and accommodation,” Vision Res.43(22), 2363–2375 (2003). [CrossRef] [PubMed]
  28. K. Richdale, L. T. Sinnott, M. A. Bullimore, P. A. Wassenaar, P. Schmalbrock, C. Y. Kao, S. Patz, D. O. Mutti, A. Glasser, and K. Zadnik, “Quantification of age-related and per diopter accommodative changes of the lens and ciliary muscle in the emmetropic human eye,” Invest. Ophthalmol. Vis. Sci.54(2), 1095–1105 (2013). [CrossRef] [PubMed]
  29. D. A. Atchison, E. L. Markwell, S. Kasthurirangan, J. M. Pope, G. Smith, and P. G. Swann, “Age-related changes in optical and biometric characteristics of emmetropic eyes,” J. Vision8(4), 29 (2008)
  30. F. J. Slataper, “Age norms of refraction and vision,” Arch. Ophthalmol.43(3), 466–481 (1950). [CrossRef]
  31. H. Saunders, “Age-dependence of human refractive errors,” Ophthalmic Physiol. Opt.1(3), 159–174 (1981). [CrossRef] [PubMed]

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