Accuracy of the reconstruction of the crystalline lens gradient index with optimization methods from Ray Tracing and Optical Coherence Tomography data

Optics Express

Volumn 19, Issue 20, 2011, Pages 19265-19279

  De Castro, Alberto ^a   Barbero, Sergio ^a   Ortiz, Sergio ^a   Marcos, Susana ^a  

^a INSTITUTO DE ÓPTICA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

CRYSTALLINE MATERIALS; INPUT OUTPUT PROGRAMS; MEASUREMENT ERRORS; OPTICAL TOMOGRAPHY; OPTIMIZATION; REFRACTIVE INDEX;

CRYSTALLINE LENS; DIRECTION COSINE; EXPERIMENTAL ERRORS; GRADIENT INDEXES; GRADIENT REFRACTIVE INDEX; INPUT DATAS; LOCAL SEARCH ALGORITHM; NOISE LEVELS; NUMBER OF RAYS; OPTICAL PATH DIFFERENCE; OPTIMIZATION METHOD; SHAPE MEASUREMENTS;

LENSES;

ALGORITHM; ARTICLE; COMPUTER SIMULATION; HISTOLOGY; HUMAN; IMAGE PROCESSING; LENS; METHODOLOGY; OPTICAL COHERENCE TOMOGRAPHY; REFRACTOMETRY;

ALGORITHMS; COMPUTER SIMULATION; HUMANS; IMAGE PROCESSING, COMPUTER-ASSISTED; LENS, CRYSTALLINE; REFRACTOMETRY; TOMOGRAPHY, OPTICAL COHERENCE;

EID: 80053291892     PISSN: None     EISSN: 10944087     Source Type: Journal    
DOI: 10.1364/OE.19.019265     Document Type: Article

References (51)

1. L. F. Garner and G. Smith, "Changes in equivalent and gradient refractive index of the crystalline lens with accommodation," Optom. Vis. Sci. 74(2), 114-119 (1997). (Pubitemid 27147886)
2. G. Smith, D. A. Atchison, and B. K. Pierscionek, "Modeling the power of the aging human eye," J. Opt. Soc. Am. A 9(12), 2111-2117 (1992).
3. 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(13), 1683-1693 (2002). (Pubitemid 34655503)
4. 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. (2011).
5. A. Huggert, The iso-indicial surfaces of the human crystalline lens (Acta Ophthalmologica supplementum, Stockholm, 1948).
6. R. Weale, "The ageing eye," in The Lens, H. K. Lewis, ed. (London, 1963).
7. B. K. Pierscionek, "Refractive index contours in the human lens," Exp. Eye Res. 64(6), 887-893 (1997). (Pubitemid 27314763)
8. M. C. Campbell and A. Hughes, "An analytic, gradient index schematic lens and eye for the rat which predicts aberrations for finite pupils," Vision Res. 21(7), 1129-1148 (1981). (Pubitemid 11095743)
9. D. Y. Chan, J. P. Ennis, B. K. Pierscionek, and G. Smith, "Determination and modeling of the 3-D gradient refractive indices in crystalline lenses," Appl. Opt. 27(5), 926-931 (1988).
10. G. Beliakov and D. Y. Chan, "Analysis of inhomogeneous optical systems by the use of ray tracing. I. Planar systems," Appl. Opt. 36(22), 5303-5309 (1997). (Pubitemid 127638480)
11. 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(3), 424-433 (2005). (Pubitemid 40384143)
12. D. Vazquez, E. Acosta, G. Smith, and L. 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(10), 2551-2565 (2006). (Pubitemid 44781656)
13. 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). (Pubitemid 40848281)
14. 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).
15. O. Pomerantzeff, M. Pankratov, G. J. Wang, and P. Dufault, "Wide-angle optical model of the eye," Am. J. Optom. Physiol. Opt. 61(3), 166-176 (1984). (Pubitemid 14140101)
16. 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(8), 973-979 (2001). (Pubitemid 32285373)
17. S. Barbero, A. Glasser, C. Clark, and S. Marcos, "Accuracy and possibilities for evaluating the lens gradientindex using a ray tracing tomography global optimization strategy," Invest. Ophthalmol. Vis. Sci. 45, 1723 (2004).
18. S. Ortiz, S. Barbero, and S. Marcos, "Computer simulations of optical coherence tomography A-scans: what can we learn about refractive index distribution?" Invest. Ophthalmol. Vis. Sci. 45, 2781 (2004).
19. Y. Verma, K. D. Rao, M. K. Suresh, H. S. Patel, and P. K. Gupta, "Measurement of gradient refractive index profile of crystalline lens of fisheye in vivo using optical coherence tomography," Appl. Phys. B 87(4), 607-610 (2007). (Pubitemid 46870868)
20. A. de Castro, S. Ortiz, E. Gambra, D. Siedlecki, and S. Marcos, "Three-dimensional reconstruction of the crystalline lens gradient index distribution from OCT imaging," Opt. Express 18(21), 21905-21917 (2010).
21. O. Pomerantzeff, H. Fish, J. Govignon, and C. L. Schepens, "Wide angle optical model of the human eye," Ann. Ophthalmol. 3(8), 815-819 (1971).
22. I. H. Al-Ahdali and M. A. El-Messiery, "Examination of the effect of the fibrous structure of a lens on the optical characteristics of the human eye: a computer-simulated model," Appl. Opt. 34(25), 5738-5745 (1995).
23. A. Popiolek Masajada, "Numerical study of the influence of the shell structure of the crystalline lens on the refractive properties of the human eye," Ophthalmic Physiol. Opt. 19(1), 41-49 (1999).
24. D. O. Mutti, K. Zadnik, and A. J. Adams, "The equivalent refractive index of the crystalline lens in childhood," Vision Res. 35(11), 1565-1573 (1995).
25. Y.-J. Liu, Z.-Q. Wang, L.-P. Song, and G.-G. Mu, "An anatomically accurate eye model with a shell-structure lens," Optik Internat. J. Light Electron. Opt. 116(6), 241-246 (2005). (Pubitemid 40786008)
26. C. E. Campbell, "Nested shell optical model of the lens of the human eye," J. Opt. Soc. Am. A 27(11), 2432-2441 (2010).
27. A. Gullstrand, Handbuch der Physiologitschen Optik, 3rd ed. 1909. J. P. Southall trans., (Optical Society of America, 1924).
28. J. W. Blaker, "Toward an adaptive model of the human eye," J. Opt. Soc. Am. 70(2), 220-223 (1980).
29. G. Smith, B. K. Pierscionek, and D. A. Atchison, "The optical modelling of the human lens," Ophthalmic Physiol. Opt. 11(4), 359-369 (1991).
30. B. K. Pierscionek and D. Y. Chan, "Refractive index gradient of human lenses," Optom. Vis. Sci. 66(12), 822-829 (1989). (Pubitemid 20078794)
31. 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. A 24(9), 2911-2920 (2007). (Pubitemid 350162024)
32. F. Manns, A. Ho, D. Borja, and J. M. Parel, "Comparison of Uniform and Gradient Paraxial Models of the Crystalline Lens," Invest. Ophthalmol. Vis. Sci. 51, 789 (2010).
33. H. L. Liou and N. A. Brennan, "Anatomically accurate, finite model eye for optical modeling," J. Opt. Soc. Am. A 14(8), 1684-1695 (1997). (Pubitemid 127569236)
34. M. A. Rama, M. V. Pérez, C. Bao, M. T. Flores-Arias, and C. Gómez-Reino, "Gradient-index crystalline lens model: A new method for determining the paraxial properties by the axial and field rays," Opt. Commun. 249(4-6), 595-609 (2005). (Pubitemid 40584324)
35. J. A. Díaz, C. Pizarro, and J. Arasa, "Single dispersive gradient-index profile for the aging human lens," J. Opt. Soc. Am. A 25(1), 250-261 (2008).
36. A. V. Goncharov and C. Dainty, "Wide-field schematic eye models with gradient-index lens," J. Opt. Soc. Am. A 24(8), 2157-2174 (2007). (Pubitemid 351193460)
37. A. V. Goncharov, M. Nowakowski, M. T. Sheehan, and C. Dainty, "Reconstruction of the optical system of the human eye with reverse ray-tracing," Opt. Express 16(3), 1692-1703 (2008). (Pubitemid 351240010)
38. I. Grulkowski, M. Gora, M. Szkulmowski, I. Gorczynska, D. Szlag, S. Marcos, A. Kowalczyk, and M. Wojtkowski, "Anterior segment imaging with Spectral OCT system using a high-speed CMOS camera," Opt. Express 17(6), 4842-4858 (2009).
39. S. Ortiz, D. Siedlecki, L. Remon, and S. Marcos, "Optical coherence tomography for quantitative surface topography," Appl. Opt. 48(35), 6708-6715 (2009).
40. S. Ortiz, D. Siedlecki, I. Grulkowski, L. Remon, D. Pascual, M. Wojtkowski, and S. Marcos, "Optical distortion correction in optical coherence tomography for quantitative ocular anterior segment by three-dimensional imaging," Opt. Express 18(3), 2782-2796 (2010).
41. O. N. Stavroudis, "Ray tracing," in The optics of rays, wavefronts and caustics, N. Y. A. Press, ed. (1972).
42. A. Sharma, D. V. Kumar, and A. K. Ghatak, "Tracing rays through graded-index media: a new method," Appl. Opt. 21(6), 984-987 (1982).
43. B. D. Stone and G. W. Forbes, "Optimal interpolants for Runge-Kutta ray tracing in inhomogeneous media," J. Opt. Soc. Am. A 7(2), 248-254 (1990).
44. J. H. Holland, Adaptation in natural and artificial systems (The University of Michigan press, 1975).
45. J. A. Nelder and R. Mead, "A Simplex Method for Function Minimization," Comput. J. 7, 308-313 (1965).
46. J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence properties of the Nelder-Mead simplex method in low dimensions," SIAM J. Optim. 9(1), 112-147 (1998).
47. D. Vasiljevic, Classical and evolutionary algorithms in the optimization of optical systems (Kluwer Academc Publishers Boston/Dordrecht/London, 2002), p. 296.
48. 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).
49. D. A. Atchison and G. Smith, "Chromatic dispersions of the ocular media of human eyes," J. Opt. Soc. Am. A 22(1), 29-37 (2005). (Pubitemid 40168105)
50. E. Moreno-Barriuso and R. Navarro, "Laser Ray Tracing versus Hartmann-Shack sensor for measuring optical aberrations in the human eye," J. Opt. Soc. Am. A 17(6), 974-985 (2000).
51. E. Moreno-Barriuso, S. Marcos, R. Navarro, and S. A. Burns, "Comparing laser ray tracing, the spatially resolved refractometer, and the Hartmann-Shack sensor to measure the ocular wave aberration," Optom. Vis. Sci. 78(3), 152-156 (2001). (Pubitemid 32299036)