Abstract

Measuring the lens gradient refractive index (GRIN) accurately and reliably has proven an extremely challenging technical problem. A fully automated laser ray tracing (LRT) system was built to address this issue. The LRT system captures images of multiple laser projections before and after traversing through an ex vivo lens. These LRT images, combined with accurate measurements of the lens geometry, are used to calculate the lens GRIN profile. Mathematically, this is an ill-conditioned problem; hence, it is essential to apply biologically relevant constraints to produce a feasible solution. The lens GRIN measurements were compared with previously published data. Our GRIN retrieval algorithm produces fast and accurate measurements of the lens GRIN profile. Experiments to study the optics of physiologically perturbed lenses are the future direction of this research.

© 2017 Optical Society of America

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2017 (1)

P. J. Donaldson, A. C. Grey, B. Maceo Heilman, J. C. Lim, and E. Vaghefi, “The physiological optics of the lens,” Prog. Retin. Eye Res. 56, e1–e24 (2017).
[PubMed]

2016 (1)

J. C. Lim, E. Vaghefi, B. Li, M. G. Nye-Wood, and P. J. Donaldson, “Characterization of the Effects of Hyperbaric Oxygen on the Biochemical and Optical Properties of the Bovine Lens,” Invest. Ophthalmol. Vis. Sci. 57(4), 1961–1973 (2016).
[PubMed]

2015 (1)

E. Vaghefi, A. Kim, and P. J. Donaldson, “Active Maintenance of the Gradient of Refractive Index Is Required to Sustain the Optical Properties of the Lens,” Invest. Ophthalmol. Vis. Sci. 56(12), 7195–7208 (2015).
[PubMed]

2011 (1)

2010 (1)

2008 (2)

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).
[PubMed]

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).
[PubMed]

2007 (1)

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).

2006 (2)

F. J. Martinez-Wittinghan, M. Srinivas, C. Sellitto, T. W. White, and R. T. Mathias, “Mefloquine effects on the lens suggest cooperative gating of gap junction channels,” J. Membr. Biol. 211(3), 163–171 (2006).
[PubMed]

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).
[PubMed]

2005 (2)

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).
[PubMed]

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).
[PubMed]

2001 (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,” Vision Res. 41(8), 973–979 (2001).
[PubMed]

G. J. Baldo, X. Gong, F. J. Martinez-Wittinghan, N. M. Kumar, N. B. Gilula, and R. T. Mathias, “Gap junctional coupling in lenses from alpha(8) connexin knockout mice,” J. Gen. Physiol. 118(5), 447–456 (2001).
[PubMed]

2000 (1)

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).

1998 (1)

1997 (1)

R. T. Mathias, J. L. Rae, and G. J. Baldo, “Physiological properties of the normal lens,” Physiol. Rev. 77(1), 21–50 (1997).
[PubMed]

1995 (2)

B. K. Pierscionek, “The refractive index along the optic axis of the bovine lens,” Eye (Lond.) 9(Pt 6), 776–782 (1995).
[PubMed]

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]

1993 (1)

1989 (1)

B. K. Pierscionek, “Growth and ageing effects on the refractive index in the equatorial plane of the bovine lens,” Vision Res. 29(12), 1759–1766 (1989).
[PubMed]

1988 (1)

D. Axelrod, D. Lerner, and P. J. Sands, “Refractive index within the lens of a goldfish eye determined from the paths of thin laser beams,” Vision Res. 28(1), 57–65 (1988).
[PubMed]

1984 (2)

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).
[PubMed]

M. C. W. Campbell, “Measurement of refractive index in an intact crystalline lens,” Vision Res. 24(5), 409–415 (1984).
[PubMed]

1982 (1)

1977 (1)

P. L. Chu, “Nondestructive measurement of index profile of an optical-fibre preform,” Electron. Lett. 13(24), 736–738 (1977).

1972 (1)

O. Pomerantzeff, H. Fish, J. Govignon, and C. L. Schepens, “Wide-angle Optical Model of the Eye,” Opt. Acta (Lond.) 19, 387–388 (1972).

Acosta, E.

Atchison, D. A.

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).
[PubMed]

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).
[PubMed]

Augusteyn, R. C.

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).
[PubMed]

Axelrod, D.

D. Axelrod, D. Lerner, and P. J. Sands, “Refractive index within the lens of a goldfish eye determined from the paths of thin laser beams,” Vision Res. 28(1), 57–65 (1988).
[PubMed]

Baldo, G. J.

G. J. Baldo, X. Gong, F. J. Martinez-Wittinghan, N. M. Kumar, N. B. Gilula, and R. T. Mathias, “Gap junctional coupling in lenses from alpha(8) connexin knockout mice,” J. Gen. Physiol. 118(5), 447–456 (2001).
[PubMed]

R. T. Mathias, J. L. Rae, and G. J. Baldo, “Physiological properties of the normal lens,” Physiol. Rev. 77(1), 21–50 (1997).
[PubMed]

Barbero, S.

Beliakov, G.

Borja, D.

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).
[PubMed]

Campbell, M. C. W.

M. C. W. Campbell, “Measurement of refractive index in an intact crystalline lens,” Vision Res. 24(5), 409–415 (1984).
[PubMed]

Chan, D. Y.

Chu, P. L.

P. L. Chu, “Nondestructive measurement of index profile of an optical-fibre preform,” Electron. Lett. 13(24), 736–738 (1977).

de Castro, A.

Donaldson, P. J.

P. J. Donaldson, A. C. Grey, B. Maceo Heilman, J. C. Lim, and E. Vaghefi, “The physiological optics of the lens,” Prog. Retin. Eye Res. 56, e1–e24 (2017).
[PubMed]

J. C. Lim, E. Vaghefi, B. Li, M. G. Nye-Wood, and P. J. Donaldson, “Characterization of the Effects of Hyperbaric Oxygen on the Biochemical and Optical Properties of the Bovine Lens,” Invest. Ophthalmol. Vis. Sci. 57(4), 1961–1973 (2016).
[PubMed]

E. Vaghefi, A. Kim, and P. J. Donaldson, “Active Maintenance of the Gradient of Refractive Index Is Required to Sustain the Optical Properties of the Lens,” Invest. Ophthalmol. Vis. Sci. 56(12), 7195–7208 (2015).
[PubMed]

Dufault, P.

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).
[PubMed]

Fish, H.

O. Pomerantzeff, H. Fish, J. Govignon, and C. L. Schepens, “Wide-angle Optical Model of the Eye,” Opt. Acta (Lond.) 19, 387–388 (1972).

Gambra, E.

Garner, L.

Garner, L. F.

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).
[PubMed]

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]

Ghatak, A. K.

Gilula, N. B.

G. J. Baldo, X. Gong, F. J. Martinez-Wittinghan, N. M. Kumar, N. B. Gilula, and R. T. Mathias, “Gap junctional coupling in lenses from alpha(8) connexin knockout mice,” J. Gen. Physiol. 118(5), 447–456 (2001).
[PubMed]

Gong, X.

G. J. Baldo, X. Gong, F. J. Martinez-Wittinghan, N. M. Kumar, N. B. Gilula, and R. T. Mathias, “Gap junctional coupling in lenses from alpha(8) connexin knockout mice,” J. Gen. Physiol. 118(5), 447–456 (2001).
[PubMed]

Govignon, J.

O. Pomerantzeff, H. Fish, J. Govignon, and C. L. Schepens, “Wide-angle Optical Model of the Eye,” Opt. Acta (Lond.) 19, 387–388 (1972).

Grey, A. C.

P. J. Donaldson, A. C. Grey, B. Maceo Heilman, J. C. Lim, and E. Vaghefi, “The physiological optics of the lens,” Prog. Retin. Eye Res. 56, e1–e24 (2017).
[PubMed]

Gupta, P. K.

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).

Heikkila, J.

J. Heikkila and O. Silven, “A four-step camera calibration procedure with implicit image correction,” in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition. 1106–1112 (1997).

Hemenger, R. P.

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]

Jones, C. E.

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).
[PubMed]

Kasthurirangan, S.

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).
[PubMed]

Kim, A.

E. Vaghefi, A. Kim, and P. J. Donaldson, “Active Maintenance of the Gradient of Refractive Index Is Required to Sustain the Optical Properties of the Lens,” Invest. Ophthalmol. Vis. Sci. 56(12), 7195–7208 (2015).
[PubMed]

Kumar, D. V.

Kumar, N. M.

G. J. Baldo, X. Gong, F. J. Martinez-Wittinghan, N. M. Kumar, N. B. Gilula, and R. T. Mathias, “Gap junctional coupling in lenses from alpha(8) connexin knockout mice,” J. Gen. Physiol. 118(5), 447–456 (2001).
[PubMed]

Lerner, D.

D. Axelrod, D. Lerner, and P. J. Sands, “Refractive index within the lens of a goldfish eye determined from the paths of thin laser beams,” Vision Res. 28(1), 57–65 (1988).
[PubMed]

Li, B.

J. C. Lim, E. Vaghefi, B. Li, M. G. Nye-Wood, and P. J. Donaldson, “Characterization of the Effects of Hyperbaric Oxygen on the Biochemical and Optical Properties of the Bovine Lens,” Invest. Ophthalmol. Vis. Sci. 57(4), 1961–1973 (2016).
[PubMed]

Lim, J. C.

P. J. Donaldson, A. C. Grey, B. Maceo Heilman, J. C. Lim, and E. Vaghefi, “The physiological optics of the lens,” Prog. Retin. Eye Res. 56, e1–e24 (2017).
[PubMed]

J. C. Lim, E. Vaghefi, B. Li, M. G. Nye-Wood, and P. J. Donaldson, “Characterization of the Effects of Hyperbaric Oxygen on the Biochemical and Optical Properties of the Bovine Lens,” Invest. Ophthalmol. Vis. Sci. 57(4), 1961–1973 (2016).
[PubMed]

Maceo Heilman, B.

P. J. Donaldson, A. C. Grey, B. Maceo Heilman, J. C. Lim, and E. Vaghefi, “The physiological optics of the lens,” Prog. Retin. Eye Res. 56, e1–e24 (2017).
[PubMed]

Manns, F.

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).
[PubMed]

Marcos, S.

Markwell, E. L.

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).
[PubMed]

Martinez-Wittinghan, F. J.

F. J. Martinez-Wittinghan, M. Srinivas, C. Sellitto, T. W. White, and R. T. Mathias, “Mefloquine effects on the lens suggest cooperative gating of gap junction channels,” J. Membr. Biol. 211(3), 163–171 (2006).
[PubMed]

G. J. Baldo, X. Gong, F. J. Martinez-Wittinghan, N. M. Kumar, N. B. Gilula, and R. T. Mathias, “Gap junctional coupling in lenses from alpha(8) connexin knockout mice,” J. Gen. Physiol. 118(5), 447–456 (2001).
[PubMed]

Mathias, R. T.

F. J. Martinez-Wittinghan, M. Srinivas, C. Sellitto, T. W. White, and R. T. Mathias, “Mefloquine effects on the lens suggest cooperative gating of gap junction channels,” J. Membr. Biol. 211(3), 163–171 (2006).
[PubMed]

G. J. Baldo, X. Gong, F. J. Martinez-Wittinghan, N. M. Kumar, N. B. Gilula, and R. T. Mathias, “Gap junctional coupling in lenses from alpha(8) connexin knockout mice,” J. Gen. Physiol. 118(5), 447–456 (2001).
[PubMed]

R. T. Mathias, J. L. Rae, and G. J. Baldo, “Physiological properties of the normal lens,” Physiol. Rev. 77(1), 21–50 (1997).
[PubMed]

Meder, R.

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).
[PubMed]

Nye-Wood, M. G.

J. C. Lim, E. Vaghefi, B. Li, M. G. Nye-Wood, and P. J. Donaldson, “Characterization of the Effects of Hyperbaric Oxygen on the Biochemical and Optical Properties of the Bovine Lens,” Invest. Ophthalmol. Vis. Sci. 57(4), 1961–1973 (2016).
[PubMed]

Ooi, C. S.

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]

Ortiz, S.

Oskar Xaver Schlömilch, B. W.

B. W. Oskar Xaver Schlömilch, Zeitschrift für Mathematik und Physik. (1901).

Pankratov, M.

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).
[PubMed]

Parel, J.-M.

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).
[PubMed]

Patel, H. S.

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).

Pierscionek, B. K.

B. K. Pierscionek, “The refractive index along the optic axis of the bovine lens,” Eye (Lond.) 9(Pt 6), 776–782 (1995).
[PubMed]

B. K. Pierscionek, “Surface refractive index of the eye lens determined with an optic fiber sensor,” J. Opt. Soc. Am. A 10(9), 1867–1871 (1993).
[PubMed]

B. K. Pierscionek, “Growth and ageing effects on the refractive index in the equatorial plane of the bovine lens,” Vision Res. 29(12), 1759–1766 (1989).
[PubMed]

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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).
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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).
[PubMed]

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).
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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).

Sands, P. J.

D. Axelrod, D. Lerner, and P. J. Sands, “Refractive index within the lens of a goldfish eye determined from the paths of thin laser beams,” Vision Res. 28(1), 57–65 (1988).
[PubMed]

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O. Pomerantzeff, H. Fish, J. Govignon, and C. L. Schepens, “Wide-angle Optical Model of the Eye,” Opt. Acta (Lond.) 19, 387–388 (1972).

Sellitto, C.

F. J. Martinez-Wittinghan, M. Srinivas, C. Sellitto, T. W. White, and R. T. Mathias, “Mefloquine effects on the lens suggest cooperative gating of gap junction channels,” J. Membr. Biol. 211(3), 163–171 (2006).
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Smith, G.

Srinivas, M.

F. J. Martinez-Wittinghan, M. Srinivas, C. Sellitto, T. W. White, and R. T. Mathias, “Mefloquine effects on the lens suggest cooperative gating of gap junction channels,” J. Membr. Biol. 211(3), 163–171 (2006).
[PubMed]

Suresh, M. K.

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).

Uhlhorn, S. R.

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).
[PubMed]

Vaghefi, E.

P. J. Donaldson, A. C. Grey, B. Maceo Heilman, J. C. Lim, and E. Vaghefi, “The physiological optics of the lens,” Prog. Retin. Eye Res. 56, e1–e24 (2017).
[PubMed]

J. C. Lim, E. Vaghefi, B. Li, M. G. Nye-Wood, and P. J. Donaldson, “Characterization of the Effects of Hyperbaric Oxygen on the Biochemical and Optical Properties of the Bovine Lens,” Invest. Ophthalmol. Vis. Sci. 57(4), 1961–1973 (2016).
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E. Vaghefi, A. Kim, and P. J. Donaldson, “Active Maintenance of the Gradient of Refractive Index Is Required to Sustain the Optical Properties of the Lens,” Invest. Ophthalmol. Vis. Sci. 56(12), 7195–7208 (2015).
[PubMed]

Vazquez, D.

Verma, Y.

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).

Wang, G. J.

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).
[PubMed]

White, T. W.

F. J. Martinez-Wittinghan, M. Srinivas, C. Sellitto, T. W. White, and R. T. Mathias, “Mefloquine effects on the lens suggest cooperative gating of gap junction channels,” J. Membr. Biol. 211(3), 163–171 (2006).
[PubMed]

Yao, S.

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).
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Zhang, Z.

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).

Am. J. Optom. Physiol. Opt. (1)

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).
[PubMed]

Appl. Opt. (2)

Appl. Phys. B (1)

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).

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Eye (Lond.) (1)

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[PubMed]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).

Invest. Ophthalmol. Vis. Sci. (4)

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).
[PubMed]

J. C. Lim, E. Vaghefi, B. Li, M. G. Nye-Wood, and P. J. Donaldson, “Characterization of the Effects of Hyperbaric Oxygen on the Biochemical and Optical Properties of the Bovine Lens,” Invest. Ophthalmol. Vis. Sci. 57(4), 1961–1973 (2016).
[PubMed]

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]

E. Vaghefi, A. Kim, and P. J. Donaldson, “Active Maintenance of the Gradient of Refractive Index Is Required to Sustain the Optical Properties of the Lens,” Invest. Ophthalmol. Vis. Sci. 56(12), 7195–7208 (2015).
[PubMed]

J. Gen. Physiol. (1)

G. J. Baldo, X. Gong, F. J. Martinez-Wittinghan, N. M. Kumar, N. B. Gilula, and R. T. Mathias, “Gap junctional coupling in lenses from alpha(8) connexin knockout mice,” J. Gen. Physiol. 118(5), 447–456 (2001).
[PubMed]

J. Membr. Biol. (1)

F. J. Martinez-Wittinghan, M. Srinivas, C. Sellitto, T. W. White, and R. T. Mathias, “Mefloquine effects on the lens suggest cooperative gating of gap junction channels,” J. Membr. Biol. 211(3), 163–171 (2006).
[PubMed]

J. Opt. Soc. Am. A (3)

Opt. Acta (Lond.) (1)

O. Pomerantzeff, H. Fish, J. Govignon, and C. L. Schepens, “Wide-angle Optical Model of the Eye,” Opt. Acta (Lond.) 19, 387–388 (1972).

Opt. Express (2)

Physiol. Rev. (1)

R. T. Mathias, J. L. Rae, and G. J. Baldo, “Physiological properties of the normal lens,” Physiol. Rev. 77(1), 21–50 (1997).
[PubMed]

Prog. Retin. Eye Res. (1)

P. J. Donaldson, A. C. Grey, B. Maceo Heilman, J. C. Lim, and E. Vaghefi, “The physiological optics of the lens,” Prog. Retin. Eye Res. 56, e1–e24 (2017).
[PubMed]

Vision Res. (6)

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).
[PubMed]

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).
[PubMed]

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).
[PubMed]

D. Axelrod, D. Lerner, and P. J. Sands, “Refractive index within the lens of a goldfish eye determined from the paths of thin laser beams,” Vision Res. 28(1), 57–65 (1988).
[PubMed]

M. C. W. Campbell, “Measurement of refractive index in an intact crystalline lens,” Vision Res. 24(5), 409–415 (1984).
[PubMed]

B. K. Pierscionek, “Growth and ageing effects on the refractive index in the equatorial plane of the bovine lens,” Vision Res. 29(12), 1759–1766 (1989).
[PubMed]

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J. Heikkila and O. Silven, “A four-step camera calibration procedure with implicit image correction,” in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition. 1106–1112 (1997).

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Figures (6)

Fig. 1
Fig. 1 (A) Solidworks assembly of the LRT system. A1: Specimen tank #1 consisting of a glass tank which houses the bovine lens and lens holder. A2: Specimen tank #2. A3: Larger glass tank used as a water bath. A4: Platform made from a 5 mm clear Perspex sheet. A5-8: Mounting post and post bracket. A9: Laser. A10: Rotation stage. A11: 25 mm linear stage. A12: 200 mm linear stage. (B) LRT system setup. B1: Monitor for LCD backlight. B2: Specimen tanks. B3: Side-facing (Alignment) camera. B4: Front-facing (Main) camera. B5: Optical Table. (C) Close up of the laser delivery. Labels correspond with those shown in (A). (D) Experimental setup for scanning two bovine lenses. D1: Lens #1 submerged in artificial aqueous humor. D2: Lens # 2 submerged in perturbation media. D3-4: Lens holders made from 0.55 mm thick stainless steel.
Fig. 2
Fig. 2 (A) Specimen tank components. A1: Custom-made glass tank. A2: Stainless steel plate which acts as a lens holder. A3: 12 mm hole for the lens to rest upon. A4: 4 threaded screws. (B) Sample experimental setup. B1: Heater. B2: Larger glass tank. B3-4: Assembled specimen tanks.
Fig. 3
Fig. 3 (A) Distortion corrected image of the lens. The yellow line indicates the approximate optical axis. Note that the right side of the lens equator is higher than the left, but the plate is horizontal. The aspheric lens equation would not fit accurately to this image. (B) Distortion corrected and rotated image of the lens. The aspheric lens equation will fit accurately to this image. (C) Output from the growcut edge segmentation showing the brushed segmented lens geometry (green points on the surface). The aspheric lens equation has not yet been fitted. (D) Fitted aspheric equation to the anterior (blue) and posterior lens surfaces (red).
Fig. 4
Fig. 4 (A) Distortion corrected, rotated, ray trace image. (B) Image showing the segmented incident and refracted ray path. (C) Image of a zoomed in region of (B). (D) Image showing an overlay of 75 segmented rays along the meridional plane of the lens at one projection angle (20°). The black lines represent the planes A, B, C and D. The points of intersection of the rays along the planes are the data points described in Section 2.2.2.
Fig. 5
Fig. 5 (A), (B), (C) Visual representation of the three solution space constraints used to retrieve the GRIN of the lens with measurement noise. These constraints help the optimization problem to avoid local minima solutions by imposing biologically appropriate solutions on the lens domain. (D) The unconstrained solution from experimental data, (E) the solution from imposing constraints 1 and 2, (F) the solution from imposing constraints 1, 2 and 3.
Fig. 6
Fig. 6 Overlay of refractive index values retrieved with our LRT system, the Pierscionek model [28] and MRI [2] along the lens equator. The plot in dark blue indicates the average of four bovine lenses and the lighter blue indicates the 95% confidence interval. The red plot shows the predicted GRIN using the Pierscionek model given the anatomical equatorial radius. The green plot indicates the GRIN profile measured using MRI. Good consistency is observed in the cortex regions of the lens but larger discrepancies in the RI are observed at the core region. Accurate retrieval at the lens core using MRI is difficult due to low signals.

Tables (2)

Tables Icon

Table 1 LRT respeatability result showing the lens shape parameters (Ra - anterior surface radius of curvature, Rp - posterio surface radius of curvature, Ka - anterior conic factor, Ka - posterior conic factor, t-lens thickness) of one bovine lens scanned five times. The maximum, minimum and average RI values obtained from the GRIN retrieval algorithm are also shown.

Tables Icon

Table 2 Mean RI in different regions of the lens using three different measurement methods. The outer cortex is defined as r/a = −1 to −0.75 and r/a = 0.75 to 1, the inner cortex is defined as r/a = −0.75 to −0.5 and r/a = 0.5 to 0.75, the core is defined as r/a = −0.5 to 0 and r/a = 0 to 0.5.

Equations (9)

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x d i s t o r t e d = x ( 1 + k 1 r 2 + k 2 r 4 + k 3 r 6 )
y d i s t o r t e d = y ( 1 + k 1 r 2 + k 2 r 4 + k 3 r 6 )
v ¯ = [ p 1 ( x ) p 2 ( x ) p 1 ( z ) p 2 ( z ) ] [ p 1 ( x ) p 2 ( x ) p 1 ( z ) p 2 ( z ) ]
I m a g e R o t a t i o n A n g l e ( γ ) = arc tan 2 ( u ¯ × v ¯ , u ¯ v ¯ )
R o t a t i o n M a t r i x = [ cos ( γ ) sin ( γ ) sin ( γ ) cos ( γ ) ] `
z ( x ) = x 2 R ( 1 + 1 ( 1 + κ ) x 2 R 2 )
S ( B C ) = 0 x sin α d x
min 1 2 A x b 2 2 { A i n e q x b i n e q A e q x = b e q l b x u b
n ( r ) = 1.4575 0.702 p 2 + 0.471 r p 2 0.186 r 2 p 2   0.00583 r + 0.00131 r 2

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