Abstract

We created a computational optical model of spherical fish lenses that takes into account the effects of the peripheral layers, which differ in cellular composition from the bulk of the lens. A constant refractive index, except for the lens capsule, in the outer about 6% of lens radius made it possible to uniquely infer the refractive index gradient in more central layers from a known or desired longitudinal spherical aberration curve using the inverse Abel transform. Since the zone of constant refractive index is wider than necessary to make the solution unique and for optimal optical performance of the lens, we propose that its width be set by the metabolic needs of the lens.

© 2008 Optical Society of America

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    [CrossRef]
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  49. S. Bassnett and D. C. Beebe, “Coincident loss of mitochondria and nuclei during lens fiber cell differentiation,” Dev. Dyn. 194, 85-93 (1992).
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    [CrossRef]
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    [CrossRef] [PubMed]
  53. R. H. H. Kröger, M. C. W. Campbell, and R. D. Fernald, “The development of the crystalline lens is sensitive to visual input in the African cichlid fish, Haplochromis burtoni,” Vision Res. 41, 549-559 (2001).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  59. B. K. Pierscionek, “Refractive index of the human lens surface measured with an optic fibre sensor,” Ophthalmic Res. 26, 32-35 (1994).
    [CrossRef] [PubMed]
  60. B. K. Pierscionek and R. C. Augusteyn, “The refractive index and protein distribution in the blue eye trevally lens,” J. Am. Optom. Assoc. 66, 739-743 (1995).
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    [CrossRef]
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    [CrossRef] [PubMed]

2007 (2)

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: Photophys. Laser Chem. 87, 607-610 (2007).
[CrossRef]

B. Karpestam, J. Gustafsson, N. Shashar, G. Katzir, and R. H. H. Kröger, “Multifocal lenses in coral reef fishes,” J. Exp. Biol. 210, 2923-2931 (2007).
[CrossRef] [PubMed]

2006 (2)

2005 (3)

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).
[CrossRef]

P. E. Malkki and R. H. H. Kröger, “Visualization of chromatic correction of fish lenses by multiple focal lengths,” J. Opt. A, Pure Appl. Opt. 7, 691-700 (2005).
[CrossRef]

D.-E. Nilsson, L. Gislen, M. M. Coates, C. Skogh, and A. Garm, “Advanced optics in a jellyfish eye,” Nature 435, 201-205 (2005).
[CrossRef] [PubMed]

2004 (2)

V. Bantseev, K. L. Moran, D. G. Dixon, J. R. Trevithick, and J. G. Sivak, “Optical properties, mitochondria, and sutures of lenses of fishes: a comparative study of nine species,” Can. J. Zool. 82, 86-93 (2004).
[CrossRef]

J. R. Kuszak, R. K. Zoltoski, and C. Sivertson, “Fibre cell organization in crystalline lenses,” Exp. Eye Res. 78, 673-687 (2004).
[CrossRef] [PubMed]

2001 (2)

R. H. H. Kröger, M. C. W. Campbell, and R. D. Fernald, “The development of the crystalline lens is sensitive to visual input in the African cichlid fish, Haplochromis burtoni,” Vision Res. 41, 549-559 (2001).
[CrossRef] [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, 973-979 (2001).
[CrossRef] [PubMed]

1999 (2)

R. H. H. Kröger, M. C. W. Campbell, R. D. Fernald, and H.-J. Wagner, “Multifocal lenses compensate for chromatic defocus in vertebrate eyes,” J. Comp. Physiol., A 184, 361-369 (1999).
[CrossRef]

V. Bantseev, K. L. Herbert, J. R. Trevithick, and J. G. Sivak, “Mitochondria of rat lenses: distribution near and at the sutures,” Invest. Ophthalmol. Visual Sci. 40, S881 (1999).

1996 (1)

R. H. H. Kröger and M. C. W. Campbell, “Dispersion and longitudinal chromatic aberration of the crystalline lens of the African cichlid fish Haplochromis burtoni,” J. Opt. Soc. Am. A 13, 2341--2347 (1996).
[CrossRef]

1995 (2)

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

B. K. Pierscionek and R. C. Augusteyn, “The refractive index and protein distribution in the blue eye trevally lens,” J. Am. Optom. Assoc. 66, 739-743 (1995).
[PubMed]

1994 (3)

B. K. Pierscionek, “Refractive index of the human lens surface measured with an optic fibre sensor,” Ophthalmic Res. 26, 32-35 (1994).
[CrossRef] [PubMed]

B. K. Pierscionek, “Refractive index of decapsulated bovine lens surfaces measured with a reflectometric sensor,” Vision Res. 34, 1927-1933 (1994).
[CrossRef] [PubMed]

R. H. H. Kröger, M. C. W. Campbell, R. Munger, and R. D. Fernald, “Refractive index distribution and spherical aberration in the crystalline lens of the African cichlid fish Haplochromis burtoni,” Vision Res. 34, 1815-1822 (1994).
[CrossRef] [PubMed]

1992 (2)

W. S. Jagger, “The optics of the spherical fish lens,” Vision Res. 32, 1271-1284 (1992).
[CrossRef] [PubMed]

S. Bassnett and D. C. Beebe, “Coincident loss of mitochondria and nuclei during lens fiber cell differentiation,” Dev. Dyn. 194, 85-93 (1992).
[CrossRef] [PubMed]

1991 (2)

J. K. Bowmaker, A. Thorpe, and R. H. Douglas, “UV-sensitive cones in the goldfish,” Vision Res. 31, 349-352 (1991).
[CrossRef] [PubMed]

J. G. Sivak and C. A. Luer, “Optical development of the ocular lens of an elasmobranch Raja eglanteria,” Vision Res. 31, 373-382 (1991).
[CrossRef] [PubMed]

1990 (2)

M. C. Campbell, E. M. Harrison, and P. Simonet, “Psychophysical measurement of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587-1602 (1990).
[CrossRef] [PubMed]

P. Schiebener, J. Straub, L. S. J. M. H., and J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature and density,” J. Phys. Chem. 19, 677 (1990).

1988 (2)

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, 57-66 (1988).
[CrossRef] [PubMed]

B. K. Pierscionek, “Nondestructive method of constructing 3-dimensional gradient index models for crystalline lenses. 1. Theory and experiment,” Am. J. Optom. Physiol. Opt. 65, 481-491 (1988).
[PubMed]

1987 (1)

J. K. Bowmaker and Y. W. Kunz, “UV receptors tetrachromatic color vision and retinal mosaics in the brown trout Salmo trutta age-dependent changes,” Vision Res. 27, 2101-2108 (1987).
[CrossRef] [PubMed]

1984 (2)

M. C. W. Campbell and P. J. Sands, “Optical quality during crystalline lens growth,” Nature 312, 291-292 (1984).
[CrossRef] [PubMed]

M. C. W. Campbell, “Measurement of refractive index in an intact crystalline lens,” Vision Res. 24, 409-416 (1984).
[CrossRef] [PubMed]

1983 (4)

J. G. Sivak and R. O. Kreuzer, “Spherical aberration of the crystalline lens,” Vision Res. 23, 59-70 (1983).
[CrossRef] [PubMed]

T. Mandelman and J. G. Sivak, “Longitudinal chromatic aberration of the vertebrate eye,” Vision Res. 23, 1555-1560 (1983).
[CrossRef] [PubMed]

R. D. Fernald and S. E. Wright, “Maintenance of optical quality during crystalline lens growth,” Nature 301, 618-620 (1983).
[CrossRef] [PubMed]

D.-E. Nilsson, M. Andersson, E. Hallberg, and P. McIntyre, “A micro interferometric method for analysis of rotation symmetric refractive index gradients in intact objects,” J. Microsc. 132, 21-30 (1983).
[CrossRef]

1982 (2)

J. G. Sivak, “Optical properties of a cephalopod eye the short finned squid Illex illecebrosus,” J. Comp. Physiol., A 147, 323-328 (1982).
[CrossRef]

J. G. Sivak, “Optical characteristics of the eye of the flounder,” J. Comp. Physiol., A 146, 345-350 (1982).
[CrossRef]

1981 (2)

P. P. Fagerholm, B. Philipson, and B. Lindström, “Normal human lens--the distribution of protein,” Exp. Eye Res. 33, 615-620 (1981).
[CrossRef] [PubMed]

M. C. W. Campbell and A. Hughes, “An analytic, gradient index schematic lens and eye for the rat which predicts aberrations for finite pupils,” Vision Res. 21, 1129-1148 (1981).
[CrossRef] [PubMed]

1979 (1)

S. Sroczyński, “Das optische System des Auges des Flussbarsches (Perca fluviatilis, L.),” Zool. Jahrb. Physiol. 83, 224-252 (1979).

1978 (2)

S. Sroczyński, “Die chromatische Aberration der Augenlinse der Bachforelle (Salmo trutta fario, L.),” Zool. Jahrb. Physiol. 82, 113-133 (1978).

K. F. Barrell and C. Pask, “Nondestructive index profile measurement of noncircular optical fibre preforms,” Opt. Commun. 27, 230-234 (1978).
[CrossRef]

1977 (2)

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

S. Sroczyński, “Spherical aberration of crystalline lens in the roach Rutilus rutilus,” J. Comp. Physiol., A 121, 135-144 (1977).
[CrossRef]

1976 (1)

M. Bando, A. Nakajima, M. Nakagawa, and T. Hiraoka, “Measurement of protein distribution in human lens by micro spectrophotometry,” Exp. Eye Res. 22, 389-392 (1976).
[CrossRef] [PubMed]

1975 (2)

S. Sroczyński, “Die sphärische Aberration der Augenlinse der Regenbogenforelle (Salmo gairdneri, Rich.),” Zool. Jahrb. Physiol. 79, 204-212 (1975).

S. Sroczyński, “Die sphärische Aberration der Augenlinse des Hechts (Esox lucius L.),” Zool. Jahrb. Physiol. 79, 547-558 (1975).

1969 (1)

B. Philipson, “Distribution of protein within the normal rat lens,” Invest. Ophthalmol. Visual Sci. 8, 258-270 (1969).

1968 (1)

1967 (1)

F. W. Campbell and R. W. Gubish, “The effect of chromatic aberration on visual acuity,” J. Physiol. (London) 186, 558-578 (1967).

1963 (1)

E. S. Reynolds, “The use of lead citrate at high pH as an electron-opaque stain in electron microscopy,” J. Cell Biol. 17, 208-212 (1963).
[CrossRef] [PubMed]

1957 (1)

R. Barer, “Refractometry and interferometry of living cells,” J. Opt. Soc. Am. 47, 54-556 (1957).
[CrossRef]

1954 (1)

A. Fletcher, T. Murphy, and A. Young, “Solutions of two optical problems,” Proc. R. Soc. London, Ser. A 223, 216-225 (1954).
[CrossRef]

1948 (1)

A. Huggart, “On the form of the iso-indicial surfaces of the human crystalline lens,” Acta Ophthalmol. Scand. 64, 1-126 (1948).

1893 (1)

L. Matthiessen, “X. Beiträge zur Dioptrik der Kristalllinse,” Z. vergleich. Augen. 7, 102-146 (1893).

1886 (1)

L. Matthiessen, “Ueber den physikalisch-optischen Bau des Auges der Cetaceen und der Fische,” Pfluegers Arch. 38, 521-528 (1886).
[CrossRef]

1882 (1)

L. Matthiessen, “Ueber die Beziehungen, welche zwischen dem Brechungsindex des Kerncentrums der Krystalllinse und den Dimensionen des Auges bestehen,” Pfluegers Arch. 27, 510-523 (1882).
[CrossRef]

1880 (1)

L. Matthiessen, “Untersuchungen über Aplanatismus und die Periskopie der Kristalllinsen in den Augen der Fische,” Pfluegers Arch. 21, 287-307 (1880).
[CrossRef]

1854 (1)

J. C. Maxwell, “Some solutions of problems 2,” Cambridge Dublin Math. J. 8, 188-195 (1854).

Acosta, E.

Andersson, M.

D.-E. Nilsson, M. Andersson, E. Hallberg, and P. McIntyre, “A micro interferometric method for analysis of rotation symmetric refractive index gradients in intact objects,” J. Microsc. 132, 21-30 (1983).
[CrossRef]

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, 973-979 (2001).
[CrossRef] [PubMed]

B. K. Pierscionek and R. C. Augusteyn, “The refractive index and protein distribution in the blue eye trevally lens,” J. Am. Optom. Assoc. 66, 739-743 (1995).
[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, 57-66 (1988).
[CrossRef] [PubMed]

Bando, M.

M. Bando, A. Nakajima, M. Nakagawa, and T. Hiraoka, “Measurement of protein distribution in human lens by micro spectrophotometry,” Exp. Eye Res. 22, 389-392 (1976).
[CrossRef] [PubMed]

Bantseev, V.

V. Bantseev, K. L. Moran, D. G. Dixon, J. R. Trevithick, and J. G. Sivak, “Optical properties, mitochondria, and sutures of lenses of fishes: a comparative study of nine species,” Can. J. Zool. 82, 86-93 (2004).
[CrossRef]

V. Bantseev, K. L. Herbert, J. R. Trevithick, and J. G. Sivak, “Mitochondria of rat lenses: distribution near and at the sutures,” Invest. Ophthalmol. Visual Sci. 40, S881 (1999).

Barer, R.

R. Barer, “Refractometry and interferometry of living cells,” J. Opt. Soc. Am. 47, 54-556 (1957).
[CrossRef]

Barrell, K. F.

K. F. Barrell and C. Pask, “Nondestructive index profile measurement of noncircular optical fibre preforms,” Opt. Commun. 27, 230-234 (1978).
[CrossRef]

Bassnett, S.

S. Bassnett and D. C. Beebe, “Coincident loss of mitochondria and nuclei during lens fiber cell differentiation,” Dev. Dyn. 194, 85-93 (1992).
[CrossRef] [PubMed]

Beebe, D. C.

S. Bassnett and D. C. Beebe, “Coincident loss of mitochondria and nuclei during lens fiber cell differentiation,” Dev. Dyn. 194, 85-93 (1992).
[CrossRef] [PubMed]

Bowmaker, J. K.

J. K. Bowmaker, A. Thorpe, and R. H. Douglas, “UV-sensitive cones in the goldfish,” Vision Res. 31, 349-352 (1991).
[CrossRef] [PubMed]

J. K. Bowmaker and Y. W. Kunz, “UV receptors tetrachromatic color vision and retinal mosaics in the brown trout Salmo trutta age-dependent changes,” Vision Res. 27, 2101-2108 (1987).
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M. C. Campbell, E. M. Harrison, and P. Simonet, “Psychophysical measurement of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587-1602 (1990).
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Campbell, M. C. W.

R. H. H. Kröger, M. C. W. Campbell, and R. D. Fernald, “The development of the crystalline lens is sensitive to visual input in the African cichlid fish, Haplochromis burtoni,” Vision Res. 41, 549-559 (2001).
[CrossRef] [PubMed]

R. H. H. Kröger, M. C. W. Campbell, R. D. Fernald, and H.-J. Wagner, “Multifocal lenses compensate for chromatic defocus in vertebrate eyes,” J. Comp. Physiol., A 184, 361-369 (1999).
[CrossRef]

R. H. H. Kröger and M. C. W. Campbell, “Dispersion and longitudinal chromatic aberration of the crystalline lens of the African cichlid fish Haplochromis burtoni,” J. Opt. Soc. Am. A 13, 2341--2347 (1996).
[CrossRef]

R. H. H. Kröger, M. C. W. Campbell, R. Munger, and R. D. Fernald, “Refractive index distribution and spherical aberration in the crystalline lens of the African cichlid fish Haplochromis burtoni,” Vision Res. 34, 1815-1822 (1994).
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M. C. W. Campbell and P. J. Sands, “Optical quality during crystalline lens growth,” Nature 312, 291-292 (1984).
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D.-E. Nilsson, L. Gislen, M. M. Coates, C. Skogh, and A. Garm, “Advanced optics in a jellyfish eye,” Nature 435, 201-205 (2005).
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V. Bantseev, K. L. Moran, D. G. Dixon, J. R. Trevithick, and J. G. Sivak, “Optical properties, mitochondria, and sutures of lenses of fishes: a comparative study of nine species,” Can. J. Zool. 82, 86-93 (2004).
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J. K. Bowmaker, A. Thorpe, and R. H. Douglas, “UV-sensitive cones in the goldfish,” Vision Res. 31, 349-352 (1991).
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P. P. Fagerholm, B. Philipson, and B. Lindström, “Normal human lens--the distribution of protein,” Exp. Eye Res. 33, 615-620 (1981).
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R. H. H. Kröger, M. C. W. Campbell, and R. D. Fernald, “The development of the crystalline lens is sensitive to visual input in the African cichlid fish, Haplochromis burtoni,” Vision Res. 41, 549-559 (2001).
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R. H. H. Kröger, M. C. W. Campbell, R. Munger, and R. D. Fernald, “Refractive index distribution and spherical aberration in the crystalline lens of the African cichlid fish Haplochromis burtoni,” Vision Res. 34, 1815-1822 (1994).
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J. M. Schartau, B. Sjögreen, Y. L. Gagnon, and R. H. H. Kröger, “Optical plasticity in fish crystalline lenses,” submitted to Curr. Biol. (posted July 25, 2008).

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P. Schiebener, J. Straub, L. S. J. M. H., and J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature and density,” J. Phys. Chem. 19, 677 (1990).

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D.-E. Nilsson, L. Gislen, M. M. Coates, C. Skogh, and A. Garm, “Advanced optics in a jellyfish eye,” Nature 435, 201-205 (2005).
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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, 973-979 (2001).
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D.-E. Nilsson, L. Gislen, M. M. Coates, C. Skogh, and A. Garm, “Advanced optics in a jellyfish eye,” Nature 435, 201-205 (2005).
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F. W. Campbell and R. W. Gubish, “The effect of chromatic aberration on visual acuity,” J. Physiol. (London) 186, 558-578 (1967).

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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: Photophys. Laser Chem. 87, 607-610 (2007).
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B. Karpestam, J. Gustafsson, N. Shashar, G. Katzir, and R. H. H. Kröger, “Multifocal lenses in coral reef fishes,” J. Exp. Biol. 210, 2923-2931 (2007).
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P. Schiebener, J. Straub, L. S. J. M. H., and J. S. Gallagher, “Refractive index of water and steam as function of wavelength, temperature and density,” J. Phys. Chem. 19, 677 (1990).

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D.-E. Nilsson, M. Andersson, E. Hallberg, and P. McIntyre, “A micro interferometric method for analysis of rotation symmetric refractive index gradients in intact objects,” J. Microsc. 132, 21-30 (1983).
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M. C. Campbell, E. M. Harrison, and P. Simonet, “Psychophysical measurement of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587-1602 (1990).
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V. Bantseev, K. L. Herbert, J. R. Trevithick, and J. G. Sivak, “Mitochondria of rat lenses: distribution near and at the sutures,” Invest. Ophthalmol. Visual Sci. 40, S881 (1999).

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M. Bando, A. Nakajima, M. Nakagawa, and T. Hiraoka, “Measurement of protein distribution in human lens by micro spectrophotometry,” Exp. Eye Res. 22, 389-392 (1976).
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B. Karpestam, J. Gustafsson, N. Shashar, G. Katzir, and R. H. H. Kröger, “Multifocal lenses in coral reef fishes,” J. Exp. Biol. 210, 2923-2931 (2007).
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B. Karpestam, J. Gustafsson, N. Shashar, G. Katzir, and R. H. H. Kröger, “Multifocal lenses in coral reef fishes,” J. Exp. Biol. 210, 2923-2931 (2007).
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B. Karpestam, J. Gustafsson, N. Shashar, G. Katzir, and R. H. H. Kröger, “Multifocal lenses in coral reef fishes,” J. Exp. Biol. 210, 2923-2931 (2007).
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J. K. Bowmaker and Y. W. Kunz, “UV receptors tetrachromatic color vision and retinal mosaics in the brown trout Salmo trutta age-dependent changes,” Vision Res. 27, 2101-2108 (1987).
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J. R. Kuszak, R. K. Zoltoski, and C. Sivertson, “Fibre cell organization in crystalline lenses,” Exp. Eye Res. 78, 673-687 (2004).
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R. H. H. Kröger, M. C. W. Campbell, R. Munger, and R. D. Fernald, “Refractive index distribution and spherical aberration in the crystalline lens of the African cichlid fish Haplochromis burtoni,” Vision Res. 34, 1815-1822 (1994).
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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: Photophys. Laser Chem. 87, 607-610 (2007).
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J. M. Schartau, B. Sjögreen, Y. L. Gagnon, and R. H. H. Kröger, “Optical plasticity in fish crystalline lenses,” submitted to Curr. Biol. (posted July 25, 2008).

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B. Karpestam, J. Gustafsson, N. Shashar, G. Katzir, and R. H. H. Kröger, “Multifocal lenses in coral reef fishes,” J. Exp. Biol. 210, 2923-2931 (2007).
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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: Photophys. Laser Chem. 87, 607-610 (2007).
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V. Bantseev, K. L. Moran, D. G. Dixon, J. R. Trevithick, and J. G. Sivak, “Optical properties, mitochondria, and sutures of lenses of fishes: a comparative study of nine species,” Can. J. Zool. 82, 86-93 (2004).
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V. Bantseev, K. L. Herbert, J. R. Trevithick, and J. G. Sivak, “Mitochondria of rat lenses: distribution near and at the sutures,” Invest. Ophthalmol. Visual Sci. 40, S881 (1999).

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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: Photophys. Laser Chem. 87, 607-610 (2007).
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R. H. H. Kröger, M. C. W. Campbell, R. D. Fernald, and H.-J. Wagner, “Multifocal lenses compensate for chromatic defocus in vertebrate eyes,” J. Comp. Physiol., A 184, 361-369 (1999).
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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).
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J. R. Kuszak, R. K. Zoltoski, and C. Sivertson, “Fibre cell organization in crystalline lenses,” Exp. Eye Res. 78, 673-687 (2004).
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Acta Ophthalmol. Scand. (1)

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Appl. Phys. B: Photophys. Laser Chem. (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: Photophys. Laser Chem. 87, 607-610 (2007).
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Can. J. Zool. (1)

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Figures (4)

Fig. 1
Fig. 1

Trajectory of a ray (dotted line) passing through the lens. R denotes the radius of the lens, while r min is the distance from the lens center to the point where the ray comes closest to the center. This point is called the symmetry point because the ray’s trajectory outward from this point is symmetrically identical to its way inward. Δ ψ is the total deflection angle, Δ φ is the angular extent of the ray’s trajectory in the lens, b is the ray’s entrance position, which is the lateral distance between the incoming ray and the optical axis, OA, and BCD is the back center distance, i.e., the distance from the lens center to where the beam intercepts the OA.

Fig. 2
Fig. 2

Interference micrograph of a piece of a lens capsule. Note the large orange area that indicates constant phase shift. Other colors occur because of folds and edge disturbances.

Fig. 3
Fig. 3

(a) Transmission electron micrograph of the peripheral region of a meridional section of an A. burtoni lens. CP, capsule; EP, epithelium. The concentric layers of lens fiber cells are divided into two zones: CZ, the constant-index zone, and GZ, the gradient zone. (b) Pixel brightness is plotted as a function of radial distance from the lens center in micrometers. Note that the y axis is reversed. The thick black curve is a windowed average of all the slices, while the dotted curves indicate the standard deviations ( N = 47 ) . The vertical lines separate the different lens zones shown in (a). The 92% R border more central to which cell organelles are absent is also marked in the figure.

Fig. 4
Fig. 4

A, Refractive index gradient of a hypothetical monofocal fish lens with a zone of constant RI in the periphery of the lens (epithelium and CZ) equal to 1.361 and a capsule of higher RI (1.394). B, LSA curve, i.e., back center distance, BCD, as a function of beam entrance position, b, for a spherical lens with the RIG shown in A. Note the strong longitudinal spherical aberration for peripheral b values. C, Same as in A with an epithelium/CZ refractive index of 1.394. D, Same as in B with the gradient shown in C. E, The relative intensity transmitted through the lens as a function of b (solid curve). The transmission as a function of b is represented by the dashed curve. The relative amount of light incident on the lens’s entire aperture at different b values is represented by the dotted line. F, An image taken from a laser scanning experiment on a fish lens [44]. The original image was manipulated to clearly show the laser beam (Gaussian blur, enhanced contrast, and gray scaling). Note how the peripheral longitudinal spherical aberration splits up the exiting laser beam, resulting in long back center distances for some of the visible portions of the beam (white arrowheads).

Tables (1)

Tables Icon

Table 1 Mean Lens Radius, Capsule Thickness, and Refractive Index with Their Corresponding Standard Deviations for Multiple Measurements from Four Individual A. burtoni Fish

Equations (3)

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Δ ψ ( b ) = 2 b r min 1 d n d r n ξ 2 b 2 d r ,
n ( ξ ) = 1 exp [ 1 π ξ 1 Δ ψ ( b ) b 2 ξ 2 d b ] .
Δ ψ ( b ) = sin 1 ( b B C D ) 2 i = 1 m [ sin 1 ( b n i r i ) sin 1 ( b n i + 1 r i ) ] ,

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