Abstract

The spherical crystalline lenses in the eyes of many fish species are well-suited models for studies on how natural selection has influenced the evolution of the optical system. Many of these lenses exhibit multiple focal lengths when illuminated with monochromatic light. Similar multifocality is present in a majority of vertebrate eyes, and it is assumed to compensate for the defocusing effect of longitudinal chromatic aberration. In order to identify potential optical advantages of multifocal lenses, we studied their information transfer capacity by computer modeling. We investigated four lens types: the lens of Astatotilapia burtoni, an African cichlid fish species, an equivalent monofocal lens, and two artificial multifocal lenses. These lenses were combined with three detector arrays of different spectral properties: the cone photoreceptor system of A. burtoni and two artificial arrays. The optical properties compared between the lenses were longitudinal spherical aberration curves, point spread functions, modulation transfer functions, and imaging characteristics. The multifocal lenses had a better balance between spatial and spectral information than the monofocal lenses. Additionally, the lens and detector array had to be matched to each other for optimal function.

© 2012 Optical Society of America

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2010

O. S. Gustafsson, P. Ekström, and R. H. Kröger, “A fibrous membrane suspends the multifocal lens in the eyes of lampreys and African lungfishes,” J. Morphol. 271, 980–989 (2010).

J. M. Schartau, R. H. H. Kröger, and B. Sjögreen, “Short-term culturing of teleost crystalline lenses combined with high-resultotion optical measurements,” Cytotechnology 62, 167–174(2010).
[CrossRef]

J. M. Schartau, R. H. H. Kröger, and B. Sjögreen, “Dopamine induces optical changes in the cichlid fish lens,” PLoS ONE 5, e10402 (2010).

K. E. O’Quin, C. M. Hofmann, H. A. Hofmann, and K. L. Carleton, “Parallel evolution of opsin gene expression in African cichlid fishes,” Mol. Biol. Evol. 27, 2839–2854 (2010).
[CrossRef]

Y. L. Gagnon, R. H. H. Kröger, and B. Söderberg, “Adjusting a light dispersion model to fit measurements from vertebrate ocular media as well as ray-tracing in fish lenses,” Vis. Res. 50, 850–853 (2010).
[CrossRef]

2009

R. H. H. Kröger, K. A. Fritsches, and E. J. Warrant, “Lens optical properties in the eyes of large marine predatory teleosts,” J. Comp. Physiol. A 195, 175–182 (2009).
[CrossRef]

J. M. Schartau, B. Sjögreen, Y. L. Gagnon, and R. H. H. Kröger, “Optical plasticity in the crystalline lenses of the cichlid fish Aequidens pulcher,” Curr. Biol. 19, 122–126 (2009).
[CrossRef]

Y. Shichida and T. Matsuyama, “Evolution of opsins and phototransduction,” Phil. Trans. R. Soc. B 364, 2881–2895 (2009).
[CrossRef]

L. S. V. Roth, L. Lundström, A. Kelber, R. H. H. Kröger, and P. Unsbo, “The pupils and optical systems of gecko eyes,” J. Vision 9(3): 27, 1–11 (2009).
[CrossRef]

2008

O. S. E. Gustafsson, S. P. Collin, and R. H. H. Kröger, “Early evolution of multifocal optics for well-focused colour vision in vertebrates,” J. Exp. Biol. 211, 1559–1564 (2008).
[CrossRef]

F. D. Hanke, R. H. H. Kröger, U. Siebert, and G. Dehnhardt, “Multifocal lenses in a monochromat: the harbour seal,” J. Exp. Biol. 211, 3315–3322 (2008).
[CrossRef]

O. E. Lind, A. Kelber, and R. H. H. Kröger, “Multifocal optical systems and pupil dynamics in birds,” J. Exp. Biol. 211, 2752–2758 (2008).
[CrossRef]

Y. L. Gagnon, B. Söderberg, and R. H. H. Kröger, “Effects of the peripheral layers on the optical properties of spherical fish lenses,” J. Opt. Soc. Am. A 25, 2468–2475 (2008).
[CrossRef]

2007

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]

2006

T. Malmström and R. H. H. Kröger, “Pupil shapes and lens optics in the eyes of terrestrial vertebrates,” J. Exp. Biol. 209, 18–25 (2006).
[CrossRef]

J. K. Bowmaker and D. M. Hunt, “Evolution of vertebrate visual pigments,” Curr. Biol. 16, R484–R489 (2006).
[CrossRef]

2005

J. W. Parry, K. L. Carleton, T. Spady, A. Carboo, D. M. Hunt, and J. K. Bowmaker, “Mix and match color vision: tuning spectral sensitivity by differential opsin gene expression in Lake Malawi cichlids,” Curr. Biol. 15, 1734–1739 (2005).
[CrossRef]

A. E. Trezise and S. P. Collin, “Opsins: evolution in waiting,” Curr. Biol. 15R794–R796 (2005).
[CrossRef]

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

2004

R. H. H. Kröger, “Anti-aliasing features in fish retina,” Investig. Ophthalmol. Vis. Sci. 45, 2785 (2004).

2003

N. J. Marshall, K. Jennings, W. N. McFarland, E. R. Loew, G. S. Losey, and W. L. Montgomery, “Visual biology of Hawaiian coral reef fishes. II. Colors of Hawaiian coral reef fish,” Am. Soc. Ichthyol. Herpetol. 3, 455–466 (2003).

2001

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,” Vis. Res. 41, 549–559 (2001).
[CrossRef]

2000

S. Yokoyama, “Molecular evolution of vertebrate visual pigments,” Prog. Retinal Eye Res. 19, 385–419 (2000).
[CrossRef]

V. I. Govardovskii, N. Fyhrquist, T. O. M. Reuter, D. G. Kuzmin, and K. Donner, “In search of the visual pigment template,” Vis. Neurosci. 17, 509–528 (2000).
[CrossRef]

1999

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]

1998

E. Warrant and D. Nilsson, “Absorption of white light in photoreceptors,” Vis. Res. 38, 195–207 (1998).
[CrossRef]

1996

J. Stark and W. Fitzgerald, “An alternative algorithm for adaptive histogram equalization,” Graph. Models Image Process. 58, 180–185 (1996).

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

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

B. K. Pierscionek and R. C. Augusteyn, “The refractive index and protein distribution in the blue eye trevally lens,” J. Am. Optometric Assoc. 66, 739–43 (1995).

1994

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

J. N. Lythgoe, W. R. A. Muntz, J. C. Partridge, J. Shand, and D. M. B. Williams, “The ecology of the visual pigments of snappers (Lutjanidae) on the great barrier reef,” J. Comp. Physiol. A 174, 461–467 (1994).
[CrossRef]

J. Bowmaker, V. Govardovskii, S. Shukolyukov, J. L. Zueva, D. Hunt, V. G. Sideleva, and O. G. Smirnova, “Visual pigments and the photic environment: the cottoid fish of Lake Baikal,” Vis. Res. 34, 591–605 (1994).
[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,” Vis. Res. 34, 1815–1822 (1994).
[CrossRef]

1991

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

1988

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

1987

R. Wehner, “‘matched filters’—neural models of the external world,” J. Comp. Physiol. A 161, 511–531 (1987).
[CrossRef]

1984

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

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

1983

T. Mandelman and J. G. Sivak, “Longitudinal chromatic aberration of the vertebrate eye,” Vis. Res. 23, 1555–1559 (1983).
[CrossRef]

1980

R. D. Fernald and P. A. Liebman, “Visual receptor pigments in the African cichlid fish Haplochromis burtoni,” Vis. Res. 20, 857–864 (1980).
[CrossRef]

1978

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

1977

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

1954

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

1893

L. Matthiessen, “Beiträge zur dioptrik der kristalllinse,” X. Zeitschrift für vergleichende Augenheilkunde 7, 102–146 (1893).

1882

L. Matthiessen, “Ueber die beziehungen, welche zwischen dem brechungsindex des kerncentrums der krystalllinse und den dimensionen des auges bestehen,” Pflüger’s Archiv. 27, 510–523 (1882).

1854

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

Augusteyn, R. C.

B. K. Pierscionek and R. C. Augusteyn, “The refractive index and protein distribution in the blue eye trevally lens,” J. Am. Optometric Assoc. 66, 739–43 (1995).

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]

Bowmaker, J.

J. Bowmaker, V. Govardovskii, S. Shukolyukov, J. L. Zueva, D. Hunt, V. G. Sideleva, and O. G. Smirnova, “Visual pigments and the photic environment: the cottoid fish of Lake Baikal,” Vis. Res. 34, 591–605 (1994).
[CrossRef]

Bowmaker, J. K.

J. K. Bowmaker and D. M. Hunt, “Evolution of vertebrate visual pigments,” Curr. Biol. 16, R484–R489 (2006).
[CrossRef]

J. W. Parry, K. L. Carleton, T. Spady, A. Carboo, D. M. Hunt, and J. K. Bowmaker, “Mix and match color vision: tuning spectral sensitivity by differential opsin gene expression in Lake Malawi cichlids,” Curr. Biol. 15, 1734–1739 (2005).
[CrossRef]

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,” Vis. Res. 41, 549–559 (2001).
[CrossRef]

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,” Vis. Res. 34, 1815–1822 (1994).
[CrossRef]

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

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

Carboo, A.

J. W. Parry, K. L. Carleton, T. Spady, A. Carboo, D. M. Hunt, and J. K. Bowmaker, “Mix and match color vision: tuning spectral sensitivity by differential opsin gene expression in Lake Malawi cichlids,” Curr. Biol. 15, 1734–1739 (2005).
[CrossRef]

Carleton, K. L.

K. E. O’Quin, C. M. Hofmann, H. A. Hofmann, and K. L. Carleton, “Parallel evolution of opsin gene expression in African cichlid fishes,” Mol. Biol. Evol. 27, 2839–2854 (2010).
[CrossRef]

J. W. Parry, K. L. Carleton, T. Spady, A. Carboo, D. M. Hunt, and J. K. Bowmaker, “Mix and match color vision: tuning spectral sensitivity by differential opsin gene expression in Lake Malawi cichlids,” Curr. Biol. 15, 1734–1739 (2005).
[CrossRef]

Chu, P. L.

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

Collin, S. P.

O. S. E. Gustafsson, S. P. Collin, and R. H. H. Kröger, “Early evolution of multifocal optics for well-focused colour vision in vertebrates,” J. Exp. Biol. 211, 1559–1564 (2008).
[CrossRef]

A. E. Trezise and S. P. Collin, “Opsins: evolution in waiting,” Curr. Biol. 15R794–R796 (2005).
[CrossRef]

Dehnhardt, G.

F. D. Hanke, R. H. H. Kröger, U. Siebert, and G. Dehnhardt, “Multifocal lenses in a monochromat: the harbour seal,” J. Exp. Biol. 211, 3315–3322 (2008).
[CrossRef]

Donner, K.

V. I. Govardovskii, N. Fyhrquist, T. O. M. Reuter, D. G. Kuzmin, and K. Donner, “In search of the visual pigment template,” Vis. Neurosci. 17, 509–528 (2000).
[CrossRef]

Ekström, P.

O. S. Gustafsson, P. Ekström, and R. H. Kröger, “A fibrous membrane suspends the multifocal lens in the eyes of lampreys and African lungfishes,” J. Morphol. 271, 980–989 (2010).

Fernald, R. D.

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,” Vis. Res. 41, 549–559 (2001).
[CrossRef]

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, 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,” Vis. Res. 34, 1815–1822 (1994).
[CrossRef]

R. D. Fernald and P. A. Liebman, “Visual receptor pigments in the African cichlid fish Haplochromis burtoni,” Vis. Res. 20, 857–864 (1980).
[CrossRef]

Fitzgerald, W.

J. Stark and W. Fitzgerald, “An alternative algorithm for adaptive histogram equalization,” Graph. Models Image Process. 58, 180–185 (1996).

Fletcher, A.

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

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R. H. H. Kröger, K. A. Fritsches, and E. J. Warrant, “Lens optical properties in the eyes of large marine predatory teleosts,” J. Comp. Physiol. A 195, 175–182 (2009).
[CrossRef]

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V. I. Govardovskii, N. Fyhrquist, T. O. M. Reuter, D. G. Kuzmin, and K. Donner, “In search of the visual pigment template,” Vis. Neurosci. 17, 509–528 (2000).
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Y. L. Gagnon, R. H. H. Kröger, and B. Söderberg, “Adjusting a light dispersion model to fit measurements from vertebrate ocular media as well as ray-tracing in fish lenses,” Vis. Res. 50, 850–853 (2010).
[CrossRef]

J. M. Schartau, B. Sjögreen, Y. L. Gagnon, and R. H. H. Kröger, “Optical plasticity in the crystalline lenses of the cichlid fish Aequidens pulcher,” Curr. Biol. 19, 122–126 (2009).
[CrossRef]

Y. L. Gagnon, B. Söderberg, and R. H. H. Kröger, “Effects of the peripheral layers on the optical properties of spherical fish lenses,” J. Opt. Soc. Am. A 25, 2468–2475 (2008).
[CrossRef]

Govardovskii, V.

J. Bowmaker, V. Govardovskii, S. Shukolyukov, J. L. Zueva, D. Hunt, V. G. Sideleva, and O. G. Smirnova, “Visual pigments and the photic environment: the cottoid fish of Lake Baikal,” Vis. Res. 34, 591–605 (1994).
[CrossRef]

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V. I. Govardovskii, N. Fyhrquist, T. O. M. Reuter, D. G. Kuzmin, and K. Donner, “In search of the visual pigment template,” Vis. Neurosci. 17, 509–528 (2000).
[CrossRef]

Gustafsson, J.

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]

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O. S. Gustafsson, P. Ekström, and R. H. Kröger, “A fibrous membrane suspends the multifocal lens in the eyes of lampreys and African lungfishes,” J. Morphol. 271, 980–989 (2010).

Gustafsson, O. S. E.

O. S. E. Gustafsson, S. P. Collin, and R. H. H. Kröger, “Early evolution of multifocal optics for well-focused colour vision in vertebrates,” J. Exp. Biol. 211, 1559–1564 (2008).
[CrossRef]

Hanke, F. D.

F. D. Hanke, R. H. H. Kröger, U. Siebert, and G. Dehnhardt, “Multifocal lenses in a monochromat: the harbour seal,” J. Exp. Biol. 211, 3315–3322 (2008).
[CrossRef]

Hofmann, C. M.

K. E. O’Quin, C. M. Hofmann, H. A. Hofmann, and K. L. Carleton, “Parallel evolution of opsin gene expression in African cichlid fishes,” Mol. Biol. Evol. 27, 2839–2854 (2010).
[CrossRef]

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K. E. O’Quin, C. M. Hofmann, H. A. Hofmann, and K. L. Carleton, “Parallel evolution of opsin gene expression in African cichlid fishes,” Mol. Biol. Evol. 27, 2839–2854 (2010).
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J. Bowmaker, V. Govardovskii, S. Shukolyukov, J. L. Zueva, D. Hunt, V. G. Sideleva, and O. G. Smirnova, “Visual pigments and the photic environment: the cottoid fish of Lake Baikal,” Vis. Res. 34, 591–605 (1994).
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J. K. Bowmaker and D. M. Hunt, “Evolution of vertebrate visual pigments,” Curr. Biol. 16, R484–R489 (2006).
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N. J. Marshall, K. Jennings, W. N. McFarland, E. R. Loew, G. S. Losey, and W. L. Montgomery, “Visual biology of Hawaiian coral reef fishes. II. Colors of Hawaiian coral reef fish,” Am. Soc. Ichthyol. Herpetol. 3, 455–466 (2003).

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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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L. S. V. Roth, L. Lundström, A. Kelber, R. H. H. Kröger, and P. Unsbo, “The pupils and optical systems of gecko eyes,” J. Vision 9(3): 27, 1–11 (2009).
[CrossRef]

O. E. Lind, A. Kelber, and R. H. H. Kröger, “Multifocal optical systems and pupil dynamics in birds,” J. Exp. Biol. 211, 2752–2758 (2008).
[CrossRef]

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O. S. Gustafsson, P. Ekström, and R. H. Kröger, “A fibrous membrane suspends the multifocal lens in the eyes of lampreys and African lungfishes,” J. Morphol. 271, 980–989 (2010).

Kröger, R. H. H.

J. M. Schartau, R. H. H. Kröger, and B. Sjögreen, “Dopamine induces optical changes in the cichlid fish lens,” PLoS ONE 5, e10402 (2010).

Y. L. Gagnon, R. H. H. Kröger, and B. Söderberg, “Adjusting a light dispersion model to fit measurements from vertebrate ocular media as well as ray-tracing in fish lenses,” Vis. Res. 50, 850–853 (2010).
[CrossRef]

J. M. Schartau, R. H. H. Kröger, and B. Sjögreen, “Short-term culturing of teleost crystalline lenses combined with high-resultotion optical measurements,” Cytotechnology 62, 167–174(2010).
[CrossRef]

L. S. V. Roth, L. Lundström, A. Kelber, R. H. H. Kröger, and P. Unsbo, “The pupils and optical systems of gecko eyes,” J. Vision 9(3): 27, 1–11 (2009).
[CrossRef]

J. M. Schartau, B. Sjögreen, Y. L. Gagnon, and R. H. H. Kröger, “Optical plasticity in the crystalline lenses of the cichlid fish Aequidens pulcher,” Curr. Biol. 19, 122–126 (2009).
[CrossRef]

R. H. H. Kröger, K. A. Fritsches, and E. J. Warrant, “Lens optical properties in the eyes of large marine predatory teleosts,” J. Comp. Physiol. A 195, 175–182 (2009).
[CrossRef]

O. E. Lind, A. Kelber, and R. H. H. Kröger, “Multifocal optical systems and pupil dynamics in birds,” J. Exp. Biol. 211, 2752–2758 (2008).
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F. D. Hanke, R. H. H. Kröger, U. Siebert, and G. Dehnhardt, “Multifocal lenses in a monochromat: the harbour seal,” J. Exp. Biol. 211, 3315–3322 (2008).
[CrossRef]

O. S. E. Gustafsson, S. P. Collin, and R. H. H. Kröger, “Early evolution of multifocal optics for well-focused colour vision in vertebrates,” J. Exp. Biol. 211, 1559–1564 (2008).
[CrossRef]

Y. L. Gagnon, B. Söderberg, and R. H. H. Kröger, “Effects of the peripheral layers on the optical properties of spherical fish lenses,” J. Opt. Soc. Am. A 25, 2468–2475 (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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V. I. Govardovskii, N. Fyhrquist, T. O. M. Reuter, D. G. Kuzmin, and K. Donner, “In search of the visual pigment template,” Vis. Neurosci. 17, 509–528 (2000).
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N. J. Marshall, K. Jennings, W. N. McFarland, E. R. Loew, G. S. Losey, and W. L. Montgomery, “Visual biology of Hawaiian coral reef fishes. II. Colors of Hawaiian coral reef fish,” Am. Soc. Ichthyol. Herpetol. 3, 455–466 (2003).

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N. J. Marshall, K. Jennings, W. N. McFarland, E. R. Loew, G. S. Losey, and W. L. Montgomery, “Visual biology of Hawaiian coral reef fishes. II. Colors of Hawaiian coral reef fish,” Am. Soc. Ichthyol. Herpetol. 3, 455–466 (2003).

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N. J. Marshall, K. Jennings, W. N. McFarland, E. R. Loew, G. S. Losey, and W. L. Montgomery, “Visual biology of Hawaiian coral reef fishes. II. Colors of Hawaiian coral reef fish,” Am. Soc. Ichthyol. Herpetol. 3, 455–466 (2003).

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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,” Vis. Res. 34, 1815–1822 (1994).
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J. N. Lythgoe, W. R. A. Muntz, J. C. Partridge, J. Shand, and D. M. B. Williams, “The ecology of the visual pigments of snappers (Lutjanidae) on the great barrier reef,” J. Comp. Physiol. A 174, 461–467 (1994).
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J. W. Parry, K. L. Carleton, T. Spady, A. Carboo, D. M. Hunt, and J. K. Bowmaker, “Mix and match color vision: tuning spectral sensitivity by differential opsin gene expression in Lake Malawi cichlids,” Curr. Biol. 15, 1734–1739 (2005).
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J. N. Lythgoe, W. R. A. Muntz, J. C. Partridge, J. Shand, and D. M. B. Williams, “The ecology of the visual pigments of snappers (Lutjanidae) on the great barrier reef,” J. Comp. Physiol. A 174, 461–467 (1994).
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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. M. Schartau, R. H. H. Kröger, and B. Sjögreen, “Short-term culturing of teleost crystalline lenses combined with high-resultotion optical measurements,” Cytotechnology 62, 167–174(2010).
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J. M. Schartau, B. Sjögreen, Y. L. Gagnon, and R. H. H. Kröger, “Optical plasticity in the crystalline lenses of the cichlid fish Aequidens pulcher,” Curr. Biol. 19, 122–126 (2009).
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J. W. Parry, K. L. Carleton, T. Spady, A. Carboo, D. M. Hunt, and J. K. Bowmaker, “Mix and match color vision: tuning spectral sensitivity by differential opsin gene expression in Lake Malawi cichlids,” Curr. Biol. 15, 1734–1739 (2005).
[CrossRef]

J. K. Bowmaker and D. M. Hunt, “Evolution of vertebrate visual pigments,” Curr. Biol. 16, R484–R489 (2006).
[CrossRef]

A. E. Trezise and S. P. Collin, “Opsins: evolution in waiting,” Curr. Biol. 15R794–R796 (2005).
[CrossRef]

Cytotechnology

J. M. Schartau, R. H. H. Kröger, and B. Sjögreen, “Short-term culturing of teleost crystalline lenses combined with high-resultotion optical measurements,” Cytotechnology 62, 167–174(2010).
[CrossRef]

Electron. Lett.

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

Eye

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

Graph. Models Image Process.

J. Stark and W. Fitzgerald, “An alternative algorithm for adaptive histogram equalization,” Graph. Models Image Process. 58, 180–185 (1996).

Investig. Ophthalmol. Vis. Sci.

R. H. H. Kröger, “Anti-aliasing features in fish retina,” Investig. Ophthalmol. Vis. Sci. 45, 2785 (2004).

J. Am. Optometric Assoc.

B. K. Pierscionek and R. C. Augusteyn, “The refractive index and protein distribution in the blue eye trevally lens,” J. Am. Optometric Assoc. 66, 739–43 (1995).

J. Comp. Physiol. A

R. Wehner, “‘matched filters’—neural models of the external world,” J. Comp. Physiol. A 161, 511–531 (1987).
[CrossRef]

J. N. Lythgoe, W. R. A. Muntz, J. C. Partridge, J. Shand, and D. M. B. Williams, “The ecology of the visual pigments of snappers (Lutjanidae) on the great barrier reef,” J. Comp. Physiol. A 174, 461–467 (1994).
[CrossRef]

R. H. H. Kröger, K. A. Fritsches, and E. J. Warrant, “Lens optical properties in the eyes of large marine predatory teleosts,” J. Comp. Physiol. A 195, 175–182 (2009).
[CrossRef]

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]

J. Exp. Biol.

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]

F. D. Hanke, R. H. H. Kröger, U. Siebert, and G. Dehnhardt, “Multifocal lenses in a monochromat: the harbour seal,” J. Exp. Biol. 211, 3315–3322 (2008).
[CrossRef]

O. E. Lind, A. Kelber, and R. H. H. Kröger, “Multifocal optical systems and pupil dynamics in birds,” J. Exp. Biol. 211, 2752–2758 (2008).
[CrossRef]

T. Malmström and R. H. H. Kröger, “Pupil shapes and lens optics in the eyes of terrestrial vertebrates,” J. Exp. Biol. 209, 18–25 (2006).
[CrossRef]

O. S. E. Gustafsson, S. P. Collin, and R. H. H. Kröger, “Early evolution of multifocal optics for well-focused colour vision in vertebrates,” J. Exp. Biol. 211, 1559–1564 (2008).
[CrossRef]

J. Morphol.

O. S. Gustafsson, P. Ekström, and R. H. Kröger, “A fibrous membrane suspends the multifocal lens in the eyes of lampreys and African lungfishes,” J. Morphol. 271, 980–989 (2010).

J. Opt. A

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

J. Opt. Soc. Am. A

J. Vision

L. S. V. Roth, L. Lundström, A. Kelber, R. H. H. Kröger, and P. Unsbo, “The pupils and optical systems of gecko eyes,” J. Vision 9(3): 27, 1–11 (2009).
[CrossRef]

Mol. Biol. Evol.

K. E. O’Quin, C. M. Hofmann, H. A. Hofmann, and K. L. Carleton, “Parallel evolution of opsin gene expression in African cichlid fishes,” Mol. Biol. Evol. 27, 2839–2854 (2010).
[CrossRef]

Nature

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

Ophthalmic Res.

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

Opt. Commun.

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

Pflüger’s Archiv.

L. Matthiessen, “Ueber die beziehungen, welche zwischen dem brechungsindex des kerncentrums der krystalllinse und den dimensionen des auges bestehen,” Pflüger’s Archiv. 27, 510–523 (1882).

Phil. Trans. R. Soc. B

Y. Shichida and T. Matsuyama, “Evolution of opsins and phototransduction,” Phil. Trans. R. Soc. B 364, 2881–2895 (2009).
[CrossRef]

PLoS ONE

J. M. Schartau, R. H. H. Kröger, and B. Sjögreen, “Dopamine induces optical changes in the cichlid fish lens,” PLoS ONE 5, e10402 (2010).

Proc. R. Soc. A

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

Prog. Retinal Eye Res.

S. Yokoyama, “Molecular evolution of vertebrate visual pigments,” Prog. Retinal Eye Res. 19, 385–419 (2000).
[CrossRef]

Vis. Neurosci.

V. I. Govardovskii, N. Fyhrquist, T. O. M. Reuter, D. G. Kuzmin, and K. Donner, “In search of the visual pigment template,” Vis. Neurosci. 17, 509–528 (2000).
[CrossRef]

Vis. Res.

E. Warrant and D. Nilsson, “Absorption of white light in photoreceptors,” Vis. Res. 38, 195–207 (1998).
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R. D. Fernald and P. A. Liebman, “Visual receptor pigments in the African cichlid fish Haplochromis burtoni,” Vis. Res. 20, 857–864 (1980).
[CrossRef]

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

J. Bowmaker, V. Govardovskii, S. Shukolyukov, J. L. Zueva, D. Hunt, V. G. Sideleva, and O. G. Smirnova, “Visual pigments and the photic environment: the cottoid fish of Lake Baikal,” Vis. Res. 34, 591–605 (1994).
[CrossRef]

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,” Vis. Res. 41, 549–559 (2001).
[CrossRef]

T. Mandelman and J. G. Sivak, “Longitudinal chromatic aberration of the vertebrate eye,” Vis. Res. 23, 1555–1559 (1983).
[CrossRef]

J. G. Sivak and C. A. Luer, “Optical development of the ocular lens of an elasmobranch Raja eglanteria,” Vis. Res. 31, 373–382 (1991).
[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,” Vis. Res. 34, 1815–1822 (1994).
[CrossRef]

Y. L. Gagnon, R. H. H. Kröger, and B. Söderberg, “Adjusting a light dispersion model to fit measurements from vertebrate ocular media as well as ray-tracing in fish lenses,” Vis. Res. 50, 850–853 (2010).
[CrossRef]

X. Zeitschrift für vergleichende Augenheilkunde

L. Matthiessen, “Beiträge zur dioptrik der kristalllinse,” X. Zeitschrift für vergleichende Augenheilkunde 7, 102–146 (1893).

Other

R. J. Pumphrey, Concerning Vision (Cambridge University, 1961), pp. 193–208.

G. L. Walls, The Vertebrate Eye and its Adaptive Radiation (Cranbrook, 1964).

M. F. Land and D. E. Nilsson, Animal Eyes, Animal Biology Series (Oxford, 2002).

L. N. Trefethen, N. Hale, R. B. Platte, T. A. Driscoll, and R. Pachón, Chebfun version 3. Oxford University. http://www.maths.ox.ac.uk/chebfun/ (2009).

J. K. Lein, “Hyperspectral sensing,” in Environmental Sensing: Analytical Techniques for Earth Observation (Springer, 2012), p. 213.

R. H. H. Kröger, “Physiological optics in fishes,” in Encyclopedia of Fish Physiology: From Genome to Environment (Elsevier, 2011) pp. 102–109.

P. E. Malkki, E. Löfblad, and R. H. H. Kröger, “Species-specific differences in the optical properties of crystalline lenses of fishes,” in ARVO Annual Meeting Abstract Search and Program Planner 2003 (2003), p. 3483.

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