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 (5)

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]

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).

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. 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).

2009 (4)

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]

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]

2008 (4)

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]

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]

2007 (1)

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 (2)

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 (3)

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 (1)

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

2003 (1)

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 (1)

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 (2)

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 (1)

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 (1)

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

1996 (2)

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 (2)

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 (4)

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]

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]

1991 (1)

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 (1)

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 (1)

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

1984 (2)

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 (1)

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

1980 (1)

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 (1)

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

1977 (1)

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

1954 (1)

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

1893 (1)

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

1882 (1)

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 (1)

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, “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]

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]

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

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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]

Fyhrquist, N.

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]

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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).
[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]

Gustafsson, O. S.

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).
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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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[CrossRef]

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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).
[CrossRef]

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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, “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).

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]

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]

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. 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]

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

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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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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).
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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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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).
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T. Mandelman and J. G. Sivak, “Longitudinal chromatic aberration of the vertebrate eye,” Vis. Res. 23, 1555–1559 (1983).
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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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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).
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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. 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. 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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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).
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J. M. Schartau, R. H. H. Kröger, and B. Sjögreen, “Dopamine induces optical changes in the cichlid fish lens,” PLoS ONE 5, e10402 (2010).

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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).
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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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Am. Soc. Ichthyol. Herpetol. (1)

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

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

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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).

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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).
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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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J. Exp. Biol. (5)

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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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).
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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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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).
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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).
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J. Morphol. (1)

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 (1)

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

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

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Figures (6)

Fig. 1.
Fig. 1.

Absorption curves of the three retinas: natural, camera, and mismatch. The x-axis denotes the wavelength in nanometers. The y-axis is the absorption. From right to left, the red, green, and blue photoreceptors are color-coded. Note that the curves are normalized so that their sum equals 1.

Fig. 2.
Fig. 2.

A, LSA curves of the four lenses. The different lenses are color-coded (legend in panel B): Burtoni (blue), monofocal (black), step-function (red), mismatch (green). The x-axis denotes the BEP, while the y-axis is the BCD of the laser beam; both are in lens radius (R) units (i.e., 1 represents the lens’ surface). B, RIG of the four lenses. The lenses are color-coded as in A. The x-axis is the distance from the lens center in units of R. The y-axis is the RI at wavelength 633 nm.

Fig. 3.
Fig. 3.

A hyperspectral image stack was imaged by the four lenses and sampled by the three detector arrays. The lenses are displayed per row (from top to bottom: none, Burtoni, monofocal, step-function, and mismatch), and the arrays are per column (from left to right: natural, camera, and mismatch). The first row, “none,” includes the hyperspectral images sampled by the arrays without any optical filtering (i.e., these retained all spatial information before being sampled). Note the greenish hue of the monofocal row. The mismatch row is sharper when sampled with the mismatch retina, while it produces a blurrier image with the other two retinae. The opposite is true for the step-function lens. This figure displays the estimated signals received at the first layer of the retina. Post processing (e.g., white-balancing, histogram equalization, opponent processing, etc.) that occurs in subsequent layers (both morphological and physiological) may considerably change the information transmitted to the brain. It is therefore important to remember that certain image aspects being presented here in their “raw” form, such as haziness, can be corrected for higher up in the visual pathway. Because of the raw nature of this representation, certain aspects of these images can be misleading. The false contrast perceived in the monofocal lens sampled by the camera array does not represent a real increase in the information content of that image (see Fig. 4 for a better understanding of the comparison between the images).

Fig. 4.
Fig. 4.

A comparison of corresponding slices (enlarged) taken from each row in the camera array column in Fig. 3 (second column). The slices were rotated and fitted into a wheel to facilitate comparisons. The slices are from the none, Burtoni, monofocal, step-function, and mismatch images in Fig. 3 and are labeled A, B, C, D, and E, respectively. The red, green, and blue wheels display the three color channels present in the RGB wheel. Note the poor color representation in the monofocal slice, where all the smaller patches have shades of green or purple. The mismatch slices have reduced contrast in all three channels. No obvious differences are present between the Burtoni and step-function slices.

Fig. 5.
Fig. 5.

Left column shows the PSFs of all four lenses and the MTF are on the right. Each row depicts one lens; from top to bottom: Burtoni, monofocal, step-function, and mismatch. The x-axis in the PSF panels is the wavelength of light. The y-axis is the spread angle in degrees, i.e., the angle between the intersection of the optical axis with the retina, the nodal point of the lens, and the intersection of the exiting ray of light with the retina. This angle is a measure for the deviation from a perfect focus. The z-axis is the relative light intensity on the retina surface (before it gets absorbed by the photoreceptor). The x-axis in the MTF panels is the wavelength of light. The y-axis is the spatial frequency in units of cycles per degree (logarithmic scale) of the signal being focused. This frequency has a cutoff at 27 cycles per degree, matching the maximum sampling frequency by cone photoreceptors in the A. burtoni retina. The z-axis represents the contrast at each wavelength. The surface color denotes the height along the z-axis in all panels. The three λmax values of A. burtoni cones are represented as color-coded lines superimposed on the surfaces.

Fig. 6.
Fig. 6.

Image histograms for the filtered and sampled hyperspectral images presented in Fig. 3. The lenses are displayed per row (from top to bottom: none, Burtoni, monofocal, step-function, and mismatch), and the arrays are per column (from left to right: natural, camera, and mismatch). The first row includes the histogram of the hyperspectral images sampled by the arrays without any optical filtering (i.e., these retained all spatial information before being sampled). The x-axis is the pixel intensity ranging from 0 to 255 (28 intensity steps). The y-axis is the frequency of pixels with the corresponding intensity. The trichromatic arrays have one histogram for each of their color channels, red, green, and blue (color-coded). The histograms describe the distribution of pixel intensities in the images. This can be used to compare contrast between similar images. A broad distribution of pixel intensities, such as in the histogram of the unfiltered images (none), results in a higher contrast. A pointy narrow histogram indicates that the image has a very limited range of pixel intensities resulting in a bland image poor in contrast. Notice that while the green channel of the monofocal image sampled by the camera array has a broad histogram indicating high contrast, its red and blue channels are pointy and narrow, indicating low contrast.

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