Abstract

Dispersion and longitudinal chromatic aberration (LCA) of the crystalline lens of the African cichlid fish Haplochromis burtoni were measured with laser lights of four wavelengths: 457, 488, 515, and 633 nm. LCA and spherical aberration, as an indicator of image quality, were determined from the back vertex distances of laser beams deflected by the lens. In the green range between 488 and 515 nm, dispersion is almost constant in the entire lens. In the blue and the red ranges (457–488 and 515–633 nm, respectively), dispersion of lens material increases approximately linearly with increasing refractive index from the periphery to the center of the lens. Spherical aberration and thus monochromatic image quality are independent of the wavelength of light. Dispersion and LCA of the lens are lower than expected from the dispersive properties of ocular media measured in other vertebrate species. Since the lens in fish sets the limit on optical performance, reduction of chromatic aberration of the crystalline lens improves the image quality of the eye.

© 1996 Optical Society of America

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  1. R. S. Longhurst, Geometrical and Physical Optics, 3rd ed. (Longman, London, 1973).
  2. R. D. Fernald, “Aquatic adaptations in fish eyes,” in Sensory Biology of Aquatic Animals, J. Atema, R. R. Fay, A. N. Popper, W. N. Tavolga, eds. (Springer, Berlin, 1988), pp. 435–466.
    [Crossref]
  3. E. Otten, “Vision during growth of a generalized Haplochromis species: H. elegansTrewavas 1933 (Pisces, Cichlidae),” Neth. J. Zool. 31, 650–700 (1981).
    [Crossref]
  4. R. D. Fernald, S. Wright, “Growth of the visual system of the African cichlid fish, Haplochromis burtoni: optics,” Vision Res. 25, 155–161 (1985).
    [Crossref]
  5. R. H. H. Kröger, M. C. W. Campbell, R. Munger, 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]
  6. L. Matthiessen, “Ueber den physikalisch-optischen Bau des Auges der Cetaceen und der Fische,” Pflüger’s Arch. 38, 521–528 (1886).
  7. T. Mandelman, J. G. Sivak, “Longitudinal chromatic aberration of the vertebrate eye,” Vision Res. 23, 1555–1559 (1983).
    [Crossref] [PubMed]
  8. D. A. Palmer, J. G. Sivak, “Crystalline lens dispersion,” J. Opt. Soc. Am. 71, 780–782 (1981).
    [Crossref] [PubMed]
  9. J. G. Sivak, T. Mandelman, “Chromatic dispersion of the ocular media,” Vision Res. 22, 997–1003 (1982).
    [Crossref] [PubMed]
  10. R. H. H. Kröger, “Methods to estimate dispersion in vertebrate ocular media,” J. Opt. Soc. Am. A 9, 1486–1490 (1992).We used Eq. (13). Kröger’s formulas are based on the data of Sivak and Mandelman (Ref. 9), who measured refractive indices of the ocular media of a variety of vertebrate species at several wavelengths and described the dispersive properties of “average” vertebrate ocular media including the crystalline lens.
    [Crossref] [PubMed]
  11. R. D. Fernald, P. Liebman, “Visual receptor pigments in the African cichlid fish, Haplochromis burtoni,” Vision Res. 20, 857–864 (1980).
    [Crossref] [PubMed]
  12. R. D. Fernald, “Chromatic organization of a cichlid fish retina,” Vision Res. 21, 1749–1753 (1981).
    [Crossref] [PubMed]
  13. R. D. Fernald, “Vision and behavior in an African cichlid fish,” Am. Sci. 72, 58–65 (1984).
  14. R. D. Fernald, S. Wright, “Maintenance of optical quality during crystalline lens growth,” Nature 301, 618–620 (1983).
    [Crossref] [PubMed]
  15. R. D. Fernald, N. R. Hirata, “Field study of Haplochromis burtoni: habitats and co-habitants,” Environ. Biol. Fish 2, 299–308 (1977).
    [Crossref]
  16. R. H. H. Kröger, R. D. Fernald, “Regulation of eye growth in the African cichlid fish Haplochromis burtoni,” Vision Res. 34, 1807–1814 (1994).
    [Crossref] [PubMed]
  17. M. C. W. Campbell, “Measurement of refractive index in an intact crystalline lens,” Vision Res. 24, 409–415 (1984).
    [Crossref] [PubMed]
  18. M. C. W. Campbell, E. M. Harrison, “Refractive-index distribution within the crystalline lens of the rock bass and its variation with age,” in Annual Meeting, Vol. 17 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 169.
  19. R. Munger, M. C. W. Campbell, R. H. H. Kröger, “Gradient index profile calculation using cubic splines,” in Ophthalmic and Visual Optics, Vol. 3 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 59–62.
  20. R. H. H. Kröger, R. D. Fernald, M. C. W. Campbell, “The refractive index distribution and optical quality of the crystalline lens of the African cichlid fish, Haplochromis burtoni, as a function of lens size and lighting condition during development,” submitted to Vision Res.
  21. D. Axelrod, D. Lerner, P. J. Sands, “Refractive index within the lens of a goldfish eye determined from the paths of thin laser beams,” Vision Res. 28, 57–65 (1988).
    [PubMed]
  22. S. Iwata, M. Hikida, “Studies of the eye lens in poikilothermal animals. I. Comparative studies of cation maintenance systems in rainbow trout and rat lenses,” Exp. Eye Res. 41, 171–178 (1985).
    [Crossref] [PubMed]
  23. M. Hikida, S. Iwata, “Studies of eye lens in poikilothermal animals. III. Long-term incubation of rainbow trout lenses,” Jpn. J. Ophthalmol. 30, 43–50 (1986).
    [PubMed]
  24. P. L. Chu, “Nondestructive measurement of index profile of an optical-fibre preform,” Electron. Lett. 13, 736–738 (1977).
    [Crossref]
  25. R. H.H. Kröger, “Dioptrik, Funktion der Pupille und Akkommodation bei Zahnwalen,” Ph. D. dissertation (Eberhard-Karls-Universität, Tübingen, Germany, 1989).
  26. S. Sroczyński, “Die chromatische Aberration der Augenlinse der Regenbogenforelle (Salmo gairdneri Rich.),” Zool. Jb. (Physiol.) 80, 432–450 (1976).
  27. H.-J. Bartsch, Taschenbuch Mathematischer Formeln (Harri Deutsch, Thun, Switzerland, 1986).
  28. J. G. Sivak, W. R. Bobier, “Chromatic aberration of the fish eye and its effect on refractive state,” Vision Res. 18, 453–455 (1978).This work refers to data by Sivak and Roth (unpublished).
    [Crossref] [PubMed]
  29. G. L. Walls, H. D. Judd, “The intra-ocular colour-filters of vertebrates,” Br. J. Ophthalmol. 17, 641–675 (1933).
    [Crossref] [PubMed]
  30. R. H. Douglas, C. M. McGuigan, “The spectral transmission of freshwater teleost ocular media—an interspecific comparison and guide to potential ultraviolet sensitivity,” Vision Res. 29, 871–879 (1989).
    [Crossref]
  31. R. J. Pumphrey, “Concerning vision,” in The Cell and the Organism, J. A. Ramsey, ed. (Condor, Cambridge, 1961), pp. 193–208.
  32. H. Eberle, “Zapfenbau, Zapfenlänge und chromatische Aberration im Auge von Lebistes reticulatus Peters (guppy),” Zool. Jb. (Physiol.) 74, 121–154 (1968).
  33. J. H. Scholes, “Colour receptors and the synaptic connexions in the retina of a cyprinid fish,” Philos. Trans. R. Soc. London, Ser. B 270, 61–118 (1975).
    [Crossref]
  34. S. Sroczyński, “Die chromatische Aberration der Augelinse der Bachforelle (Salmo trutta fario L.),” Zool. Jb. (Physiol.) 82, 113–133 (1978).
  35. S. Sroczyński, “Das optische System des Auges des Flussbarsches (Perca fluviatilis L.),” Zool. Jb. (Physiol.) 83, 224–252 (1979).
  36. A. Chaudhuri, P. E. Hallet, J. A. Parker, “Aspheric curvatures, refractive indices and chromatic aberration for the rat eye,” Vision Res. 23, 1351–1361 (1983).
    [Crossref] [PubMed]

1994 (2)

R. H. H. Kröger, M. C. W. Campbell, R. Munger, 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]

R. H. H. Kröger, R. D. Fernald, “Regulation of eye growth in the African cichlid fish Haplochromis burtoni,” Vision Res. 34, 1807–1814 (1994).
[Crossref] [PubMed]

1992 (1)

1989 (1)

R. H. Douglas, C. M. McGuigan, “The spectral transmission of freshwater teleost ocular media—an interspecific comparison and guide to potential ultraviolet sensitivity,” Vision Res. 29, 871–879 (1989).
[Crossref]

1988 (1)

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

1986 (1)

M. Hikida, S. Iwata, “Studies of eye lens in poikilothermal animals. III. Long-term incubation of rainbow trout lenses,” Jpn. J. Ophthalmol. 30, 43–50 (1986).
[PubMed]

1985 (2)

S. Iwata, M. Hikida, “Studies of the eye lens in poikilothermal animals. I. Comparative studies of cation maintenance systems in rainbow trout and rat lenses,” Exp. Eye Res. 41, 171–178 (1985).
[Crossref] [PubMed]

R. D. Fernald, S. Wright, “Growth of the visual system of the African cichlid fish, Haplochromis burtoni: optics,” Vision Res. 25, 155–161 (1985).
[Crossref]

1984 (2)

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

R. D. Fernald, “Vision and behavior in an African cichlid fish,” Am. Sci. 72, 58–65 (1984).

1983 (3)

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

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

A. Chaudhuri, P. E. Hallet, J. A. Parker, “Aspheric curvatures, refractive indices and chromatic aberration for the rat eye,” Vision Res. 23, 1351–1361 (1983).
[Crossref] [PubMed]

1982 (1)

J. G. Sivak, T. Mandelman, “Chromatic dispersion of the ocular media,” Vision Res. 22, 997–1003 (1982).
[Crossref] [PubMed]

1981 (3)

R. D. Fernald, “Chromatic organization of a cichlid fish retina,” Vision Res. 21, 1749–1753 (1981).
[Crossref] [PubMed]

D. A. Palmer, J. G. Sivak, “Crystalline lens dispersion,” J. Opt. Soc. Am. 71, 780–782 (1981).
[Crossref] [PubMed]

E. Otten, “Vision during growth of a generalized Haplochromis species: H. elegansTrewavas 1933 (Pisces, Cichlidae),” Neth. J. Zool. 31, 650–700 (1981).
[Crossref]

1980 (1)

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

1979 (1)

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

1978 (2)

J. G. Sivak, W. R. Bobier, “Chromatic aberration of the fish eye and its effect on refractive state,” Vision Res. 18, 453–455 (1978).This work refers to data by Sivak and Roth (unpublished).
[Crossref] [PubMed]

S. Sroczyński, “Die chromatische Aberration der Augelinse der Bachforelle (Salmo trutta fario L.),” Zool. Jb. (Physiol.) 82, 113–133 (1978).

1977 (2)

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

R. D. Fernald, N. R. Hirata, “Field study of Haplochromis burtoni: habitats and co-habitants,” Environ. Biol. Fish 2, 299–308 (1977).
[Crossref]

1976 (1)

S. Sroczyński, “Die chromatische Aberration der Augenlinse der Regenbogenforelle (Salmo gairdneri Rich.),” Zool. Jb. (Physiol.) 80, 432–450 (1976).

1975 (1)

J. H. Scholes, “Colour receptors and the synaptic connexions in the retina of a cyprinid fish,” Philos. Trans. R. Soc. London, Ser. B 270, 61–118 (1975).
[Crossref]

1968 (1)

H. Eberle, “Zapfenbau, Zapfenlänge und chromatische Aberration im Auge von Lebistes reticulatus Peters (guppy),” Zool. Jb. (Physiol.) 74, 121–154 (1968).

1933 (1)

G. L. Walls, H. D. Judd, “The intra-ocular colour-filters of vertebrates,” Br. J. Ophthalmol. 17, 641–675 (1933).
[Crossref] [PubMed]

1886 (1)

L. Matthiessen, “Ueber den physikalisch-optischen Bau des Auges der Cetaceen und der Fische,” Pflüger’s Arch. 38, 521–528 (1886).

Axelrod, D.

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

Bartsch, H.-J.

H.-J. Bartsch, Taschenbuch Mathematischer Formeln (Harri Deutsch, Thun, Switzerland, 1986).

Bobier, W. R.

J. G. Sivak, W. R. Bobier, “Chromatic aberration of the fish eye and its effect on refractive state,” Vision Res. 18, 453–455 (1978).This work refers to data by Sivak and Roth (unpublished).
[Crossref] [PubMed]

Campbell, M. C. W.

R. H. H. Kröger, M. C. W. Campbell, R. Munger, 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]

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

M. C. W. Campbell, E. M. Harrison, “Refractive-index distribution within the crystalline lens of the rock bass and its variation with age,” in Annual Meeting, Vol. 17 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 169.

R. Munger, M. C. W. Campbell, R. H. H. Kröger, “Gradient index profile calculation using cubic splines,” in Ophthalmic and Visual Optics, Vol. 3 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 59–62.

R. H. H. Kröger, R. D. Fernald, M. C. W. Campbell, “The refractive index distribution and optical quality of the crystalline lens of the African cichlid fish, Haplochromis burtoni, as a function of lens size and lighting condition during development,” submitted to Vision Res.

Chaudhuri, A.

A. Chaudhuri, P. E. Hallet, J. A. Parker, “Aspheric curvatures, refractive indices and chromatic aberration for the rat eye,” Vision Res. 23, 1351–1361 (1983).
[Crossref] [PubMed]

Chu, P. L.

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

Douglas, R. H.

R. H. Douglas, C. M. McGuigan, “The spectral transmission of freshwater teleost ocular media—an interspecific comparison and guide to potential ultraviolet sensitivity,” Vision Res. 29, 871–879 (1989).
[Crossref]

Eberle, H.

H. Eberle, “Zapfenbau, Zapfenlänge und chromatische Aberration im Auge von Lebistes reticulatus Peters (guppy),” Zool. Jb. (Physiol.) 74, 121–154 (1968).

Fernald, R. D.

R. H. H. Kröger, R. D. Fernald, “Regulation of eye growth in the African cichlid fish Haplochromis burtoni,” Vision Res. 34, 1807–1814 (1994).
[Crossref] [PubMed]

R. H. H. Kröger, M. C. W. Campbell, R. Munger, 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]

R. D. Fernald, S. Wright, “Growth of the visual system of the African cichlid fish, Haplochromis burtoni: optics,” Vision Res. 25, 155–161 (1985).
[Crossref]

R. D. Fernald, “Vision and behavior in an African cichlid fish,” Am. Sci. 72, 58–65 (1984).

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

R. D. Fernald, “Chromatic organization of a cichlid fish retina,” Vision Res. 21, 1749–1753 (1981).
[Crossref] [PubMed]

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

R. D. Fernald, N. R. Hirata, “Field study of Haplochromis burtoni: habitats and co-habitants,” Environ. Biol. Fish 2, 299–308 (1977).
[Crossref]

R. H. H. Kröger, R. D. Fernald, M. C. W. Campbell, “The refractive index distribution and optical quality of the crystalline lens of the African cichlid fish, Haplochromis burtoni, as a function of lens size and lighting condition during development,” submitted to Vision Res.

R. D. Fernald, “Aquatic adaptations in fish eyes,” in Sensory Biology of Aquatic Animals, J. Atema, R. R. Fay, A. N. Popper, W. N. Tavolga, eds. (Springer, Berlin, 1988), pp. 435–466.
[Crossref]

Hallet, P. E.

A. Chaudhuri, P. E. Hallet, J. A. Parker, “Aspheric curvatures, refractive indices and chromatic aberration for the rat eye,” Vision Res. 23, 1351–1361 (1983).
[Crossref] [PubMed]

Harrison, E. M.

M. C. W. Campbell, E. M. Harrison, “Refractive-index distribution within the crystalline lens of the rock bass and its variation with age,” in Annual Meeting, Vol. 17 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), p. 169.

Hikida, M.

M. Hikida, S. Iwata, “Studies of eye lens in poikilothermal animals. III. Long-term incubation of rainbow trout lenses,” Jpn. J. Ophthalmol. 30, 43–50 (1986).
[PubMed]

S. Iwata, M. Hikida, “Studies of the eye lens in poikilothermal animals. I. Comparative studies of cation maintenance systems in rainbow trout and rat lenses,” Exp. Eye Res. 41, 171–178 (1985).
[Crossref] [PubMed]

Hirata, N. R.

R. D. Fernald, N. R. Hirata, “Field study of Haplochromis burtoni: habitats and co-habitants,” Environ. Biol. Fish 2, 299–308 (1977).
[Crossref]

Iwata, S.

M. Hikida, S. Iwata, “Studies of eye lens in poikilothermal animals. III. Long-term incubation of rainbow trout lenses,” Jpn. J. Ophthalmol. 30, 43–50 (1986).
[PubMed]

S. Iwata, M. Hikida, “Studies of the eye lens in poikilothermal animals. I. Comparative studies of cation maintenance systems in rainbow trout and rat lenses,” Exp. Eye Res. 41, 171–178 (1985).
[Crossref] [PubMed]

Judd, H. D.

G. L. Walls, H. D. Judd, “The intra-ocular colour-filters of vertebrates,” Br. J. Ophthalmol. 17, 641–675 (1933).
[Crossref] [PubMed]

Kröger, R. H. H.

R. H. H. Kröger, M. C. W. Campbell, R. Munger, 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]

R. H. H. Kröger, R. D. Fernald, “Regulation of eye growth in the African cichlid fish Haplochromis burtoni,” Vision Res. 34, 1807–1814 (1994).
[Crossref] [PubMed]

R. H. H. Kröger, “Methods to estimate dispersion in vertebrate ocular media,” J. Opt. Soc. Am. A 9, 1486–1490 (1992).We used Eq. (13). Kröger’s formulas are based on the data of Sivak and Mandelman (Ref. 9), who measured refractive indices of the ocular media of a variety of vertebrate species at several wavelengths and described the dispersive properties of “average” vertebrate ocular media including the crystalline lens.
[Crossref] [PubMed]

R. Munger, M. C. W. Campbell, R. H. H. Kröger, “Gradient index profile calculation using cubic splines,” in Ophthalmic and Visual Optics, Vol. 3 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 59–62.

R. H. H. Kröger, R. D. Fernald, M. C. W. Campbell, “The refractive index distribution and optical quality of the crystalline lens of the African cichlid fish, Haplochromis burtoni, as a function of lens size and lighting condition during development,” submitted to Vision Res.

Kröger, R. H.H.

R. H.H. Kröger, “Dioptrik, Funktion der Pupille und Akkommodation bei Zahnwalen,” Ph. D. dissertation (Eberhard-Karls-Universität, Tübingen, Germany, 1989).

Lerner, D.

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

Liebman, P.

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

Longhurst, R. S.

R. S. Longhurst, Geometrical and Physical Optics, 3rd ed. (Longman, London, 1973).

Mandelman, T.

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

J. G. Sivak, T. Mandelman, “Chromatic dispersion of the ocular media,” Vision Res. 22, 997–1003 (1982).
[Crossref] [PubMed]

Matthiessen, L.

L. Matthiessen, “Ueber den physikalisch-optischen Bau des Auges der Cetaceen und der Fische,” Pflüger’s Arch. 38, 521–528 (1886).

McGuigan, C. M.

R. H. Douglas, C. M. McGuigan, “The spectral transmission of freshwater teleost ocular media—an interspecific comparison and guide to potential ultraviolet sensitivity,” Vision Res. 29, 871–879 (1989).
[Crossref]

Munger, R.

R. H. H. Kröger, M. C. W. Campbell, R. Munger, 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]

R. Munger, M. C. W. Campbell, R. H. H. Kröger, “Gradient index profile calculation using cubic splines,” in Ophthalmic and Visual Optics, Vol. 3 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 59–62.

Otten, E.

E. Otten, “Vision during growth of a generalized Haplochromis species: H. elegansTrewavas 1933 (Pisces, Cichlidae),” Neth. J. Zool. 31, 650–700 (1981).
[Crossref]

Palmer, D. A.

Parker, J. A.

A. Chaudhuri, P. E. Hallet, J. A. Parker, “Aspheric curvatures, refractive indices and chromatic aberration for the rat eye,” Vision Res. 23, 1351–1361 (1983).
[Crossref] [PubMed]

Pumphrey, R. J.

R. J. Pumphrey, “Concerning vision,” in The Cell and the Organism, J. A. Ramsey, ed. (Condor, Cambridge, 1961), pp. 193–208.

Sands, P. J.

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

Scholes, J. H.

J. H. Scholes, “Colour receptors and the synaptic connexions in the retina of a cyprinid fish,” Philos. Trans. R. Soc. London, Ser. B 270, 61–118 (1975).
[Crossref]

Sivak, J. G.

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

J. G. Sivak, T. Mandelman, “Chromatic dispersion of the ocular media,” Vision Res. 22, 997–1003 (1982).
[Crossref] [PubMed]

D. A. Palmer, J. G. Sivak, “Crystalline lens dispersion,” J. Opt. Soc. Am. 71, 780–782 (1981).
[Crossref] [PubMed]

J. G. Sivak, W. R. Bobier, “Chromatic aberration of the fish eye and its effect on refractive state,” Vision Res. 18, 453–455 (1978).This work refers to data by Sivak and Roth (unpublished).
[Crossref] [PubMed]

Sroczynski, S.

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

S. Sroczyński, “Die chromatische Aberration der Augelinse der Bachforelle (Salmo trutta fario L.),” Zool. Jb. (Physiol.) 82, 113–133 (1978).

S. Sroczyński, “Die chromatische Aberration der Augenlinse der Regenbogenforelle (Salmo gairdneri Rich.),” Zool. Jb. (Physiol.) 80, 432–450 (1976).

Walls, G. L.

G. L. Walls, H. D. Judd, “The intra-ocular colour-filters of vertebrates,” Br. J. Ophthalmol. 17, 641–675 (1933).
[Crossref] [PubMed]

Wright, S.

R. D. Fernald, S. Wright, “Growth of the visual system of the African cichlid fish, Haplochromis burtoni: optics,” Vision Res. 25, 155–161 (1985).
[Crossref]

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

Am. Sci. (1)

R. D. Fernald, “Vision and behavior in an African cichlid fish,” Am. Sci. 72, 58–65 (1984).

Br. J. Ophthalmol. (1)

G. L. Walls, H. D. Judd, “The intra-ocular colour-filters of vertebrates,” Br. J. Ophthalmol. 17, 641–675 (1933).
[Crossref] [PubMed]

Electron. Lett. (1)

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

Environ. Biol. Fish (1)

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[Crossref]

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R. H. H. Kröger, M. C. W. Campbell, R. Munger, 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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[Crossref]

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Figures (6)

Fig. 1
Fig. 1

Top view of the experimental setup. For description see Section 2.

Fig. 2
Fig. 2

Results from a typical lens normalized to unit lens radius. A, Refractive-index profiles. Note the small depressions in the profiles close to the surface (arrowhead) that indicate that the refractive index of the immersion medium was slightly higher than the surface index of the lens. B, Spherical aberrations predicted by ray tracing from the refractive-index profiles shown in A (upper traces) and measured directly (lower traces). Note that predicted and measured spherical aberrations are similar and that spherical aberrations at the four wavelengths are parallel over most of the aperture. Repeatability is better in directly measured than in predicted spherical aberrations. Accuracy of measured spherical aberrations is low very close to the optical axis, because a small error in the position of the optical axis and/or the measured beam leads to a large error in back vertex distance.

Fig. 3
Fig. 3

Mean refractive index (n = 7) as a function of wavelength and radial position in the lens. In general, dispersion increases with increasing refractive index and radial position. Error bars indicate standard deviations.

Fig. 4
Fig. 4

Measured differences that are due to dispersion in mean refractive index as functions of n633 (thick traces). Dispersion increases approximately linearly with increasing n633 in the blue and the red ranges. Dispersion is almost independent of n633 in the green range. The thin traces are calculated from the refractive index at 633 nm.10

Fig. 5
Fig. 5

Differences in BCD’s between 633 and 457 nm expressed in percent f633 as a function of beam entrance position. The black areas delimit the standard deviations. Longitudinal chromatic aberration is independent of beam entrance position if calculated from either measurements or model calculations with inferred refractive-index profiles. The slopes of the differences in BCD’s as functions of beam entrance positions were not significantly different from zero in any of the possible combinations of wavelengths.

Fig. 6
Fig. 6

Differences in mean focal lengths of the lenses as a function of the wavelength of light expressed in percent f633. The line is the best fit of Eq. (1) to differences in focal lengths calculated from measured BVD’s. The symbols mark the differences in focal length expected from the best fit of Eq. (1) at the wavelengths of maximum absorbances of the photoreceptor types in the H. burtoni retina and at the wavelengths of the C and F Fraunhofer lines. The differences in focal length predicted from inferred refractive-index profiles are also indicated. Error bars indicate standard deviations.

Tables (4)

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Table 1 Linear Correlation Analysis of Dispersion as a Function of n633a

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Table 2 LCA Expressed As Differences in Focal Length in Percent f633a

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Table 3 LCA for the Wavelengths of the C and F Fraunhofer Lines and the Wavelengths of Cone Maximum Absorbances, Interpolated with Eq. (1)

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Table 4 Longitudinal Chromatic Aberration (LCA) of Fish Lenses in Percent Focal Lengtha

Equations (1)

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Δ f = U + ( 1 nm / λ + V ) exp W ,

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