Abstract

A mathematical model of multiple layer skin coloration in cephalopods, a class of aquatic animals, is presented. The model incorporates diffuse and specular reflection from both pigment and structural photonic components found in the skin of these animals. Specific physical processes of this coloration are identified and modeled utilizing available biological materials data. Several examples of combination spectra are calculated to illustrate multiple layer and incident light effects as well as the potentially rich repertoire of color schemes available to these animals. A detailed understanding of the physical principles underlying cephalopod coloration is expected to yield insights into their possible functions.

© 2008 Optical Society of America

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References

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  1. R. T. Hanlon and J. B. Messenger, Cephalopod Behaviour (Cambridge U. Press, 1996).
  2. L. Mäthger and R. T. Hanlon, “Malleable skin coloration in cephalopods: Selective reflectance, transmission and absorbance of light by chromatophores and iridophores,” Cell Tissue Res. 329, 179-186 (2007).
    [CrossRef] [PubMed]
  3. M. B. Masthay, “Color changes induced by pigment granule aggregation in chromatophores: A quantitative model based on Beer's law,” Photochem. Photobiol. 66, 649-658 (1997).
    [CrossRef]
  4. E. J. Denton and M. F. Land, “Mechanism of reflexion in silvery layers of fish and cephalopods,” Proc. R. Soc. London, Ser. A 178, 43-61 (1971).
    [CrossRef]
  5. L. M. Mäthger and E. J. Denton, “Reflective properties of iridophores and fluorescent 'eyespots' in the loliginid squid Alloteuthis subulata and Loligo vulgaris,” J. Exp. Biol. 204, 2103-2118 (2001).
    [PubMed]
  6. R. L. Sutherland, L. M. Mäthger, R. T. Hanlon, A. M. Urbas, and M. O. Stone, “Cephalopod coloration model. I. Squid chromatophores and iridophores,” J. Opt. Soc. Am. A 25, 588-599 (2008).
    [CrossRef]
  7. R. T. Hanlon, “Cephalopod dynamic camouflage,” Curr. Biol. 17, R400-R404 (2007).
    [CrossRef] [PubMed]
  8. W. J. Crookes, L. Ding, Q. L. Huang, J. R. Kimbell, J. Horwitz, and M. J. McFall-Ngai, “Reflectins: The unusual proteins of squid reflective tissues,” Science 303, 235-238 (2004).
    [CrossRef] [PubMed]
  9. K. M. Cooper and R. T. Hanlon, “Correlation of iridescence with changes in iridophore platelet ultrastructure in the squid Lolliguncula brevis,” J. Exp. Biol. 121, 451-455 (1986).
    [PubMed]
  10. L. M. Mäthger, A. M. Kuzirian, and R. T. Hanlon, “Exceptional bright white diffusion by cephalopod leucophores” (manuscript in preparation).
  11. D. Froesch and J. B. Messenger, “On leucophores and the chromatic unit of Octopus vulgaris,” J. Zool. 186, 163-173 (1978).
    [CrossRef]
  12. L. M. Mäthger and R. T. Hanlon, “Anatomical basis for camouflaged polarized light communication in squid,” Cell. Mol. Biol. Lett. 2, 494-496 (2006).
  13. B. Maheu, J. N. Letoulouzan, and G. Gouesbet, “Four-flux models to solve the scattering transfer equation in terms of Lorenz-Mie parameters,” Appl. Opt. 23, 3353-3362 (1984).
    [CrossRef] [PubMed]
  14. P. Kubelka, “New contributions to the optics of intensely light-scattering materials. Part I,” J. Opt. Soc. Am. 38, 448-457 (1948).
    [CrossRef] [PubMed]
  15. R. Levinson, P. Berdahl, and H. Akbari, “Solar spectral optical properties of pigments--Part I: Model for deriving scattering and absorption coefficients from transmittance and reflectance measurements,” Sol. Energy Mater. Sol. Cells 89, 319-349 (2005).
    [CrossRef]
  16. R. M. Kramer, W. J. Crookes-Goodson, and R. R. Naik, “The self-organizing properties of squid reflectin protein,” Nat. Mater. 6, 533-538 (2007).
    [CrossRef] [PubMed]
  17. R. T. Hanlon and J. B. Messenger, “Adaptive coloration in young cuttlefish (Sepia officinalis L.): The morphology and development of body patterns and their relation to behaviour,” Philos. Trans. R. Soc. London, Ser. B 320, 437-487 (1988).
    [CrossRef]
  18. R. T. Hanlon, L. M. Mäthger, A. M. Kuzirian, and J. B. Messenger, “White reflection from cuttlefish skin (Mollusca: Cephalopoda)” (manuscript in preparation).
  19. J. Bellingham, A. G. Morris, and D. M. Hunt, “The rhodopsin gene of the cuttlefish Sepia officinalis: Sequence and spectral tuning,” J. Exp. Biol. 201, 2299-2306 (1998).
    [PubMed]
  20. P. K. Brown and P. S. Brown, “Visual pigments of the octopus and cuttlefish,” Nature (London) 182, 1288-1290 (1958).
    [CrossRef]
  21. R. Levinson, P. Berdahl, and H. Akbari, “Solar spectral optical properties of pigments--Part II: Survey of common colorants,” Sol. Energy Mater. Sol. Cells 89, 351-389 (2005).
    [CrossRef]
  22. W. E. Vargas and G. A. Niklasson, “Forward-scattering ratios and average pathlength parameter in radiative transfer models,” J. Phys. Condens. Matter 9, 9083-9096 (1997).
    [CrossRef]

2008 (1)

2007 (3)

L. Mäthger and R. T. Hanlon, “Malleable skin coloration in cephalopods: Selective reflectance, transmission and absorbance of light by chromatophores and iridophores,” Cell Tissue Res. 329, 179-186 (2007).
[CrossRef] [PubMed]

R. T. Hanlon, “Cephalopod dynamic camouflage,” Curr. Biol. 17, R400-R404 (2007).
[CrossRef] [PubMed]

R. M. Kramer, W. J. Crookes-Goodson, and R. R. Naik, “The self-organizing properties of squid reflectin protein,” Nat. Mater. 6, 533-538 (2007).
[CrossRef] [PubMed]

2006 (1)

L. M. Mäthger and R. T. Hanlon, “Anatomical basis for camouflaged polarized light communication in squid,” Cell. Mol. Biol. Lett. 2, 494-496 (2006).

2005 (2)

R. Levinson, P. Berdahl, and H. Akbari, “Solar spectral optical properties of pigments--Part I: Model for deriving scattering and absorption coefficients from transmittance and reflectance measurements,” Sol. Energy Mater. Sol. Cells 89, 319-349 (2005).
[CrossRef]

R. Levinson, P. Berdahl, and H. Akbari, “Solar spectral optical properties of pigments--Part II: Survey of common colorants,” Sol. Energy Mater. Sol. Cells 89, 351-389 (2005).
[CrossRef]

2004 (1)

W. J. Crookes, L. Ding, Q. L. Huang, J. R. Kimbell, J. Horwitz, and M. J. McFall-Ngai, “Reflectins: The unusual proteins of squid reflective tissues,” Science 303, 235-238 (2004).
[CrossRef] [PubMed]

2001 (1)

L. M. Mäthger and E. J. Denton, “Reflective properties of iridophores and fluorescent 'eyespots' in the loliginid squid Alloteuthis subulata and Loligo vulgaris,” J. Exp. Biol. 204, 2103-2118 (2001).
[PubMed]

1998 (1)

J. Bellingham, A. G. Morris, and D. M. Hunt, “The rhodopsin gene of the cuttlefish Sepia officinalis: Sequence and spectral tuning,” J. Exp. Biol. 201, 2299-2306 (1998).
[PubMed]

1997 (2)

M. B. Masthay, “Color changes induced by pigment granule aggregation in chromatophores: A quantitative model based on Beer's law,” Photochem. Photobiol. 66, 649-658 (1997).
[CrossRef]

W. E. Vargas and G. A. Niklasson, “Forward-scattering ratios and average pathlength parameter in radiative transfer models,” J. Phys. Condens. Matter 9, 9083-9096 (1997).
[CrossRef]

1996 (1)

R. T. Hanlon and J. B. Messenger, Cephalopod Behaviour (Cambridge U. Press, 1996).

1988 (1)

R. T. Hanlon and J. B. Messenger, “Adaptive coloration in young cuttlefish (Sepia officinalis L.): The morphology and development of body patterns and their relation to behaviour,” Philos. Trans. R. Soc. London, Ser. B 320, 437-487 (1988).
[CrossRef]

1986 (1)

K. M. Cooper and R. T. Hanlon, “Correlation of iridescence with changes in iridophore platelet ultrastructure in the squid Lolliguncula brevis,” J. Exp. Biol. 121, 451-455 (1986).
[PubMed]

1984 (1)

1978 (1)

D. Froesch and J. B. Messenger, “On leucophores and the chromatic unit of Octopus vulgaris,” J. Zool. 186, 163-173 (1978).
[CrossRef]

1971 (1)

E. J. Denton and M. F. Land, “Mechanism of reflexion in silvery layers of fish and cephalopods,” Proc. R. Soc. London, Ser. A 178, 43-61 (1971).
[CrossRef]

1958 (1)

P. K. Brown and P. S. Brown, “Visual pigments of the octopus and cuttlefish,” Nature (London) 182, 1288-1290 (1958).
[CrossRef]

1948 (1)

Akbari, H.

R. Levinson, P. Berdahl, and H. Akbari, “Solar spectral optical properties of pigments--Part I: Model for deriving scattering and absorption coefficients from transmittance and reflectance measurements,” Sol. Energy Mater. Sol. Cells 89, 319-349 (2005).
[CrossRef]

R. Levinson, P. Berdahl, and H. Akbari, “Solar spectral optical properties of pigments--Part II: Survey of common colorants,” Sol. Energy Mater. Sol. Cells 89, 351-389 (2005).
[CrossRef]

Bellingham, J.

J. Bellingham, A. G. Morris, and D. M. Hunt, “The rhodopsin gene of the cuttlefish Sepia officinalis: Sequence and spectral tuning,” J. Exp. Biol. 201, 2299-2306 (1998).
[PubMed]

Berdahl, P.

R. Levinson, P. Berdahl, and H. Akbari, “Solar spectral optical properties of pigments--Part I: Model for deriving scattering and absorption coefficients from transmittance and reflectance measurements,” Sol. Energy Mater. Sol. Cells 89, 319-349 (2005).
[CrossRef]

R. Levinson, P. Berdahl, and H. Akbari, “Solar spectral optical properties of pigments--Part II: Survey of common colorants,” Sol. Energy Mater. Sol. Cells 89, 351-389 (2005).
[CrossRef]

Brown, P. K.

P. K. Brown and P. S. Brown, “Visual pigments of the octopus and cuttlefish,” Nature (London) 182, 1288-1290 (1958).
[CrossRef]

Brown, P. S.

P. K. Brown and P. S. Brown, “Visual pigments of the octopus and cuttlefish,” Nature (London) 182, 1288-1290 (1958).
[CrossRef]

Cooper, K. M.

K. M. Cooper and R. T. Hanlon, “Correlation of iridescence with changes in iridophore platelet ultrastructure in the squid Lolliguncula brevis,” J. Exp. Biol. 121, 451-455 (1986).
[PubMed]

Crookes, W. J.

W. J. Crookes, L. Ding, Q. L. Huang, J. R. Kimbell, J. Horwitz, and M. J. McFall-Ngai, “Reflectins: The unusual proteins of squid reflective tissues,” Science 303, 235-238 (2004).
[CrossRef] [PubMed]

Crookes-Goodson, W. J.

R. M. Kramer, W. J. Crookes-Goodson, and R. R. Naik, “The self-organizing properties of squid reflectin protein,” Nat. Mater. 6, 533-538 (2007).
[CrossRef] [PubMed]

Denton, E. J.

L. M. Mäthger and E. J. Denton, “Reflective properties of iridophores and fluorescent 'eyespots' in the loliginid squid Alloteuthis subulata and Loligo vulgaris,” J. Exp. Biol. 204, 2103-2118 (2001).
[PubMed]

E. J. Denton and M. F. Land, “Mechanism of reflexion in silvery layers of fish and cephalopods,” Proc. R. Soc. London, Ser. A 178, 43-61 (1971).
[CrossRef]

Ding, L.

W. J. Crookes, L. Ding, Q. L. Huang, J. R. Kimbell, J. Horwitz, and M. J. McFall-Ngai, “Reflectins: The unusual proteins of squid reflective tissues,” Science 303, 235-238 (2004).
[CrossRef] [PubMed]

Froesch, D.

D. Froesch and J. B. Messenger, “On leucophores and the chromatic unit of Octopus vulgaris,” J. Zool. 186, 163-173 (1978).
[CrossRef]

Gouesbet, G.

Hanlon, R. T.

R. L. Sutherland, L. M. Mäthger, R. T. Hanlon, A. M. Urbas, and M. O. Stone, “Cephalopod coloration model. I. Squid chromatophores and iridophores,” J. Opt. Soc. Am. A 25, 588-599 (2008).
[CrossRef]

L. Mäthger and R. T. Hanlon, “Malleable skin coloration in cephalopods: Selective reflectance, transmission and absorbance of light by chromatophores and iridophores,” Cell Tissue Res. 329, 179-186 (2007).
[CrossRef] [PubMed]

R. T. Hanlon, “Cephalopod dynamic camouflage,” Curr. Biol. 17, R400-R404 (2007).
[CrossRef] [PubMed]

L. M. Mäthger and R. T. Hanlon, “Anatomical basis for camouflaged polarized light communication in squid,” Cell. Mol. Biol. Lett. 2, 494-496 (2006).

R. T. Hanlon and J. B. Messenger, Cephalopod Behaviour (Cambridge U. Press, 1996).

R. T. Hanlon and J. B. Messenger, “Adaptive coloration in young cuttlefish (Sepia officinalis L.): The morphology and development of body patterns and their relation to behaviour,” Philos. Trans. R. Soc. London, Ser. B 320, 437-487 (1988).
[CrossRef]

K. M. Cooper and R. T. Hanlon, “Correlation of iridescence with changes in iridophore platelet ultrastructure in the squid Lolliguncula brevis,” J. Exp. Biol. 121, 451-455 (1986).
[PubMed]

L. M. Mäthger, A. M. Kuzirian, and R. T. Hanlon, “Exceptional bright white diffusion by cephalopod leucophores” (manuscript in preparation).

R. T. Hanlon, L. M. Mäthger, A. M. Kuzirian, and J. B. Messenger, “White reflection from cuttlefish skin (Mollusca: Cephalopoda)” (manuscript in preparation).

Horwitz, J.

W. J. Crookes, L. Ding, Q. L. Huang, J. R. Kimbell, J. Horwitz, and M. J. McFall-Ngai, “Reflectins: The unusual proteins of squid reflective tissues,” Science 303, 235-238 (2004).
[CrossRef] [PubMed]

Huang, Q. L.

W. J. Crookes, L. Ding, Q. L. Huang, J. R. Kimbell, J. Horwitz, and M. J. McFall-Ngai, “Reflectins: The unusual proteins of squid reflective tissues,” Science 303, 235-238 (2004).
[CrossRef] [PubMed]

Hunt, D. M.

J. Bellingham, A. G. Morris, and D. M. Hunt, “The rhodopsin gene of the cuttlefish Sepia officinalis: Sequence and spectral tuning,” J. Exp. Biol. 201, 2299-2306 (1998).
[PubMed]

Kimbell, J. R.

W. J. Crookes, L. Ding, Q. L. Huang, J. R. Kimbell, J. Horwitz, and M. J. McFall-Ngai, “Reflectins: The unusual proteins of squid reflective tissues,” Science 303, 235-238 (2004).
[CrossRef] [PubMed]

Kramer, R. M.

R. M. Kramer, W. J. Crookes-Goodson, and R. R. Naik, “The self-organizing properties of squid reflectin protein,” Nat. Mater. 6, 533-538 (2007).
[CrossRef] [PubMed]

Kubelka, P.

Kuzirian, A. M.

L. M. Mäthger, A. M. Kuzirian, and R. T. Hanlon, “Exceptional bright white diffusion by cephalopod leucophores” (manuscript in preparation).

R. T. Hanlon, L. M. Mäthger, A. M. Kuzirian, and J. B. Messenger, “White reflection from cuttlefish skin (Mollusca: Cephalopoda)” (manuscript in preparation).

Land, M. F.

E. J. Denton and M. F. Land, “Mechanism of reflexion in silvery layers of fish and cephalopods,” Proc. R. Soc. London, Ser. A 178, 43-61 (1971).
[CrossRef]

Letoulouzan, J. N.

Levinson, R.

R. Levinson, P. Berdahl, and H. Akbari, “Solar spectral optical properties of pigments--Part I: Model for deriving scattering and absorption coefficients from transmittance and reflectance measurements,” Sol. Energy Mater. Sol. Cells 89, 319-349 (2005).
[CrossRef]

R. Levinson, P. Berdahl, and H. Akbari, “Solar spectral optical properties of pigments--Part II: Survey of common colorants,” Sol. Energy Mater. Sol. Cells 89, 351-389 (2005).
[CrossRef]

Maheu, B.

Masthay, M. B.

M. B. Masthay, “Color changes induced by pigment granule aggregation in chromatophores: A quantitative model based on Beer's law,” Photochem. Photobiol. 66, 649-658 (1997).
[CrossRef]

Mäthger, L.

L. Mäthger and R. T. Hanlon, “Malleable skin coloration in cephalopods: Selective reflectance, transmission and absorbance of light by chromatophores and iridophores,” Cell Tissue Res. 329, 179-186 (2007).
[CrossRef] [PubMed]

Mäthger, L. M.

R. L. Sutherland, L. M. Mäthger, R. T. Hanlon, A. M. Urbas, and M. O. Stone, “Cephalopod coloration model. I. Squid chromatophores and iridophores,” J. Opt. Soc. Am. A 25, 588-599 (2008).
[CrossRef]

L. M. Mäthger and R. T. Hanlon, “Anatomical basis for camouflaged polarized light communication in squid,” Cell. Mol. Biol. Lett. 2, 494-496 (2006).

L. M. Mäthger and E. J. Denton, “Reflective properties of iridophores and fluorescent 'eyespots' in the loliginid squid Alloteuthis subulata and Loligo vulgaris,” J. Exp. Biol. 204, 2103-2118 (2001).
[PubMed]

L. M. Mäthger, A. M. Kuzirian, and R. T. Hanlon, “Exceptional bright white diffusion by cephalopod leucophores” (manuscript in preparation).

R. T. Hanlon, L. M. Mäthger, A. M. Kuzirian, and J. B. Messenger, “White reflection from cuttlefish skin (Mollusca: Cephalopoda)” (manuscript in preparation).

McFall-Ngai, M. J.

W. J. Crookes, L. Ding, Q. L. Huang, J. R. Kimbell, J. Horwitz, and M. J. McFall-Ngai, “Reflectins: The unusual proteins of squid reflective tissues,” Science 303, 235-238 (2004).
[CrossRef] [PubMed]

Messenger, J. B.

R. T. Hanlon and J. B. Messenger, Cephalopod Behaviour (Cambridge U. Press, 1996).

R. T. Hanlon and J. B. Messenger, “Adaptive coloration in young cuttlefish (Sepia officinalis L.): The morphology and development of body patterns and their relation to behaviour,” Philos. Trans. R. Soc. London, Ser. B 320, 437-487 (1988).
[CrossRef]

D. Froesch and J. B. Messenger, “On leucophores and the chromatic unit of Octopus vulgaris,” J. Zool. 186, 163-173 (1978).
[CrossRef]

R. T. Hanlon, L. M. Mäthger, A. M. Kuzirian, and J. B. Messenger, “White reflection from cuttlefish skin (Mollusca: Cephalopoda)” (manuscript in preparation).

Morris, A. G.

J. Bellingham, A. G. Morris, and D. M. Hunt, “The rhodopsin gene of the cuttlefish Sepia officinalis: Sequence and spectral tuning,” J. Exp. Biol. 201, 2299-2306 (1998).
[PubMed]

Naik, R. R.

R. M. Kramer, W. J. Crookes-Goodson, and R. R. Naik, “The self-organizing properties of squid reflectin protein,” Nat. Mater. 6, 533-538 (2007).
[CrossRef] [PubMed]

Niklasson, G. A.

W. E. Vargas and G. A. Niklasson, “Forward-scattering ratios and average pathlength parameter in radiative transfer models,” J. Phys. Condens. Matter 9, 9083-9096 (1997).
[CrossRef]

Stone, M. O.

Sutherland, R. L.

Urbas, A. M.

Vargas, W. E.

W. E. Vargas and G. A. Niklasson, “Forward-scattering ratios and average pathlength parameter in radiative transfer models,” J. Phys. Condens. Matter 9, 9083-9096 (1997).
[CrossRef]

Appl. Opt. (1)

Cell Tissue Res. (1)

L. Mäthger and R. T. Hanlon, “Malleable skin coloration in cephalopods: Selective reflectance, transmission and absorbance of light by chromatophores and iridophores,” Cell Tissue Res. 329, 179-186 (2007).
[CrossRef] [PubMed]

Cell. Mol. Biol. Lett. (1)

L. M. Mäthger and R. T. Hanlon, “Anatomical basis for camouflaged polarized light communication in squid,” Cell. Mol. Biol. Lett. 2, 494-496 (2006).

Curr. Biol. (1)

R. T. Hanlon, “Cephalopod dynamic camouflage,” Curr. Biol. 17, R400-R404 (2007).
[CrossRef] [PubMed]

J. Exp. Biol. (3)

K. M. Cooper and R. T. Hanlon, “Correlation of iridescence with changes in iridophore platelet ultrastructure in the squid Lolliguncula brevis,” J. Exp. Biol. 121, 451-455 (1986).
[PubMed]

L. M. Mäthger and E. J. Denton, “Reflective properties of iridophores and fluorescent 'eyespots' in the loliginid squid Alloteuthis subulata and Loligo vulgaris,” J. Exp. Biol. 204, 2103-2118 (2001).
[PubMed]

J. Bellingham, A. G. Morris, and D. M. Hunt, “The rhodopsin gene of the cuttlefish Sepia officinalis: Sequence and spectral tuning,” J. Exp. Biol. 201, 2299-2306 (1998).
[PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Phys. Condens. Matter (1)

W. E. Vargas and G. A. Niklasson, “Forward-scattering ratios and average pathlength parameter in radiative transfer models,” J. Phys. Condens. Matter 9, 9083-9096 (1997).
[CrossRef]

J. Zool. (1)

D. Froesch and J. B. Messenger, “On leucophores and the chromatic unit of Octopus vulgaris,” J. Zool. 186, 163-173 (1978).
[CrossRef]

Nat. Mater. (1)

R. M. Kramer, W. J. Crookes-Goodson, and R. R. Naik, “The self-organizing properties of squid reflectin protein,” Nat. Mater. 6, 533-538 (2007).
[CrossRef] [PubMed]

Nature (London) (1)

P. K. Brown and P. S. Brown, “Visual pigments of the octopus and cuttlefish,” Nature (London) 182, 1288-1290 (1958).
[CrossRef]

Philos. Trans. R. Soc. London, Ser. B (1)

R. T. Hanlon and J. B. Messenger, “Adaptive coloration in young cuttlefish (Sepia officinalis L.): The morphology and development of body patterns and their relation to behaviour,” Philos. Trans. R. Soc. London, Ser. B 320, 437-487 (1988).
[CrossRef]

Photochem. Photobiol. (1)

M. B. Masthay, “Color changes induced by pigment granule aggregation in chromatophores: A quantitative model based on Beer's law,” Photochem. Photobiol. 66, 649-658 (1997).
[CrossRef]

Proc. R. Soc. London, Ser. A (1)

E. J. Denton and M. F. Land, “Mechanism of reflexion in silvery layers of fish and cephalopods,” Proc. R. Soc. London, Ser. A 178, 43-61 (1971).
[CrossRef]

Science (1)

W. J. Crookes, L. Ding, Q. L. Huang, J. R. Kimbell, J. Horwitz, and M. J. McFall-Ngai, “Reflectins: The unusual proteins of squid reflective tissues,” Science 303, 235-238 (2004).
[CrossRef] [PubMed]

Sol. Energy Mater. Sol. Cells (2)

R. Levinson, P. Berdahl, and H. Akbari, “Solar spectral optical properties of pigments--Part I: Model for deriving scattering and absorption coefficients from transmittance and reflectance measurements,” Sol. Energy Mater. Sol. Cells 89, 319-349 (2005).
[CrossRef]

R. Levinson, P. Berdahl, and H. Akbari, “Solar spectral optical properties of pigments--Part II: Survey of common colorants,” Sol. Energy Mater. Sol. Cells 89, 351-389 (2005).
[CrossRef]

Other (3)

R. T. Hanlon and J. B. Messenger, Cephalopod Behaviour (Cambridge U. Press, 1996).

R. T. Hanlon, L. M. Mäthger, A. M. Kuzirian, and J. B. Messenger, “White reflection from cuttlefish skin (Mollusca: Cephalopoda)” (manuscript in preparation).

L. M. Mäthger, A. M. Kuzirian, and R. T. Hanlon, “Exceptional bright white diffusion by cephalopod leucophores” (manuscript in preparation).

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Figures (11)

Fig. 1
Fig. 1

Illustration of the photometric problem addressed by the cephalopod coloration model.

Fig. 2
Fig. 2

Simplified schematic illustration of cephalopod skin structure.

Fig. 3
Fig. 3

Four-flux model of collimated and diffuse reflectance from multiple layers in a cephalopod skin. Skin layers are numbered 1 , 2 , m . Forward and backward components of flux are labeled as I and J, respectively, with numerical subscripts j indicating values in the space following layer j. Subscripts c collimated , d diffuse .

Fig. 4
Fig. 4

Spectral backscattering ( S ) coefficients (normalized to thickness d) derived from reflectance measurements of leucophores and muscle of the cuttlefish Sepia officinalis. (a) Fin spot, zebra stripe, head bar, white spot, and muscle spectra. (b) Head bar and white square spectra with an expanded vertical scale.

Fig. 5
Fig. 5

Comparison of calculated reflectance for bare chromatophores to reflectance with leucophore and leuco phore plus muscle backgrounds. The white square leucophore was used for these calculations. (a) Brown chromatophore. (b) Red chromatophore. (c) Yellow chromatophore.

Fig. 6
Fig. 6

Theoretical calculations of specular, diffuse, and total reflectance for a red iridophore over a zebra stripe leucophore background. The incident light is collimated, and the angle of incidence is 30°.

Fig. 7
Fig. 7

Theoretical calculations of total (s and p polarization) and unpolarized diffuse reflectance for a yellow chromatophore over a red iridophore. The incident light is collimated, and the angle of incidence is 30°. The reflectance of a bare yellow chromatophore is also given for comparison.

Fig. 8
Fig. 8

Theoretical calculations of total reflectance for an expanding red chromatophore over a green iridophore with a head bar leucophore background. The incident light is collimated, and the angle of incidence is 0°. The size of the chromatophore (relative to the default value) is indicated by the scale factor ρ.

Fig. 9
Fig. 9

Theoretical calculations of total reflectance for a partially retracted red chromatophore ( ρ = 0.4 ) occupying 12 % of the field of view above a green iridophore with a head bar leucophore background illustrating the effects of a varying q of the incident light. Normal incidence for collimated light was assumed.

Fig. 10
Fig. 10

Theoretical calculations of total reflectance for a partially retracted red chromatophore ( ρ = 0.4 ) occupying 80 % of the field of view above a green iridophore (no background) illustrating the effects of a varying q of the incident light. Normal incidence for collimated light was assumed.

Fig. 11
Fig. 11

Calculated chromaticity coordinates for the spectra presented in Figs. 8, 9, 10 and for a bare yellow chromatophore and a bare green iridophore under conditions where q = 1 (collimated light) and q = 0 (diffuse light). Also shown is the CIE 1931 chromaticity diagram. CIE standard daylight illuminant D65 was used for these calculations.

Equations (41)

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I ¯ = R ( λ ) T e ( λ ) V ( λ ) I λ d λ .
I c , j = T cc , j I c , j 1 + R cc , j J c , j ,
I d , j = T cd , j I c , j 1 + T d d , j I d , j 1 + R cd , j J c , j + R d d , j J d , j ,
J c , j 1 = R cc , j I c , j 1 + T cc , j J cc , j ,
J d , j 1 = R cd , j I c , j 1 + R d d , j I d , j 1 + T cd , j J c , j + T d d , j J d , j .
[ I c , j 1 I d , j 1 J c , j 1 J d , j 1 ] = S j [ I c , j I d , j J c , j J d , j ] .
S j = [ S j , 11 0 S j , 13 0 S j , 21 S j , 22 S j , 23 S j , 24 S j , 13 0 S j , 33 0 S j , 41 S j , 24 S j , 43 S j , 44 ] ,
S j , 11 = T cc , j 1 ,
S j , 12 = S j , 14 = S j , 32 = S j , 34 = 0 ,
S j , 13 = S j , 31 = T cc , j 1 R cc , j ,
S j , 21 = T cc , j 1 T d d , j 1 T cd , j ,
S j , 22 = T d d , j 1 ,
S j , 23 = T cc , j 1 T d d , j 1 ( T cd , j R cc , j T cc , j R cd , j ) ,
S j , 24 = S j , 42 = T d d , j 1 R d d , j ,
S j , 33 = T cc , j 1 ( T cc , j 2 R cc , j 2 ) ,
S j , 41 = T cc , j 1 T d d , j 1 ( T cd , j R d d , j T d d , j R cd , j ) ,
S j , 43 = R cc , j S j , 41 T d d , j 1 R cd , j R d d , j + T cd , j ,
S j , 44 = T d d , j 1 ( T d d , j 2 R d d , j 2 ) .
[ I c , 0 I d , 0 J c , 0 J d , 0 ] = S [ I c , m I d , m 0 0 ]
S = j = 1 m S j ,
R s = J c , 0 I c , 0 + I d , 0 = q S 31 S 11 ,
R d = J d , 0 I c , 0 + I d , 0 = q ( S 41 S 11 S 21 S 42 S 11 S 22 ) + ( 1 q ) S 42 S 22 .
T s = I c , m I c , 0 + I d , 0 = q S 11 ,
T d = I d , m I c , 0 + I d , 0 = 1 q S 22 q S 21 S 11 S 22 .
T cc = exp [ ( α + σ ) d ] ,
T d d = κ κ cosh η κ d + [ α + ( 1 ξ ) σ ] sinh η κ d ,
R d d = ( 1 ξ ) σ sinh η κ d κ cosh η κ d + [ α + ( 1 ξ ) σ ] sinh η κ d ,
κ = α 2 + 2 ( 1 ξ ) σ α ;
T cd κ κ cosh κ d + [ α + ( 1 ξ ) σ ] sinh κ d exp [ ( α + σ ) d ] ,
R cd ( 1 ξ ) σ sinh κ d κ cosh κ d + [ α + ( 1 ξ ) σ ] sinh κ d .
a = 1 + R cd 2 T 2 2 R cd ,
b = a 2 1 ,
S ( 1 ξ ) σ = 1 b d sinh 1 ( b R cd T ) ,
K α = ( 1 a ) S .
T cc = exp ( σ d ) ,
T d d = 1 1 + η ( 1 ξ ) σ d ,
R d d = η ( 1 ξ ) σ d 1 + η ( 1 ξ ) σ d ,
T cd 1 1 + ( 1 ξ ) σ d exp ( σ d ) ,
R cd ( 1 ξ ) σ d 1 + ( 1 ξ ) σ d ,
S = R cd d T = R cd d ( 1 R cd ) ,
T d d ( λ ) = 0 π 2 T cc , u ( λ , θ ) sin 2 θ d θ ,

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