Abstract

Photonic structures in the skin of pelagic fishes and squids evolved specifically for hiding in the complex light field of the open ocean. To understand the principles under which these structures operate, a detailed characterization of their optical properties is required. An optical scatterometer has been developed to measure one important property, the bidirectional reflectance distribution function (BRDF). The instrument was used to collect reflectance functions from the squid Pterygioteuthis microlampas and fish Sternoptyx sp. Although the animals appear very different to a casual observer, the results reveal interesting similarities in their scattering patterns, suggesting a similar optical strategy for hiding in open water.

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  1. J. B. Messenger, “Reflecting elements in cephalopod skin and their importance for camouflage,” J. Zool.174, 387–395 (1974).
    [CrossRef]
  2. E. J. Denton and M. F. Land, “Mechanism of reflexion in silvery layers of fish and cephalopods,” P. R. Soc. B178, 43–61 (1971).
    [CrossRef]
  3. E. J. Denton, “On the organization of reflecting surfaces in some marine animals,” Philos. T. R. Soc. B258, 285–313 (1970).
    [CrossRef]
  4. S. Johnsen, “Cryptic and conspicuous coloration in the pelagic environment,” P. R. Soc. B269, 243–256 (2002).
    [CrossRef]
  5. S. Johnsen, “Lifting the cloak of invisibility: The effects of changing optical conditions on pelagic crypsis,” Integr. Comp. Biol.43, 580–590 (2003).
    [CrossRef] [PubMed]
  6. S. Johnsen and H. M. Sosik, “Cryptic coloration and mirrored sides as camouflage strategies in near-surface pelagic habitats: Implications for foraging and predator avoidance,” Limnol. Oceanogr.48, 1277–1288 (2003).
    [CrossRef]
  7. D. R. McKenzie, Y. Yin, and W. D. McFall, “Silvery fish skin as an example of a chaotic reflector,” Philos. T. R. Soc. S-A451, 579–584 (1995).
  8. A. L. Holt, A. M. Sweeney, S. Johnsen, and D. E. Morse, “A highly distributed Bragg stack with unique geometry provides effective camouflage for Loliginid squid eyes,” J. R. Soc. Interface8, 1386–1399 (2011).
    [CrossRef] [PubMed]
  9. F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Geometrical Considerations and Nomenclature for Reflectance (National Bureau of Standards (U.S.), 1977), Monograph 160.
  10. T. Weyrich, J. Lawrence, H. Lensch, S. Rusinkiewicz, and T. Zickler, “Principles of appearance acquisition and representation,” Found. Trends Comput. Graph. Vis.4, 75–191 (2009).
    [CrossRef]
  11. B. D. Wilts, H. L. Leertouwer, and D. G. Stavenga, “Imaging scatterometry and microspectrophotometry of lycaenid butterfly wing scales with perforated multilayers,” J. R. Soc. Interface6, S185–S192 (2009).
    [CrossRef]
  12. D. G. Stavenga, H. L. Leertouwer, P. Pirih, and M. F. Wehling, “Imaging scatterometry of butterfly wing scales,” Opt. Express17, 193–202 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]
  14. M. Ben-Ezra, J. Wang, B. Wilburn, X. Li, and L. Ma, “An LED-only BRDF measurement device,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2008), pp. 1–8.
  15. Y. Lan, Y. Dong, J. Wang, X. Tong, and B. Guo, “Condenser-based instant reflectometry,” Comput. Graph. Forum29, 2091–2098 (2010).
    [CrossRef]
  16. Y. Mukaigawa, K. Sumino, and Y. Yagi, “Multiplexed illumination for measuring BRDF using an ellipsoidal mirror and a projector,” in Proceedings of the 8th Asian Conference on Computer Vision, Part II, Y. Yagi, S. B. Kang, I. S. Kweon, and H. Zha, eds. (Springer-Verlag, 2007), pp. 246–257.
  17. Z. Zhang, “A flexible new technique for camera calibration,” IEEE T. Pattern Anal.22, 1330–1334 (2000).
    [CrossRef]
  18. M. Grossberg and S. Nayar, “Determining the camera response from images: What is knowable?” IEEE T. Pattern Anal.25, 1455–1467 (2003).
    [CrossRef]
  19. F. O. Bartell, E. L. Dereniak, and W. L. Wolfe, “The theory and measurement of bidirectional reflectance distribution function (BRDF) and bidirectional transmittance distribution function (BTDF),” Proc. SPIE0257, 154–160 (1981).
    [CrossRef]
  20. J. Murray-Coleman and A. Smith, “The automated measurement of BRDFs and their application to luminaire modeling,” J. Illum. Eng. Soc.19, 87–99 (1990).
  21. A. Lindgren, “Systematics and distribution of the squid genus Pterygioteuthis (Cephalopoda: Oegopsida) in the eastern tropical Pacific Ocean,” J. Mollus. Stud.76, 389–398 (2010).
    [CrossRef]
  22. R. C. Baird, “The systematics, distribution, and zoogeography of the marine hatchetfishes (family Sternoptychidae),” Bull. Mus. Comp. Zool.142, 1–128 (1971).
  23. P. Vukusic and D. G. Stavenga, “Physical methods for investigating structural colors in biological systems,” J. R. Soc. Interface6, 133–148 (2009).
    [CrossRef]
  24. M. Levoy, Z. Zhang, and I. McDowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc-Oxford235, 144–162 (2009).
    [CrossRef]
  25. L. M. 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]
  26. T. M. Jordan, J. C. Partridge, and N. W. Roberts, “Non-polarizing broadband multilayer reflectors in fish,” Nature Photon.6, 759–763 (2012).
    [CrossRef]

2012 (1)

T. M. Jordan, J. C. Partridge, and N. W. Roberts, “Non-polarizing broadband multilayer reflectors in fish,” Nature Photon.6, 759–763 (2012).
[CrossRef]

2011 (1)

A. L. Holt, A. M. Sweeney, S. Johnsen, and D. E. Morse, “A highly distributed Bragg stack with unique geometry provides effective camouflage for Loliginid squid eyes,” J. R. Soc. Interface8, 1386–1399 (2011).
[CrossRef] [PubMed]

2010 (2)

Y. Lan, Y. Dong, J. Wang, X. Tong, and B. Guo, “Condenser-based instant reflectometry,” Comput. Graph. Forum29, 2091–2098 (2010).
[CrossRef]

A. Lindgren, “Systematics and distribution of the squid genus Pterygioteuthis (Cephalopoda: Oegopsida) in the eastern tropical Pacific Ocean,” J. Mollus. Stud.76, 389–398 (2010).
[CrossRef]

2009 (5)

T. Weyrich, J. Lawrence, H. Lensch, S. Rusinkiewicz, and T. Zickler, “Principles of appearance acquisition and representation,” Found. Trends Comput. Graph. Vis.4, 75–191 (2009).
[CrossRef]

B. D. Wilts, H. L. Leertouwer, and D. G. Stavenga, “Imaging scatterometry and microspectrophotometry of lycaenid butterfly wing scales with perforated multilayers,” J. R. Soc. Interface6, S185–S192 (2009).
[CrossRef]

D. G. Stavenga, H. L. Leertouwer, P. Pirih, and M. F. Wehling, “Imaging scatterometry of butterfly wing scales,” Opt. Express17, 193–202 (2009).
[CrossRef] [PubMed]

P. Vukusic and D. G. Stavenga, “Physical methods for investigating structural colors in biological systems,” J. R. Soc. Interface6, 133–148 (2009).
[CrossRef]

M. Levoy, Z. Zhang, and I. McDowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc-Oxford235, 144–162 (2009).
[CrossRef]

2007 (1)

L. M. 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]

2003 (3)

S. Johnsen, “Lifting the cloak of invisibility: The effects of changing optical conditions on pelagic crypsis,” Integr. Comp. Biol.43, 580–590 (2003).
[CrossRef] [PubMed]

S. Johnsen and H. M. Sosik, “Cryptic coloration and mirrored sides as camouflage strategies in near-surface pelagic habitats: Implications for foraging and predator avoidance,” Limnol. Oceanogr.48, 1277–1288 (2003).
[CrossRef]

M. Grossberg and S. Nayar, “Determining the camera response from images: What is knowable?” IEEE T. Pattern Anal.25, 1455–1467 (2003).
[CrossRef]

2002 (1)

S. Johnsen, “Cryptic and conspicuous coloration in the pelagic environment,” P. R. Soc. B269, 243–256 (2002).
[CrossRef]

2000 (2)

1995 (1)

D. R. McKenzie, Y. Yin, and W. D. McFall, “Silvery fish skin as an example of a chaotic reflector,” Philos. T. R. Soc. S-A451, 579–584 (1995).

1990 (1)

J. Murray-Coleman and A. Smith, “The automated measurement of BRDFs and their application to luminaire modeling,” J. Illum. Eng. Soc.19, 87–99 (1990).

1981 (1)

F. O. Bartell, E. L. Dereniak, and W. L. Wolfe, “The theory and measurement of bidirectional reflectance distribution function (BRDF) and bidirectional transmittance distribution function (BTDF),” Proc. SPIE0257, 154–160 (1981).
[CrossRef]

1974 (1)

J. B. Messenger, “Reflecting elements in cephalopod skin and their importance for camouflage,” J. Zool.174, 387–395 (1974).
[CrossRef]

1971 (2)

E. J. Denton and M. F. Land, “Mechanism of reflexion in silvery layers of fish and cephalopods,” P. R. Soc. B178, 43–61 (1971).
[CrossRef]

R. C. Baird, “The systematics, distribution, and zoogeography of the marine hatchetfishes (family Sternoptychidae),” Bull. Mus. Comp. Zool.142, 1–128 (1971).

1970 (1)

E. J. Denton, “On the organization of reflecting surfaces in some marine animals,” Philos. T. R. Soc. B258, 285–313 (1970).
[CrossRef]

Baird, R. C.

R. C. Baird, “The systematics, distribution, and zoogeography of the marine hatchetfishes (family Sternoptychidae),” Bull. Mus. Comp. Zool.142, 1–128 (1971).

Bartell, F. O.

F. O. Bartell, E. L. Dereniak, and W. L. Wolfe, “The theory and measurement of bidirectional reflectance distribution function (BRDF) and bidirectional transmittance distribution function (BTDF),” Proc. SPIE0257, 154–160 (1981).
[CrossRef]

Ben-Ezra, M.

M. Ben-Ezra, J. Wang, B. Wilburn, X. Li, and L. Ma, “An LED-only BRDF measurement device,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2008), pp. 1–8.

Chapin, A.

Denton, E. J.

E. J. Denton and M. F. Land, “Mechanism of reflexion in silvery layers of fish and cephalopods,” P. R. Soc. B178, 43–61 (1971).
[CrossRef]

E. J. Denton, “On the organization of reflecting surfaces in some marine animals,” Philos. T. R. Soc. B258, 285–313 (1970).
[CrossRef]

Dereniak, E. L.

F. O. Bartell, E. L. Dereniak, and W. L. Wolfe, “The theory and measurement of bidirectional reflectance distribution function (BRDF) and bidirectional transmittance distribution function (BTDF),” Proc. SPIE0257, 154–160 (1981).
[CrossRef]

Dong, Y.

Y. Lan, Y. Dong, J. Wang, X. Tong, and B. Guo, “Condenser-based instant reflectometry,” Comput. Graph. Forum29, 2091–2098 (2010).
[CrossRef]

Ginsberg, I. W.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Geometrical Considerations and Nomenclature for Reflectance (National Bureau of Standards (U.S.), 1977), Monograph 160.

Grossberg, M.

M. Grossberg and S. Nayar, “Determining the camera response from images: What is knowable?” IEEE T. Pattern Anal.25, 1455–1467 (2003).
[CrossRef]

Guo, B.

Y. Lan, Y. Dong, J. Wang, X. Tong, and B. Guo, “Condenser-based instant reflectometry,” Comput. Graph. Forum29, 2091–2098 (2010).
[CrossRef]

Hanlon, R. T.

L. M. 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]

Holt, A. L.

A. L. Holt, A. M. Sweeney, S. Johnsen, and D. E. Morse, “A highly distributed Bragg stack with unique geometry provides effective camouflage for Loliginid squid eyes,” J. R. Soc. Interface8, 1386–1399 (2011).
[CrossRef] [PubMed]

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Geometrical Considerations and Nomenclature for Reflectance (National Bureau of Standards (U.S.), 1977), Monograph 160.

Johnsen, S.

A. L. Holt, A. M. Sweeney, S. Johnsen, and D. E. Morse, “A highly distributed Bragg stack with unique geometry provides effective camouflage for Loliginid squid eyes,” J. R. Soc. Interface8, 1386–1399 (2011).
[CrossRef] [PubMed]

S. Johnsen, “Lifting the cloak of invisibility: The effects of changing optical conditions on pelagic crypsis,” Integr. Comp. Biol.43, 580–590 (2003).
[CrossRef] [PubMed]

S. Johnsen and H. M. Sosik, “Cryptic coloration and mirrored sides as camouflage strategies in near-surface pelagic habitats: Implications for foraging and predator avoidance,” Limnol. Oceanogr.48, 1277–1288 (2003).
[CrossRef]

S. Johnsen, “Cryptic and conspicuous coloration in the pelagic environment,” P. R. Soc. B269, 243–256 (2002).
[CrossRef]

Jordan, T. M.

T. M. Jordan, J. C. Partridge, and N. W. Roberts, “Non-polarizing broadband multilayer reflectors in fish,” Nature Photon.6, 759–763 (2012).
[CrossRef]

Lan, Y.

Y. Lan, Y. Dong, J. Wang, X. Tong, and B. Guo, “Condenser-based instant reflectometry,” Comput. Graph. Forum29, 2091–2098 (2010).
[CrossRef]

Land, M. F.

E. J. Denton and M. F. Land, “Mechanism of reflexion in silvery layers of fish and cephalopods,” P. R. Soc. B178, 43–61 (1971).
[CrossRef]

Lawrence, J.

T. Weyrich, J. Lawrence, H. Lensch, S. Rusinkiewicz, and T. Zickler, “Principles of appearance acquisition and representation,” Found. Trends Comput. Graph. Vis.4, 75–191 (2009).
[CrossRef]

Leertouwer, H. L.

B. D. Wilts, H. L. Leertouwer, and D. G. Stavenga, “Imaging scatterometry and microspectrophotometry of lycaenid butterfly wing scales with perforated multilayers,” J. R. Soc. Interface6, S185–S192 (2009).
[CrossRef]

D. G. Stavenga, H. L. Leertouwer, P. Pirih, and M. F. Wehling, “Imaging scatterometry of butterfly wing scales,” Opt. Express17, 193–202 (2009).
[CrossRef] [PubMed]

Lensch, H.

T. Weyrich, J. Lawrence, H. Lensch, S. Rusinkiewicz, and T. Zickler, “Principles of appearance acquisition and representation,” Found. Trends Comput. Graph. Vis.4, 75–191 (2009).
[CrossRef]

Levoy, M.

M. Levoy, Z. Zhang, and I. McDowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc-Oxford235, 144–162 (2009).
[CrossRef]

Li, X.

M. Ben-Ezra, J. Wang, B. Wilburn, X. Li, and L. Ma, “An LED-only BRDF measurement device,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2008), pp. 1–8.

Limperis, T.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Geometrical Considerations and Nomenclature for Reflectance (National Bureau of Standards (U.S.), 1977), Monograph 160.

Lindgren, A.

A. Lindgren, “Systematics and distribution of the squid genus Pterygioteuthis (Cephalopoda: Oegopsida) in the eastern tropical Pacific Ocean,” J. Mollus. Stud.76, 389–398 (2010).
[CrossRef]

Ma, L.

M. Ben-Ezra, J. Wang, B. Wilburn, X. Li, and L. Ma, “An LED-only BRDF measurement device,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2008), pp. 1–8.

Mäthger, L. M.

L. M. 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]

McDowall, I.

M. Levoy, Z. Zhang, and I. McDowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc-Oxford235, 144–162 (2009).
[CrossRef]

McFall, W. D.

D. R. McKenzie, Y. Yin, and W. D. McFall, “Silvery fish skin as an example of a chaotic reflector,” Philos. T. R. Soc. S-A451, 579–584 (1995).

McKenzie, D. R.

D. R. McKenzie, Y. Yin, and W. D. McFall, “Silvery fish skin as an example of a chaotic reflector,” Philos. T. R. Soc. S-A451, 579–584 (1995).

Messenger, J. B.

J. B. Messenger, “Reflecting elements in cephalopod skin and their importance for camouflage,” J. Zool.174, 387–395 (1974).
[CrossRef]

Monti, M.

Morse, D. E.

A. L. Holt, A. M. Sweeney, S. Johnsen, and D. E. Morse, “A highly distributed Bragg stack with unique geometry provides effective camouflage for Loliginid squid eyes,” J. R. Soc. Interface8, 1386–1399 (2011).
[CrossRef] [PubMed]

Mukaigawa, Y.

Y. Mukaigawa, K. Sumino, and Y. Yagi, “Multiplexed illumination for measuring BRDF using an ellipsoidal mirror and a projector,” in Proceedings of the 8th Asian Conference on Computer Vision, Part II, Y. Yagi, S. B. Kang, I. S. Kweon, and H. Zha, eds. (Springer-Verlag, 2007), pp. 246–257.

Murray-Coleman, J.

J. Murray-Coleman and A. Smith, “The automated measurement of BRDFs and their application to luminaire modeling,” J. Illum. Eng. Soc.19, 87–99 (1990).

Nayar, S.

M. Grossberg and S. Nayar, “Determining the camera response from images: What is knowable?” IEEE T. Pattern Anal.25, 1455–1467 (2003).
[CrossRef]

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Geometrical Considerations and Nomenclature for Reflectance (National Bureau of Standards (U.S.), 1977), Monograph 160.

Partridge, J. C.

T. M. Jordan, J. C. Partridge, and N. W. Roberts, “Non-polarizing broadband multilayer reflectors in fish,” Nature Photon.6, 759–763 (2012).
[CrossRef]

Pirih, P.

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Geometrical Considerations and Nomenclature for Reflectance (National Bureau of Standards (U.S.), 1977), Monograph 160.

Roberts, N. W.

T. M. Jordan, J. C. Partridge, and N. W. Roberts, “Non-polarizing broadband multilayer reflectors in fish,” Nature Photon.6, 759–763 (2012).
[CrossRef]

Rusinkiewicz, S.

T. Weyrich, J. Lawrence, H. Lensch, S. Rusinkiewicz, and T. Zickler, “Principles of appearance acquisition and representation,” Found. Trends Comput. Graph. Vis.4, 75–191 (2009).
[CrossRef]

Smith, A.

J. Murray-Coleman and A. Smith, “The automated measurement of BRDFs and their application to luminaire modeling,” J. Illum. Eng. Soc.19, 87–99 (1990).

Sosik, H. M.

S. Johnsen and H. M. Sosik, “Cryptic coloration and mirrored sides as camouflage strategies in near-surface pelagic habitats: Implications for foraging and predator avoidance,” Limnol. Oceanogr.48, 1277–1288 (2003).
[CrossRef]

Stavenga, D. G.

B. D. Wilts, H. L. Leertouwer, and D. G. Stavenga, “Imaging scatterometry and microspectrophotometry of lycaenid butterfly wing scales with perforated multilayers,” J. R. Soc. Interface6, S185–S192 (2009).
[CrossRef]

D. G. Stavenga, H. L. Leertouwer, P. Pirih, and M. F. Wehling, “Imaging scatterometry of butterfly wing scales,” Opt. Express17, 193–202 (2009).
[CrossRef] [PubMed]

P. Vukusic and D. G. Stavenga, “Physical methods for investigating structural colors in biological systems,” J. R. Soc. Interface6, 133–148 (2009).
[CrossRef]

Sumino, K.

Y. Mukaigawa, K. Sumino, and Y. Yagi, “Multiplexed illumination for measuring BRDF using an ellipsoidal mirror and a projector,” in Proceedings of the 8th Asian Conference on Computer Vision, Part II, Y. Yagi, S. B. Kang, I. S. Kweon, and H. Zha, eds. (Springer-Verlag, 2007), pp. 246–257.

Sweeney, A. M.

A. L. Holt, A. M. Sweeney, S. Johnsen, and D. E. Morse, “A highly distributed Bragg stack with unique geometry provides effective camouflage for Loliginid squid eyes,” J. R. Soc. Interface8, 1386–1399 (2011).
[CrossRef] [PubMed]

Tong, X.

Y. Lan, Y. Dong, J. Wang, X. Tong, and B. Guo, “Condenser-based instant reflectometry,” Comput. Graph. Forum29, 2091–2098 (2010).
[CrossRef]

Voss, K. J.

Vukusic, P.

P. Vukusic and D. G. Stavenga, “Physical methods for investigating structural colors in biological systems,” J. R. Soc. Interface6, 133–148 (2009).
[CrossRef]

Wang, J.

Y. Lan, Y. Dong, J. Wang, X. Tong, and B. Guo, “Condenser-based instant reflectometry,” Comput. Graph. Forum29, 2091–2098 (2010).
[CrossRef]

M. Ben-Ezra, J. Wang, B. Wilburn, X. Li, and L. Ma, “An LED-only BRDF measurement device,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2008), pp. 1–8.

Wehling, M. F.

Weyrich, T.

T. Weyrich, J. Lawrence, H. Lensch, S. Rusinkiewicz, and T. Zickler, “Principles of appearance acquisition and representation,” Found. Trends Comput. Graph. Vis.4, 75–191 (2009).
[CrossRef]

Wilburn, B.

M. Ben-Ezra, J. Wang, B. Wilburn, X. Li, and L. Ma, “An LED-only BRDF measurement device,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2008), pp. 1–8.

Wilts, B. D.

B. D. Wilts, H. L. Leertouwer, and D. G. Stavenga, “Imaging scatterometry and microspectrophotometry of lycaenid butterfly wing scales with perforated multilayers,” J. R. Soc. Interface6, S185–S192 (2009).
[CrossRef]

Wolfe, W. L.

F. O. Bartell, E. L. Dereniak, and W. L. Wolfe, “The theory and measurement of bidirectional reflectance distribution function (BRDF) and bidirectional transmittance distribution function (BTDF),” Proc. SPIE0257, 154–160 (1981).
[CrossRef]

Yagi, Y.

Y. Mukaigawa, K. Sumino, and Y. Yagi, “Multiplexed illumination for measuring BRDF using an ellipsoidal mirror and a projector,” in Proceedings of the 8th Asian Conference on Computer Vision, Part II, Y. Yagi, S. B. Kang, I. S. Kweon, and H. Zha, eds. (Springer-Verlag, 2007), pp. 246–257.

Yin, Y.

D. R. McKenzie, Y. Yin, and W. D. McFall, “Silvery fish skin as an example of a chaotic reflector,” Philos. T. R. Soc. S-A451, 579–584 (1995).

Zhang, H.

Zhang, Z.

M. Levoy, Z. Zhang, and I. McDowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc-Oxford235, 144–162 (2009).
[CrossRef]

Z. Zhang, “A flexible new technique for camera calibration,” IEEE T. Pattern Anal.22, 1330–1334 (2000).
[CrossRef]

Zickler, T.

T. Weyrich, J. Lawrence, H. Lensch, S. Rusinkiewicz, and T. Zickler, “Principles of appearance acquisition and representation,” Found. Trends Comput. Graph. Vis.4, 75–191 (2009).
[CrossRef]

Appl. Opt. (1)

Bull. Mus. Comp. Zool. (1)

R. C. Baird, “The systematics, distribution, and zoogeography of the marine hatchetfishes (family Sternoptychidae),” Bull. Mus. Comp. Zool.142, 1–128 (1971).

Cell Tissue Res. (1)

L. M. 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]

Comput. Graph. Forum (1)

Y. Lan, Y. Dong, J. Wang, X. Tong, and B. Guo, “Condenser-based instant reflectometry,” Comput. Graph. Forum29, 2091–2098 (2010).
[CrossRef]

Found. Trends Comput. Graph. Vis. (1)

T. Weyrich, J. Lawrence, H. Lensch, S. Rusinkiewicz, and T. Zickler, “Principles of appearance acquisition and representation,” Found. Trends Comput. Graph. Vis.4, 75–191 (2009).
[CrossRef]

IEEE T. Pattern Anal. (2)

Z. Zhang, “A flexible new technique for camera calibration,” IEEE T. Pattern Anal.22, 1330–1334 (2000).
[CrossRef]

M. Grossberg and S. Nayar, “Determining the camera response from images: What is knowable?” IEEE T. Pattern Anal.25, 1455–1467 (2003).
[CrossRef]

Integr. Comp. Biol. (1)

S. Johnsen, “Lifting the cloak of invisibility: The effects of changing optical conditions on pelagic crypsis,” Integr. Comp. Biol.43, 580–590 (2003).
[CrossRef] [PubMed]

J. Illum. Eng. Soc. (1)

J. Murray-Coleman and A. Smith, “The automated measurement of BRDFs and their application to luminaire modeling,” J. Illum. Eng. Soc.19, 87–99 (1990).

J. Microsc-Oxford (1)

M. Levoy, Z. Zhang, and I. McDowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc-Oxford235, 144–162 (2009).
[CrossRef]

J. Mollus. Stud. (1)

A. Lindgren, “Systematics and distribution of the squid genus Pterygioteuthis (Cephalopoda: Oegopsida) in the eastern tropical Pacific Ocean,” J. Mollus. Stud.76, 389–398 (2010).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Definition of the bidirectional reflectance distribution function (BRDF) parameters. Subscripts i and o represent incident and viewing (outgoing) angles respectively.

Fig. 2
Fig. 2

System layout and design schematic of optical scatterometer for measurement of angular reflectance (OSMAR). Projector light source S produces a beam at a particular angle that is collimated by lens L1. The beam is reflected by beamsplitter B onto objective lens L2 and focused to its back focal point at the location of sample M. The beam simultaneously transmitted by beamsplitter B is focused by lens L3 onto the collection aperture of power meter P. Light scattered from sample M is collected by lens L2, transmitted by beamsplitter B, and focused by lens L4 onto the pinhole aperture A. The light not blocked by pinhole aperture A is collected by lens L5 and directed with normal incidence onto the sensor of camera C. The process is repeated for all desired incident angles.

Fig. 3
Fig. 3

Example pinhole occluder images used for geometric camera calibration and viewing angle mapping estimation. (a) Original image. (b) Undistorted image.

Fig. 4
Fig. 4

The animals of interest. (a) Pterygioteuthis microlampas. (b) Sternoptyx sp. Scale bars are approximately 10 mm.

Fig. 5
Fig. 5

Directional reflectance of Pterygioteuthis microlampas mantle skin measured at λ = 532 nm. (a) Dissected mantle tissue with measurement points indicated. (b) In-illumination-plane BRDF line scans. (c) BRDF map for left lateral (blue) point. (d) BRDF map for right lateral (red) point. The BRDF maps show the BRDF for each measured point from θo = 0 to 45° and φo = 0 to 360° for the incident illumination angle indicated by the white asterisk. Each green circle represents an increment of the angle θo by 15°. The pink asterisk indicates the estimated specular point. In-illumination-plane scanlines are marked by blue and red dashed lines.

Fig. 6
Fig. 6

Directional reflectance of Sternoptyx sp. scales measured at λ = 532 nm. (a) Whole fish with measurement points indicated. (b) In-illumination-plane BRDF line scans. (c) BRDF map for head (blue) point. (d) BRDF map for tail (red) point. The BRDF maps show the BRDF for each measured point from θo = 0 to 45° and φo = 0 to 360° for the incident illumination angle indicated by the white asterisk. Each green circle represents an increment of the angle θo by 15°. The pink asterisk indicates the estimated specular point. In-illumination-plane scanlines are marked by blue and red dashed lines.

Fig. 7
Fig. 7

Microscope image of P. microlampas mantle enlarged to show detail. Scale bar is approximately 1 mm.

Equations (3)

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B R D F ( θ i , φ i , θ o , φ o ) = d L o ( θ o , φ o ) d E i ( θ i , φ i )
θ o = tan 1 ( y PC z PS )
B R D F sample = B R D F reference R sample R reference

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