Abstract

Animals use color vision for a number of tasks including food localization, object recognition, communication, and mate selection. For these and other specific behaviors involving the use of color cues, models that quantify color discriminability have been developed. These models take as input the photoreceptor spectral sensitivities of the animal and radiance spectra of the surfaces of interest. These spectra are usually acquired using spectroscopic instruments that collect point-by-point data and can easily yield signals contaminated with neighboring colors if not operated carefully. In this paper, I present an equation that relates the optical fiber diameter and numerical aperture to the measurement angle and distance needed to record uncontaminated spectra. I demonstrate its utility by testing the discriminability of two solid colors for the visual systems of a dichromatic ferret and a trichromatic frog in (1) a conspicuous scenario where the colors have little spectral overlap and (2) a perfect camouflage scenario where the spectra are identical. This equation is derived from geometrical optics and is applicable to spectroscopic measurements in all fields.

© 2013 Optical Society of America

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  1. D. Brainard, “Color vision theory,” in International Encyclopedia of the Social and Behavioral Sciences, N. Smelser and P. Baltes, eds. (Elsevier, 2001), pp. 2256–2263.
  2. M. E. Maan and M. E. Cummings, “Female preferences for aposematic signal components in a polymorphic poison frog,” Evolution 62, 2334–2345 (2008).
    [CrossRef]
  3. A. Kelber, M. Vorobyev, and D. Osorio, “Animal colour vision, behavioural tests and physiological concepts,” Biol. Rev. 78, 81–118 (2003).
    [CrossRef]
  4. M. C. Stoddard and M. Stevens, “Avian vision and the evolution of egg color mimicry in the common cuckoo,” Evolution 65, 2004–2013 (2011).
    [CrossRef]
  5. J. A. Endler and P. W. Mielke, “Comparing entire colour patterns as birds see them,” Biol. J. Linn. Soc. 86, 405–431 (2005).
    [CrossRef]
  6. G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data, and Formulae, 2nd ed. (Wiley, 2000).
  7. D. Akkaynak, T. Treibitz, B. Xiao, U. A. Gurkan, J. J. Allen, U. Demirci, and R. T. Hanlon, “Use of commercial off-the-shelf (COTS) digital cameras for scientific data acquisition and scene-specific color calibration,” J. Opt. Soc. Am. A (to be published).
  8. D. Akkaynak, J. Allen, L. Mäthger, C.-C. Chiao, and R. Hanlon, “Quantification of cuttlefish (Sepia officinalis) camouflage: a study of color and luminance using in situ spectrometry,” J. Comp. Physiol. A 199, 211–225 (2013).
    [CrossRef]
  9. R. T. Hanlon, C.-C. Chiao, L. M. Mäthger, and N. J. Marshall, “A fish-eye view of cuttlefish camouflage using in situ spectrometry,” Biol. J. Linn. Soc. 109, 535–551 (2013).
    [CrossRef]
  10. C. C. Chiao, J. K. Wickiser, J. J. Allen, B. Genter, and R. T. Hanlon, “Hyperspectral imaging of cuttlefish camouflage indicates good color match in the eyes of fish predators,” Proc. Natl. Acad. Sci. USA 108, 9148–9153 (2011).
    [CrossRef]
  11. L. A. Isaac and P. T. Gregory, “Can snakes hide in plain view? Chromatic and achromatic crypsis of two colour forms of the Western terrestrial garter snake (Thamnophis elegans),” Biol. J. Linn. Soc. 108, 756–772 (2013).
  12. S. D. Finkbeiner, A. D. Briscoe, and R. D. Reed, “The benefit of being a social butterfly: communal roosting deters predation,” Proc. R. Soc. B 279, 2769–2776 (2012).
    [CrossRef]
  13. O. Lind, M. Mitkus, P. Olsson, and A. Kelber, “Ultraviolet sensitivity and colour vision in raptor foraging,” J. Exp. Biol. 216, 1819–1826 (2013).
    [CrossRef]
  14. M. E. Maan and M. E. Cummings, “Poison frog colors are honest signals of toxicity, particularly for bird predators,” Am. Nat. 179, E1–E14 (2012).
    [CrossRef]
  15. S. M. Bybee, F. Yuan, M. D. Ramstetter, J. Llorente-Bousquets, R. D. Reed, D. Osorio, and A. D. Briscoe, “UV photoreceptors and UV-yellow wing pigments in Heliconius butterflies allow a color signal to serve both mimicry and intraspecific communication,” Am. Nat. 179, 38–51 (2012).
    [CrossRef]
  16. F. Cortesi and K. Cheney, “Conspicuousness is correlated with toxicity in marine opisthobranchs,” J. Evol. Biol. 23, 1509–1518 (2010).
    [CrossRef]
  17. N. Langmore, M. Stevens, G. Maurer, and R. Kilner, “Are dark cuckoo eggs cryptic in host nests?” Anim. Behav. 78, 461–468 (2009).
    [CrossRef]
  18. J. Baldwin and S. n. Johnsen, “The male blue crab, Callinectes sapidus, uses both chromatic and achromatic cues during mate choice,” J. Exp. Biol. 215, 1184–1191 (2012).
    [CrossRef]
  19. O. Nokelainen, R. H. Hegna, J. H. Reudler, C. Lindstedt, and J. Mappes, “Trade-off between warning signal efficacy and mating success in the wood tiger moth,” Proc. R. Soc. B 279, 257–265 (2012).
    [CrossRef]
  20. A. Siddiqi, T. W. Cronin, E. R. Loew, M. Vorobyev, and K. Summers, “Interspecific and intraspecific views of color signals in the strawberry poison frog Dendrobates pumilio,” J. Exp. Biol. 207, 2471–2485 (2004).
    [CrossRef]
  21. M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, Volume II: Design, Fabrication and Testing, Sources and Detectors, Radiometry and Photometry (McGraw-Hill, 2009).
  22. M. D. Fairchild and G. M. Johnson, “METACOW: a public-domain, high-resolution, fully-digital, noise-free, metameric, extended-dynamic-range, spectral test target for imaging system analysis and simulation,” in Color and Imaging Conference (Society for Imaging Science and Technology, 2004), pp. 239–245.
  23. R. H. Yuhas, A. F. H. Goetz, and J. W. Boardman, “Discrimination among semiarid landscape endmembers using the spectral angle mapper (SAM) algorithm,” in Summaries of the Third Annual JPL Airborne Geoscience Workshop, Pasadena, California (1992), Vol. l, pp 147–149.
  24. M. Vorobyev and D. Osorio, “Receptor noise as a determinant of colour thresholds,” Proc. R. Soc. B 265, 351–358 (1998).
    [CrossRef]

2013

D. Akkaynak, J. Allen, L. Mäthger, C.-C. Chiao, and R. Hanlon, “Quantification of cuttlefish (Sepia officinalis) camouflage: a study of color and luminance using in situ spectrometry,” J. Comp. Physiol. A 199, 211–225 (2013).
[CrossRef]

R. T. Hanlon, C.-C. Chiao, L. M. Mäthger, and N. J. Marshall, “A fish-eye view of cuttlefish camouflage using in situ spectrometry,” Biol. J. Linn. Soc. 109, 535–551 (2013).
[CrossRef]

L. A. Isaac and P. T. Gregory, “Can snakes hide in plain view? Chromatic and achromatic crypsis of two colour forms of the Western terrestrial garter snake (Thamnophis elegans),” Biol. J. Linn. Soc. 108, 756–772 (2013).

O. Lind, M. Mitkus, P. Olsson, and A. Kelber, “Ultraviolet sensitivity and colour vision in raptor foraging,” J. Exp. Biol. 216, 1819–1826 (2013).
[CrossRef]

2012

M. E. Maan and M. E. Cummings, “Poison frog colors are honest signals of toxicity, particularly for bird predators,” Am. Nat. 179, E1–E14 (2012).
[CrossRef]

S. M. Bybee, F. Yuan, M. D. Ramstetter, J. Llorente-Bousquets, R. D. Reed, D. Osorio, and A. D. Briscoe, “UV photoreceptors and UV-yellow wing pigments in Heliconius butterflies allow a color signal to serve both mimicry and intraspecific communication,” Am. Nat. 179, 38–51 (2012).
[CrossRef]

J. Baldwin and S. n. Johnsen, “The male blue crab, Callinectes sapidus, uses both chromatic and achromatic cues during mate choice,” J. Exp. Biol. 215, 1184–1191 (2012).
[CrossRef]

O. Nokelainen, R. H. Hegna, J. H. Reudler, C. Lindstedt, and J. Mappes, “Trade-off between warning signal efficacy and mating success in the wood tiger moth,” Proc. R. Soc. B 279, 257–265 (2012).
[CrossRef]

S. D. Finkbeiner, A. D. Briscoe, and R. D. Reed, “The benefit of being a social butterfly: communal roosting deters predation,” Proc. R. Soc. B 279, 2769–2776 (2012).
[CrossRef]

2011

C. C. Chiao, J. K. Wickiser, J. J. Allen, B. Genter, and R. T. Hanlon, “Hyperspectral imaging of cuttlefish camouflage indicates good color match in the eyes of fish predators,” Proc. Natl. Acad. Sci. USA 108, 9148–9153 (2011).
[CrossRef]

M. C. Stoddard and M. Stevens, “Avian vision and the evolution of egg color mimicry in the common cuckoo,” Evolution 65, 2004–2013 (2011).
[CrossRef]

2010

F. Cortesi and K. Cheney, “Conspicuousness is correlated with toxicity in marine opisthobranchs,” J. Evol. Biol. 23, 1509–1518 (2010).
[CrossRef]

2009

N. Langmore, M. Stevens, G. Maurer, and R. Kilner, “Are dark cuckoo eggs cryptic in host nests?” Anim. Behav. 78, 461–468 (2009).
[CrossRef]

2008

M. E. Maan and M. E. Cummings, “Female preferences for aposematic signal components in a polymorphic poison frog,” Evolution 62, 2334–2345 (2008).
[CrossRef]

2005

J. A. Endler and P. W. Mielke, “Comparing entire colour patterns as birds see them,” Biol. J. Linn. Soc. 86, 405–431 (2005).
[CrossRef]

2004

A. Siddiqi, T. W. Cronin, E. R. Loew, M. Vorobyev, and K. Summers, “Interspecific and intraspecific views of color signals in the strawberry poison frog Dendrobates pumilio,” J. Exp. Biol. 207, 2471–2485 (2004).
[CrossRef]

2003

A. Kelber, M. Vorobyev, and D. Osorio, “Animal colour vision, behavioural tests and physiological concepts,” Biol. Rev. 78, 81–118 (2003).
[CrossRef]

1998

M. Vorobyev and D. Osorio, “Receptor noise as a determinant of colour thresholds,” Proc. R. Soc. B 265, 351–358 (1998).
[CrossRef]

Akkaynak, D.

D. Akkaynak, J. Allen, L. Mäthger, C.-C. Chiao, and R. Hanlon, “Quantification of cuttlefish (Sepia officinalis) camouflage: a study of color and luminance using in situ spectrometry,” J. Comp. Physiol. A 199, 211–225 (2013).
[CrossRef]

D. Akkaynak, T. Treibitz, B. Xiao, U. A. Gurkan, J. J. Allen, U. Demirci, and R. T. Hanlon, “Use of commercial off-the-shelf (COTS) digital cameras for scientific data acquisition and scene-specific color calibration,” J. Opt. Soc. Am. A (to be published).

Allen, J.

D. Akkaynak, J. Allen, L. Mäthger, C.-C. Chiao, and R. Hanlon, “Quantification of cuttlefish (Sepia officinalis) camouflage: a study of color and luminance using in situ spectrometry,” J. Comp. Physiol. A 199, 211–225 (2013).
[CrossRef]

Allen, J. J.

C. C. Chiao, J. K. Wickiser, J. J. Allen, B. Genter, and R. T. Hanlon, “Hyperspectral imaging of cuttlefish camouflage indicates good color match in the eyes of fish predators,” Proc. Natl. Acad. Sci. USA 108, 9148–9153 (2011).
[CrossRef]

D. Akkaynak, T. Treibitz, B. Xiao, U. A. Gurkan, J. J. Allen, U. Demirci, and R. T. Hanlon, “Use of commercial off-the-shelf (COTS) digital cameras for scientific data acquisition and scene-specific color calibration,” J. Opt. Soc. Am. A (to be published).

Baldwin, J.

J. Baldwin and S. n. Johnsen, “The male blue crab, Callinectes sapidus, uses both chromatic and achromatic cues during mate choice,” J. Exp. Biol. 215, 1184–1191 (2012).
[CrossRef]

Bass, M.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, Volume II: Design, Fabrication and Testing, Sources and Detectors, Radiometry and Photometry (McGraw-Hill, 2009).

Boardman, J. W.

R. H. Yuhas, A. F. H. Goetz, and J. W. Boardman, “Discrimination among semiarid landscape endmembers using the spectral angle mapper (SAM) algorithm,” in Summaries of the Third Annual JPL Airborne Geoscience Workshop, Pasadena, California (1992), Vol. l, pp 147–149.

Brainard, D.

D. Brainard, “Color vision theory,” in International Encyclopedia of the Social and Behavioral Sciences, N. Smelser and P. Baltes, eds. (Elsevier, 2001), pp. 2256–2263.

Briscoe, A. D.

S. M. Bybee, F. Yuan, M. D. Ramstetter, J. Llorente-Bousquets, R. D. Reed, D. Osorio, and A. D. Briscoe, “UV photoreceptors and UV-yellow wing pigments in Heliconius butterflies allow a color signal to serve both mimicry and intraspecific communication,” Am. Nat. 179, 38–51 (2012).
[CrossRef]

S. D. Finkbeiner, A. D. Briscoe, and R. D. Reed, “The benefit of being a social butterfly: communal roosting deters predation,” Proc. R. Soc. B 279, 2769–2776 (2012).
[CrossRef]

Bybee, S. M.

S. M. Bybee, F. Yuan, M. D. Ramstetter, J. Llorente-Bousquets, R. D. Reed, D. Osorio, and A. D. Briscoe, “UV photoreceptors and UV-yellow wing pigments in Heliconius butterflies allow a color signal to serve both mimicry and intraspecific communication,” Am. Nat. 179, 38–51 (2012).
[CrossRef]

Cheney, K.

F. Cortesi and K. Cheney, “Conspicuousness is correlated with toxicity in marine opisthobranchs,” J. Evol. Biol. 23, 1509–1518 (2010).
[CrossRef]

Chiao, C. C.

C. C. Chiao, J. K. Wickiser, J. J. Allen, B. Genter, and R. T. Hanlon, “Hyperspectral imaging of cuttlefish camouflage indicates good color match in the eyes of fish predators,” Proc. Natl. Acad. Sci. USA 108, 9148–9153 (2011).
[CrossRef]

Chiao, C.-C.

D. Akkaynak, J. Allen, L. Mäthger, C.-C. Chiao, and R. Hanlon, “Quantification of cuttlefish (Sepia officinalis) camouflage: a study of color and luminance using in situ spectrometry,” J. Comp. Physiol. A 199, 211–225 (2013).
[CrossRef]

R. T. Hanlon, C.-C. Chiao, L. M. Mäthger, and N. J. Marshall, “A fish-eye view of cuttlefish camouflage using in situ spectrometry,” Biol. J. Linn. Soc. 109, 535–551 (2013).
[CrossRef]

Cortesi, F.

F. Cortesi and K. Cheney, “Conspicuousness is correlated with toxicity in marine opisthobranchs,” J. Evol. Biol. 23, 1509–1518 (2010).
[CrossRef]

Cronin, T. W.

A. Siddiqi, T. W. Cronin, E. R. Loew, M. Vorobyev, and K. Summers, “Interspecific and intraspecific views of color signals in the strawberry poison frog Dendrobates pumilio,” J. Exp. Biol. 207, 2471–2485 (2004).
[CrossRef]

Cummings, M. E.

M. E. Maan and M. E. Cummings, “Poison frog colors are honest signals of toxicity, particularly for bird predators,” Am. Nat. 179, E1–E14 (2012).
[CrossRef]

M. E. Maan and M. E. Cummings, “Female preferences for aposematic signal components in a polymorphic poison frog,” Evolution 62, 2334–2345 (2008).
[CrossRef]

DeCusatis, C.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, Volume II: Design, Fabrication and Testing, Sources and Detectors, Radiometry and Photometry (McGraw-Hill, 2009).

Demirci, U.

D. Akkaynak, T. Treibitz, B. Xiao, U. A. Gurkan, J. J. Allen, U. Demirci, and R. T. Hanlon, “Use of commercial off-the-shelf (COTS) digital cameras for scientific data acquisition and scene-specific color calibration,” J. Opt. Soc. Am. A (to be published).

Endler, J. A.

J. A. Endler and P. W. Mielke, “Comparing entire colour patterns as birds see them,” Biol. J. Linn. Soc. 86, 405–431 (2005).
[CrossRef]

Enoch, J.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, Volume II: Design, Fabrication and Testing, Sources and Detectors, Radiometry and Photometry (McGraw-Hill, 2009).

Fairchild, M. D.

M. D. Fairchild and G. M. Johnson, “METACOW: a public-domain, high-resolution, fully-digital, noise-free, metameric, extended-dynamic-range, spectral test target for imaging system analysis and simulation,” in Color and Imaging Conference (Society for Imaging Science and Technology, 2004), pp. 239–245.

Finkbeiner, S. D.

S. D. Finkbeiner, A. D. Briscoe, and R. D. Reed, “The benefit of being a social butterfly: communal roosting deters predation,” Proc. R. Soc. B 279, 2769–2776 (2012).
[CrossRef]

Genter, B.

C. C. Chiao, J. K. Wickiser, J. J. Allen, B. Genter, and R. T. Hanlon, “Hyperspectral imaging of cuttlefish camouflage indicates good color match in the eyes of fish predators,” Proc. Natl. Acad. Sci. USA 108, 9148–9153 (2011).
[CrossRef]

Goetz, A. F. H.

R. H. Yuhas, A. F. H. Goetz, and J. W. Boardman, “Discrimination among semiarid landscape endmembers using the spectral angle mapper (SAM) algorithm,” in Summaries of the Third Annual JPL Airborne Geoscience Workshop, Pasadena, California (1992), Vol. l, pp 147–149.

Gregory, P. T.

L. A. Isaac and P. T. Gregory, “Can snakes hide in plain view? Chromatic and achromatic crypsis of two colour forms of the Western terrestrial garter snake (Thamnophis elegans),” Biol. J. Linn. Soc. 108, 756–772 (2013).

Gurkan, U. A.

D. Akkaynak, T. Treibitz, B. Xiao, U. A. Gurkan, J. J. Allen, U. Demirci, and R. T. Hanlon, “Use of commercial off-the-shelf (COTS) digital cameras for scientific data acquisition and scene-specific color calibration,” J. Opt. Soc. Am. A (to be published).

Hanlon, R.

D. Akkaynak, J. Allen, L. Mäthger, C.-C. Chiao, and R. Hanlon, “Quantification of cuttlefish (Sepia officinalis) camouflage: a study of color and luminance using in situ spectrometry,” J. Comp. Physiol. A 199, 211–225 (2013).
[CrossRef]

Hanlon, R. T.

R. T. Hanlon, C.-C. Chiao, L. M. Mäthger, and N. J. Marshall, “A fish-eye view of cuttlefish camouflage using in situ spectrometry,” Biol. J. Linn. Soc. 109, 535–551 (2013).
[CrossRef]

C. C. Chiao, J. K. Wickiser, J. J. Allen, B. Genter, and R. T. Hanlon, “Hyperspectral imaging of cuttlefish camouflage indicates good color match in the eyes of fish predators,” Proc. Natl. Acad. Sci. USA 108, 9148–9153 (2011).
[CrossRef]

D. Akkaynak, T. Treibitz, B. Xiao, U. A. Gurkan, J. J. Allen, U. Demirci, and R. T. Hanlon, “Use of commercial off-the-shelf (COTS) digital cameras for scientific data acquisition and scene-specific color calibration,” J. Opt. Soc. Am. A (to be published).

Hegna, R. H.

O. Nokelainen, R. H. Hegna, J. H. Reudler, C. Lindstedt, and J. Mappes, “Trade-off between warning signal efficacy and mating success in the wood tiger moth,” Proc. R. Soc. B 279, 257–265 (2012).
[CrossRef]

Isaac, L. A.

L. A. Isaac and P. T. Gregory, “Can snakes hide in plain view? Chromatic and achromatic crypsis of two colour forms of the Western terrestrial garter snake (Thamnophis elegans),” Biol. J. Linn. Soc. 108, 756–772 (2013).

Johnsen, S. n.

J. Baldwin and S. n. Johnsen, “The male blue crab, Callinectes sapidus, uses both chromatic and achromatic cues during mate choice,” J. Exp. Biol. 215, 1184–1191 (2012).
[CrossRef]

Johnson, G. M.

M. D. Fairchild and G. M. Johnson, “METACOW: a public-domain, high-resolution, fully-digital, noise-free, metameric, extended-dynamic-range, spectral test target for imaging system analysis and simulation,” in Color and Imaging Conference (Society for Imaging Science and Technology, 2004), pp. 239–245.

Kelber, A.

O. Lind, M. Mitkus, P. Olsson, and A. Kelber, “Ultraviolet sensitivity and colour vision in raptor foraging,” J. Exp. Biol. 216, 1819–1826 (2013).
[CrossRef]

A. Kelber, M. Vorobyev, and D. Osorio, “Animal colour vision, behavioural tests and physiological concepts,” Biol. Rev. 78, 81–118 (2003).
[CrossRef]

Kilner, R.

N. Langmore, M. Stevens, G. Maurer, and R. Kilner, “Are dark cuckoo eggs cryptic in host nests?” Anim. Behav. 78, 461–468 (2009).
[CrossRef]

Lakshminarayanan, V.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, Volume II: Design, Fabrication and Testing, Sources and Detectors, Radiometry and Photometry (McGraw-Hill, 2009).

Langmore, N.

N. Langmore, M. Stevens, G. Maurer, and R. Kilner, “Are dark cuckoo eggs cryptic in host nests?” Anim. Behav. 78, 461–468 (2009).
[CrossRef]

Li, G.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, Volume II: Design, Fabrication and Testing, Sources and Detectors, Radiometry and Photometry (McGraw-Hill, 2009).

Lind, O.

O. Lind, M. Mitkus, P. Olsson, and A. Kelber, “Ultraviolet sensitivity and colour vision in raptor foraging,” J. Exp. Biol. 216, 1819–1826 (2013).
[CrossRef]

Lindstedt, C.

O. Nokelainen, R. H. Hegna, J. H. Reudler, C. Lindstedt, and J. Mappes, “Trade-off between warning signal efficacy and mating success in the wood tiger moth,” Proc. R. Soc. B 279, 257–265 (2012).
[CrossRef]

Llorente-Bousquets, J.

S. M. Bybee, F. Yuan, M. D. Ramstetter, J. Llorente-Bousquets, R. D. Reed, D. Osorio, and A. D. Briscoe, “UV photoreceptors and UV-yellow wing pigments in Heliconius butterflies allow a color signal to serve both mimicry and intraspecific communication,” Am. Nat. 179, 38–51 (2012).
[CrossRef]

Loew, E. R.

A. Siddiqi, T. W. Cronin, E. R. Loew, M. Vorobyev, and K. Summers, “Interspecific and intraspecific views of color signals in the strawberry poison frog Dendrobates pumilio,” J. Exp. Biol. 207, 2471–2485 (2004).
[CrossRef]

Maan, M. E.

M. E. Maan and M. E. Cummings, “Poison frog colors are honest signals of toxicity, particularly for bird predators,” Am. Nat. 179, E1–E14 (2012).
[CrossRef]

M. E. Maan and M. E. Cummings, “Female preferences for aposematic signal components in a polymorphic poison frog,” Evolution 62, 2334–2345 (2008).
[CrossRef]

Macdonald, C.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, Volume II: Design, Fabrication and Testing, Sources and Detectors, Radiometry and Photometry (McGraw-Hill, 2009).

Mahajan, V.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, Volume II: Design, Fabrication and Testing, Sources and Detectors, Radiometry and Photometry (McGraw-Hill, 2009).

Mappes, J.

O. Nokelainen, R. H. Hegna, J. H. Reudler, C. Lindstedt, and J. Mappes, “Trade-off between warning signal efficacy and mating success in the wood tiger moth,” Proc. R. Soc. B 279, 257–265 (2012).
[CrossRef]

Marshall, N. J.

R. T. Hanlon, C.-C. Chiao, L. M. Mäthger, and N. J. Marshall, “A fish-eye view of cuttlefish camouflage using in situ spectrometry,” Biol. J. Linn. Soc. 109, 535–551 (2013).
[CrossRef]

Mäthger, L.

D. Akkaynak, J. Allen, L. Mäthger, C.-C. Chiao, and R. Hanlon, “Quantification of cuttlefish (Sepia officinalis) camouflage: a study of color and luminance using in situ spectrometry,” J. Comp. Physiol. A 199, 211–225 (2013).
[CrossRef]

Mäthger, L. M.

R. T. Hanlon, C.-C. Chiao, L. M. Mäthger, and N. J. Marshall, “A fish-eye view of cuttlefish camouflage using in situ spectrometry,” Biol. J. Linn. Soc. 109, 535–551 (2013).
[CrossRef]

Maurer, G.

N. Langmore, M. Stevens, G. Maurer, and R. Kilner, “Are dark cuckoo eggs cryptic in host nests?” Anim. Behav. 78, 461–468 (2009).
[CrossRef]

Mielke, P. W.

J. A. Endler and P. W. Mielke, “Comparing entire colour patterns as birds see them,” Biol. J. Linn. Soc. 86, 405–431 (2005).
[CrossRef]

Mitkus, M.

O. Lind, M. Mitkus, P. Olsson, and A. Kelber, “Ultraviolet sensitivity and colour vision in raptor foraging,” J. Exp. Biol. 216, 1819–1826 (2013).
[CrossRef]

Nokelainen, O.

O. Nokelainen, R. H. Hegna, J. H. Reudler, C. Lindstedt, and J. Mappes, “Trade-off between warning signal efficacy and mating success in the wood tiger moth,” Proc. R. Soc. B 279, 257–265 (2012).
[CrossRef]

Olsson, P.

O. Lind, M. Mitkus, P. Olsson, and A. Kelber, “Ultraviolet sensitivity and colour vision in raptor foraging,” J. Exp. Biol. 216, 1819–1826 (2013).
[CrossRef]

Osorio, D.

S. M. Bybee, F. Yuan, M. D. Ramstetter, J. Llorente-Bousquets, R. D. Reed, D. Osorio, and A. D. Briscoe, “UV photoreceptors and UV-yellow wing pigments in Heliconius butterflies allow a color signal to serve both mimicry and intraspecific communication,” Am. Nat. 179, 38–51 (2012).
[CrossRef]

A. Kelber, M. Vorobyev, and D. Osorio, “Animal colour vision, behavioural tests and physiological concepts,” Biol. Rev. 78, 81–118 (2003).
[CrossRef]

M. Vorobyev and D. Osorio, “Receptor noise as a determinant of colour thresholds,” Proc. R. Soc. B 265, 351–358 (1998).
[CrossRef]

Ramstetter, M. D.

S. M. Bybee, F. Yuan, M. D. Ramstetter, J. Llorente-Bousquets, R. D. Reed, D. Osorio, and A. D. Briscoe, “UV photoreceptors and UV-yellow wing pigments in Heliconius butterflies allow a color signal to serve both mimicry and intraspecific communication,” Am. Nat. 179, 38–51 (2012).
[CrossRef]

Reed, R. D.

S. M. Bybee, F. Yuan, M. D. Ramstetter, J. Llorente-Bousquets, R. D. Reed, D. Osorio, and A. D. Briscoe, “UV photoreceptors and UV-yellow wing pigments in Heliconius butterflies allow a color signal to serve both mimicry and intraspecific communication,” Am. Nat. 179, 38–51 (2012).
[CrossRef]

S. D. Finkbeiner, A. D. Briscoe, and R. D. Reed, “The benefit of being a social butterfly: communal roosting deters predation,” Proc. R. Soc. B 279, 2769–2776 (2012).
[CrossRef]

Reudler, J. H.

O. Nokelainen, R. H. Hegna, J. H. Reudler, C. Lindstedt, and J. Mappes, “Trade-off between warning signal efficacy and mating success in the wood tiger moth,” Proc. R. Soc. B 279, 257–265 (2012).
[CrossRef]

Siddiqi, A.

A. Siddiqi, T. W. Cronin, E. R. Loew, M. Vorobyev, and K. Summers, “Interspecific and intraspecific views of color signals in the strawberry poison frog Dendrobates pumilio,” J. Exp. Biol. 207, 2471–2485 (2004).
[CrossRef]

Stevens, M.

M. C. Stoddard and M. Stevens, “Avian vision and the evolution of egg color mimicry in the common cuckoo,” Evolution 65, 2004–2013 (2011).
[CrossRef]

N. Langmore, M. Stevens, G. Maurer, and R. Kilner, “Are dark cuckoo eggs cryptic in host nests?” Anim. Behav. 78, 461–468 (2009).
[CrossRef]

Stiles, W. S.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data, and Formulae, 2nd ed. (Wiley, 2000).

Stoddard, M. C.

M. C. Stoddard and M. Stevens, “Avian vision and the evolution of egg color mimicry in the common cuckoo,” Evolution 65, 2004–2013 (2011).
[CrossRef]

Summers, K.

A. Siddiqi, T. W. Cronin, E. R. Loew, M. Vorobyev, and K. Summers, “Interspecific and intraspecific views of color signals in the strawberry poison frog Dendrobates pumilio,” J. Exp. Biol. 207, 2471–2485 (2004).
[CrossRef]

Treibitz, T.

D. Akkaynak, T. Treibitz, B. Xiao, U. A. Gurkan, J. J. Allen, U. Demirci, and R. T. Hanlon, “Use of commercial off-the-shelf (COTS) digital cameras for scientific data acquisition and scene-specific color calibration,” J. Opt. Soc. Am. A (to be published).

Van Stryland, E.

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, Volume II: Design, Fabrication and Testing, Sources and Detectors, Radiometry and Photometry (McGraw-Hill, 2009).

Vorobyev, M.

A. Siddiqi, T. W. Cronin, E. R. Loew, M. Vorobyev, and K. Summers, “Interspecific and intraspecific views of color signals in the strawberry poison frog Dendrobates pumilio,” J. Exp. Biol. 207, 2471–2485 (2004).
[CrossRef]

A. Kelber, M. Vorobyev, and D. Osorio, “Animal colour vision, behavioural tests and physiological concepts,” Biol. Rev. 78, 81–118 (2003).
[CrossRef]

M. Vorobyev and D. Osorio, “Receptor noise as a determinant of colour thresholds,” Proc. R. Soc. B 265, 351–358 (1998).
[CrossRef]

Wickiser, J. K.

C. C. Chiao, J. K. Wickiser, J. J. Allen, B. Genter, and R. T. Hanlon, “Hyperspectral imaging of cuttlefish camouflage indicates good color match in the eyes of fish predators,” Proc. Natl. Acad. Sci. USA 108, 9148–9153 (2011).
[CrossRef]

Wyszecki, G.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data, and Formulae, 2nd ed. (Wiley, 2000).

Xiao, B.

D. Akkaynak, T. Treibitz, B. Xiao, U. A. Gurkan, J. J. Allen, U. Demirci, and R. T. Hanlon, “Use of commercial off-the-shelf (COTS) digital cameras for scientific data acquisition and scene-specific color calibration,” J. Opt. Soc. Am. A (to be published).

Yuan, F.

S. M. Bybee, F. Yuan, M. D. Ramstetter, J. Llorente-Bousquets, R. D. Reed, D. Osorio, and A. D. Briscoe, “UV photoreceptors and UV-yellow wing pigments in Heliconius butterflies allow a color signal to serve both mimicry and intraspecific communication,” Am. Nat. 179, 38–51 (2012).
[CrossRef]

Yuhas, R. H.

R. H. Yuhas, A. F. H. Goetz, and J. W. Boardman, “Discrimination among semiarid landscape endmembers using the spectral angle mapper (SAM) algorithm,” in Summaries of the Third Annual JPL Airborne Geoscience Workshop, Pasadena, California (1992), Vol. l, pp 147–149.

Am. Nat.

M. E. Maan and M. E. Cummings, “Poison frog colors are honest signals of toxicity, particularly for bird predators,” Am. Nat. 179, E1–E14 (2012).
[CrossRef]

S. M. Bybee, F. Yuan, M. D. Ramstetter, J. Llorente-Bousquets, R. D. Reed, D. Osorio, and A. D. Briscoe, “UV photoreceptors and UV-yellow wing pigments in Heliconius butterflies allow a color signal to serve both mimicry and intraspecific communication,” Am. Nat. 179, 38–51 (2012).
[CrossRef]

Anim. Behav.

N. Langmore, M. Stevens, G. Maurer, and R. Kilner, “Are dark cuckoo eggs cryptic in host nests?” Anim. Behav. 78, 461–468 (2009).
[CrossRef]

Biol. J. Linn. Soc.

L. A. Isaac and P. T. Gregory, “Can snakes hide in plain view? Chromatic and achromatic crypsis of two colour forms of the Western terrestrial garter snake (Thamnophis elegans),” Biol. J. Linn. Soc. 108, 756–772 (2013).

J. A. Endler and P. W. Mielke, “Comparing entire colour patterns as birds see them,” Biol. J. Linn. Soc. 86, 405–431 (2005).
[CrossRef]

R. T. Hanlon, C.-C. Chiao, L. M. Mäthger, and N. J. Marshall, “A fish-eye view of cuttlefish camouflage using in situ spectrometry,” Biol. J. Linn. Soc. 109, 535–551 (2013).
[CrossRef]

Biol. Rev.

A. Kelber, M. Vorobyev, and D. Osorio, “Animal colour vision, behavioural tests and physiological concepts,” Biol. Rev. 78, 81–118 (2003).
[CrossRef]

Evolution

M. C. Stoddard and M. Stevens, “Avian vision and the evolution of egg color mimicry in the common cuckoo,” Evolution 65, 2004–2013 (2011).
[CrossRef]

M. E. Maan and M. E. Cummings, “Female preferences for aposematic signal components in a polymorphic poison frog,” Evolution 62, 2334–2345 (2008).
[CrossRef]

J. Comp. Physiol. A

D. Akkaynak, J. Allen, L. Mäthger, C.-C. Chiao, and R. Hanlon, “Quantification of cuttlefish (Sepia officinalis) camouflage: a study of color and luminance using in situ spectrometry,” J. Comp. Physiol. A 199, 211–225 (2013).
[CrossRef]

J. Evol. Biol.

F. Cortesi and K. Cheney, “Conspicuousness is correlated with toxicity in marine opisthobranchs,” J. Evol. Biol. 23, 1509–1518 (2010).
[CrossRef]

J. Exp. Biol.

J. Baldwin and S. n. Johnsen, “The male blue crab, Callinectes sapidus, uses both chromatic and achromatic cues during mate choice,” J. Exp. Biol. 215, 1184–1191 (2012).
[CrossRef]

O. Lind, M. Mitkus, P. Olsson, and A. Kelber, “Ultraviolet sensitivity and colour vision in raptor foraging,” J. Exp. Biol. 216, 1819–1826 (2013).
[CrossRef]

A. Siddiqi, T. W. Cronin, E. R. Loew, M. Vorobyev, and K. Summers, “Interspecific and intraspecific views of color signals in the strawberry poison frog Dendrobates pumilio,” J. Exp. Biol. 207, 2471–2485 (2004).
[CrossRef]

Proc. Natl. Acad. Sci. USA

C. C. Chiao, J. K. Wickiser, J. J. Allen, B. Genter, and R. T. Hanlon, “Hyperspectral imaging of cuttlefish camouflage indicates good color match in the eyes of fish predators,” Proc. Natl. Acad. Sci. USA 108, 9148–9153 (2011).
[CrossRef]

Proc. R. Soc. B

S. D. Finkbeiner, A. D. Briscoe, and R. D. Reed, “The benefit of being a social butterfly: communal roosting deters predation,” Proc. R. Soc. B 279, 2769–2776 (2012).
[CrossRef]

O. Nokelainen, R. H. Hegna, J. H. Reudler, C. Lindstedt, and J. Mappes, “Trade-off between warning signal efficacy and mating success in the wood tiger moth,” Proc. R. Soc. B 279, 257–265 (2012).
[CrossRef]

M. Vorobyev and D. Osorio, “Receptor noise as a determinant of colour thresholds,” Proc. R. Soc. B 265, 351–358 (1998).
[CrossRef]

Other

M. Bass, C. DeCusatis, J. Enoch, V. Lakshminarayanan, G. Li, C. Macdonald, V. Mahajan, and E. Van Stryland, Handbook of Optics, Volume II: Design, Fabrication and Testing, Sources and Detectors, Radiometry and Photometry (McGraw-Hill, 2009).

M. D. Fairchild and G. M. Johnson, “METACOW: a public-domain, high-resolution, fully-digital, noise-free, metameric, extended-dynamic-range, spectral test target for imaging system analysis and simulation,” in Color and Imaging Conference (Society for Imaging Science and Technology, 2004), pp. 239–245.

R. H. Yuhas, A. F. H. Goetz, and J. W. Boardman, “Discrimination among semiarid landscape endmembers using the spectral angle mapper (SAM) algorithm,” in Summaries of the Third Annual JPL Airborne Geoscience Workshop, Pasadena, California (1992), Vol. l, pp 147–149.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data, and Formulae, 2nd ed. (Wiley, 2000).

D. Akkaynak, T. Treibitz, B. Xiao, U. A. Gurkan, J. J. Allen, U. Demirci, and R. T. Hanlon, “Use of commercial off-the-shelf (COTS) digital cameras for scientific data acquisition and scene-specific color calibration,” J. Opt. Soc. Am. A (to be published).

D. Brainard, “Color vision theory,” in International Encyclopedia of the Social and Behavioral Sciences, N. Smelser and P. Baltes, eds. (Elsevier, 2001), pp. 2256–2263.

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Figures (5)

Fig. 1.
Fig. 1.

(a) Scuba diver extending the optical fiber attached to a spectrometer (in water and pressure proof housing) to record the spectrum of light reflected from the skin of a cuttlefish, in Urla, Turkey. Getting the optical fiber close enough to take accurate measurements from freely behaving animals in the wild is challenging. Image reproduced here with kind permission from Springer Science+Business Media: Journal of Comparative Physiology A, Quantification of cuttlefish (Sepia officinalis) camouflage: a study of color and luminance using in situ spectrometry, 199, 2013, 211–225, Fig. 1, photo credit: D. Akkaynak. (b) Spectral measurements of a specimen can be recorded in a laboratory by getting the fiber as close as possible to the specimen without touching it. Photo courtesy of M. C. Stoddard and K. Zyskowski, taken at the Ornithology Collections of the Peabody Museum of Natural History, Yale University, New Haven, Connecticut.

Fig. 2.
Fig. 2.

Field of view of an optical fiber.

Fig. 3.
Fig. 3.

Test stimuli used for assessment of color discrimination for a conspicuous animal (case 1), and a camouflaged animal (case 2). (a) The synthetic hyperspectral test target has the same layout as the Macbeth ColorChecker shown here. Patches A and B are those selected to be highly contrasting with each other for case (1). For case (2), the reflectance of patch A is copied to the location of patch B, creating two patches with identical spectra next to each other separated by a black border. (b) Reflectance spectra of patches A and B.

Fig. 4.
Fig. 4.

(a) When the optical fiber (NA=0.22) is held at 90° to the surface being measured, the cross section of the cone of acceptance is a disk. As the measurement distance increases, the radius of the disk also increases. For a measurement at 45°, the cross section is an ellipse. The concentric curves show cross sections at distances 0–20 cm, in ten equal steps. (b) Mathematical similarity of patches A (black lines) and B (gray lines) to their uncontaminated versions. Note that SAM only measures the similarity of the shape of the two spectra disregarding magnitude. Results for different fiber diameters were similar, and so only those for 100 μm are shown here.

Fig. 5.
Fig. 5.

(a) Cross section of the cone of acceptance when the fiber is held at an angle perpendicular to the surface, at measurement distances 5, 10, 15, and 20 cm (the dimension of each square is 4.1 cm). The signals measured from patches A and B are expected to remain pure up to d=10cm. (b) In the conspicuous case, patches A and B have little spectral overlap, and that translates to a high color contrast (ΔS) value for both the frog and the ferret. Beyond d=10cm, the color contrast decreases (the signals become more similar) with both distance and measurement angle. (c) In the camouflaged case, the spectrum of patch A is copied to the location of patch B. The color contrast is zero until d=10cm and after that, the spectra quickly get contaminated. The signals measured at α=90° remain slightly more pure than at α=45°. The dashed line indicates the JND threshold of 1.

Tables (1)

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Table 1. Recent Publications That Assess the Discriminability of Colors Based on Measurements Taken by Spectrometersa

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

NA=nmed·sinθ0.
(xxc)2a2+(yyc)2b2=1,
(xc,yc)=(0,HStanα1t2(tanα)2)
a2=Hs2t2(1t2(tanα)2)2
b2=a21t2(tanα)2
HS=d+df2tan(sin1(NAnmed)).
θSAM=cos1SATSBSASB.
(ΔS)2=(ΔQ1ΔQ2)2e12+e22,
(ΔS)2=e12(ΔQ3ΔQ2)2+e22(ΔQ3ΔQ1)2+e32(ΔQ1ΔQ2)2(e1e2)2+(e1e3)2+(e2e3)2,
Qi=kλminλmaxI(λ)R(λ)Si(λ)dλ,
wi=(0.05ni)nlws,
x2+y2(RH)2=(tanα·y+Hs)2.
x2(RH)2+y2(1(RH)2tan2α)2tanαHsy=Hs2.
x2Mt2+y22tanαHsMy=Hs2M.
x2Mt2C+(yHstanαM)2C=1,

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