Abstract

We describe an imaging scatterometer allowing hemispherical reflectance measurements as a function of the angle of incidence. The heart of the scatterometer is an ellipsoidal reflector, which compresses the hemispherical reflection into a cone-shaped beam that can be imaged by a normal optical system. The instrument’s performance is illustrated by measurements of the scattering profiles of the blue-iridescent dorsal wing scales of the nymphalid Morpho aega and the matte-green ventral wing scales of the lycaenid Callophrys rubi.

© 2009 Optical Society of America

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  1. M. Srinivasarao, 'Nano-optics in the biological world: Beetles, butterflies, birds and moths,' Chem. Rev. 99, 1935-1961 (1999).
    [CrossRef]
  2. P. Vukusic and J. R. Sambles, 'Photonic structures in biology,' Nature 424, 852-855 (2003).
    [CrossRef] [PubMed]
  3. S. Kinoshita and S. Yoshioka, 'Structural colors in nature: the role of regularity and irregularity in the structure,' ChemPhysChem 6, 1-19 (2005).
  4. K. Kertész, Z. Bálint, Z. Vertésy, G. I. Márk, V. Lousse, J. P. Vigneron, M. Rassart, and L. P. Biró, 'Gleaming and dull surface textures from photonic-crystal-type nanostructures in the butterfly Cyanophrys remus,' Phys. Rev. E 74, 021922 (2006).
    [CrossRef]
  5. K. Michielsen and D. G. Stavenga, 'Gyroid cuticular structures in butterfly wing scales: biological photonic crystals,' J. R. Soc. Interface 5, 85-94 (2008).
    [CrossRef]
  6. H. Ghiradella and W. Radigan, 'Development of butterfly scales: II. Struts, lattices and surface tension,' J. Morphol. 150, 279-297 (1976).
    [CrossRef]
  7. H. F. Nijhout, The Development and Evolution of Butterfly Wing Patterns (Washington, Smithsonian Institution Press, 1991).
  8. H. Ghiradella, 'Structure of iridescent lepidopteran scales: variations on several themes,' Ann. Entomol. Soc. Am. 77, 637-645 (1984).
  9. D. G. Stavenga, M. A. Giraldo, and B. J. Hoenders, 'Reflectance and transmittance of light scattering scales stacked on the wings of pierid butterflies,' Opt. Express 14, 4880-4890 (2006).
    [CrossRef] [PubMed]
  10. M. A. Giraldo and D. G. Stavenga, 'Sexual dichroism and pigment localization in the wing scales of Pieris rapae butterflies,' Proc. R. Soc. B 274, 97-102 (2007).
    [CrossRef]
  11. N. I. Morehouse, P. Vukusic, and R. Rutowski, 'Pterin pigment granules are responsible for both broadband light scattering and wavelength selective absorption in the wing scales of pierid butterflies,' Proc. R. Soc. B 274, 359-366 (2007).
    [CrossRef]
  12. D. G. Stavenga, S. Stowe, K. Siebke, J. Zeil, and K. Arikawa, 'Butterfly wing colours: scale beads make white pierid wings brighter,' Proc. R. Soc. Lond. B 271, 1577-1584 (2004).
    [CrossRef]
  13. C. W. Mason, 'Structural colors in insects. 2.,' J. Phys. Chem. 31, 321-354 (1927).
    [CrossRef]
  14. P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, 'Quantified interference and diffraction in single Morpho butterfly scales,' Proc. R. Soc. Lond. B 266, 1403-1411 (1999).
    [CrossRef]
  15. S. Kinoshita, S. Yoshioka, and K. Kawagoe, 'Mechanisms of structural colour in the Morpho butterfly: cooperation of regularity and irregularity in an iridescent scale,' Proc. R. Soc. Lond. B 269, 1417-1421 (2002).
    [CrossRef]
  16. S. Yoshioka and S. Kinoshita, 'Structural or pigmentary? Origin of the distinctive white stripe on the blue wing of a Morpho butterfly,' Proc. R. Soc. B 273, 129-134 (2006).
    [CrossRef] [PubMed]
  17. M. A. Giraldo, S. Yoshioka, and D. G. Stavenga, 'Far field scattering pattern of differently structured butterfly scales,' J. Comp. Physiol. A 194, 201-207 (2008).
    [CrossRef]
  18. F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Geometrical Considerations and Nomenclature for Reflectance (Washington, DC, National Bureau of Standards, US Department of Commerce, 1977).
  19. R. B. Morris, 'Iridescence from diffraction structures in the wing scales of Callophrys rubi, the Green Hairstreak,' J. Ent. (A) 49, 149-154 (1975).
  20. Y. L. Pan, K. B. Aptowicz, R. K. Chang, M. Hart, and J. D. Eversole, 'Characterizing and monitoring respiratory aerosols by light scattering,' Opt. Lett. 28, 589-591 (2003).
    [CrossRef] [PubMed]
  21. K. B. Aptowicz, Y. L. Pan, R. K. Chang, R. G. Pinnick, S. C. Hill, R. L. Tober, A. Goyal, T. Leys, and B. V. Bronk, 'Two-dimensional angular optical scattering patterns of microdroplets in the mid infrared with strong and weak absorption,' Opt. Lett. 29, 1965-1967 (2004).
    [CrossRef] [PubMed]
  22. O. G. Rodríguez-Herrera, M. Rosete-Aguilar, and N. C. Bruce, 'Scatterometer of visible light for 2D rough surfaces," Rev. Sci. Instr. 75, 4820-4823 (2004).
    [CrossRef]
  23. S. Yoshioka and S. Kinoshita, 'Wavelength-selective and anisotropic light-diffusing scale on the wing of the Morpho butterfly,' Proc. R. Soc. B 271, 581-587 (2004).
    [CrossRef] [PubMed]
  24. S. Berthier, Iridescences, les Couleurs Physiques des Insectes (Paris, Springer, 2003).
  25. P. Vukusic and D. G. Stavenga, 'Physical methods for investigating structural colours in biological systems,' J. R. Soc. Interface, in press (2009).
  26. 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. Interface, in press (2009).

2009 (2)

P. Vukusic and D. G. Stavenga, 'Physical methods for investigating structural colours in biological systems,' J. R. Soc. Interface, in press (2009).

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. Interface, in press (2009).

2008 (2)

K. Michielsen and D. G. Stavenga, 'Gyroid cuticular structures in butterfly wing scales: biological photonic crystals,' J. R. Soc. Interface 5, 85-94 (2008).
[CrossRef]

M. A. Giraldo, S. Yoshioka, and D. G. Stavenga, 'Far field scattering pattern of differently structured butterfly scales,' J. Comp. Physiol. A 194, 201-207 (2008).
[CrossRef]

2007 (2)

M. A. Giraldo and D. G. Stavenga, 'Sexual dichroism and pigment localization in the wing scales of Pieris rapae butterflies,' Proc. R. Soc. B 274, 97-102 (2007).
[CrossRef]

N. I. Morehouse, P. Vukusic, and R. Rutowski, 'Pterin pigment granules are responsible for both broadband light scattering and wavelength selective absorption in the wing scales of pierid butterflies,' Proc. R. Soc. B 274, 359-366 (2007).
[CrossRef]

2006 (3)

K. Kertész, Z. Bálint, Z. Vertésy, G. I. Márk, V. Lousse, J. P. Vigneron, M. Rassart, and L. P. Biró, 'Gleaming and dull surface textures from photonic-crystal-type nanostructures in the butterfly Cyanophrys remus,' Phys. Rev. E 74, 021922 (2006).
[CrossRef]

S. Yoshioka and S. Kinoshita, 'Structural or pigmentary? Origin of the distinctive white stripe on the blue wing of a Morpho butterfly,' Proc. R. Soc. B 273, 129-134 (2006).
[CrossRef] [PubMed]

D. G. Stavenga, M. A. Giraldo, and B. J. Hoenders, 'Reflectance and transmittance of light scattering scales stacked on the wings of pierid butterflies,' Opt. Express 14, 4880-4890 (2006).
[CrossRef] [PubMed]

2005 (1)

S. Kinoshita and S. Yoshioka, 'Structural colors in nature: the role of regularity and irregularity in the structure,' ChemPhysChem 6, 1-19 (2005).

2004 (4)

D. G. Stavenga, S. Stowe, K. Siebke, J. Zeil, and K. Arikawa, 'Butterfly wing colours: scale beads make white pierid wings brighter,' Proc. R. Soc. Lond. B 271, 1577-1584 (2004).
[CrossRef]

K. B. Aptowicz, Y. L. Pan, R. K. Chang, R. G. Pinnick, S. C. Hill, R. L. Tober, A. Goyal, T. Leys, and B. V. Bronk, 'Two-dimensional angular optical scattering patterns of microdroplets in the mid infrared with strong and weak absorption,' Opt. Lett. 29, 1965-1967 (2004).
[CrossRef] [PubMed]

O. G. Rodríguez-Herrera, M. Rosete-Aguilar, and N. C. Bruce, 'Scatterometer of visible light for 2D rough surfaces," Rev. Sci. Instr. 75, 4820-4823 (2004).
[CrossRef]

S. Yoshioka and S. Kinoshita, 'Wavelength-selective and anisotropic light-diffusing scale on the wing of the Morpho butterfly,' Proc. R. Soc. B 271, 581-587 (2004).
[CrossRef] [PubMed]

2003 (2)

2002 (1)

S. Kinoshita, S. Yoshioka, and K. Kawagoe, 'Mechanisms of structural colour in the Morpho butterfly: cooperation of regularity and irregularity in an iridescent scale,' Proc. R. Soc. Lond. B 269, 1417-1421 (2002).
[CrossRef]

1999 (2)

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, 'Quantified interference and diffraction in single Morpho butterfly scales,' Proc. R. Soc. Lond. B 266, 1403-1411 (1999).
[CrossRef]

M. Srinivasarao, 'Nano-optics in the biological world: Beetles, butterflies, birds and moths,' Chem. Rev. 99, 1935-1961 (1999).
[CrossRef]

1984 (1)

H. Ghiradella, 'Structure of iridescent lepidopteran scales: variations on several themes,' Ann. Entomol. Soc. Am. 77, 637-645 (1984).

1976 (1)

H. Ghiradella and W. Radigan, 'Development of butterfly scales: II. Struts, lattices and surface tension,' J. Morphol. 150, 279-297 (1976).
[CrossRef]

1975 (1)

R. B. Morris, 'Iridescence from diffraction structures in the wing scales of Callophrys rubi, the Green Hairstreak,' J. Ent. (A) 49, 149-154 (1975).

1927 (1)

C. W. Mason, 'Structural colors in insects. 2.,' J. Phys. Chem. 31, 321-354 (1927).
[CrossRef]

Aptowicz, K. B.

Arikawa, K.

D. G. Stavenga, S. Stowe, K. Siebke, J. Zeil, and K. Arikawa, 'Butterfly wing colours: scale beads make white pierid wings brighter,' Proc. R. Soc. Lond. B 271, 1577-1584 (2004).
[CrossRef]

Bálint, Z.

K. Kertész, Z. Bálint, Z. Vertésy, G. I. Márk, V. Lousse, J. P. Vigneron, M. Rassart, and L. P. Biró, 'Gleaming and dull surface textures from photonic-crystal-type nanostructures in the butterfly Cyanophrys remus,' Phys. Rev. E 74, 021922 (2006).
[CrossRef]

Biró, L. P.

K. Kertész, Z. Bálint, Z. Vertésy, G. I. Márk, V. Lousse, J. P. Vigneron, M. Rassart, and L. P. Biró, 'Gleaming and dull surface textures from photonic-crystal-type nanostructures in the butterfly Cyanophrys remus,' Phys. Rev. E 74, 021922 (2006).
[CrossRef]

Bronk, B. V.

Bruce, N. C.

O. G. Rodríguez-Herrera, M. Rosete-Aguilar, and N. C. Bruce, 'Scatterometer of visible light for 2D rough surfaces," Rev. Sci. Instr. 75, 4820-4823 (2004).
[CrossRef]

Chang, R. K.

Eversole, J. D.

Ghiradella, H.

H. Ghiradella, 'Structure of iridescent lepidopteran scales: variations on several themes,' Ann. Entomol. Soc. Am. 77, 637-645 (1984).

H. Ghiradella and W. Radigan, 'Development of butterfly scales: II. Struts, lattices and surface tension,' J. Morphol. 150, 279-297 (1976).
[CrossRef]

Giraldo, M. A.

M. A. Giraldo, S. Yoshioka, and D. G. Stavenga, 'Far field scattering pattern of differently structured butterfly scales,' J. Comp. Physiol. A 194, 201-207 (2008).
[CrossRef]

M. A. Giraldo and D. G. Stavenga, 'Sexual dichroism and pigment localization in the wing scales of Pieris rapae butterflies,' Proc. R. Soc. B 274, 97-102 (2007).
[CrossRef]

D. G. Stavenga, M. A. Giraldo, and B. J. Hoenders, 'Reflectance and transmittance of light scattering scales stacked on the wings of pierid butterflies,' Opt. Express 14, 4880-4890 (2006).
[CrossRef] [PubMed]

Goyal, A.

Hart, M.

Hill, S. C.

Hoenders, B. J.

Kawagoe, K.

S. Kinoshita, S. Yoshioka, and K. Kawagoe, 'Mechanisms of structural colour in the Morpho butterfly: cooperation of regularity and irregularity in an iridescent scale,' Proc. R. Soc. Lond. B 269, 1417-1421 (2002).
[CrossRef]

Kertész, K.

K. Kertész, Z. Bálint, Z. Vertésy, G. I. Márk, V. Lousse, J. P. Vigneron, M. Rassart, and L. P. Biró, 'Gleaming and dull surface textures from photonic-crystal-type nanostructures in the butterfly Cyanophrys remus,' Phys. Rev. E 74, 021922 (2006).
[CrossRef]

Kinoshita, S.

S. Yoshioka and S. Kinoshita, 'Structural or pigmentary? Origin of the distinctive white stripe on the blue wing of a Morpho butterfly,' Proc. R. Soc. B 273, 129-134 (2006).
[CrossRef] [PubMed]

S. Kinoshita and S. Yoshioka, 'Structural colors in nature: the role of regularity and irregularity in the structure,' ChemPhysChem 6, 1-19 (2005).

S. Yoshioka and S. Kinoshita, 'Wavelength-selective and anisotropic light-diffusing scale on the wing of the Morpho butterfly,' Proc. R. Soc. B 271, 581-587 (2004).
[CrossRef] [PubMed]

S. Kinoshita, S. Yoshioka, and K. Kawagoe, 'Mechanisms of structural colour in the Morpho butterfly: cooperation of regularity and irregularity in an iridescent scale,' Proc. R. Soc. Lond. B 269, 1417-1421 (2002).
[CrossRef]

Lawrence, C. R.

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, 'Quantified interference and diffraction in single Morpho butterfly scales,' Proc. R. Soc. Lond. B 266, 1403-1411 (1999).
[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. Interface, in press (2009).

Leys, T.

Lousse, V.

K. Kertész, Z. Bálint, Z. Vertésy, G. I. Márk, V. Lousse, J. P. Vigneron, M. Rassart, and L. P. Biró, 'Gleaming and dull surface textures from photonic-crystal-type nanostructures in the butterfly Cyanophrys remus,' Phys. Rev. E 74, 021922 (2006).
[CrossRef]

Márk, G. I.

K. Kertész, Z. Bálint, Z. Vertésy, G. I. Márk, V. Lousse, J. P. Vigneron, M. Rassart, and L. P. Biró, 'Gleaming and dull surface textures from photonic-crystal-type nanostructures in the butterfly Cyanophrys remus,' Phys. Rev. E 74, 021922 (2006).
[CrossRef]

Mason, C. W.

C. W. Mason, 'Structural colors in insects. 2.,' J. Phys. Chem. 31, 321-354 (1927).
[CrossRef]

Michielsen, K.

K. Michielsen and D. G. Stavenga, 'Gyroid cuticular structures in butterfly wing scales: biological photonic crystals,' J. R. Soc. Interface 5, 85-94 (2008).
[CrossRef]

Morehouse, N. I.

N. I. Morehouse, P. Vukusic, and R. Rutowski, 'Pterin pigment granules are responsible for both broadband light scattering and wavelength selective absorption in the wing scales of pierid butterflies,' Proc. R. Soc. B 274, 359-366 (2007).
[CrossRef]

Morris, R. B.

R. B. Morris, 'Iridescence from diffraction structures in the wing scales of Callophrys rubi, the Green Hairstreak,' J. Ent. (A) 49, 149-154 (1975).

Pan, Y. L.

Pinnick, R. G.

Radigan, W.

H. Ghiradella and W. Radigan, 'Development of butterfly scales: II. Struts, lattices and surface tension,' J. Morphol. 150, 279-297 (1976).
[CrossRef]

Rassart, M.

K. Kertész, Z. Bálint, Z. Vertésy, G. I. Márk, V. Lousse, J. P. Vigneron, M. Rassart, and L. P. Biró, 'Gleaming and dull surface textures from photonic-crystal-type nanostructures in the butterfly Cyanophrys remus,' Phys. Rev. E 74, 021922 (2006).
[CrossRef]

Rodríguez-Herrera, O. G.

O. G. Rodríguez-Herrera, M. Rosete-Aguilar, and N. C. Bruce, 'Scatterometer of visible light for 2D rough surfaces," Rev. Sci. Instr. 75, 4820-4823 (2004).
[CrossRef]

Rosete-Aguilar, M.

O. G. Rodríguez-Herrera, M. Rosete-Aguilar, and N. C. Bruce, 'Scatterometer of visible light for 2D rough surfaces," Rev. Sci. Instr. 75, 4820-4823 (2004).
[CrossRef]

Rutowski, R.

N. I. Morehouse, P. Vukusic, and R. Rutowski, 'Pterin pigment granules are responsible for both broadband light scattering and wavelength selective absorption in the wing scales of pierid butterflies,' Proc. R. Soc. B 274, 359-366 (2007).
[CrossRef]

Sambles, J. R.

P. Vukusic and J. R. Sambles, 'Photonic structures in biology,' Nature 424, 852-855 (2003).
[CrossRef] [PubMed]

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, 'Quantified interference and diffraction in single Morpho butterfly scales,' Proc. R. Soc. Lond. B 266, 1403-1411 (1999).
[CrossRef]

Siebke, K.

D. G. Stavenga, S. Stowe, K. Siebke, J. Zeil, and K. Arikawa, 'Butterfly wing colours: scale beads make white pierid wings brighter,' Proc. R. Soc. Lond. B 271, 1577-1584 (2004).
[CrossRef]

Srinivasarao, M.

M. Srinivasarao, 'Nano-optics in the biological world: Beetles, butterflies, birds and moths,' Chem. Rev. 99, 1935-1961 (1999).
[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. Interface, in press (2009).

P. Vukusic and D. G. Stavenga, 'Physical methods for investigating structural colours in biological systems,' J. R. Soc. Interface, in press (2009).

M. A. Giraldo, S. Yoshioka, and D. G. Stavenga, 'Far field scattering pattern of differently structured butterfly scales,' J. Comp. Physiol. A 194, 201-207 (2008).
[CrossRef]

K. Michielsen and D. G. Stavenga, 'Gyroid cuticular structures in butterfly wing scales: biological photonic crystals,' J. R. Soc. Interface 5, 85-94 (2008).
[CrossRef]

M. A. Giraldo and D. G. Stavenga, 'Sexual dichroism and pigment localization in the wing scales of Pieris rapae butterflies,' Proc. R. Soc. B 274, 97-102 (2007).
[CrossRef]

D. G. Stavenga, M. A. Giraldo, and B. J. Hoenders, 'Reflectance and transmittance of light scattering scales stacked on the wings of pierid butterflies,' Opt. Express 14, 4880-4890 (2006).
[CrossRef] [PubMed]

D. G. Stavenga, S. Stowe, K. Siebke, J. Zeil, and K. Arikawa, 'Butterfly wing colours: scale beads make white pierid wings brighter,' Proc. R. Soc. Lond. B 271, 1577-1584 (2004).
[CrossRef]

Stowe, S.

D. G. Stavenga, S. Stowe, K. Siebke, J. Zeil, and K. Arikawa, 'Butterfly wing colours: scale beads make white pierid wings brighter,' Proc. R. Soc. Lond. B 271, 1577-1584 (2004).
[CrossRef]

Tober, R. L.

Vertésy, Z.

K. Kertész, Z. Bálint, Z. Vertésy, G. I. Márk, V. Lousse, J. P. Vigneron, M. Rassart, and L. P. Biró, 'Gleaming and dull surface textures from photonic-crystal-type nanostructures in the butterfly Cyanophrys remus,' Phys. Rev. E 74, 021922 (2006).
[CrossRef]

Vigneron, J. P.

K. Kertész, Z. Bálint, Z. Vertésy, G. I. Márk, V. Lousse, J. P. Vigneron, M. Rassart, and L. P. Biró, 'Gleaming and dull surface textures from photonic-crystal-type nanostructures in the butterfly Cyanophrys remus,' Phys. Rev. E 74, 021922 (2006).
[CrossRef]

Vukusic, P.

P. Vukusic and D. G. Stavenga, 'Physical methods for investigating structural colours in biological systems,' J. R. Soc. Interface, in press (2009).

N. I. Morehouse, P. Vukusic, and R. Rutowski, 'Pterin pigment granules are responsible for both broadband light scattering and wavelength selective absorption in the wing scales of pierid butterflies,' Proc. R. Soc. B 274, 359-366 (2007).
[CrossRef]

P. Vukusic and J. R. Sambles, 'Photonic structures in biology,' Nature 424, 852-855 (2003).
[CrossRef] [PubMed]

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, 'Quantified interference and diffraction in single Morpho butterfly scales,' Proc. R. Soc. Lond. B 266, 1403-1411 (1999).
[CrossRef]

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. Interface, in press (2009).

Wootton, R. J.

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, 'Quantified interference and diffraction in single Morpho butterfly scales,' Proc. R. Soc. Lond. B 266, 1403-1411 (1999).
[CrossRef]

Yoshioka, S.

M. A. Giraldo, S. Yoshioka, and D. G. Stavenga, 'Far field scattering pattern of differently structured butterfly scales,' J. Comp. Physiol. A 194, 201-207 (2008).
[CrossRef]

S. Yoshioka and S. Kinoshita, 'Structural or pigmentary? Origin of the distinctive white stripe on the blue wing of a Morpho butterfly,' Proc. R. Soc. B 273, 129-134 (2006).
[CrossRef] [PubMed]

S. Kinoshita and S. Yoshioka, 'Structural colors in nature: the role of regularity and irregularity in the structure,' ChemPhysChem 6, 1-19 (2005).

S. Yoshioka and S. Kinoshita, 'Wavelength-selective and anisotropic light-diffusing scale on the wing of the Morpho butterfly,' Proc. R. Soc. B 271, 581-587 (2004).
[CrossRef] [PubMed]

S. Kinoshita, S. Yoshioka, and K. Kawagoe, 'Mechanisms of structural colour in the Morpho butterfly: cooperation of regularity and irregularity in an iridescent scale,' Proc. R. Soc. Lond. B 269, 1417-1421 (2002).
[CrossRef]

Zeil, J.

D. G. Stavenga, S. Stowe, K. Siebke, J. Zeil, and K. Arikawa, 'Butterfly wing colours: scale beads make white pierid wings brighter,' Proc. R. Soc. Lond. B 271, 1577-1584 (2004).
[CrossRef]

Ann. Entomol. Soc. Am. (1)

H. Ghiradella, 'Structure of iridescent lepidopteran scales: variations on several themes,' Ann. Entomol. Soc. Am. 77, 637-645 (1984).

Chem. Rev. (1)

M. Srinivasarao, 'Nano-optics in the biological world: Beetles, butterflies, birds and moths,' Chem. Rev. 99, 1935-1961 (1999).
[CrossRef]

ChemPhysChem (1)

S. Kinoshita and S. Yoshioka, 'Structural colors in nature: the role of regularity and irregularity in the structure,' ChemPhysChem 6, 1-19 (2005).

J. Comp. Physiol. A (1)

M. A. Giraldo, S. Yoshioka, and D. G. Stavenga, 'Far field scattering pattern of differently structured butterfly scales,' J. Comp. Physiol. A 194, 201-207 (2008).
[CrossRef]

J. Ent. (A) (1)

R. B. Morris, 'Iridescence from diffraction structures in the wing scales of Callophrys rubi, the Green Hairstreak,' J. Ent. (A) 49, 149-154 (1975).

J. Morphol. (1)

H. Ghiradella and W. Radigan, 'Development of butterfly scales: II. Struts, lattices and surface tension,' J. Morphol. 150, 279-297 (1976).
[CrossRef]

J. Phys. Chem. (1)

C. W. Mason, 'Structural colors in insects. 2.,' J. Phys. Chem. 31, 321-354 (1927).
[CrossRef]

J. R. Soc. Interface (3)

K. Michielsen and D. G. Stavenga, 'Gyroid cuticular structures in butterfly wing scales: biological photonic crystals,' J. R. Soc. Interface 5, 85-94 (2008).
[CrossRef]

P. Vukusic and D. G. Stavenga, 'Physical methods for investigating structural colours in biological systems,' J. R. Soc. Interface, in press (2009).

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. Interface, in press (2009).

Nature (1)

P. Vukusic and J. R. Sambles, 'Photonic structures in biology,' Nature 424, 852-855 (2003).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. E (1)

K. Kertész, Z. Bálint, Z. Vertésy, G. I. Márk, V. Lousse, J. P. Vigneron, M. Rassart, and L. P. Biró, 'Gleaming and dull surface textures from photonic-crystal-type nanostructures in the butterfly Cyanophrys remus,' Phys. Rev. E 74, 021922 (2006).
[CrossRef]

Proc. R. Soc. B (4)

M. A. Giraldo and D. G. Stavenga, 'Sexual dichroism and pigment localization in the wing scales of Pieris rapae butterflies,' Proc. R. Soc. B 274, 97-102 (2007).
[CrossRef]

N. I. Morehouse, P. Vukusic, and R. Rutowski, 'Pterin pigment granules are responsible for both broadband light scattering and wavelength selective absorption in the wing scales of pierid butterflies,' Proc. R. Soc. B 274, 359-366 (2007).
[CrossRef]

S. Yoshioka and S. Kinoshita, 'Structural or pigmentary? Origin of the distinctive white stripe on the blue wing of a Morpho butterfly,' Proc. R. Soc. B 273, 129-134 (2006).
[CrossRef] [PubMed]

S. Yoshioka and S. Kinoshita, 'Wavelength-selective and anisotropic light-diffusing scale on the wing of the Morpho butterfly,' Proc. R. Soc. B 271, 581-587 (2004).
[CrossRef] [PubMed]

Proc. R. Soc. Lond. B (3)

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, 'Quantified interference and diffraction in single Morpho butterfly scales,' Proc. R. Soc. Lond. B 266, 1403-1411 (1999).
[CrossRef]

S. Kinoshita, S. Yoshioka, and K. Kawagoe, 'Mechanisms of structural colour in the Morpho butterfly: cooperation of regularity and irregularity in an iridescent scale,' Proc. R. Soc. Lond. B 269, 1417-1421 (2002).
[CrossRef]

D. G. Stavenga, S. Stowe, K. Siebke, J. Zeil, and K. Arikawa, 'Butterfly wing colours: scale beads make white pierid wings brighter,' Proc. R. Soc. Lond. B 271, 1577-1584 (2004).
[CrossRef]

Rev. Sci. Instr. (1)

O. G. Rodríguez-Herrera, M. Rosete-Aguilar, and N. C. Bruce, 'Scatterometer of visible light for 2D rough surfaces," Rev. Sci. Instr. 75, 4820-4823 (2004).
[CrossRef]

Other (3)

S. Berthier, Iridescences, les Couleurs Physiques des Insectes (Paris, Springer, 2003).

H. F. Nijhout, The Development and Evolution of Butterfly Wing Patterns (Washington, Smithsonian Institution Press, 1991).

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Geometrical Considerations and Nomenclature for Reflectance (Washington, DC, National Bureau of Standards, US Department of Commerce, 1977).

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Figures (5)

Fig. 1.
Fig. 1.

Diagram of the imaging scatterometer. The primary beam, delivered by light source S1 and diaphragm D1, is focused by lenses L1 and L2, via a central hole in the ellipsoidal reflector, M, on the sample, positioned in the first focal point of the reflector, F1. The positioning of the sample is visually controlled with the epi-illumination microscope consisting of lenses L2 and L3 to which camera C1 is connected. The beam aperture is determined by diaphragm D2. The secondary beam, delivered by light source S2, via diaphragms D3-5 and lenses L4 and L5, is focused via a beam splitter, H, and the ellipsoidal reflector at the sample. Light scattered by the sample is focused at the second focal point of the reflector, F2, which coincides with the front-focal point of a large-aperture photographical lens, L6. The far-field scattering pattern, projected in plane I, is imaged by lens L7 at a digital camera, C2. A reflected light ray, having an angle θ with the axis, leaves the second focal point with an angle α, has a distance r to the axis in the back focal plane of lens L6, and is projected at the camera chip at a distance p from the axis. A spatial filter in plane I blocks the zeroth-order transmitted light.

Fig. 2.
Fig. 2.

Coordinate systems for the spatial relationships of light fluxes. (a) The bidirectional reflectance distribution function relates the reflected radiance L r(θ r,φ r) with the incident irradiance E i(θ i, φ i) ; see Eq. 2. (b) Polar diagram where the area of the spatial element (grey) equals = s ds dφ. The coordinate s is the pixel distance p or the angle θ r, and φ = φ r.

Fig. 3.
Fig. 3.

Calibration of the scatterometer with a small mirror, positioned in focal point F1 of the scatterometer. (a) The mirror, reflecting the primary light beam, was rotated around a horizontal axis in steps of 5°, and the images of the light beam were superimposed. A light spot is missing in the center, because the mirror blocks the reflection of the axial beam. (b) The mirror, reflecting the secondary light beam, was in an approximately vertical position, and the vertical position of diaphragm D4 (Fig. 1) was varied in steps; the resulting images were superimposed. The step size of the diaphragm was 0.5 mm, but only every third image was used in the superposition. (c) The centers of the image spots of (a) were determined, and their distance to the axial pixel was then normalized to the value obtained with a mirror angle of 45°, which corresponds to an angle of the reflected beam θ max = 90°. (d) The centers of the image spots of (b) were determined, and the distances to the axial pixel, normalized to the maximal value, were plotted as a function of the relative displacement d * of diaphragm D4 in the secondary beam. (e) Relative correction factor K * for the radiance in a polar plot (Eq. 3c). (f) Relationship between the angle of illumination, θ, and relative diaphragm position, d * (Eq. 4). The red circles in (a) and (b) indicate the boundary of the image corresponding to θ max = 90°. The blue and green symbols in (c) and (d) represent the image spots above (φ r = π/2) and below (φ r = 3π/2) the horizontal axis, respectively. The image spots are not perfectly in a vertical plane, because the mirror plane and the rotation axis of the pin, to which the mirror is glued, were not perfectly parallel.

Fig. 4.
Fig. 4.

Scattering by a dorsal wing scale of the butterfly Morpho aega. (a) A small wing fragment was positioned in the scatterometer and the primary beam was projected as a 40 μm spot at a single scale (a much wider area was illuminated by a weaker beam delivered by the secondary source); bar 100 μm. (b) The scattering pattern resulting from the primary beam. (c) Scattering patterns created by the secondary beam with diaphragm D4 positioned at d = 0, ±2, ±4, and ±6 mm with respect to the axis (corresponding to an angle of incidence of θ i = 0°, ±20.5°, ±39.9° and ±57.1°, respectively). The long, pointed, black object at 9 o’clock is the glass micropipette holding the about circular wing fragment. The red circles in (b) and (c) indicate scattering angles of θ r = 5, 30, 60, and 90 degrees.

Fig. 5.
Fig. 5.

Scattering characteristics of the ventral wings of the Green Hairstreak, Callophrys rubi. (a) A small wing fragment was positioned in the scatterometer, and the primary beam was projected as a 40 μm spot at a scale (a wider secondary light beam caused the additional scattering of the scale assembly); bar 100 μm. (b) The scattering pattern is quite random and covers a major part of the hemisphere. (c) The integral of the scattered light for circular areas bounded by scattering angles θ r = 30°, 60°, and 90° was divided by the incident light flux, resulting in reflectance spectra that peak in the green wavelength range (inset: the ventral side of the Green Hairstreak; bar 1 cm).

Equations (9)

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α=asin[(1ε2)sinθ/(1+ε2+2εcosθ)]
αmax=asin[(1ε2)/(1+ε2)]
p*=p/pmax =α/αmax
Rλ(θi,φi,θr,φr)=Lr(θr,φr)dωrEi(θi,φi)cosθidωi
Ecor=Ecam pθdp=EcamM2αθ =EcamK
K=M2 αθ
K*=K/K0
θ=asin[(1ε2)sinα/(1+ε2+2εcosα)]
α=(αmax/dmax) d=αmaxd*

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