Abstract

We have determined the reflectance spectra of colored metallic coatings with high spatial resolution by using a hyperspectral imaging system. Reflectance spectra were converted to color coordinates revealing characteristic color maps in the color space. Principal-component analysis was applied to decorrelate the spatial variability of the reflectance spectra. We found that the eigenvalue spectra follow different power laws. The scaling exponent was analyzed by considering random-walk-type processes. An estimation of the Hurst exponent was done, suggesting anomalous diffusion from multiple light scattering. The results show that hyperspectral imaging combined with principal-component analysis provides a valuable method for nondestructive testing of complex turbid media.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. W. Billmeyer and J. G. Davidson, “Color and appearance of metallized paint films. 1. Characterization,” J. Paint Technol. 46, 31–37 (1974).
  2. C. S. McCamy, “Observation and measurement of the appearance of metallic materials. 1. Macro appearance,” Color Res. Appl. 21, 292–304 (1996).
    [CrossRef]
  3. G. Pfaff and P. Reynders, “Angle-dependent optical effects deriving from submicron structures of films and pigments,” Chem. Rev. 99, 1963–1981 (1999).
    [CrossRef]
  4. S. Kinoshita, S. Yoshioka, and J. Miyazaki, “Physics of structural colors,” Rep. Prog. Phys. 71, 076401 (2008).
    [CrossRef]
  5. P. A. Lewis, Pigment Handbook, Properties and Economics, 2nd ed. (Wiley, 1988), Vol.  1.
  6. A. A. Tracton, Coatings Technology Handbook, 3rd ed. (Taylor & Francis Group, 2006).
    [CrossRef]
  7. H.-J. Streitberger and K.-F. Dössel, Automotive Paints and Coatings, 2nd ed. (Wiley-VCH, 2008).
    [CrossRef]
  8. C. S. McCamy, “Observation and measurement of the appearance of metallic materials. Part II. Micro appearance,” Color Res. Appl. 23, 362–373 (1998).
    [CrossRef]
  9. M. E. Nadal and E. A. Early, “Color measurements for pearlescent coatings,” Color Res. Appl. 29, 38–42 (2004).
    [CrossRef]
  10. E. Kirchner, G. J. van den Kieboom, L. Njo, R. Super, and R. Gottenbos, “Observation of visual texture of metallic and pearlescent materials,” Color Res. Appl. 32, 256–266 (2007).
    [CrossRef]
  11. N. Dekker, E. J. J. Kirchner, R. Super, G. J. van den Kieboom, and R. Gottenbos, “Total appearance differences for metallic and pearlescent materials: contributions from color and texture,” Color Res. Appl. 36, 4–14 (2011).
    [CrossRef]
  12. H. G. Völz, Industrial Color Testing, Fundamentals and Techniques, 2nd ed. (Wiley-VCH, 2001).
    [CrossRef]
  13. G. A. Klein, Industrial Color Physics, Springer Series in Optical Sciences (Springer, 2010).
    [CrossRef]
  14. R. Hunter and R. W. Harold, The Measurement of Appearance, 2nd ed. (Wiley, 1987).
  15. F. W. Billmeyer and E. C. Carter, “Color and appearance of metallized paint films. 2. Initial application of turbid-medium theory,” J. Coat. Technol. 48, 53–60 (1976).
  16. A. B. Murphy, “Modified Kubelka-Munk model for calculation of the reflectance of coatings with optically-rough surfaces,” J. Phys. D Appl. Phys. 39, 3571–3581 (2006).
    [CrossRef]
  17. “Standard terminology of appearance,” Rep. No. ASTM E284-95a (American Society for Testing and Materials, 1995).
  18. H. J. A. Saris, R. J. B. Gottenbos, and H. Vanhouwelingen, “Correlation between visual and instrumental color differecnes of metallic paint films,” Color Res. Appl. 15, 200–2051990).
    [CrossRef]
  19. “Farbtoleranzen für Automobillackierungen—Teil 2: Effektlackierungen,” Rep. No. DIN 6175-2 (Deutsches Institut für Normung e.V., 2001).
  20. “Standard practice for specifying the geometry of multiangle spectrophotometers,” Rep. No. ASTM E2175-01 (American Society for Testing and Materials, 2001).
  21. “Standard practice for multiangle color measurement of interference pigments,” Rep. No. ASTM E2539-08 (American Society for Testing and Materials, 2008).
  22. G. Baba and H. Arai, “Gonio-spectrophotometry of metal-flake and pearl-mica pigmented paint surfaces,” Proc. SPIE 4826, 79–86 (2003)..
    [CrossRef]
  23. A. F. H. Goetz, G. Vane, J. E. Solomon, and B. N. Rock, “Imaging spectrometry for Earth remote sensing,” Science 228, 1147–1153 (1985).
    [CrossRef] [PubMed]
  24. N. Gat, “Imaging spectroscopy using tunable filters: A review,” Proc. SPIE 4056, 50–64 (2000).
    [CrossRef]
  25. J. Y. Hardeberg, F. Schmitt, and H. Brettel, “Multispectral color image capture using a liquid crystal tunable filter,” Opt. Eng. 41, 2532–2548 (2002).
    [CrossRef]
  26. H. F. Grahn and P. Geladi, Techniques and Applications of Hyperspectral Image Analysis (Wiley, 2007).
    [CrossRef]
  27. D. B. Kim, M. K. Seo, K. Y. Kim, and K. H. Lee, “Developing a multi-spectral HDR imaging module for a BRDF measurement system,” in Reflection, Scattering, and Diffraction from Surfaces II, Proceedings of SPIE-The International Society for Optical Engineering (SPIE, 2010).
    [PubMed]
  28. D. B. Kim, M. K. Seo, K. Y. Kim, and K. H. Lee, “Acquisition and representation of pearlescent paints using an image-based goniospectrophotometer,” Opt. Eng. 49, 043604 (2010).
    [CrossRef]
  29. J. M. Medina, S. Nascimento, and P. Vukusic, “Hyperspectral optical imaging of two different species of lepidoptera,” Nanoscale Res. Lett. 6, 1–5 (2011).
    [CrossRef]
  30. N. Ohta, “Estimating absorption-bands of component dyes by means of principal component analysis,” Anal. Chem. 45, 553–557 (1973).
    [CrossRef]
  31. I. T. Jollitffe, Principal Component Analysis, 2nd ed., Springer Series in Statistics (Springer-Verlag, 2002).
  32. D. Y. Tzeng and R. S. Berns, “A review of principal component analysis and its applications to color technology,” Color Res. Appl. 30, 84–98 (2005).
    [CrossRef]
  33. J. M. Medina, “Linear basis for metallic and iridescent colors,” Appl. Opt. 47, 5644–5653 (2008).
    [CrossRef] [PubMed]
  34. G. L. Rogers, “Multiple path analysis of reflectance from turbid media,” J. Opt. Soc. Am. A 25, 2879–2883 (2008).
    [CrossRef]
  35. P. Barthelemy, J. Bertolotti, and D. S. Wiersma, “A Levy flight for light,” Nature 453, 495–498 (2008).
    [CrossRef] [PubMed]
  36. J. B. Gao, Y. H. Cao, and J. M. Lee, “Principal component analysis of 1/f(alpha) noise,” Phys. Lett. A 314, 392–400 (2003).
    [CrossRef]
  37. P. J. B. Hancock, R. J. Baddeley, and L. S. Smith, “The principal components of natural images,” Netw. Comput. Neural Syst. 3, 61–70 (1992).
    [CrossRef]
  38. M. Kurylowicz, C. H. Yu, and R. Pomes, “Systematic study of anharmonic features in a principal component analysis of gramicidin A,” Biophys. J. 98, 386–395 (2010).
    [CrossRef] [PubMed]
  39. B. B. Mandelbrot, The Fractal Geometry of Nature (W. H. Freeman, 1982).
  40. J. M. Medina, L. M. Pereira, H. T. Correia, and S. Nascimento, “Hyperspectral optical imaging of human iris in vivo: characteristics of reflectance spectra,” J. Biomed. Opt. 16, 076001–076012 (2011).
    [CrossRef] [PubMed]
  41. G. E. Healey and R. Kondepudy, “Radiometric CCD camera calibration and noise estimation,” IEEE Trans. Pattern Anal. Machine Intell. 16, 267–276 (1994).
    [CrossRef]
  42. R. A. Yotter and D. M. Wilson, “A review of photodetectors for sensing light-emitting reporters in biological systems,” IEEE Sens. J. 3, 288–303 (2003).
    [CrossRef]
  43. E. Kirchner, “Film shrinkage and flake orientation,” Prog. Org. Coatings 65, 333–336 (2009).
    [CrossRef]
  44. G. Stolovitzky and K. R. Sreenivasan, “Kolmogorov refined similarity hypotheses for turbulence and general stochastic processes,” Rev. Mod. Phys. 66, 229–240 (1994).
    [CrossRef]
  45. G. Funes, D. Gulich, L. Zunino, D. G. Perez, and M. Garavaglia, “Behavior of the laser beam wandering variance with the turbulent path length,” Opt. Commun. 272, 476–479(2007).
    [CrossRef]
  46. J. Bertolotti, K. Vynck, L. Pattelli, P. Barthelemy, S. Lepri, and D. S. Wiersma, “Engineering disorder in superdiffusive Levy glasses,” Adv. Funct. Mater. 20, 965–968 (2010).
    [CrossRef]
  47. P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Quantified interference and diffraction in single Morpho butterfly scales,” Proc. R. Soc. London Ser. B 266, 1403–1411(1999).
    [CrossRef]
  48. P. Vukusic, R. Sambles, C. Lawrence, and G. Wakely, “Sculpted-multilayer optical effects in two species of Papilio butterfly,” Appl. Opt. 40, 1116–1125 (2001).
    [CrossRef]
  49. E. Kirchner and J. Houweling, “Measuring flake orientation for metallic coatings,” Prog. Org. Coatings 64, 287–293 (2009).
    [CrossRef]
  50. L. P. Sung, M. E. Nadal, M. E. McKnight, E. Marx, and B. Laurenti, “Optical reflectance of metallic coatings: Effect of aluminum flake orientation,” J. Coat. Technol. 74, 55–63(2002).
    [CrossRef]
  51. P. Barthelemy, J. Bertolotti, K. Vynck, S. Lepri, and D. S. Wiersma, “Role of quenching on superdiffusive transport in two-dimensional random media,” Phys. Rev. E 82, 011101(2010).
    [CrossRef]

2011 (3)

N. Dekker, E. J. J. Kirchner, R. Super, G. J. van den Kieboom, and R. Gottenbos, “Total appearance differences for metallic and pearlescent materials: contributions from color and texture,” Color Res. Appl. 36, 4–14 (2011).
[CrossRef]

J. M. Medina, S. Nascimento, and P. Vukusic, “Hyperspectral optical imaging of two different species of lepidoptera,” Nanoscale Res. Lett. 6, 1–5 (2011).
[CrossRef]

J. M. Medina, L. M. Pereira, H. T. Correia, and S. Nascimento, “Hyperspectral optical imaging of human iris in vivo: characteristics of reflectance spectra,” J. Biomed. Opt. 16, 076001–076012 (2011).
[CrossRef] [PubMed]

2010 (4)

M. Kurylowicz, C. H. Yu, and R. Pomes, “Systematic study of anharmonic features in a principal component analysis of gramicidin A,” Biophys. J. 98, 386–395 (2010).
[CrossRef] [PubMed]

J. Bertolotti, K. Vynck, L. Pattelli, P. Barthelemy, S. Lepri, and D. S. Wiersma, “Engineering disorder in superdiffusive Levy glasses,” Adv. Funct. Mater. 20, 965–968 (2010).
[CrossRef]

D. B. Kim, M. K. Seo, K. Y. Kim, and K. H. Lee, “Acquisition and representation of pearlescent paints using an image-based goniospectrophotometer,” Opt. Eng. 49, 043604 (2010).
[CrossRef]

P. Barthelemy, J. Bertolotti, K. Vynck, S. Lepri, and D. S. Wiersma, “Role of quenching on superdiffusive transport in two-dimensional random media,” Phys. Rev. E 82, 011101(2010).
[CrossRef]

2009 (2)

E. Kirchner and J. Houweling, “Measuring flake orientation for metallic coatings,” Prog. Org. Coatings 64, 287–293 (2009).
[CrossRef]

E. Kirchner, “Film shrinkage and flake orientation,” Prog. Org. Coatings 65, 333–336 (2009).
[CrossRef]

2008 (4)

P. Barthelemy, J. Bertolotti, and D. S. Wiersma, “A Levy flight for light,” Nature 453, 495–498 (2008).
[CrossRef] [PubMed]

S. Kinoshita, S. Yoshioka, and J. Miyazaki, “Physics of structural colors,” Rep. Prog. Phys. 71, 076401 (2008).
[CrossRef]

J. M. Medina, “Linear basis for metallic and iridescent colors,” Appl. Opt. 47, 5644–5653 (2008).
[CrossRef] [PubMed]

G. L. Rogers, “Multiple path analysis of reflectance from turbid media,” J. Opt. Soc. Am. A 25, 2879–2883 (2008).
[CrossRef]

2007 (2)

E. Kirchner, G. J. van den Kieboom, L. Njo, R. Super, and R. Gottenbos, “Observation of visual texture of metallic and pearlescent materials,” Color Res. Appl. 32, 256–266 (2007).
[CrossRef]

G. Funes, D. Gulich, L. Zunino, D. G. Perez, and M. Garavaglia, “Behavior of the laser beam wandering variance with the turbulent path length,” Opt. Commun. 272, 476–479(2007).
[CrossRef]

2006 (1)

A. B. Murphy, “Modified Kubelka-Munk model for calculation of the reflectance of coatings with optically-rough surfaces,” J. Phys. D Appl. Phys. 39, 3571–3581 (2006).
[CrossRef]

2005 (1)

D. Y. Tzeng and R. S. Berns, “A review of principal component analysis and its applications to color technology,” Color Res. Appl. 30, 84–98 (2005).
[CrossRef]

2004 (1)

M. E. Nadal and E. A. Early, “Color measurements for pearlescent coatings,” Color Res. Appl. 29, 38–42 (2004).
[CrossRef]

2003 (3)

G. Baba and H. Arai, “Gonio-spectrophotometry of metal-flake and pearl-mica pigmented paint surfaces,” Proc. SPIE 4826, 79–86 (2003)..
[CrossRef]

J. B. Gao, Y. H. Cao, and J. M. Lee, “Principal component analysis of 1/f(alpha) noise,” Phys. Lett. A 314, 392–400 (2003).
[CrossRef]

R. A. Yotter and D. M. Wilson, “A review of photodetectors for sensing light-emitting reporters in biological systems,” IEEE Sens. J. 3, 288–303 (2003).
[CrossRef]

2002 (2)

L. P. Sung, M. E. Nadal, M. E. McKnight, E. Marx, and B. Laurenti, “Optical reflectance of metallic coatings: Effect of aluminum flake orientation,” J. Coat. Technol. 74, 55–63(2002).
[CrossRef]

J. Y. Hardeberg, F. Schmitt, and H. Brettel, “Multispectral color image capture using a liquid crystal tunable filter,” Opt. Eng. 41, 2532–2548 (2002).
[CrossRef]

2001 (1)

2000 (1)

N. Gat, “Imaging spectroscopy using tunable filters: A review,” Proc. SPIE 4056, 50–64 (2000).
[CrossRef]

1999 (2)

G. Pfaff and P. Reynders, “Angle-dependent optical effects deriving from submicron structures of films and pigments,” Chem. Rev. 99, 1963–1981 (1999).
[CrossRef]

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Quantified interference and diffraction in single Morpho butterfly scales,” Proc. R. Soc. London Ser. B 266, 1403–1411(1999).
[CrossRef]

1998 (1)

C. S. McCamy, “Observation and measurement of the appearance of metallic materials. Part II. Micro appearance,” Color Res. Appl. 23, 362–373 (1998).
[CrossRef]

1996 (1)

C. S. McCamy, “Observation and measurement of the appearance of metallic materials. 1. Macro appearance,” Color Res. Appl. 21, 292–304 (1996).
[CrossRef]

1994 (2)

G. Stolovitzky and K. R. Sreenivasan, “Kolmogorov refined similarity hypotheses for turbulence and general stochastic processes,” Rev. Mod. Phys. 66, 229–240 (1994).
[CrossRef]

G. E. Healey and R. Kondepudy, “Radiometric CCD camera calibration and noise estimation,” IEEE Trans. Pattern Anal. Machine Intell. 16, 267–276 (1994).
[CrossRef]

1992 (1)

P. J. B. Hancock, R. J. Baddeley, and L. S. Smith, “The principal components of natural images,” Netw. Comput. Neural Syst. 3, 61–70 (1992).
[CrossRef]

1990 (1)

H. J. A. Saris, R. J. B. Gottenbos, and H. Vanhouwelingen, “Correlation between visual and instrumental color differecnes of metallic paint films,” Color Res. Appl. 15, 200–2051990).
[CrossRef]

1985 (1)

A. F. H. Goetz, G. Vane, J. E. Solomon, and B. N. Rock, “Imaging spectrometry for Earth remote sensing,” Science 228, 1147–1153 (1985).
[CrossRef] [PubMed]

1976 (1)

F. W. Billmeyer and E. C. Carter, “Color and appearance of metallized paint films. 2. Initial application of turbid-medium theory,” J. Coat. Technol. 48, 53–60 (1976).

1974 (1)

F. W. Billmeyer and J. G. Davidson, “Color and appearance of metallized paint films. 1. Characterization,” J. Paint Technol. 46, 31–37 (1974).

1973 (1)

N. Ohta, “Estimating absorption-bands of component dyes by means of principal component analysis,” Anal. Chem. 45, 553–557 (1973).
[CrossRef]

Arai, H.

G. Baba and H. Arai, “Gonio-spectrophotometry of metal-flake and pearl-mica pigmented paint surfaces,” Proc. SPIE 4826, 79–86 (2003)..
[CrossRef]

Baba, G.

G. Baba and H. Arai, “Gonio-spectrophotometry of metal-flake and pearl-mica pigmented paint surfaces,” Proc. SPIE 4826, 79–86 (2003)..
[CrossRef]

Baddeley, R. J.

P. J. B. Hancock, R. J. Baddeley, and L. S. Smith, “The principal components of natural images,” Netw. Comput. Neural Syst. 3, 61–70 (1992).
[CrossRef]

Barthelemy, P.

P. Barthelemy, J. Bertolotti, K. Vynck, S. Lepri, and D. S. Wiersma, “Role of quenching on superdiffusive transport in two-dimensional random media,” Phys. Rev. E 82, 011101(2010).
[CrossRef]

J. Bertolotti, K. Vynck, L. Pattelli, P. Barthelemy, S. Lepri, and D. S. Wiersma, “Engineering disorder in superdiffusive Levy glasses,” Adv. Funct. Mater. 20, 965–968 (2010).
[CrossRef]

P. Barthelemy, J. Bertolotti, and D. S. Wiersma, “A Levy flight for light,” Nature 453, 495–498 (2008).
[CrossRef] [PubMed]

Berns, R. S.

D. Y. Tzeng and R. S. Berns, “A review of principal component analysis and its applications to color technology,” Color Res. Appl. 30, 84–98 (2005).
[CrossRef]

Bertolotti, J.

J. Bertolotti, K. Vynck, L. Pattelli, P. Barthelemy, S. Lepri, and D. S. Wiersma, “Engineering disorder in superdiffusive Levy glasses,” Adv. Funct. Mater. 20, 965–968 (2010).
[CrossRef]

P. Barthelemy, J. Bertolotti, K. Vynck, S. Lepri, and D. S. Wiersma, “Role of quenching on superdiffusive transport in two-dimensional random media,” Phys. Rev. E 82, 011101(2010).
[CrossRef]

P. Barthelemy, J. Bertolotti, and D. S. Wiersma, “A Levy flight for light,” Nature 453, 495–498 (2008).
[CrossRef] [PubMed]

Billmeyer, F. W.

F. W. Billmeyer and E. C. Carter, “Color and appearance of metallized paint films. 2. Initial application of turbid-medium theory,” J. Coat. Technol. 48, 53–60 (1976).

F. W. Billmeyer and J. G. Davidson, “Color and appearance of metallized paint films. 1. Characterization,” J. Paint Technol. 46, 31–37 (1974).

Brettel, H.

J. Y. Hardeberg, F. Schmitt, and H. Brettel, “Multispectral color image capture using a liquid crystal tunable filter,” Opt. Eng. 41, 2532–2548 (2002).
[CrossRef]

Cao, Y. H.

J. B. Gao, Y. H. Cao, and J. M. Lee, “Principal component analysis of 1/f(alpha) noise,” Phys. Lett. A 314, 392–400 (2003).
[CrossRef]

Carter, E. C.

F. W. Billmeyer and E. C. Carter, “Color and appearance of metallized paint films. 2. Initial application of turbid-medium theory,” J. Coat. Technol. 48, 53–60 (1976).

Correia, H. T.

J. M. Medina, L. M. Pereira, H. T. Correia, and S. Nascimento, “Hyperspectral optical imaging of human iris in vivo: characteristics of reflectance spectra,” J. Biomed. Opt. 16, 076001–076012 (2011).
[CrossRef] [PubMed]

Davidson, J. G.

F. W. Billmeyer and J. G. Davidson, “Color and appearance of metallized paint films. 1. Characterization,” J. Paint Technol. 46, 31–37 (1974).

Dekker, N.

N. Dekker, E. J. J. Kirchner, R. Super, G. J. van den Kieboom, and R. Gottenbos, “Total appearance differences for metallic and pearlescent materials: contributions from color and texture,” Color Res. Appl. 36, 4–14 (2011).
[CrossRef]

Dössel, K.-F.

H.-J. Streitberger and K.-F. Dössel, Automotive Paints and Coatings, 2nd ed. (Wiley-VCH, 2008).
[CrossRef]

Early, E. A.

M. E. Nadal and E. A. Early, “Color measurements for pearlescent coatings,” Color Res. Appl. 29, 38–42 (2004).
[CrossRef]

Funes, G.

G. Funes, D. Gulich, L. Zunino, D. G. Perez, and M. Garavaglia, “Behavior of the laser beam wandering variance with the turbulent path length,” Opt. Commun. 272, 476–479(2007).
[CrossRef]

Gao, J. B.

J. B. Gao, Y. H. Cao, and J. M. Lee, “Principal component analysis of 1/f(alpha) noise,” Phys. Lett. A 314, 392–400 (2003).
[CrossRef]

Garavaglia, M.

G. Funes, D. Gulich, L. Zunino, D. G. Perez, and M. Garavaglia, “Behavior of the laser beam wandering variance with the turbulent path length,” Opt. Commun. 272, 476–479(2007).
[CrossRef]

Gat, N.

N. Gat, “Imaging spectroscopy using tunable filters: A review,” Proc. SPIE 4056, 50–64 (2000).
[CrossRef]

Geladi, P.

H. F. Grahn and P. Geladi, Techniques and Applications of Hyperspectral Image Analysis (Wiley, 2007).
[CrossRef]

Goetz, A. F. H.

A. F. H. Goetz, G. Vane, J. E. Solomon, and B. N. Rock, “Imaging spectrometry for Earth remote sensing,” Science 228, 1147–1153 (1985).
[CrossRef] [PubMed]

Gottenbos, R.

N. Dekker, E. J. J. Kirchner, R. Super, G. J. van den Kieboom, and R. Gottenbos, “Total appearance differences for metallic and pearlescent materials: contributions from color and texture,” Color Res. Appl. 36, 4–14 (2011).
[CrossRef]

E. Kirchner, G. J. van den Kieboom, L. Njo, R. Super, and R. Gottenbos, “Observation of visual texture of metallic and pearlescent materials,” Color Res. Appl. 32, 256–266 (2007).
[CrossRef]

Gottenbos, R. J. B.

H. J. A. Saris, R. J. B. Gottenbos, and H. Vanhouwelingen, “Correlation between visual and instrumental color differecnes of metallic paint films,” Color Res. Appl. 15, 200–2051990).
[CrossRef]

Grahn, H. F.

H. F. Grahn and P. Geladi, Techniques and Applications of Hyperspectral Image Analysis (Wiley, 2007).
[CrossRef]

Gulich, D.

G. Funes, D. Gulich, L. Zunino, D. G. Perez, and M. Garavaglia, “Behavior of the laser beam wandering variance with the turbulent path length,” Opt. Commun. 272, 476–479(2007).
[CrossRef]

Hancock, P. J. B.

P. J. B. Hancock, R. J. Baddeley, and L. S. Smith, “The principal components of natural images,” Netw. Comput. Neural Syst. 3, 61–70 (1992).
[CrossRef]

Hardeberg, J. Y.

J. Y. Hardeberg, F. Schmitt, and H. Brettel, “Multispectral color image capture using a liquid crystal tunable filter,” Opt. Eng. 41, 2532–2548 (2002).
[CrossRef]

Harold, R. W.

R. Hunter and R. W. Harold, The Measurement of Appearance, 2nd ed. (Wiley, 1987).

Healey, G. E.

G. E. Healey and R. Kondepudy, “Radiometric CCD camera calibration and noise estimation,” IEEE Trans. Pattern Anal. Machine Intell. 16, 267–276 (1994).
[CrossRef]

Houweling, J.

E. Kirchner and J. Houweling, “Measuring flake orientation for metallic coatings,” Prog. Org. Coatings 64, 287–293 (2009).
[CrossRef]

Hunter, R.

R. Hunter and R. W. Harold, The Measurement of Appearance, 2nd ed. (Wiley, 1987).

Jollitffe, I. T.

I. T. Jollitffe, Principal Component Analysis, 2nd ed., Springer Series in Statistics (Springer-Verlag, 2002).

Kim, D. B.

D. B. Kim, M. K. Seo, K. Y. Kim, and K. H. Lee, “Acquisition and representation of pearlescent paints using an image-based goniospectrophotometer,” Opt. Eng. 49, 043604 (2010).
[CrossRef]

D. B. Kim, M. K. Seo, K. Y. Kim, and K. H. Lee, “Developing a multi-spectral HDR imaging module for a BRDF measurement system,” in Reflection, Scattering, and Diffraction from Surfaces II, Proceedings of SPIE-The International Society for Optical Engineering (SPIE, 2010).
[PubMed]

Kim, K. Y.

D. B. Kim, M. K. Seo, K. Y. Kim, and K. H. Lee, “Acquisition and representation of pearlescent paints using an image-based goniospectrophotometer,” Opt. Eng. 49, 043604 (2010).
[CrossRef]

D. B. Kim, M. K. Seo, K. Y. Kim, and K. H. Lee, “Developing a multi-spectral HDR imaging module for a BRDF measurement system,” in Reflection, Scattering, and Diffraction from Surfaces II, Proceedings of SPIE-The International Society for Optical Engineering (SPIE, 2010).
[PubMed]

Kinoshita, S.

S. Kinoshita, S. Yoshioka, and J. Miyazaki, “Physics of structural colors,” Rep. Prog. Phys. 71, 076401 (2008).
[CrossRef]

Kirchner, E.

E. Kirchner and J. Houweling, “Measuring flake orientation for metallic coatings,” Prog. Org. Coatings 64, 287–293 (2009).
[CrossRef]

E. Kirchner, “Film shrinkage and flake orientation,” Prog. Org. Coatings 65, 333–336 (2009).
[CrossRef]

E. Kirchner, G. J. van den Kieboom, L. Njo, R. Super, and R. Gottenbos, “Observation of visual texture of metallic and pearlescent materials,” Color Res. Appl. 32, 256–266 (2007).
[CrossRef]

Kirchner, E. J. J.

N. Dekker, E. J. J. Kirchner, R. Super, G. J. van den Kieboom, and R. Gottenbos, “Total appearance differences for metallic and pearlescent materials: contributions from color and texture,” Color Res. Appl. 36, 4–14 (2011).
[CrossRef]

Klein, G. A.

G. A. Klein, Industrial Color Physics, Springer Series in Optical Sciences (Springer, 2010).
[CrossRef]

Kondepudy, R.

G. E. Healey and R. Kondepudy, “Radiometric CCD camera calibration and noise estimation,” IEEE Trans. Pattern Anal. Machine Intell. 16, 267–276 (1994).
[CrossRef]

Kurylowicz, M.

M. Kurylowicz, C. H. Yu, and R. Pomes, “Systematic study of anharmonic features in a principal component analysis of gramicidin A,” Biophys. J. 98, 386–395 (2010).
[CrossRef] [PubMed]

Laurenti, B.

L. P. Sung, M. E. Nadal, M. E. McKnight, E. Marx, and B. Laurenti, “Optical reflectance of metallic coatings: Effect of aluminum flake orientation,” J. Coat. Technol. 74, 55–63(2002).
[CrossRef]

Lawrence, C.

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. London Ser. B 266, 1403–1411(1999).
[CrossRef]

Lee, J. M.

J. B. Gao, Y. H. Cao, and J. M. Lee, “Principal component analysis of 1/f(alpha) noise,” Phys. Lett. A 314, 392–400 (2003).
[CrossRef]

Lee, K. H.

D. B. Kim, M. K. Seo, K. Y. Kim, and K. H. Lee, “Acquisition and representation of pearlescent paints using an image-based goniospectrophotometer,” Opt. Eng. 49, 043604 (2010).
[CrossRef]

D. B. Kim, M. K. Seo, K. Y. Kim, and K. H. Lee, “Developing a multi-spectral HDR imaging module for a BRDF measurement system,” in Reflection, Scattering, and Diffraction from Surfaces II, Proceedings of SPIE-The International Society for Optical Engineering (SPIE, 2010).
[PubMed]

Lepri, S.

P. Barthelemy, J. Bertolotti, K. Vynck, S. Lepri, and D. S. Wiersma, “Role of quenching on superdiffusive transport in two-dimensional random media,” Phys. Rev. E 82, 011101(2010).
[CrossRef]

J. Bertolotti, K. Vynck, L. Pattelli, P. Barthelemy, S. Lepri, and D. S. Wiersma, “Engineering disorder in superdiffusive Levy glasses,” Adv. Funct. Mater. 20, 965–968 (2010).
[CrossRef]

Lewis, P. A.

P. A. Lewis, Pigment Handbook, Properties and Economics, 2nd ed. (Wiley, 1988), Vol.  1.

Mandelbrot, B. B.

B. B. Mandelbrot, The Fractal Geometry of Nature (W. H. Freeman, 1982).

Marx, E.

L. P. Sung, M. E. Nadal, M. E. McKnight, E. Marx, and B. Laurenti, “Optical reflectance of metallic coatings: Effect of aluminum flake orientation,” J. Coat. Technol. 74, 55–63(2002).
[CrossRef]

McCamy, C. S.

C. S. McCamy, “Observation and measurement of the appearance of metallic materials. Part II. Micro appearance,” Color Res. Appl. 23, 362–373 (1998).
[CrossRef]

C. S. McCamy, “Observation and measurement of the appearance of metallic materials. 1. Macro appearance,” Color Res. Appl. 21, 292–304 (1996).
[CrossRef]

McKnight, M. E.

L. P. Sung, M. E. Nadal, M. E. McKnight, E. Marx, and B. Laurenti, “Optical reflectance of metallic coatings: Effect of aluminum flake orientation,” J. Coat. Technol. 74, 55–63(2002).
[CrossRef]

Medina, J. M.

J. M. Medina, S. Nascimento, and P. Vukusic, “Hyperspectral optical imaging of two different species of lepidoptera,” Nanoscale Res. Lett. 6, 1–5 (2011).
[CrossRef]

J. M. Medina, L. M. Pereira, H. T. Correia, and S. Nascimento, “Hyperspectral optical imaging of human iris in vivo: characteristics of reflectance spectra,” J. Biomed. Opt. 16, 076001–076012 (2011).
[CrossRef] [PubMed]

J. M. Medina, “Linear basis for metallic and iridescent colors,” Appl. Opt. 47, 5644–5653 (2008).
[CrossRef] [PubMed]

Miyazaki, J.

S. Kinoshita, S. Yoshioka, and J. Miyazaki, “Physics of structural colors,” Rep. Prog. Phys. 71, 076401 (2008).
[CrossRef]

Murphy, A. B.

A. B. Murphy, “Modified Kubelka-Munk model for calculation of the reflectance of coatings with optically-rough surfaces,” J. Phys. D Appl. Phys. 39, 3571–3581 (2006).
[CrossRef]

Nadal, M. E.

M. E. Nadal and E. A. Early, “Color measurements for pearlescent coatings,” Color Res. Appl. 29, 38–42 (2004).
[CrossRef]

L. P. Sung, M. E. Nadal, M. E. McKnight, E. Marx, and B. Laurenti, “Optical reflectance of metallic coatings: Effect of aluminum flake orientation,” J. Coat. Technol. 74, 55–63(2002).
[CrossRef]

Nascimento, S.

J. M. Medina, S. Nascimento, and P. Vukusic, “Hyperspectral optical imaging of two different species of lepidoptera,” Nanoscale Res. Lett. 6, 1–5 (2011).
[CrossRef]

J. M. Medina, L. M. Pereira, H. T. Correia, and S. Nascimento, “Hyperspectral optical imaging of human iris in vivo: characteristics of reflectance spectra,” J. Biomed. Opt. 16, 076001–076012 (2011).
[CrossRef] [PubMed]

Njo, L.

E. Kirchner, G. J. van den Kieboom, L. Njo, R. Super, and R. Gottenbos, “Observation of visual texture of metallic and pearlescent materials,” Color Res. Appl. 32, 256–266 (2007).
[CrossRef]

Ohta, N.

N. Ohta, “Estimating absorption-bands of component dyes by means of principal component analysis,” Anal. Chem. 45, 553–557 (1973).
[CrossRef]

Pattelli, L.

J. Bertolotti, K. Vynck, L. Pattelli, P. Barthelemy, S. Lepri, and D. S. Wiersma, “Engineering disorder in superdiffusive Levy glasses,” Adv. Funct. Mater. 20, 965–968 (2010).
[CrossRef]

Pereira, L. M.

J. M. Medina, L. M. Pereira, H. T. Correia, and S. Nascimento, “Hyperspectral optical imaging of human iris in vivo: characteristics of reflectance spectra,” J. Biomed. Opt. 16, 076001–076012 (2011).
[CrossRef] [PubMed]

Perez, D. G.

G. Funes, D. Gulich, L. Zunino, D. G. Perez, and M. Garavaglia, “Behavior of the laser beam wandering variance with the turbulent path length,” Opt. Commun. 272, 476–479(2007).
[CrossRef]

Pfaff, G.

G. Pfaff and P. Reynders, “Angle-dependent optical effects deriving from submicron structures of films and pigments,” Chem. Rev. 99, 1963–1981 (1999).
[CrossRef]

Pomes, R.

M. Kurylowicz, C. H. Yu, and R. Pomes, “Systematic study of anharmonic features in a principal component analysis of gramicidin A,” Biophys. J. 98, 386–395 (2010).
[CrossRef] [PubMed]

Reynders, P.

G. Pfaff and P. Reynders, “Angle-dependent optical effects deriving from submicron structures of films and pigments,” Chem. Rev. 99, 1963–1981 (1999).
[CrossRef]

Rock, B. N.

A. F. H. Goetz, G. Vane, J. E. Solomon, and B. N. Rock, “Imaging spectrometry for Earth remote sensing,” Science 228, 1147–1153 (1985).
[CrossRef] [PubMed]

Rogers, G. L.

Sambles, J. 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. London Ser. B 266, 1403–1411(1999).
[CrossRef]

Sambles, R.

Saris, H. J. A.

H. J. A. Saris, R. J. B. Gottenbos, and H. Vanhouwelingen, “Correlation between visual and instrumental color differecnes of metallic paint films,” Color Res. Appl. 15, 200–2051990).
[CrossRef]

Schmitt, F.

J. Y. Hardeberg, F. Schmitt, and H. Brettel, “Multispectral color image capture using a liquid crystal tunable filter,” Opt. Eng. 41, 2532–2548 (2002).
[CrossRef]

Seo, M. K.

D. B. Kim, M. K. Seo, K. Y. Kim, and K. H. Lee, “Acquisition and representation of pearlescent paints using an image-based goniospectrophotometer,” Opt. Eng. 49, 043604 (2010).
[CrossRef]

D. B. Kim, M. K. Seo, K. Y. Kim, and K. H. Lee, “Developing a multi-spectral HDR imaging module for a BRDF measurement system,” in Reflection, Scattering, and Diffraction from Surfaces II, Proceedings of SPIE-The International Society for Optical Engineering (SPIE, 2010).
[PubMed]

Smith, L. S.

P. J. B. Hancock, R. J. Baddeley, and L. S. Smith, “The principal components of natural images,” Netw. Comput. Neural Syst. 3, 61–70 (1992).
[CrossRef]

Solomon, J. E.

A. F. H. Goetz, G. Vane, J. E. Solomon, and B. N. Rock, “Imaging spectrometry for Earth remote sensing,” Science 228, 1147–1153 (1985).
[CrossRef] [PubMed]

Sreenivasan, K. R.

G. Stolovitzky and K. R. Sreenivasan, “Kolmogorov refined similarity hypotheses for turbulence and general stochastic processes,” Rev. Mod. Phys. 66, 229–240 (1994).
[CrossRef]

Stolovitzky, G.

G. Stolovitzky and K. R. Sreenivasan, “Kolmogorov refined similarity hypotheses for turbulence and general stochastic processes,” Rev. Mod. Phys. 66, 229–240 (1994).
[CrossRef]

Streitberger, H.-J.

H.-J. Streitberger and K.-F. Dössel, Automotive Paints and Coatings, 2nd ed. (Wiley-VCH, 2008).
[CrossRef]

Sung, L. P.

L. P. Sung, M. E. Nadal, M. E. McKnight, E. Marx, and B. Laurenti, “Optical reflectance of metallic coatings: Effect of aluminum flake orientation,” J. Coat. Technol. 74, 55–63(2002).
[CrossRef]

Super, R.

N. Dekker, E. J. J. Kirchner, R. Super, G. J. van den Kieboom, and R. Gottenbos, “Total appearance differences for metallic and pearlescent materials: contributions from color and texture,” Color Res. Appl. 36, 4–14 (2011).
[CrossRef]

E. Kirchner, G. J. van den Kieboom, L. Njo, R. Super, and R. Gottenbos, “Observation of visual texture of metallic and pearlescent materials,” Color Res. Appl. 32, 256–266 (2007).
[CrossRef]

Tracton, A. A.

A. A. Tracton, Coatings Technology Handbook, 3rd ed. (Taylor & Francis Group, 2006).
[CrossRef]

Tzeng, D. Y.

D. Y. Tzeng and R. S. Berns, “A review of principal component analysis and its applications to color technology,” Color Res. Appl. 30, 84–98 (2005).
[CrossRef]

van den Kieboom, G. J.

N. Dekker, E. J. J. Kirchner, R. Super, G. J. van den Kieboom, and R. Gottenbos, “Total appearance differences for metallic and pearlescent materials: contributions from color and texture,” Color Res. Appl. 36, 4–14 (2011).
[CrossRef]

E. Kirchner, G. J. van den Kieboom, L. Njo, R. Super, and R. Gottenbos, “Observation of visual texture of metallic and pearlescent materials,” Color Res. Appl. 32, 256–266 (2007).
[CrossRef]

Vane, G.

A. F. H. Goetz, G. Vane, J. E. Solomon, and B. N. Rock, “Imaging spectrometry for Earth remote sensing,” Science 228, 1147–1153 (1985).
[CrossRef] [PubMed]

Vanhouwelingen, H.

H. J. A. Saris, R. J. B. Gottenbos, and H. Vanhouwelingen, “Correlation between visual and instrumental color differecnes of metallic paint films,” Color Res. Appl. 15, 200–2051990).
[CrossRef]

Völz, H. G.

H. G. Völz, Industrial Color Testing, Fundamentals and Techniques, 2nd ed. (Wiley-VCH, 2001).
[CrossRef]

Vukusic, P.

J. M. Medina, S. Nascimento, and P. Vukusic, “Hyperspectral optical imaging of two different species of lepidoptera,” Nanoscale Res. Lett. 6, 1–5 (2011).
[CrossRef]

P. Vukusic, R. Sambles, C. Lawrence, and G. Wakely, “Sculpted-multilayer optical effects in two species of Papilio butterfly,” Appl. Opt. 40, 1116–1125 (2001).
[CrossRef]

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Quantified interference and diffraction in single Morpho butterfly scales,” Proc. R. Soc. London Ser. B 266, 1403–1411(1999).
[CrossRef]

Vynck, K.

P. Barthelemy, J. Bertolotti, K. Vynck, S. Lepri, and D. S. Wiersma, “Role of quenching on superdiffusive transport in two-dimensional random media,” Phys. Rev. E 82, 011101(2010).
[CrossRef]

J. Bertolotti, K. Vynck, L. Pattelli, P. Barthelemy, S. Lepri, and D. S. Wiersma, “Engineering disorder in superdiffusive Levy glasses,” Adv. Funct. Mater. 20, 965–968 (2010).
[CrossRef]

Wakely, G.

Wiersma, D. S.

P. Barthelemy, J. Bertolotti, K. Vynck, S. Lepri, and D. S. Wiersma, “Role of quenching on superdiffusive transport in two-dimensional random media,” Phys. Rev. E 82, 011101(2010).
[CrossRef]

J. Bertolotti, K. Vynck, L. Pattelli, P. Barthelemy, S. Lepri, and D. S. Wiersma, “Engineering disorder in superdiffusive Levy glasses,” Adv. Funct. Mater. 20, 965–968 (2010).
[CrossRef]

P. Barthelemy, J. Bertolotti, and D. S. Wiersma, “A Levy flight for light,” Nature 453, 495–498 (2008).
[CrossRef] [PubMed]

Wilson, D. M.

R. A. Yotter and D. M. Wilson, “A review of photodetectors for sensing light-emitting reporters in biological systems,” IEEE Sens. J. 3, 288–303 (2003).
[CrossRef]

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. London Ser. B 266, 1403–1411(1999).
[CrossRef]

Yoshioka, S.

S. Kinoshita, S. Yoshioka, and J. Miyazaki, “Physics of structural colors,” Rep. Prog. Phys. 71, 076401 (2008).
[CrossRef]

Yotter, R. A.

R. A. Yotter and D. M. Wilson, “A review of photodetectors for sensing light-emitting reporters in biological systems,” IEEE Sens. J. 3, 288–303 (2003).
[CrossRef]

Yu, C. H.

M. Kurylowicz, C. H. Yu, and R. Pomes, “Systematic study of anharmonic features in a principal component analysis of gramicidin A,” Biophys. J. 98, 386–395 (2010).
[CrossRef] [PubMed]

Zunino, L.

G. Funes, D. Gulich, L. Zunino, D. G. Perez, and M. Garavaglia, “Behavior of the laser beam wandering variance with the turbulent path length,” Opt. Commun. 272, 476–479(2007).
[CrossRef]

Adv. Funct. Mater. (1)

J. Bertolotti, K. Vynck, L. Pattelli, P. Barthelemy, S. Lepri, and D. S. Wiersma, “Engineering disorder in superdiffusive Levy glasses,” Adv. Funct. Mater. 20, 965–968 (2010).
[CrossRef]

Anal. Chem. (1)

N. Ohta, “Estimating absorption-bands of component dyes by means of principal component analysis,” Anal. Chem. 45, 553–557 (1973).
[CrossRef]

Appl. Opt. (2)

Biophys. J. (1)

M. Kurylowicz, C. H. Yu, and R. Pomes, “Systematic study of anharmonic features in a principal component analysis of gramicidin A,” Biophys. J. 98, 386–395 (2010).
[CrossRef] [PubMed]

Chem. Rev. (1)

G. Pfaff and P. Reynders, “Angle-dependent optical effects deriving from submicron structures of films and pigments,” Chem. Rev. 99, 1963–1981 (1999).
[CrossRef]

Color Res. Appl. (7)

C. S. McCamy, “Observation and measurement of the appearance of metallic materials. Part II. Micro appearance,” Color Res. Appl. 23, 362–373 (1998).
[CrossRef]

M. E. Nadal and E. A. Early, “Color measurements for pearlescent coatings,” Color Res. Appl. 29, 38–42 (2004).
[CrossRef]

E. Kirchner, G. J. van den Kieboom, L. Njo, R. Super, and R. Gottenbos, “Observation of visual texture of metallic and pearlescent materials,” Color Res. Appl. 32, 256–266 (2007).
[CrossRef]

N. Dekker, E. J. J. Kirchner, R. Super, G. J. van den Kieboom, and R. Gottenbos, “Total appearance differences for metallic and pearlescent materials: contributions from color and texture,” Color Res. Appl. 36, 4–14 (2011).
[CrossRef]

C. S. McCamy, “Observation and measurement of the appearance of metallic materials. 1. Macro appearance,” Color Res. Appl. 21, 292–304 (1996).
[CrossRef]

H. J. A. Saris, R. J. B. Gottenbos, and H. Vanhouwelingen, “Correlation between visual and instrumental color differecnes of metallic paint films,” Color Res. Appl. 15, 200–2051990).
[CrossRef]

D. Y. Tzeng and R. S. Berns, “A review of principal component analysis and its applications to color technology,” Color Res. Appl. 30, 84–98 (2005).
[CrossRef]

IEEE Sens. J. (1)

R. A. Yotter and D. M. Wilson, “A review of photodetectors for sensing light-emitting reporters in biological systems,” IEEE Sens. J. 3, 288–303 (2003).
[CrossRef]

IEEE Trans. Pattern Anal. Machine Intell. (1)

G. E. Healey and R. Kondepudy, “Radiometric CCD camera calibration and noise estimation,” IEEE Trans. Pattern Anal. Machine Intell. 16, 267–276 (1994).
[CrossRef]

J. Biomed. Opt. (1)

J. M. Medina, L. M. Pereira, H. T. Correia, and S. Nascimento, “Hyperspectral optical imaging of human iris in vivo: characteristics of reflectance spectra,” J. Biomed. Opt. 16, 076001–076012 (2011).
[CrossRef] [PubMed]

J. Coat. Technol. (2)

F. W. Billmeyer and E. C. Carter, “Color and appearance of metallized paint films. 2. Initial application of turbid-medium theory,” J. Coat. Technol. 48, 53–60 (1976).

L. P. Sung, M. E. Nadal, M. E. McKnight, E. Marx, and B. Laurenti, “Optical reflectance of metallic coatings: Effect of aluminum flake orientation,” J. Coat. Technol. 74, 55–63(2002).
[CrossRef]

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

J. Paint Technol. (1)

F. W. Billmeyer and J. G. Davidson, “Color and appearance of metallized paint films. 1. Characterization,” J. Paint Technol. 46, 31–37 (1974).

J. Phys. D Appl. Phys. (1)

A. B. Murphy, “Modified Kubelka-Munk model for calculation of the reflectance of coatings with optically-rough surfaces,” J. Phys. D Appl. Phys. 39, 3571–3581 (2006).
[CrossRef]

Nanoscale Res. Lett. (1)

J. M. Medina, S. Nascimento, and P. Vukusic, “Hyperspectral optical imaging of two different species of lepidoptera,” Nanoscale Res. Lett. 6, 1–5 (2011).
[CrossRef]

Nature (1)

P. Barthelemy, J. Bertolotti, and D. S. Wiersma, “A Levy flight for light,” Nature 453, 495–498 (2008).
[CrossRef] [PubMed]

Netw. Comput. Neural Syst. (1)

P. J. B. Hancock, R. J. Baddeley, and L. S. Smith, “The principal components of natural images,” Netw. Comput. Neural Syst. 3, 61–70 (1992).
[CrossRef]

Opt. Commun. (1)

G. Funes, D. Gulich, L. Zunino, D. G. Perez, and M. Garavaglia, “Behavior of the laser beam wandering variance with the turbulent path length,” Opt. Commun. 272, 476–479(2007).
[CrossRef]

Opt. Eng. (2)

D. B. Kim, M. K. Seo, K. Y. Kim, and K. H. Lee, “Acquisition and representation of pearlescent paints using an image-based goniospectrophotometer,” Opt. Eng. 49, 043604 (2010).
[CrossRef]

J. Y. Hardeberg, F. Schmitt, and H. Brettel, “Multispectral color image capture using a liquid crystal tunable filter,” Opt. Eng. 41, 2532–2548 (2002).
[CrossRef]

Phys. Lett. A (1)

J. B. Gao, Y. H. Cao, and J. M. Lee, “Principal component analysis of 1/f(alpha) noise,” Phys. Lett. A 314, 392–400 (2003).
[CrossRef]

Phys. Rev. E (1)

P. Barthelemy, J. Bertolotti, K. Vynck, S. Lepri, and D. S. Wiersma, “Role of quenching on superdiffusive transport in two-dimensional random media,” Phys. Rev. E 82, 011101(2010).
[CrossRef]

Proc. R. Soc. London Ser. B (1)

P. Vukusic, J. R. Sambles, C. R. Lawrence, and R. J. Wootton, “Quantified interference and diffraction in single Morpho butterfly scales,” Proc. R. Soc. London Ser. B 266, 1403–1411(1999).
[CrossRef]

Proc. SPIE (1)

G. Baba and H. Arai, “Gonio-spectrophotometry of metal-flake and pearl-mica pigmented paint surfaces,” Proc. SPIE 4826, 79–86 (2003)..
[CrossRef]

Proc. SPIE (1)

N. Gat, “Imaging spectroscopy using tunable filters: A review,” Proc. SPIE 4056, 50–64 (2000).
[CrossRef]

Prog. Org. Coatings (2)

E. Kirchner and J. Houweling, “Measuring flake orientation for metallic coatings,” Prog. Org. Coatings 64, 287–293 (2009).
[CrossRef]

E. Kirchner, “Film shrinkage and flake orientation,” Prog. Org. Coatings 65, 333–336 (2009).
[CrossRef]

Rep. Prog. Phys. (1)

S. Kinoshita, S. Yoshioka, and J. Miyazaki, “Physics of structural colors,” Rep. Prog. Phys. 71, 076401 (2008).
[CrossRef]

Rev. Mod. Phys. (1)

G. Stolovitzky and K. R. Sreenivasan, “Kolmogorov refined similarity hypotheses for turbulence and general stochastic processes,” Rev. Mod. Phys. 66, 229–240 (1994).
[CrossRef]

Science (1)

A. F. H. Goetz, G. Vane, J. E. Solomon, and B. N. Rock, “Imaging spectrometry for Earth remote sensing,” Science 228, 1147–1153 (1985).
[CrossRef] [PubMed]

Other (14)

H. F. Grahn and P. Geladi, Techniques and Applications of Hyperspectral Image Analysis (Wiley, 2007).
[CrossRef]

D. B. Kim, M. K. Seo, K. Y. Kim, and K. H. Lee, “Developing a multi-spectral HDR imaging module for a BRDF measurement system,” in Reflection, Scattering, and Diffraction from Surfaces II, Proceedings of SPIE-The International Society for Optical Engineering (SPIE, 2010).
[PubMed]

I. T. Jollitffe, Principal Component Analysis, 2nd ed., Springer Series in Statistics (Springer-Verlag, 2002).

B. B. Mandelbrot, The Fractal Geometry of Nature (W. H. Freeman, 1982).

P. A. Lewis, Pigment Handbook, Properties and Economics, 2nd ed. (Wiley, 1988), Vol.  1.

A. A. Tracton, Coatings Technology Handbook, 3rd ed. (Taylor & Francis Group, 2006).
[CrossRef]

H.-J. Streitberger and K.-F. Dössel, Automotive Paints and Coatings, 2nd ed. (Wiley-VCH, 2008).
[CrossRef]

H. G. Völz, Industrial Color Testing, Fundamentals and Techniques, 2nd ed. (Wiley-VCH, 2001).
[CrossRef]

G. A. Klein, Industrial Color Physics, Springer Series in Optical Sciences (Springer, 2010).
[CrossRef]

R. Hunter and R. W. Harold, The Measurement of Appearance, 2nd ed. (Wiley, 1987).

“Standard terminology of appearance,” Rep. No. ASTM E284-95a (American Society for Testing and Materials, 1995).

“Farbtoleranzen für Automobillackierungen—Teil 2: Effektlackierungen,” Rep. No. DIN 6175-2 (Deutsches Institut für Normung e.V., 2001).

“Standard practice for specifying the geometry of multiangle spectrophotometers,” Rep. No. ASTM E2175-01 (American Society for Testing and Materials, 2001).

“Standard practice for multiangle color measurement of interference pigments,” Rep. No. ASTM E2539-08 (American Society for Testing and Materials, 2008).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

(a) Schematic representation of the illumination system. (b) Schematic representation of the entire hyperspectral imaging system. Light from the Xenon lamp is filtered by a liquid crystal tunable filter (LCTF) and projected to the metallic sample by two mirrors. The mirrors can be rotated to adjust the illumination angle to the CIE geometry 45 ° / 0 ° (Commission Internationale de l’Éclairage, International Commission on Illumination CIE geometry 45 ° / 0 ° ).

Fig. 2
Fig. 2

Optical image of two representative metallic samples labeled as metallic yellow and metallic blue ( 3 × ).

Fig. 3
Fig. 3

(a) Microscopic image of the two metallic samples containing lenticular aluminum and yellow iron oxide nanoparticles (metallic yellow sample) and blue indanthrone nanoparticles (metallic blue sample) ( 20 × , bright field illumination). (b) SEMs of the metallic yellow and blue samples when the lacquer was removed ( 3000 × ).

Fig. 4
Fig. 4

Semilogarithmic plot of the spectral reflectance curves at two representative CCD’s pixels labeled as “1” and “2” in the metallic yellow and blue samples. ( a.u. = arbitrary units ).

Fig. 5
Fig. 5

Color coordinates derived from reflectance spectra in the metallic yellow and blue samples. (a) CIE-1931 chromaticity diagram. (b) CIELAB color space. Data were calculated by means of the CIE 2 ° standard observer and the D65 illuminant. Only a fraction of color coordinates is represented.

Fig. 6
Fig. 6

The first six basis functions of the metallic yellow and blue samples derived from PCA. The percentage in each basis indicates the cumulative variance accounted for.

Fig. 7
Fig. 7

Double logarithmic plot of the eigenvalue spectrum for each metallic sample derived from PCA. Solid circles and squares indicate the metallic yellow and blue samples, respectively. Black solid lines show the adjusted power laws. The slope γ indicates power-law scaling at different regimes. Numbers in parentheses represent the associated standard errors.

Fig. 8
Fig. 8

Double logarithmic plot of the eigenvalue spectrum in pigmented thin films. Hyperspectral data collection of diffuse reflectance was similar to the analyzed metallic coatings. (a) Anomalous diffusive scattering in nanostructured photonic crystals exemplified by two different types of Lepidoptera: Morpho Didius (solid circles) versus Papilio Palinurus (solid squares). (b) Anomalous diffusive scattering in biological tissues exemplified by two human irises: light (bluish) versus dark pigmented (brownish) iris in vivo represented by solid circles and squares, respectively. Black solid lines show the adjusted power laws. The slope γ indicates power-law scaling at different regimes. Numbers in parentheses represent the associated standard errors.

Equations (3)

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

γ = 2 H + 1.
R i , j ( λ ) = ρ ( I i , j ( λ ) D C i , j ( λ ) W i , j ( λ ) D C i , j ( λ ) ) ,
R i , j k = R ¯ + α i , j 1 S i , j 1 + α i , j 2 S i , j 2 + + α i , j 53 S i , j 53 ,

Metrics