Abstract

A type of representation of the spectral bidirectional reflectance distribution function (BRDF) is proposed that distinctly separates the spectral variable (wavelength) from the geometrical variables (spherical coordinates of the irradiation and viewing directions). Principal components analysis (PCA) is used in order to decompose the spectral BRDF in decorrelated spectral components, and the weight that they have at every geometrical configuration of irradiation/viewing is established. This method was applied to the spectral BRDF measurement of a special effect pigment sample, and four principal components with relevant variance were identified. These four components are enough to reproduce the great diversity of spectral reflectances observed at different geometrical configurations. Since this representation is able to separate spectral and geometrical variables, it facilitates the interpretation of the color variation of special effect pigments coatings versus the geometrical configuration of irradiation/viewing.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments—past, present and future” Progr. Organic Coatings 54, 150–163 (2005).
  2. M. Mikula, M. Ceppan, and K. Vaško, “Gloss and goniocolorimetry of printed materials,” Color Res. Appl. 28, 335–342 (2003).
    [CrossRef]
  3. M. E. Nadal and E. A. Early, “Color measurements for pearlescent coatings,” Color Res. Appl. 29, 38–42 (2004).
    [CrossRef]
  4. H. J. Streitberger and K. F. Dössel, Automotive Paints and Coatings (Wiley-VCH, 2008).
  5. P. Dutré, K. Bala, and P. Bekaert, Advanced Global Illumination (A K Peters, 2006).
  6. J. Dorsey, H. Rushmeier, and F. Sillion, Digital Modelling of Material Appearance (Elsevier, 2007).
  7. G. Müller, J. Meseth, M. Sattler, R. Sarlette, and R. Klein, “Acquisition, synthesis and rendering of bidirectional texture functions,” Comput. Graph. Forum 24, 83–109 (2005).
    [CrossRef]
  8. G. Baba, “Gonio-spectrophotometric analysis of pearl-mica paint,” Die Farbe 37, 99–110 (1990).
  9. T. A. Germer and M. E. Nadal, “Modeling the appearance of special effect pigment coatings,” Proc. SPIE 4447, 77–86 (2001).
    [CrossRef]
  10. M. E. Nadal and T. A. Germer, “Colorimetric characterization of pearlescent coatings,” in Proceedings of AIC Color(2001), pp. 757–760.
  11. B. Parker, “Color shift of light interference pigments,” Surf. Coat. Aust. 39, 10–13 (2002).
  12. F. Leloup, P. Hanselaer, M. Pointer, and J. Versluys, “Characterization of gonio-apparent colours,” in Proceedings of AIC Color (2005), pp. 515–518.
  13. C. A. Nicholls, Visual and instrumental characterisation of special-effect colours, Ph.D. thesis (University of Leeds, 2000).
  14. R. Besold, “Metallic effect-characterization, parameter and methods for instrumentally determination,” Die Farbe 37, 79–85(1990).
  15. DIN standard 6175-2, “Colour tolerances for automobile lacquer finishes, Part 2: Effect lacquer finishes” (2001).
  16. DIN standard 6175-2, “Tolerances for automotive paints, Part 2: Goniochromatic paints (Farbtoleranzen für Automobillackierungen-Teil 2: Effektlackierungen)” (2001).
  17. E. Chorro, E. Perales, F. M. Martínez-Verdú, J. Campos, and A. Pons, “Colorimetric and spectral evaluation of the optical anisotropy of metallic and pearlescent samples,” J. Mod. Opt. 56, 1457–1465 (2009).
    [CrossRef]
  18. E. Kirchner, G. J. Van den Kiebomm, L. Njo, R. Supér, and R. Gottenbos, “Observation of visual texture of metallic and pearlescent materials,” Color Res. Appl. 32, 256–266 (2007).
    [CrossRef]
  19. F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Geometrical Considerations and Nomenclature for Reflectance, National Bureau of Standards Monograph 161 (National Bureau of Standards, 1977).
  20. Colorstream T20-02 WNT Artic Fire, Product Information, Colorstream. Merck KgaA (2004).
  21. A. M. Rabal, A. Ferrero, J. L. Fontecha, A. Pons, J. Campos, A. Corróns, and A. M. Rubiño, “Gonio-spectrophotometer for low-uncertainty measurements of bidirectional scattering distribution function (BSDF),” in Proceedings of CIE Expert Symposium on Spectral and Imaging Methods for Photometry and Radiometry, Publication CIE x036: 2010 (CIE, 2010), pp. 79–84.
  22. A. M. Rabal, A. Ferrero, J. L. Fontecha, A. Pons, J. Campos, and A. Corróns, “Gonio-spectrophotometer for bidirectional scattering distribution function (BSDF) measurements,” Opt. Pura Apl. 44, 137–147 (2011).
  23. A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio-spectrophotometer for the absolute measurement of the spectral BRDF at in- and out-of-plane retroreflection geometries,” Metrologia 49, 213–223 (2012).
  24. A. Ferrero, J. Campos, A. M. Rabal, A. Pons, M. L. Hernanz, and A. Corróns, “Principal components analysis on the spectral bidirectional reflectance distribution function of ceramic colour standards,” Opt. Express 19, 19199–19211 (2011).
    [CrossRef]
  25. A. Ferrero, J. Alda, J. Campos, J. M. López-Alonso, and A. Pons, “Principal components analysis of the photoresponse nonuniformity of a matrix detector,” Appl. Opt. 46, 9–17(2007).
    [CrossRef]
  26. J. L. Simonds, “Application of characteristic vector analysis to photographic and optical response data,” J. Opt. Soc. Am. 53, 968–971 (1963).
    [CrossRef]
  27. J. M. López-Alonso, J. Alda, and E. Bernabéu, “Principal-component characterization of noise for infrared images,” Appl. Opt. 41, 320–331 (2002).
    [CrossRef]

2012 (1)

A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio-spectrophotometer for the absolute measurement of the spectral BRDF at in- and out-of-plane retroreflection geometries,” Metrologia 49, 213–223 (2012).

2011 (2)

A. Ferrero, J. Campos, A. M. Rabal, A. Pons, M. L. Hernanz, and A. Corróns, “Principal components analysis on the spectral bidirectional reflectance distribution function of ceramic colour standards,” Opt. Express 19, 19199–19211 (2011).
[CrossRef]

A. M. Rabal, A. Ferrero, J. L. Fontecha, A. Pons, J. Campos, and A. Corróns, “Gonio-spectrophotometer for bidirectional scattering distribution function (BSDF) measurements,” Opt. Pura Apl. 44, 137–147 (2011).

2009 (1)

E. Chorro, E. Perales, F. M. Martínez-Verdú, J. Campos, and A. Pons, “Colorimetric and spectral evaluation of the optical anisotropy of metallic and pearlescent samples,” J. Mod. Opt. 56, 1457–1465 (2009).
[CrossRef]

2007 (2)

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

A. Ferrero, J. Alda, J. Campos, J. M. López-Alonso, and A. Pons, “Principal components analysis of the photoresponse nonuniformity of a matrix detector,” Appl. Opt. 46, 9–17(2007).
[CrossRef]

2005 (2)

F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments—past, present and future” Progr. Organic Coatings 54, 150–163 (2005).

G. Müller, J. Meseth, M. Sattler, R. Sarlette, and R. Klein, “Acquisition, synthesis and rendering of bidirectional texture functions,” Comput. Graph. Forum 24, 83–109 (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 (1)

M. Mikula, M. Ceppan, and K. Vaško, “Gloss and goniocolorimetry of printed materials,” Color Res. Appl. 28, 335–342 (2003).
[CrossRef]

2002 (2)

2001 (1)

T. A. Germer and M. E. Nadal, “Modeling the appearance of special effect pigment coatings,” Proc. SPIE 4447, 77–86 (2001).
[CrossRef]

1990 (2)

R. Besold, “Metallic effect-characterization, parameter and methods for instrumentally determination,” Die Farbe 37, 79–85(1990).

G. Baba, “Gonio-spectrophotometric analysis of pearl-mica paint,” Die Farbe 37, 99–110 (1990).

1963 (1)

Alda, J.

Baba, G.

G. Baba, “Gonio-spectrophotometric analysis of pearl-mica paint,” Die Farbe 37, 99–110 (1990).

Bala, K.

P. Dutré, K. Bala, and P. Bekaert, Advanced Global Illumination (A K Peters, 2006).

Bekaert, P.

P. Dutré, K. Bala, and P. Bekaert, Advanced Global Illumination (A K Peters, 2006).

Bernabéu, E.

Besold, R.

R. Besold, “Metallic effect-characterization, parameter and methods for instrumentally determination,” Die Farbe 37, 79–85(1990).

Campos, J.

A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio-spectrophotometer for the absolute measurement of the spectral BRDF at in- and out-of-plane retroreflection geometries,” Metrologia 49, 213–223 (2012).

A. M. Rabal, A. Ferrero, J. L. Fontecha, A. Pons, J. Campos, and A. Corróns, “Gonio-spectrophotometer for bidirectional scattering distribution function (BSDF) measurements,” Opt. Pura Apl. 44, 137–147 (2011).

A. Ferrero, J. Campos, A. M. Rabal, A. Pons, M. L. Hernanz, and A. Corróns, “Principal components analysis on the spectral bidirectional reflectance distribution function of ceramic colour standards,” Opt. Express 19, 19199–19211 (2011).
[CrossRef]

E. Chorro, E. Perales, F. M. Martínez-Verdú, J. Campos, and A. Pons, “Colorimetric and spectral evaluation of the optical anisotropy of metallic and pearlescent samples,” J. Mod. Opt. 56, 1457–1465 (2009).
[CrossRef]

A. Ferrero, J. Alda, J. Campos, J. M. López-Alonso, and A. Pons, “Principal components analysis of the photoresponse nonuniformity of a matrix detector,” Appl. Opt. 46, 9–17(2007).
[CrossRef]

A. M. Rabal, A. Ferrero, J. L. Fontecha, A. Pons, J. Campos, A. Corróns, and A. M. Rubiño, “Gonio-spectrophotometer for low-uncertainty measurements of bidirectional scattering distribution function (BSDF),” in Proceedings of CIE Expert Symposium on Spectral and Imaging Methods for Photometry and Radiometry, Publication CIE x036: 2010 (CIE, 2010), pp. 79–84.

Ceppan, M.

M. Mikula, M. Ceppan, and K. Vaško, “Gloss and goniocolorimetry of printed materials,” Color Res. Appl. 28, 335–342 (2003).
[CrossRef]

Chorro, E.

E. Chorro, E. Perales, F. M. Martínez-Verdú, J. Campos, and A. Pons, “Colorimetric and spectral evaluation of the optical anisotropy of metallic and pearlescent samples,” J. Mod. Opt. 56, 1457–1465 (2009).
[CrossRef]

Corróns, A.

A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio-spectrophotometer for the absolute measurement of the spectral BRDF at in- and out-of-plane retroreflection geometries,” Metrologia 49, 213–223 (2012).

A. Ferrero, J. Campos, A. M. Rabal, A. Pons, M. L. Hernanz, and A. Corróns, “Principal components analysis on the spectral bidirectional reflectance distribution function of ceramic colour standards,” Opt. Express 19, 19199–19211 (2011).
[CrossRef]

A. M. Rabal, A. Ferrero, J. L. Fontecha, A. Pons, J. Campos, and A. Corróns, “Gonio-spectrophotometer for bidirectional scattering distribution function (BSDF) measurements,” Opt. Pura Apl. 44, 137–147 (2011).

A. M. Rabal, A. Ferrero, J. L. Fontecha, A. Pons, J. Campos, A. Corróns, and A. M. Rubiño, “Gonio-spectrophotometer for low-uncertainty measurements of bidirectional scattering distribution function (BSDF),” in Proceedings of CIE Expert Symposium on Spectral and Imaging Methods for Photometry and Radiometry, Publication CIE x036: 2010 (CIE, 2010), pp. 79–84.

Dorsey, J.

J. Dorsey, H. Rushmeier, and F. Sillion, Digital Modelling of Material Appearance (Elsevier, 2007).

Dössel, K. F.

H. J. Streitberger and K. F. Dössel, Automotive Paints and Coatings (Wiley-VCH, 2008).

Dutré, P.

P. Dutré, K. Bala, and P. Bekaert, Advanced Global Illumination (A K Peters, 2006).

Early, E. A.

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

Ferrero, A.

A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio-spectrophotometer for the absolute measurement of the spectral BRDF at in- and out-of-plane retroreflection geometries,” Metrologia 49, 213–223 (2012).

A. Ferrero, J. Campos, A. M. Rabal, A. Pons, M. L. Hernanz, and A. Corróns, “Principal components analysis on the spectral bidirectional reflectance distribution function of ceramic colour standards,” Opt. Express 19, 19199–19211 (2011).
[CrossRef]

A. M. Rabal, A. Ferrero, J. L. Fontecha, A. Pons, J. Campos, and A. Corróns, “Gonio-spectrophotometer for bidirectional scattering distribution function (BSDF) measurements,” Opt. Pura Apl. 44, 137–147 (2011).

A. Ferrero, J. Alda, J. Campos, J. M. López-Alonso, and A. Pons, “Principal components analysis of the photoresponse nonuniformity of a matrix detector,” Appl. Opt. 46, 9–17(2007).
[CrossRef]

A. M. Rabal, A. Ferrero, J. L. Fontecha, A. Pons, J. Campos, A. Corróns, and A. M. Rubiño, “Gonio-spectrophotometer for low-uncertainty measurements of bidirectional scattering distribution function (BSDF),” in Proceedings of CIE Expert Symposium on Spectral and Imaging Methods for Photometry and Radiometry, Publication CIE x036: 2010 (CIE, 2010), pp. 79–84.

Fontecha, J. L.

A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio-spectrophotometer for the absolute measurement of the spectral BRDF at in- and out-of-plane retroreflection geometries,” Metrologia 49, 213–223 (2012).

A. M. Rabal, A. Ferrero, J. L. Fontecha, A. Pons, J. Campos, and A. Corróns, “Gonio-spectrophotometer for bidirectional scattering distribution function (BSDF) measurements,” Opt. Pura Apl. 44, 137–147 (2011).

A. M. Rabal, A. Ferrero, J. L. Fontecha, A. Pons, J. Campos, A. Corróns, and A. M. Rubiño, “Gonio-spectrophotometer for low-uncertainty measurements of bidirectional scattering distribution function (BSDF),” in Proceedings of CIE Expert Symposium on Spectral and Imaging Methods for Photometry and Radiometry, Publication CIE x036: 2010 (CIE, 2010), pp. 79–84.

Germer, T. A.

T. A. Germer and M. E. Nadal, “Modeling the appearance of special effect pigment coatings,” Proc. SPIE 4447, 77–86 (2001).
[CrossRef]

M. E. Nadal and T. A. Germer, “Colorimetric characterization of pearlescent coatings,” in Proceedings of AIC Color(2001), pp. 757–760.

Ginsberg, I. W.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Geometrical Considerations and Nomenclature for Reflectance, National Bureau of Standards Monograph 161 (National Bureau of Standards, 1977).

Gottenbos, R.

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

Hanselaer, P.

F. Leloup, P. Hanselaer, M. Pointer, and J. Versluys, “Characterization of gonio-apparent colours,” in Proceedings of AIC Color (2005), pp. 515–518.

Hernanz, M. L.

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Geometrical Considerations and Nomenclature for Reflectance, National Bureau of Standards Monograph 161 (National Bureau of Standards, 1977).

Kirchner, E.

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

Klein, R.

G. Müller, J. Meseth, M. Sattler, R. Sarlette, and R. Klein, “Acquisition, synthesis and rendering of bidirectional texture functions,” Comput. Graph. Forum 24, 83–109 (2005).
[CrossRef]

Leloup, F.

F. Leloup, P. Hanselaer, M. Pointer, and J. Versluys, “Characterization of gonio-apparent colours,” in Proceedings of AIC Color (2005), pp. 515–518.

Limperis, T.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Geometrical Considerations and Nomenclature for Reflectance, National Bureau of Standards Monograph 161 (National Bureau of Standards, 1977).

López-Alonso, J. M.

Maile, F. J.

F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments—past, present and future” Progr. Organic Coatings 54, 150–163 (2005).

Martínez-Verdú, F. M.

E. Chorro, E. Perales, F. M. Martínez-Verdú, J. Campos, and A. Pons, “Colorimetric and spectral evaluation of the optical anisotropy of metallic and pearlescent samples,” J. Mod. Opt. 56, 1457–1465 (2009).
[CrossRef]

Meseth, J.

G. Müller, J. Meseth, M. Sattler, R. Sarlette, and R. Klein, “Acquisition, synthesis and rendering of bidirectional texture functions,” Comput. Graph. Forum 24, 83–109 (2005).
[CrossRef]

Mikula, M.

M. Mikula, M. Ceppan, and K. Vaško, “Gloss and goniocolorimetry of printed materials,” Color Res. Appl. 28, 335–342 (2003).
[CrossRef]

Müller, G.

G. Müller, J. Meseth, M. Sattler, R. Sarlette, and R. Klein, “Acquisition, synthesis and rendering of bidirectional texture functions,” Comput. Graph. Forum 24, 83–109 (2005).
[CrossRef]

Nadal, M. E.

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

T. A. Germer and M. E. Nadal, “Modeling the appearance of special effect pigment coatings,” Proc. SPIE 4447, 77–86 (2001).
[CrossRef]

M. E. Nadal and T. A. Germer, “Colorimetric characterization of pearlescent coatings,” in Proceedings of AIC Color(2001), pp. 757–760.

Nicholls, C. A.

C. A. Nicholls, Visual and instrumental characterisation of special-effect colours, Ph.D. thesis (University of Leeds, 2000).

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Geometrical Considerations and Nomenclature for Reflectance, National Bureau of Standards Monograph 161 (National Bureau of Standards, 1977).

Njo, L.

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

Parker, B.

B. Parker, “Color shift of light interference pigments,” Surf. Coat. Aust. 39, 10–13 (2002).

Perales, E.

E. Chorro, E. Perales, F. M. Martínez-Verdú, J. Campos, and A. Pons, “Colorimetric and spectral evaluation of the optical anisotropy of metallic and pearlescent samples,” J. Mod. Opt. 56, 1457–1465 (2009).
[CrossRef]

Pfaff, G.

F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments—past, present and future” Progr. Organic Coatings 54, 150–163 (2005).

Pointer, M.

F. Leloup, P. Hanselaer, M. Pointer, and J. Versluys, “Characterization of gonio-apparent colours,” in Proceedings of AIC Color (2005), pp. 515–518.

Pons, A.

A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio-spectrophotometer for the absolute measurement of the spectral BRDF at in- and out-of-plane retroreflection geometries,” Metrologia 49, 213–223 (2012).

A. M. Rabal, A. Ferrero, J. L. Fontecha, A. Pons, J. Campos, and A. Corróns, “Gonio-spectrophotometer for bidirectional scattering distribution function (BSDF) measurements,” Opt. Pura Apl. 44, 137–147 (2011).

A. Ferrero, J. Campos, A. M. Rabal, A. Pons, M. L. Hernanz, and A. Corróns, “Principal components analysis on the spectral bidirectional reflectance distribution function of ceramic colour standards,” Opt. Express 19, 19199–19211 (2011).
[CrossRef]

E. Chorro, E. Perales, F. M. Martínez-Verdú, J. Campos, and A. Pons, “Colorimetric and spectral evaluation of the optical anisotropy of metallic and pearlescent samples,” J. Mod. Opt. 56, 1457–1465 (2009).
[CrossRef]

A. Ferrero, J. Alda, J. Campos, J. M. López-Alonso, and A. Pons, “Principal components analysis of the photoresponse nonuniformity of a matrix detector,” Appl. Opt. 46, 9–17(2007).
[CrossRef]

A. M. Rabal, A. Ferrero, J. L. Fontecha, A. Pons, J. Campos, A. Corróns, and A. M. Rubiño, “Gonio-spectrophotometer for low-uncertainty measurements of bidirectional scattering distribution function (BSDF),” in Proceedings of CIE Expert Symposium on Spectral and Imaging Methods for Photometry and Radiometry, Publication CIE x036: 2010 (CIE, 2010), pp. 79–84.

Rabal, A. M.

A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio-spectrophotometer for the absolute measurement of the spectral BRDF at in- and out-of-plane retroreflection geometries,” Metrologia 49, 213–223 (2012).

A. Ferrero, J. Campos, A. M. Rabal, A. Pons, M. L. Hernanz, and A. Corróns, “Principal components analysis on the spectral bidirectional reflectance distribution function of ceramic colour standards,” Opt. Express 19, 19199–19211 (2011).
[CrossRef]

A. M. Rabal, A. Ferrero, J. L. Fontecha, A. Pons, J. Campos, and A. Corróns, “Gonio-spectrophotometer for bidirectional scattering distribution function (BSDF) measurements,” Opt. Pura Apl. 44, 137–147 (2011).

A. M. Rabal, A. Ferrero, J. L. Fontecha, A. Pons, J. Campos, A. Corróns, and A. M. Rubiño, “Gonio-spectrophotometer for low-uncertainty measurements of bidirectional scattering distribution function (BSDF),” in Proceedings of CIE Expert Symposium on Spectral and Imaging Methods for Photometry and Radiometry, Publication CIE x036: 2010 (CIE, 2010), pp. 79–84.

Reynders, P.

F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments—past, present and future” Progr. Organic Coatings 54, 150–163 (2005).

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Geometrical Considerations and Nomenclature for Reflectance, National Bureau of Standards Monograph 161 (National Bureau of Standards, 1977).

Rubiño, A. M.

A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio-spectrophotometer for the absolute measurement of the spectral BRDF at in- and out-of-plane retroreflection geometries,” Metrologia 49, 213–223 (2012).

A. M. Rabal, A. Ferrero, J. L. Fontecha, A. Pons, J. Campos, A. Corróns, and A. M. Rubiño, “Gonio-spectrophotometer for low-uncertainty measurements of bidirectional scattering distribution function (BSDF),” in Proceedings of CIE Expert Symposium on Spectral and Imaging Methods for Photometry and Radiometry, Publication CIE x036: 2010 (CIE, 2010), pp. 79–84.

Rushmeier, H.

J. Dorsey, H. Rushmeier, and F. Sillion, Digital Modelling of Material Appearance (Elsevier, 2007).

Sarlette, R.

G. Müller, J. Meseth, M. Sattler, R. Sarlette, and R. Klein, “Acquisition, synthesis and rendering of bidirectional texture functions,” Comput. Graph. Forum 24, 83–109 (2005).
[CrossRef]

Sattler, M.

G. Müller, J. Meseth, M. Sattler, R. Sarlette, and R. Klein, “Acquisition, synthesis and rendering of bidirectional texture functions,” Comput. Graph. Forum 24, 83–109 (2005).
[CrossRef]

Sillion, F.

J. Dorsey, H. Rushmeier, and F. Sillion, Digital Modelling of Material Appearance (Elsevier, 2007).

Simonds, J. L.

Streitberger, H. J.

H. J. Streitberger and K. F. Dössel, Automotive Paints and Coatings (Wiley-VCH, 2008).

Supér, R.

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

Van den Kiebomm, G. J.

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

Vaško, K.

M. Mikula, M. Ceppan, and K. Vaško, “Gloss and goniocolorimetry of printed materials,” Color Res. Appl. 28, 335–342 (2003).
[CrossRef]

Versluys, J.

F. Leloup, P. Hanselaer, M. Pointer, and J. Versluys, “Characterization of gonio-apparent colours,” in Proceedings of AIC Color (2005), pp. 515–518.

Appl. Opt. (2)

Color Res. Appl. (3)

M. Mikula, M. Ceppan, and K. Vaško, “Gloss and goniocolorimetry of printed materials,” Color Res. Appl. 28, 335–342 (2003).
[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 Kiebomm, L. Njo, R. Supér, and R. Gottenbos, “Observation of visual texture of metallic and pearlescent materials,” Color Res. Appl. 32, 256–266 (2007).
[CrossRef]

Comput. Graph. Forum (1)

G. Müller, J. Meseth, M. Sattler, R. Sarlette, and R. Klein, “Acquisition, synthesis and rendering of bidirectional texture functions,” Comput. Graph. Forum 24, 83–109 (2005).
[CrossRef]

Die Farbe (2)

G. Baba, “Gonio-spectrophotometric analysis of pearl-mica paint,” Die Farbe 37, 99–110 (1990).

R. Besold, “Metallic effect-characterization, parameter and methods for instrumentally determination,” Die Farbe 37, 79–85(1990).

J. Mod. Opt. (1)

E. Chorro, E. Perales, F. M. Martínez-Verdú, J. Campos, and A. Pons, “Colorimetric and spectral evaluation of the optical anisotropy of metallic and pearlescent samples,” J. Mod. Opt. 56, 1457–1465 (2009).
[CrossRef]

J. Opt. Soc. Am. (1)

Metrologia (1)

A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio-spectrophotometer for the absolute measurement of the spectral BRDF at in- and out-of-plane retroreflection geometries,” Metrologia 49, 213–223 (2012).

Opt. Express (1)

Opt. Pura Apl. (1)

A. M. Rabal, A. Ferrero, J. L. Fontecha, A. Pons, J. Campos, and A. Corróns, “Gonio-spectrophotometer for bidirectional scattering distribution function (BSDF) measurements,” Opt. Pura Apl. 44, 137–147 (2011).

Proc. SPIE (1)

T. A. Germer and M. E. Nadal, “Modeling the appearance of special effect pigment coatings,” Proc. SPIE 4447, 77–86 (2001).
[CrossRef]

Progr. Organic Coatings (1)

F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments—past, present and future” Progr. Organic Coatings 54, 150–163 (2005).

Surf. Coat. Aust. (1)

B. Parker, “Color shift of light interference pigments,” Surf. Coat. Aust. 39, 10–13 (2002).

Other (11)

F. Leloup, P. Hanselaer, M. Pointer, and J. Versluys, “Characterization of gonio-apparent colours,” in Proceedings of AIC Color (2005), pp. 515–518.

C. A. Nicholls, Visual and instrumental characterisation of special-effect colours, Ph.D. thesis (University of Leeds, 2000).

DIN standard 6175-2, “Colour tolerances for automobile lacquer finishes, Part 2: Effect lacquer finishes” (2001).

DIN standard 6175-2, “Tolerances for automotive paints, Part 2: Goniochromatic paints (Farbtoleranzen für Automobillackierungen-Teil 2: Effektlackierungen)” (2001).

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Geometrical Considerations and Nomenclature for Reflectance, National Bureau of Standards Monograph 161 (National Bureau of Standards, 1977).

Colorstream T20-02 WNT Artic Fire, Product Information, Colorstream. Merck KgaA (2004).

A. M. Rabal, A. Ferrero, J. L. Fontecha, A. Pons, J. Campos, A. Corróns, and A. M. Rubiño, “Gonio-spectrophotometer for low-uncertainty measurements of bidirectional scattering distribution function (BSDF),” in Proceedings of CIE Expert Symposium on Spectral and Imaging Methods for Photometry and Radiometry, Publication CIE x036: 2010 (CIE, 2010), pp. 79–84.

M. E. Nadal and T. A. Germer, “Colorimetric characterization of pearlescent coatings,” in Proceedings of AIC Color(2001), pp. 757–760.

H. J. Streitberger and K. F. Dössel, Automotive Paints and Coatings (Wiley-VCH, 2008).

P. Dutré, K. Bala, and P. Bekaert, Advanced Global Illumination (A K Peters, 2006).

J. Dorsey, H. Rushmeier, and F. Sillion, Digital Modelling of Material Appearance (Elsevier, 2007).

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 (7)

Fig. 1.
Fig. 1.

Sample coordinate system showing spherical coordinates for irradiation (θi, ϕi) and viewing directions (θs, ϕs).

Fig. 2.
Fig. 2.

Representation of fr(θi,ϕi;θs,ϕs)λ versus viewing polar angles. Every plot corresponds to a different incident polar angle (θi).

Fig. 3.
Fig. 3.

The four components of Hj(λ) containing 99.4% of the total relative variance of the data, arranged from the highest to the lowest variance.

Fig. 4.
Fig. 4.

Weights cj at different in-plane geometrical configurations corresponding to H1, H2, H3, and H4, respectively.

Fig. 5.
Fig. 5.

Weights cj at different out-of-plane geometrical configurations corresponding to H1, H2, H3, and H4, respectively.

Fig. 6.
Fig. 6.

Integration-calculated weights CHD,j corresponding to the HD radiance factor.

Fig. 7.
Fig. 7.

Comparison between the principal component H1 and the modified H1 (H1).

Equations (7)

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

fr(θi,ϕi;θs,ϕs;λ)=fr(θi,ϕi;θs,ϕs)λ[1+Σj=1Mcj(θi,ϕi;θs,ϕs)Hj(λ)].
fr,rel(θi,ϕi;θs,ϕs;λ)=fr(θi,ϕi;θs,ϕs;λ)fr(θi,ϕi;θs,ϕs)λ1.
Hj(λ)=Aj(λ)σ[Aj(λ)],
cj(θi,ϕi;θs,ϕs)=ej(θi,ϕi;θs,ϕs)σ[Aj(λ)].
fr=frλ[1+c1H1+(c2c1c2,min)H2+(c3c1c3,min)H3+(c4c1c4,min)H4],
H1=H1+c2,minH2+c3,minH3+c4,minH4.
fr,abs(θi,ϕi;θs,ϕs;λ)=fr(θi,ϕi;θs,ϕs;λ)fr(θi,ϕi;θs,ϕs)λ.

Metrics