Abstract

A reduced set of measurement geometries allows the spectral reflectance of special effect coatings to be predicted for any other geometry. A physical model based on flake-related parameters has been used to determine nonredundant measurement geometries for the complete description of the spectral bidirectional reflectance distribution function (BRDF). The analysis of experimental spectral BRDF was carried out by means of principal component analysis. From this analysis, a set of nine measurement geometries was proposed to characterize special effect coatings. It was shown that, for two different special effect coatings, these geometries provide a good prediction of their complete color shift.

© 2013 Optical Society of America

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References

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  1. F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments—past, present and future,” Prog. Org. Coat. 54, 150–163 (2005).
    [CrossRef]
  2. H. J. Streitberger and K. F. Dössel, Automotive Paints and Coatings (Wiley-VCH, 2008).
  3. M. E. Nadal and E. A. Early, “Color measurements for pearlescent coatings,” Color Res. Appl. 29, 38–42 (2004).
    [CrossRef]
  4. G. Baba, “Gonio-spectrophotometric analysis of pearl-mica paint,” Die Farbe 37, 99–110 (1990).
  5. T. A. Germer and M. E. Nadal, “Modeling the appearance of special effect pigment coatings,” Proc. SPIE 4447, 77–86 (2001).
    [CrossRef]
  6. M. E. Nadal and T. A. Germer, “Colorimetric characterization of pearlescent coatings,” Proc. SPIE 4421, 757–760 (2001).
    [CrossRef]
  7. B. Parker, “Color shift of light interference pigments,” Surf. Coat. Aust. 39, 10–13 (2002).
  8. F. Leloup, P. Hanselaer, M. Pointer, and J. Versluys, “Characterization of gonio-apparent colours,” in Congress of the International Colour Association, 10th ed. (AIC, 2005), pp. 515–518.
  9. C. A. Nicholls, “Visual and instrumental characterisation of special-effect colours,” Ph.D. Thesis (University of Leeds, 2000).
  10. R. Besold, “Metallic effect-characterization, parameter and methods for instrumentally determination,” Die Farbe 37, 79–85 (1990).
  11. “Tolerances for automotive paints, Part 2: Goniochromatic paints (Farbtoleranzen für Automobillackierungen-Teil 2: Effektlackierungen), DIN 6175-2” (Deutsche Institut für Normung e. V., 2001).
  12. 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]
  13. E. Kirchner, G. J. Van den Kieboom, L. Njo, R. Supér, and R. Gottenbos, “Observation of visual texture of metallic and pearlescent materials,” Color Res. Appl. 32, 256–266 (2007).
    [CrossRef]
  14. W. R. Cramer, “Reflections on the right angle,” Eur. Coat. J. 4, 32–37 (2012).
  15. E. Perales, E. Chorro, W. R. Cramer, and F. M. Martínez-Verdú, “Analysis of the colorimetric properties of goniochromatic colors using the MacAdam limits under different light sources,” Appl. Opt. 50, 5271–5278 (2011).
    [CrossRef]
  16. F. E. Nicodemus, J. C. Richmond, and J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” NBS Monogr. 160, 3–7 (1977).
  17. A. Takagi, S. Sato, and G. Baba, “Prediction of spectral reflectance factor distribution of color-shift paint finishes,” Color Res. Appl. 32, 378–387 (2007).
    [CrossRef]
  18. “Standard practice for multiangle color measurement of interference pigments,” ASTM E 2539-08 (American Society for the Testing of Materials, 2009).
  19. E. Kirchner and W. Cramer, “Making sense of measurement geometries for multi-angle spectrophotometers,” Color Res. Appl. 37, 186–198 (2012).
    [CrossRef]
  20. 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]
  21. A. Ferrero, J. Campos, A. M. Rabal, A. Pons, M. L. Hernanz, and A. Corróns, “Variables separation of the spectral BRDF for better understanding color variation in special effect pigment coatings,” J. Opt. Soc. Am. A 29, 842–847 (2012).
    [CrossRef]
  22. 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 & out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
    [CrossRef]
  23. G. Pfaff and P. Reynders, “Angle-dependent optical effects deriving from submicron structures of films and pigments,” Chem. Rev. 99, 1963–1982 (1999).
    [CrossRef]
  24. E. J. J. Kirchner and J. Houweling, “Measuring flake orientation for metallic coatings,” Prog. Org. Coat. 64, 287–293 (2009).
    [CrossRef]
  25. Colorstream T20-02 WNT Artic Fire, Product Information, Colorstream (Merck KgaA,2004).
  26. Colorstream T20-04 WNT Lapis Sunlight, Product Information, Colorstream (Merck KgaA,2004).

2012 (4)

W. R. Cramer, “Reflections on the right angle,” Eur. Coat. J. 4, 32–37 (2012).

E. Kirchner and W. Cramer, “Making sense of measurement geometries for multi-angle spectrophotometers,” Color Res. Appl. 37, 186–198 (2012).
[CrossRef]

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 & out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
[CrossRef]

A. Ferrero, J. Campos, A. M. Rabal, A. Pons, M. L. Hernanz, and A. Corróns, “Variables separation of the spectral BRDF for better understanding color variation in special effect pigment coatings,” J. Opt. Soc. Am. A 29, 842–847 (2012).
[CrossRef]

2011 (2)

2009 (2)

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

2007 (2)

E. Kirchner, G. J. Van den Kieboom, 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. Takagi, S. Sato, and G. Baba, “Prediction of spectral reflectance factor distribution of color-shift paint finishes,” Color Res. Appl. 32, 378–387 (2007).
[CrossRef]

2005 (1)

F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments—past, present and future,” Prog. Org. Coat. 54, 150–163 (2005).
[CrossRef]

2004 (1)

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

2002 (1)

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

2001 (2)

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,” Proc. SPIE 4421, 757–760 (2001).
[CrossRef]

1999 (1)

G. Pfaff and P. Reynders, “Angle-dependent optical effects deriving from submicron structures of films and pigments,” Chem. Rev. 99, 1963–1982 (1999).
[CrossRef]

1990 (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).

1977 (1)

F. E. Nicodemus, J. C. Richmond, and J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” NBS Monogr. 160, 3–7 (1977).

Baba, G.

A. Takagi, S. Sato, and G. Baba, “Prediction of spectral reflectance factor distribution of color-shift paint finishes,” Color Res. Appl. 32, 378–387 (2007).
[CrossRef]

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

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 & out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
[CrossRef]

A. Ferrero, J. Campos, A. M. Rabal, A. Pons, M. L. Hernanz, and A. Corróns, “Variables separation of the spectral BRDF for better understanding color variation in special effect pigment coatings,” J. Opt. Soc. Am. A 29, 842–847 (2012).
[CrossRef]

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]

Chorro, E.

E. Perales, E. Chorro, W. R. Cramer, and F. M. Martínez-Verdú, “Analysis of the colorimetric properties of goniochromatic colors using the MacAdam limits under different light sources,” Appl. Opt. 50, 5271–5278 (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]

Corróns, A.

Cramer, W.

E. Kirchner and W. Cramer, “Making sense of measurement geometries for multi-angle spectrophotometers,” Color Res. Appl. 37, 186–198 (2012).
[CrossRef]

Cramer, W. R.

Dössel, K. F.

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

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.

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 & out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
[CrossRef]

Germer, T. A.

M. E. Nadal and T. A. Germer, “Colorimetric characterization of pearlescent coatings,” Proc. SPIE 4421, 757–760 (2001).
[CrossRef]

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

Gottenbos, R.

E. Kirchner, G. J. Van den Kieboom, 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 Congress of the International Colour Association, 10th ed. (AIC, 2005), pp. 515–518.

Hernanz, M. L.

Houweling, J.

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

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, and J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” NBS Monogr. 160, 3–7 (1977).

Kirchner, E.

E. Kirchner and W. Cramer, “Making sense of measurement geometries for multi-angle spectrophotometers,” Color Res. Appl. 37, 186–198 (2012).
[CrossRef]

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

Kirchner, E. J. J.

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

Leloup, F.

F. Leloup, P. Hanselaer, M. Pointer, and J. Versluys, “Characterization of gonio-apparent colours,” in Congress of the International Colour Association, 10th ed. (AIC, 2005), pp. 515–518.

Maile, F. J.

F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments—past, present and future,” Prog. Org. Coat. 54, 150–163 (2005).
[CrossRef]

Martínez-Verdú, F. M.

E. Perales, E. Chorro, W. R. Cramer, and F. M. Martínez-Verdú, “Analysis of the colorimetric properties of goniochromatic colors using the MacAdam limits under different light sources,” Appl. Opt. 50, 5271–5278 (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]

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,” Proc. SPIE 4421, 757–760 (2001).
[CrossRef]

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, and J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” NBS Monogr. 160, 3–7 (1977).

Njo, L.

E. Kirchner, G. J. Van den Kieboom, 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. Perales, E. Chorro, W. R. Cramer, and F. M. Martínez-Verdú, “Analysis of the colorimetric properties of goniochromatic colors using the MacAdam limits under different light sources,” Appl. Opt. 50, 5271–5278 (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]

Pfaff, G.

F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments—past, present and future,” Prog. Org. Coat. 54, 150–163 (2005).
[CrossRef]

G. Pfaff and P. Reynders, “Angle-dependent optical effects deriving from submicron structures of films and pigments,” Chem. Rev. 99, 1963–1982 (1999).
[CrossRef]

Pointer, M.

F. Leloup, P. Hanselaer, M. Pointer, and J. Versluys, “Characterization of gonio-apparent colours,” in Congress of the International Colour Association, 10th ed. (AIC, 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 & out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
[CrossRef]

A. Ferrero, J. Campos, A. M. Rabal, A. Pons, M. L. Hernanz, and A. Corróns, “Variables separation of the spectral BRDF for better understanding color variation in special effect pigment coatings,” J. Opt. Soc. Am. A 29, 842–847 (2012).
[CrossRef]

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]

Rabal, A. M.

Reynders, P.

F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments—past, present and future,” Prog. Org. Coat. 54, 150–163 (2005).
[CrossRef]

G. Pfaff and P. Reynders, “Angle-dependent optical effects deriving from submicron structures of films and pigments,” Chem. Rev. 99, 1963–1982 (1999).
[CrossRef]

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, and J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” NBS Monogr. 160, 3–7 (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 & out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
[CrossRef]

Sato, S.

A. Takagi, S. Sato, and G. Baba, “Prediction of spectral reflectance factor distribution of color-shift paint finishes,” Color Res. Appl. 32, 378–387 (2007).
[CrossRef]

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 Kieboom, L. Njo, R. Supér, and R. Gottenbos, “Observation of visual texture of metallic and pearlescent materials,” Color Res. Appl. 32, 256–266 (2007).
[CrossRef]

Takagi, A.

A. Takagi, S. Sato, and G. Baba, “Prediction of spectral reflectance factor distribution of color-shift paint finishes,” Color Res. Appl. 32, 378–387 (2007).
[CrossRef]

Van den Kieboom, G. J.

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

Versluys, J.

F. Leloup, P. Hanselaer, M. Pointer, and J. Versluys, “Characterization of gonio-apparent colours,” in Congress of the International Colour Association, 10th ed. (AIC, 2005), pp. 515–518.

Appl. Opt. (1)

Chem. Rev. (1)

G. Pfaff and P. Reynders, “Angle-dependent optical effects deriving from submicron structures of films and pigments,” Chem. Rev. 99, 1963–1982 (1999).
[CrossRef]

Color Res. Appl. (4)

E. Kirchner, G. J. Van den Kieboom, 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. Takagi, S. Sato, and G. Baba, “Prediction of spectral reflectance factor distribution of color-shift paint finishes,” Color Res. Appl. 32, 378–387 (2007).
[CrossRef]

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

E. Kirchner and W. Cramer, “Making sense of measurement geometries for multi-angle spectrophotometers,” Color Res. Appl. 37, 186–198 (2012).
[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).

Eur. Coat. J. (1)

W. R. Cramer, “Reflections on the right angle,” Eur. Coat. J. 4, 32–37 (2012).

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. A (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 & out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
[CrossRef]

NBS Monogr. (1)

F. E. Nicodemus, J. C. Richmond, and J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” NBS Monogr. 160, 3–7 (1977).

Opt. Express (1)

Proc. SPIE (2)

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,” Proc. SPIE 4421, 757–760 (2001).
[CrossRef]

Prog. Org. Coat. (2)

F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments—past, present and future,” Prog. Org. Coat. 54, 150–163 (2005).
[CrossRef]

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

Surf. Coat. Aust. (1)

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

Other (7)

F. Leloup, P. Hanselaer, M. Pointer, and J. Versluys, “Characterization of gonio-apparent colours,” in Congress of the International Colour Association, 10th ed. (AIC, 2005), pp. 515–518.

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

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

“Tolerances for automotive paints, Part 2: Goniochromatic paints (Farbtoleranzen für Automobillackierungen-Teil 2: Effektlackierungen), DIN 6175-2” (Deutsche Institut für Normung e. V., 2001).

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

Colorstream T20-04 WNT Lapis Sunlight, Product Information, Colorstream (Merck KgaA,2004).

“Standard practice for multiangle color measurement of interference pigments,” ASTM E 2539-08 (American Society for the Testing of Materials, 2009).

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Figures (12)

Fig. 1.
Fig. 1.

Sample coordinate system, defined by the set of spherical coordinates for the irradiation (θi, ϕi) and the viewing directions (θs, ϕs).

Fig. 2.
Fig. 2.

Geometrical variables needed to describe the flake-related reflection mechanism.

Fig. 3.
Fig. 3.

Relation between θflake and θasp for 648 measurement geometries (θi and θs range from 0° to 85° at steps of 5°), for ϕs=0° and 180°.

Fig. 4.
Fig. 4.

Scattering of the optical radiation due to the disorientation of the flakes. Lλ is the spectral radiance.

Fig. 5.
Fig. 5.

Weights cj as a function of the viewing angle θs for different in-plane geometrical configurations corresponding, respectively, to H1, H2, H3, and H4. Positive and negative θs indicate ϕs=180° and 0°, respectively (Arctic Fire). This figure corresponds to Fig. 4 in [21].

Fig. 6.
Fig. 6.

Relation of the weights of H2 with θflake for 0°<θinc7°, 7°<θinc10°, 10°<θinc25°, and 25°<θinc35°.

Fig. 7.
Fig. 7.

Relative weights alow,p and ahigh,p as a function of the incidence angle on the flake. In this case, sixth-degree polynomials were fitted to the experimental points.

Fig. 8.
Fig. 8.

Histogram of color differences between the measurement and the estimation from the nine proposed geometries (Arctic Fire). The binning is 0.4.

Fig. 9.
Fig. 9.

Histogram of color differences between the measurement and estimation from the nine proposed geometries (Lapis Sunlight). The binning is 0.35.

Fig. 10.
Fig. 10.

Color representation of Arctic Fire in CIE-a*,b* coordinates.

Fig. 11.
Fig. 11.

Color representation of Lapis SunLight in CIE-a*,b* coordinates.

Fig. 12.
Fig. 12.

Summary of color shifts for Arctic Fire and Lapis Sunlight.

Tables (2)

Tables Icon

Table 1. Proposal for the Optimal Measurement Geometries for Predicting the Color Appearance Variance of Special Effect Coatings

Tables Icon

Table 2. Comparison of the Measurement Geometries That We Propose with the Geometries of Those Instruments That Are Commercially Available

Equations (16)

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

fr(θi,ϕi;θs,ϕs;λ)=fr,eff(θi,ϕi;θs,ϕs;λ)+fr,0(θi,ϕi;θs,ϕs;λ).
fr,eff(θi,ϕi;θs,ϕs;λ)=D(θflake)fr,flake(θi,ϕi;θs,ϕs;λ),
fr,flake(θi,ϕi;θs,ϕs;λ)=T(θi,λ)Rflake(θinc,λ)T(θs,λ)Ωs(θs,ϕs),
fr(θi,ϕi;θs,ϕs;λ)=fr(θi,ϕi;θs,ϕs)λ[1+Σj=1Mcj(θi,ϕi;θs,ϕs)Hj(λ)].
Rflake(θinc,λ)=alow(θinc)Rlow(λ)+ahigh(θinc)Rhigh(λ),
fr,m(θi,ϕi;θs,ϕs;λ)=fr,m(θi,ϕi;θs,ϕs)λΣj=13cj,m(θi,ϕi;θs,ϕs)Hj,m(λ),
c1,m(θi,ϕi;θs,ϕs)=fr,0(θi,ϕi;θs,ϕsλfr,m(θi,ϕi;θs,ϕs)λ,
c2,m(θi,ϕi;θs,ϕs)=D(θflake)alow(θinc)T(θi)T(θs)fr,m(θi,ϕi;θs,ϕs)λΩs(θs,ϕs),
c3,m(θi,ϕi;θs,ϕs)=D(θflake)ahigh(θinc)T(θi)T(θs)fr,m(θi,ϕi;θs,ϕs)λΩs(θs,ϕs),
H1,m(λ)=fr,0(λ),
H2,m(λ)=Rlow(λ)T2(λ),
H3,m(λ)=Rhigh(λ)T2(λ),
alow,p=c2c2,mind(θflake),
ahigh,p=c3c3,mind(θflake).
feff,pca(θi,ϕi;θs,ϕs;λ)=d(θflake)[alow,pHlow(λ)+ahigh,pHhigh(λ)],
θiasp(θasp)(θiθasp)asp(θasp).

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