Abstract

Colors of special-effect coatings have strong dependence on illumination/viewing geometry and an appealing appearance. An open question is to ask about the minimum number of measurement geometries required to completely characterize their observed color shift. A recently published principal components analysis (PCA)-based procedure to estimate the color of special-effect coatings at any geometry from measurements at a reduced set of geometries was tested in this work by using the measurement geometries of commercial portable multiangle spectrophotometers X-Rite MA98, Datacolor FX10, and BYK-mac as reduced sets. The performance of the proposed PCA procedure for the color-shift estimation for these commercial geometries has been examined for 15 special-effect coatings. Our results suggest that for rendering the color appearance of 3D objects covered with special-effect coatings, the color accuracy obtained with this procedure may be sufficient. This is the case especially if geometries of X-Rite MA98 or Datacolor FX10 are used.

© 2014 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
  6. G. Obein, R. Bousquet, and M. E. Nadal, “New NIST reference goniospectrometer,” Proc. SPIE 5880, 58800T (2005).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  21. A. Ferrero, B. Bernad, J. Campos, F. M. Martínez-Verdú, E. Perales, I. van der Lans, and E. Kirchner, “Towards a better understanding of the color shift of effect coatings by densely sampled spectral BRDF measurement,” Proc. SPIE 9018, 90180K (2014).
    [Crossref]
  22. A. Ferrero, E. Perales, A. M. Rabal, J. Campos, F. M. Martínez-Verdú, E. Chorro, and A. Pons, “Color representation and interpretation of special effect coatings,” J. Opt. Soc. Am. A 31, 436–447 (2014).
    [Crossref]

2014 (3)

2013 (3)

N. Matsapey, J. Faucheu, M. Flury, and D. Delafosse, “Design of a gonio-spectrophotometer for optical characterization of gonio-apparent materials,” Meas. Sci. Technol. 24, 065901 (2013).
[Crossref]

H. J. Patrick, C. J. Zarobila, and T. A. Germer, “The NIST robotic optical scatter instrument (ROSI) and its application to BRDF measurements of diffuse reflectance standards for remote sensing,” Proc. SPIE 8866, 886615 (2013).
[Crossref]

A. Ferrero, A. M. Rabal, J. Campos, F. Martínez-Verdú, E. Chorro, E. Perales, A. Pons, and M. L. Hernanz, “Spectral BRDF-based determination of proper measurement geometries to characterize color shift of special effect coatings,” J. Opt. Soc. Am. A 30, 206–214 (2013).
[Crossref]

2012 (2)

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]

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

2009 (1)

R. Baribeau, W. S. Neil, and É. Côté, “Development of a robot-based gonioreflectometer for spectral BRDF measurement,” J. Mod. Opt. 56, 1497–1503 (2009).
[Crossref]

2008 (1)

2007 (1)

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]

2006 (1)

D. Hünerhoff, U. Grusemann, and A. Höpe, “New robot-based gonioreflectometer for measuring spectral diffuse reflection,” Metrologia 43, S11–S16 (2006).
[Crossref]

2005 (2)

G. Obein, R. Bousquet, and M. E. Nadal, “New NIST reference goniospectrometer,” Proc. SPIE 5880, 58800T (2005).
[Crossref]

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

2004 (2)

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

S. Nevas, F. Manoocheri, and E. Ikonen, “Gonioreflectometer for measuring spectral diffuse reflectance,” Appl. Opt. 43, 6391–6399 (2004).
[Crossref]

1999 (2)

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

T. A. Germer and C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70, 3688–3695 (1999).
[Crossref]

Asmail, C. C.

T. A. Germer and C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70, 3688–3695 (1999).
[Crossref]

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]

Baribeau, R.

R. Baribeau, W. S. Neil, and É. Côté, “Development of a robot-based gonioreflectometer for spectral BRDF measurement,” J. Mod. Opt. 56, 1497–1503 (2009).
[Crossref]

Bernad, B.

A. Ferrero, B. Bernad, J. Campos, F. M. Martínez-Verdú, E. Perales, I. van der Lans, and E. Kirchner, “Towards a better understanding of the color shift of effect coatings by densely sampled spectral BRDF measurement,” Proc. SPIE 9018, 90180K (2014).
[Crossref]

Bousquet, R.

G. Obein, R. Bousquet, and M. E. Nadal, “New NIST reference goniospectrometer,” Proc. SPIE 5880, 58800T (2005).
[Crossref]

Campos, J.

A. Ferrero, B. Bernad, J. Campos, F. M. Martínez-Verdú, E. Perales, I. van der Lans, and E. Kirchner, “Towards a better understanding of the color shift of effect coatings by densely sampled spectral BRDF measurement,” Proc. SPIE 9018, 90180K (2014).
[Crossref]

A. Ferrero, E. Perales, A. M. Rabal, J. Campos, F. M. Martínez-Verdú, E. Chorro, and A. Pons, “Color representation and interpretation of special effect coatings,” J. Opt. Soc. Am. A 31, 436–447 (2014).
[Crossref]

A. Ferrero, A. M. Rabal, J. Campos, F. Martínez-Verdú, E. Chorro, E. Perales, A. Pons, and M. L. Hernanz, “Spectral BRDF-based determination of proper measurement geometries to characterize color shift of special effect coatings,” J. Opt. Soc. Am. A 30, 206–214 (2013).
[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]

Chorro, E.

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

Côté, É.

R. Baribeau, W. S. Neil, and É. Côté, “Development of a robot-based gonioreflectometer for spectral BRDF measurement,” J. Mod. Opt. 56, 1497–1503 (2009).
[Crossref]

Cramer, W.

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

Delafosse, D.

N. Matsapey, J. Faucheu, M. Flury, and D. Delafosse, “Design of a gonio-spectrophotometer for optical characterization of gonio-apparent materials,” Meas. Sci. Technol. 24, 065901 (2013).
[Crossref]

Dössel, K. F.

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

Dutré, P.

Early, E. A.

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

Faucheu, J.

N. Matsapey, J. Faucheu, M. Flury, and D. Delafosse, “Design of a gonio-spectrophotometer for optical characterization of gonio-apparent materials,” Meas. Sci. Technol. 24, 065901 (2013).
[Crossref]

Ferrero, A.

E. Kirchner and A. Ferrero, “Isochromatic lines as extension of the Helmholtz reciprocity principle for effect paints,” J. Opt. Soc. Am. A, 31, 1861–1867 (2014).
[Crossref]

A. Ferrero, B. Bernad, J. Campos, F. M. Martínez-Verdú, E. Perales, I. van der Lans, and E. Kirchner, “Towards a better understanding of the color shift of effect coatings by densely sampled spectral BRDF measurement,” Proc. SPIE 9018, 90180K (2014).
[Crossref]

A. Ferrero, E. Perales, A. M. Rabal, J. Campos, F. M. Martínez-Verdú, E. Chorro, and A. Pons, “Color representation and interpretation of special effect coatings,” J. Opt. Soc. Am. A 31, 436–447 (2014).
[Crossref]

A. Ferrero, A. M. Rabal, J. Campos, F. Martínez-Verdú, E. Chorro, E. Perales, A. Pons, and M. L. Hernanz, “Spectral BRDF-based determination of proper measurement geometries to characterize color shift of special effect coatings,” J. Opt. Soc. Am. A 30, 206–214 (2013).
[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]

Flury, M.

N. Matsapey, J. Faucheu, M. Flury, and D. Delafosse, “Design of a gonio-spectrophotometer for optical characterization of gonio-apparent materials,” Meas. Sci. Technol. 24, 065901 (2013).
[Crossref]

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]

Forment, S.

Ged, G.

S. Ouarets, G. Ged, A. Razet, and G. Obein, “A new gonioreflectometer for the measurement of the bidirectional reflectance distribution function (BRDF) at LNE-CNAM,” in Proceedings of CIE 2012 Lighting Quality and Energy Efficiency (2012), pp. 687–691.

Germer, T. A.

H. J. Patrick, C. J. Zarobila, and T. A. Germer, “The NIST robotic optical scatter instrument (ROSI) and its application to BRDF measurements of diffuse reflectance standards for remote sensing,” Proc. SPIE 8866, 886615 (2013).
[Crossref]

T. A. Germer and C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70, 3688–3695 (1999).
[Crossref]

Ginsberg, I. W.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” (1977).

Grusemann, U.

D. Hünerhoff, U. Grusemann, and A. Höpe, “New robot-based gonioreflectometer for measuring spectral diffuse reflection,” Metrologia 43, S11–S16 (2006).
[Crossref]

Hanselaer, P.

Hernanz, M. L.

Höpe, A.

D. Hünerhoff, U. Grusemann, and A. Höpe, “New robot-based gonioreflectometer for measuring spectral diffuse reflection,” Metrologia 43, S11–S16 (2006).
[Crossref]

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” (1977).

Hünerhoff, D.

D. Hünerhoff, U. Grusemann, and A. Höpe, “New robot-based gonioreflectometer for measuring spectral diffuse reflection,” Metrologia 43, S11–S16 (2006).
[Crossref]

Ikonen, E.

Kirchner, E.

E. Kirchner and A. Ferrero, “Isochromatic lines as extension of the Helmholtz reciprocity principle for effect paints,” J. Opt. Soc. Am. A, 31, 1861–1867 (2014).
[Crossref]

A. Ferrero, B. Bernad, J. Campos, F. M. Martínez-Verdú, E. Perales, I. van der Lans, and E. Kirchner, “Towards a better understanding of the color shift of effect coatings by densely sampled spectral BRDF measurement,” Proc. SPIE 9018, 90180K (2014).
[Crossref]

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

Leloup, F. B.

Limperis, T.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” (1977).

Maile, F. J.

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

Manoocheri, F.

Martínez-Verdú, F.

Martínez-Verdú, F. M.

A. Ferrero, B. Bernad, J. Campos, F. M. Martínez-Verdú, E. Perales, I. van der Lans, and E. Kirchner, “Towards a better understanding of the color shift of effect coatings by densely sampled spectral BRDF measurement,” Proc. SPIE 9018, 90180K (2014).
[Crossref]

A. Ferrero, E. Perales, A. M. Rabal, J. Campos, F. M. Martínez-Verdú, E. Chorro, and A. Pons, “Color representation and interpretation of special effect coatings,” J. Opt. Soc. Am. A 31, 436–447 (2014).
[Crossref]

Matsapey, N.

N. Matsapey, J. Faucheu, M. Flury, and D. Delafosse, “Design of a gonio-spectrophotometer for optical characterization of gonio-apparent materials,” Meas. Sci. Technol. 24, 065901 (2013).
[Crossref]

Nadal, M. E.

G. Obein, R. Bousquet, and M. E. Nadal, “New NIST reference goniospectrometer,” Proc. SPIE 5880, 58800T (2005).
[Crossref]

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

Neil, W. S.

R. Baribeau, W. S. Neil, and É. Côté, “Development of a robot-based gonioreflectometer for spectral BRDF measurement,” J. Mod. Opt. 56, 1497–1503 (2009).
[Crossref]

Nevas, S.

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” (1977).

Obein, G.

G. Obein, R. Bousquet, and M. E. Nadal, “New NIST reference goniospectrometer,” Proc. SPIE 5880, 58800T (2005).
[Crossref]

S. Ouarets, G. Ged, A. Razet, and G. Obein, “A new gonioreflectometer for the measurement of the bidirectional reflectance distribution function (BRDF) at LNE-CNAM,” in Proceedings of CIE 2012 Lighting Quality and Energy Efficiency (2012), pp. 687–691.

Ouarets, S.

S. Ouarets, G. Ged, A. Razet, and G. Obein, “A new gonioreflectometer for the measurement of the bidirectional reflectance distribution function (BRDF) at LNE-CNAM,” in Proceedings of CIE 2012 Lighting Quality and Energy Efficiency (2012), pp. 687–691.

Patrick, H. J.

H. J. Patrick, C. J. Zarobila, and T. A. Germer, “The NIST robotic optical scatter instrument (ROSI) and its application to BRDF measurements of diffuse reflectance standards for remote sensing,” Proc. SPIE 8866, 886615 (2013).
[Crossref]

Perales, E.

Pfaff, G.

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

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. R.

Pons, A.

Rabal, A. M.

Razet, A.

S. Ouarets, G. Ged, A. Razet, and G. Obein, “A new gonioreflectometer for the measurement of the bidirectional reflectance distribution function (BRDF) at LNE-CNAM,” in Proceedings of CIE 2012 Lighting Quality and Energy Efficiency (2012), pp. 687–691.

Reynders, P.

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

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, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” (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).

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 der Lans, I.

A. Ferrero, B. Bernad, J. Campos, F. M. Martínez-Verdú, E. Perales, I. van der Lans, and E. Kirchner, “Towards a better understanding of the color shift of effect coatings by densely sampled spectral BRDF measurement,” Proc. SPIE 9018, 90180K (2014).
[Crossref]

Zarobila, C. J.

H. J. Patrick, C. J. Zarobila, and T. A. Germer, “The NIST robotic optical scatter instrument (ROSI) and its application to BRDF measurements of diffuse reflectance standards for remote sensing,” Proc. SPIE 8866, 886615 (2013).
[Crossref]

Appl. Opt. (2)

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. (3)

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]

J. Mod. Opt. (1)

R. Baribeau, W. S. Neil, and É. Côté, “Development of a robot-based gonioreflectometer for spectral BRDF measurement,” J. Mod. Opt. 56, 1497–1503 (2009).
[Crossref]

J. Opt. Soc. Am. A (3)

Meas. Sci. Technol. (1)

N. Matsapey, J. Faucheu, M. Flury, and D. Delafosse, “Design of a gonio-spectrophotometer for optical characterization of gonio-apparent materials,” Meas. Sci. Technol. 24, 065901 (2013).
[Crossref]

Metrologia (2)

D. Hünerhoff, U. Grusemann, and A. Höpe, “New robot-based gonioreflectometer for measuring spectral diffuse reflection,” Metrologia 43, S11–S16 (2006).
[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]

Proc. SPIE (3)

G. Obein, R. Bousquet, and M. E. Nadal, “New NIST reference goniospectrometer,” Proc. SPIE 5880, 58800T (2005).
[Crossref]

H. J. Patrick, C. J. Zarobila, and T. A. Germer, “The NIST robotic optical scatter instrument (ROSI) and its application to BRDF measurements of diffuse reflectance standards for remote sensing,” Proc. SPIE 8866, 886615 (2013).
[Crossref]

A. Ferrero, B. Bernad, J. Campos, F. M. Martínez-Verdú, E. Perales, I. van der Lans, and E. Kirchner, “Towards a better understanding of the color shift of effect coatings by densely sampled spectral BRDF measurement,” Proc. SPIE 9018, 90180K (2014).
[Crossref]

Prog. Organic Coat. (1)

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

Rev. Sci. Instrum. (1)

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Figures (12)

Fig. 1.
Fig. 1. Representative examples of the color behavior of the studied coatings. The four displayed coatings correspond to different types of pigment (Iriodin, Xirallic, Colorstream, and Chromaflair).
Fig. 2.
Fig. 2. Total hue angle variation and chroma variation for the 15 studied special-effect coatings. Total hue angle variation was calculated as the highest hue angle difference in the set of geometries with fixed θ asp = 10 ° and with θ i from 0° to 70° in steps of 10°. Total chroma angle variation was calculated as the highest hue angle difference in the set of geometries with fixed θ bi = 10 ° and with θ i from 0° to 70° in steps of 10°. The bistatic angle θ bi is defined as the angular distance between incidence and viewing directions.
Fig. 3.
Fig. 3. Plot θ inc versus θ flake for the measurement geometries of the commercial portable multiangle spectrophotometers (X-Rite MA98, Datacolor FX10, and BYK-mac) and the nine geometries proposed by some of the authors in [18] (big black circles). The very small marks represent measurement geometries used in this study.
Fig. 4.
Fig. 4. Average of Δ E ab * over all geometries (except specular and retroreflection geometries) for the 15 samples.
Fig. 5.
Fig. 5. Bubble chart to show the variation of Δ E ab * with the geometry, when color estimation is accomplished from measurements at geometries available in X-Rite MA98, Datacolor FX10, BYK-mac, and at those proposed in [18]. White circles with maximum radii correspond to values of Δ E ab * of 10 or more.
Fig. 6.
Fig. 6. Average of Δ E ab * over geometries with θ flake < 7 ° (except specular and retroreflection geometries) for the 15 samples.
Fig. 7.
Fig. 7. Estimation of color shift for sample #4, for which the color estimation is poor for the three sets of geometries. Δ E ab * is 8.6, 10.8, and 7.3 for X-Rite MA98, Datacolor FX10, and [18] geometries, respectively.
Fig. 8.
Fig. 8. Estimation of color shift for sample #7, for which the color estimation is good for the geometries in [18] and X-Rite MA98, but not so good for Datacolor FX10. Δ E ab * is 3.8, 7.4, and 3.1 for the geometries in X-Rite MA98, Datacolor FX10, and [18], respectively.
Fig. 9.
Fig. 9. Estimation of color shift for sample #9, which presents the highest chroma variation and whose color estimation is acceptable for the geometries in X-Rite MA98, Datacolor FX10, and [18]. Δ E ab * is 2.6, 4.6 and 2.5 for the geometries in X-Rite MA98, Datacolor FX10, and [18], respectively.
Fig. 10.
Fig. 10. Estimation of color shift for sample #3, whose color estimation is almost acceptable for the geometries in X-Rite MA98 and Datacolor FX10 but not so acceptable for [18]. Δ E ab * is 5.4, 5, and 11.2 for the geometries in X-Rite MA98, Datacolor FX10, and [18], respectively.
Fig. 11.
Fig. 11. Estimation of color shift for sample #15, whose color estimation is good for the geometries in X-Rite MA98, Datacolor FX10, and [18]. Δ E ab * is 2.5, 4.3 and 3.8 for the geometries in X-Rite MA98, Datacolor FX10, and [18], respectively.
Fig. 12.
Fig. 12. Estimated color, from the geometries of BYK-mac, for samples #4 (top left), #7 (top right), #3 (bottom left), and #15 (bottom right), which must be compared with top-left subplots in Figs. 7, 8, 10, and 11. Δ E ab * is 48.1, 13.1, 19.1, and 6.5 for samples #4, #7, #3, and #15, respectively.

Tables (3)

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Table 1. Special-Effect Coatings Studied in this Work

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Table 2. Measurement Geometries Used by Multiangle Spectrophotometers: X-Rite MA98, Datacolor FX10, and BYK-mac

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Table 3. Average of Δ E ab * Over Geometries with θ flake < 7 ° a

Equations (2)

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f r ( θ i , ϕ i ; θ s , ϕ s ; λ ) = f r ( θ i , ϕ i ; θ s , ϕ s ) λ [ 1 + Σ j = 1 M c j ( θ i , ϕ i ; θ s , ϕ s ) H j ( λ ) ] .
f r , int ( θ flake , θ inc ; λ ) = e G ( θ flake ) [ 1 + F bcoat ( θ flake , θ inc ) H 1 ( λ ) + P D ( θ flake ) Σ j = 1 M 1 P j ( θ inc ) H j ( λ ) ] .

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