Abstract

I have examined the correlation structure in goniochromism by principal-component analysis. Reflectance spectra were collected in synthetic samples that reproduce metallic, nacreous, and iridescent effects under different viewing angles. Although three principal components take into account 99% of the variance, between seven and eight are needed to reach 99.99%. The results were also confirmed by analyzing each viewing condition separately. It was found that although the viewing angle does not modify the first three basis functions, it affects the higher-order ones. These angle-dependent effects can be attributed to optical interference flakes. The implications for pigment identification are discussed.

© 2008 Optical Society of America

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    [CrossRef]
  3. H. Tabata, K. Kumazawa, M. Funakawa, J. Takimoto, and M. Akimoto, “Microstructures and optical properties of scales of butterfly wings,” Opt. Rev. 3, 139-145 (1996).
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2008 (1)

M.V. Diamantini, B. del Curto, and M. Pedeferri , “Interference colors of thin oxide layers on titanium,” Color Res. Appl. 33, 221-228 (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]

S. Yoshioka and S. Kinoshita, “Polarization-sensitive color mixing in the wing of the Madagascan sunset moth,” Opt. Express 15, 2691-2701 (2007).
[CrossRef] [PubMed]

2006 (1)

O. Kohonen, J. Parkkinen, and T. Jaaskelainen, “Databases for spectral color science,” Color Res. Appl. 31, 381-390 (2006).
[CrossRef]

2005 (3)

S. M. Nascimento, D. H. Foster, and K. Amano, “Psychophysical estimates of the number of spectral-reflectance basis functions needed to reproduce natural scenes,” J. Opt. Soc. Am. A 22, 1017-1022 (2005).
[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]

A. Takagi, A. Watanabe, and G. Baba, “Prediction of spectral reflectance factor distribution of automotive paint finishes,” Color Res. Appl. 30, 275-282 (2005).
[CrossRef]

2004 (2)

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

J. A. Worthey and M. H. Brill, “Principal components applied to modeling: dealing with the mean vector,” Color Res. Appl. 29, 261-266 (2004).
[CrossRef]

2003 (2)

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

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

2002 (2)

W. R. Cramer, “Examples of interference and the color pigment mixtures green with red and red with green,” Color Res. Appl. 27, 276-281 (2002).
[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]

2001 (1)

2000 (1)

A. R. Parker, “515 million years of structural colour,” J. Opt. A Pure Appl. Opt. 2, R15-R28 (2000).
[CrossRef]

1998 (2)

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

A. Garcia-Beltran, J. L. Nieves, J. Hernandez-Andres, and J. Romero, “Linear bases for spectral reflectance functions of acrylic paints,” Color Res. Appl. 23, 39-45 (1998).
[CrossRef]

1997 (2)

1996 (2)

H. Tabata, K. Kumazawa, M. Funakawa, J. Takimoto, and M. Akimoto, “Microstructures and optical properties of scales of butterfly wings,” Opt. Rev. 3, 139-145 (1996).
[CrossRef]

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

1990 (1)

H. J. A. Saris, R. J. B. Gottenbos, and H. Vanhouwelingen, “Correlation between visual and instrumental color differences of metallic paint films,” Color Res. Appl. 15, 200-205(1990).
[CrossRef]

1986 (1)

1976 (1)

F. W. Billmeyer and E. C. Carter, “Color and appearance of metallized paint films. II. 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. I. 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]

Akimoto, M.

H. Tabata, K. Kumazawa, M. Funakawa, J. Takimoto, and M. Akimoto, “Microstructures and optical properties of scales of butterfly wings,” Opt. Rev. 3, 139-145 (1996).
[CrossRef]

Amano, K.

Arai, H.

G. Baba and H. Arai, “Gonio-spectrophotometry of metal-flake and pearl-mica pigmented paint surfaces,” in Fourth Oxford Conference on Spectroscopy, A. Springsteen and M. Pointer, eds., Proc SPIE 4826, 79-86 (2003).

Baba, G.

A. Takagi, A. Watanabe, and G. Baba, “Prediction of spectral reflectance factor distribution of automotive paint finishes,” Color Res. Appl. 30, 275-282 (2005).
[CrossRef]

G. Baba and H. Arai, “Gonio-spectrophotometry of metal-flake and pearl-mica pigmented paint surfaces,” in Fourth Oxford Conference on Spectroscopy, A. Springsteen and M. Pointer, eds., Proc SPIE 4826, 79-86 (2003).

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]

R. S. Berns, “A generic approach to color modeling,” Color Res. Appl. 22, 318-325 (1997).
[CrossRef]

Billmeyer, F. W.

F. W. Billmeyer and E. C. Carter, “Color and appearance of metallized paint films. II. 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. I. Characterization,” J. Paint Technol. 46, 31-37 (1974).

Brill, M. H.

J. A. Worthey and M. H. Brill, “Principal components applied to modeling: dealing with the mean vector,” Color Res. Appl. 29, 261-266 (2004).
[CrossRef]

Carter, E. C.

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

Ceppan, M.

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

Cramer, W. R.

W. R. Cramer, “Examples of interference and the color pigment mixtures green with red and red with green,” Color Res. Appl. 27, 276-281 (2002).
[CrossRef]

Davidson, J. G.

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

del Curto, B.

M.V. Diamantini, B. del Curto, and M. Pedeferri , “Interference colors of thin oxide layers on titanium,” Color Res. Appl. 33, 221-228 (2008).
[CrossRef]

Diamantini, M. V.

M.V. Diamantini, B. del Curto, and M. Pedeferri , “Interference colors of thin oxide layers on titanium,” Color Res. Appl. 33, 221-228 (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]

Enoch, S.

Flannery, B.

W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes in C (Cambridge University, 1992), p. 994.

Foster, D. H.

Funakawa, M.

H. Tabata, K. Kumazawa, M. Funakawa, J. Takimoto, and M. Akimoto, “Microstructures and optical properties of scales of butterfly wings,” Opt. Rev. 3, 139-145 (1996).
[CrossRef]

Garcia-Beltran, A.

A. Garcia-Beltran, J. L. Nieves, J. Hernandez-Andres, and J. Romero, “Linear bases for spectral reflectance functions of acrylic paints,” Color Res. Appl. 23, 39-45 (1998).
[CrossRef]

J. Romero, A. Garcia-Beltran, and J. Hernandez-Andres, “Linear bases for representation of natural and artificial illuminants,” J. Opt. Soc. Am. A 14, 1007-1014 (1997).
[CrossRef]

Gottenbos, R.

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 differences of metallic paint films,” Color Res. Appl. 15, 200-205(1990).
[CrossRef]

Gralak, B.

Hecht, E.

E. Hecht and A. Zajac, Optics (Addison-Wesley, 1974), p. 565.

Hernandez-Andres, J.

A. Garcia-Beltran, J. L. Nieves, J. Hernandez-Andres, and J. Romero, “Linear bases for spectral reflectance functions of acrylic paints,” Color Res. Appl. 23, 39-45 (1998).
[CrossRef]

J. Romero, A. Garcia-Beltran, and J. Hernandez-Andres, “Linear bases for representation of natural and artificial illuminants,” J. Opt. Soc. Am. A 14, 1007-1014 (1997).
[CrossRef]

Jaaskelainen, T.

O. Kohonen, J. Parkkinen, and T. Jaaskelainen, “Databases for spectral color science,” Color Res. Appl. 31, 381-390 (2006).
[CrossRef]

Kinoshita, S.

Kirchner, E.

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]

Kohonen, O.

O. Kohonen, J. Parkkinen, and T. Jaaskelainen, “Databases for spectral color science,” Color Res. Appl. 31, 381-390 (2006).
[CrossRef]

Kumazawa, K.

H. Tabata, K. Kumazawa, M. Funakawa, J. Takimoto, and M. Akimoto, “Microstructures and optical properties of scales of butterfly wings,” Opt. Rev. 3, 139-145 (1996).
[CrossRef]

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]

Lewis, P. A.

P. A. Lewis, Pigment Handbook, Properties and Economics, 2nd ed. (Wiley, 1988), Vol. 1, p. 976.

Maloney, L. T.

L. T. Maloney, “Evaluation of linear models of surface spectral reflectance with small numbers of parameters,” J. Opt. Soc. Am. A 3, 1673-1683 (1986).
[CrossRef] [PubMed]

L. T. Maloney, “Physics-based approaches to modeling surface color perception,” in Color Vision: From Genes to Perception, K. R. Gengenfurtner and L. T. Sharpe, eds. (Cambridge University, 1999), pp. 387-422.

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. II. Micro appearance,” Color Res. Appl. 23, 362-373 (1998).
[CrossRef]

C. S. McCamy, “Observation and measurement of the appearance of metallic materials. I. 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]

Mikula, M.

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

Nieves, J. L.

A. Garcia-Beltran, J. L. Nieves, J. Hernandez-Andres, and J. Romero, “Linear bases for spectral reflectance functions of acrylic paints,” Color Res. Appl. 23, 39-45 (1998).
[CrossRef]

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]

Parker, A. R.

A. R. Parker, “515 million years of structural colour,” J. Opt. A Pure Appl. Opt. 2, R15-R28 (2000).
[CrossRef]

Parkkinen, J.

O. Kohonen, J. Parkkinen, and T. Jaaskelainen, “Databases for spectral color science,” Color Res. Appl. 31, 381-390 (2006).
[CrossRef]

Pedeferri, M.

M.V. Diamantini, B. del Curto, and M. Pedeferri , “Interference colors of thin oxide layers on titanium,” Color Res. Appl. 33, 221-228 (2008).
[CrossRef]

Press, W.

W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes in C (Cambridge University, 1992), p. 994.

Romero, J.

A. Garcia-Beltran, J. L. Nieves, J. Hernandez-Andres, and J. Romero, “Linear bases for spectral reflectance functions of acrylic paints,” Color Res. Appl. 23, 39-45 (1998).
[CrossRef]

J. Romero, A. Garcia-Beltran, and J. Hernandez-Andres, “Linear bases for representation of natural and artificial illuminants,” J. Opt. Soc. Am. A 14, 1007-1014 (1997).
[CrossRef]

Sambles, J. R.

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

Saris, H. J. A.

H. J. A. Saris, R. J. B. Gottenbos, and H. Vanhouwelingen, “Correlation between visual and instrumental color differences of metallic paint films,” Color Res. Appl. 15, 200-205(1990).
[CrossRef]

Stiles, W. S.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982), p. 950.

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.

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]

Tabata, H.

H. Tabata, K. Kumazawa, M. Funakawa, J. Takimoto, and M. Akimoto, “Microstructures and optical properties of scales of butterfly wings,” Opt. Rev. 3, 139-145 (1996).
[CrossRef]

Takagi, A.

A. Takagi, A. Watanabe, and G. Baba, “Prediction of spectral reflectance factor distribution of automotive paint finishes,” Color Res. Appl. 30, 275-282 (2005).
[CrossRef]

Takimoto, J.

H. Tabata, K. Kumazawa, M. Funakawa, J. Takimoto, and M. Akimoto, “Microstructures and optical properties of scales of butterfly wings,” Opt. Rev. 3, 139-145 (1996).
[CrossRef]

Tayeb, G.

Teukolsky, S.

W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes in C (Cambridge University, 1992), p. 994.

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.

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]

Vanhouwelingen, H.

H. J. A. Saris, R. J. B. Gottenbos, and H. Vanhouwelingen, “Correlation between visual and instrumental color differences of metallic paint films,” Color Res. Appl. 15, 200-205(1990).
[CrossRef]

Vasko, K.

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

Vetterling, W.

W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes in C (Cambridge University, 1992), p. 994.

Völz, H. G.

H. G. Völz, Industrial Color Testing, Fundamentals and Techniques, 2nd ed. (Wiley, 2001), p. 388.

Vukusic, P.

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

Watanabe, A.

A. Takagi, A. Watanabe, and G. Baba, “Prediction of spectral reflectance factor distribution of automotive paint finishes,” Color Res. Appl. 30, 275-282 (2005).
[CrossRef]

Worthey, J. A.

J. A. Worthey and M. H. Brill, “Principal components applied to modeling: dealing with the mean vector,” Color Res. Appl. 29, 261-266 (2004).
[CrossRef]

Wyszecki, G.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982), p. 950.

Yoshioka, S.

Zajac, A.

E. Hecht and A. Zajac, Optics (Addison-Wesley, 1974), p. 565.

Anal. Chem. (1)

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

Color Res. Appl. (14)

J. A. Worthey and M. H. Brill, “Principal components applied to modeling: dealing with the mean vector,” Color Res. Appl. 29, 261-266 (2004).
[CrossRef]

R. S. Berns, “A generic approach to color modeling,” Color Res. Appl. 22, 318-325 (1997).
[CrossRef]

M. Mikula, M. Ceppan, and K. Vasko, “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]

M.V. Diamantini, B. del Curto, and M. Pedeferri , “Interference colors of thin oxide layers on titanium,” Color Res. Appl. 33, 221-228 (2008).
[CrossRef]

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

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

W. R. Cramer, “Examples of interference and the color pigment mixtures green with red and red with green,” Color Res. Appl. 27, 276-281 (2002).
[CrossRef]

A. Takagi, A. Watanabe, and G. Baba, “Prediction of spectral reflectance factor distribution of automotive paint finishes,” Color Res. Appl. 30, 275-282 (2005).
[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]

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic of an interference flake (mica coated by TiO 2 ). Fringes of equal inclination are generated at the specular reflection by the metal oxide layer. Those rays not reflected are transmitted to the next interface. (b) Microscopic image of a typical metallic-green coating containing lenticular aluminum and pearl red-green interference pigments ( 50 × , dark-field illumination).

Fig. 2
Fig. 2

Schematic of a five-angle spectrophotometer. Illumination source is fixed at the standard geometry of 45 ° from the normal. Measuring geometries are defined from specular reflection (aspecular viewing angles) at 15 ° , 25 ° , 45 ° , 75 ° , and 110 ° .

Fig. 3
Fig. 3

Spectral properties and colorimetric values of four representative goniochromatic samples. (a) and (b) Examples containing high concentration of metal flakes (metallic coatings). (c) and (d) Examples containing optical interference flakes (pearlescent coatings). Left column: Semilogarithmic plot of the spectral reflectance curves. Reflectance factors are indicated for each aspecular viewing geometry separately at 15 ° , 25 ° , 45 ° , 75 ° , and 110 ° . Central column: Wavelength at maximum reflectance in relation to the viewing aspecular angle. Right column: CIELAB values for different aspecular angles. Data were calculated using CIE 10 ° standard observer and D65 illuminant.

Fig. 4
Fig. 4

CIELAB values of the synthetic goniochromatic surfaces for all the viewing angles measured. Solid black symbols represent the color coordinates in the three-dimensional color space. Solid gray symbols represent the projections in the a * b * and L * b * planes. Data were calculated using CIE 10 ° standard observer and D65 illuminant. Lightness values are in logarithmic units. The inset shows an amplification of the chromaticity coordinates in the a * b * plane.

Fig. 5
Fig. 5

PCA of goniochromatic samples at each viewing angle separately. Panels shows the first eight basis functions for near-specular ( 15 ° , solid curves), normal to the sample ( 45 ° , dashed curves), and close to the surface or far from specular ( 110 ° , dash-dotted curves). Top left corner: the first three basis functions were represented in the same panel. The first, second, and third bases are indicated by black, gray, and light gray, respectively.

Fig. 6
Fig. 6

Examples of a reconstruction of a metallic-green (left column) and a metallic-red (right column) goniochromatic samples at 15 ° and 110 ° , separately. Solid curves represent the original reflectance functions. Dashed and dash-dotted curves represent the reconstruction using the linear combination of the first three and first eight basis functions, respectively. (b) Examples of reconstruction (dashed curves) of the same examples using only those basis functions associated with aluminum (Al) and pearl-mica pigments. Solid curves represent the original reflectance functions.

Tables (3)

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Table 1 Cumulative Percentage of Variance Accounted for the First Eight Principal Components (PCs) in Goniochromatic Materials Taking into Account All the Aspecular Viewing Angles Together: γ = 15 ° , 25 ° , 45 ° , 75 ° , and 110 ° a

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Table 2 Cumulative Percentage of Variance Accounted for the First Eight Principal Components (PCs) in Goniochromatic Materials Taking into Account Each Viewing Angle Separately

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Table 3 Mean, Standard Error of the Mean ( ± 1 SEM), and Maximum Root Mean Square Error and Δ E DIN of the Reconstructed Reflectance Spectra a

Equations (4)

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( Maxima ) λ = 2 d [ n 1 2 n 0 2 sin 2 ( ϕ ) ] 1 / 2 ( m + 1 2 ) , m = 0 , ± 1 , ± 2 , ,
( Minima ) λ = 2 d [ n 1 2 n 0 2 sin 2 ( ϕ ) ] 1 / 2 m , m = ± 1 , ± 2 , ,
R j i = 1 m α i S i , j = 1 , , 540 ; m 31 ,
Δ E ( γ ) = { [ Δ L g L S L ( γ ) ] 2 + [ Δ C g C S C ( γ ) ] 2 + [ Δ H g H S H ( γ ) ] 2 } 1 / 2 ,

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