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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 16 — Jul. 30, 2012
  • pp: 17560–17565
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Low-frequency correlations (1/f α type) in paint application of metallic colors

José M. Medina and José A. Díaz  »View Author Affiliations


Optics Express, Vol. 20, Issue 16, pp. 17560-17565 (2012)
http://dx.doi.org/10.1364/OE.20.017560


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Abstract

We examine trial-to-trial variability of color coordinates in automotive coatings containing effect pigments, which are considered a reference paradigm for engineering angle-dependent color effects. We report the existence of correlations that show 1/f - Fourier spectra at low frequencies in all color coordinates. The scaling exponent was lower at near-specular conditions for lightness variations, suggesting a contribution from the deposition of metal flakes in metallic colors. However, the exponent was lower near the specular for blue-yellow variations, suggesting a contribution from chemical pigments in solid colors. These results were independent of the illuminant spectra. The methods employed are useful in the evaluation of industrial color matching among assembly parts.

© 2012 OSA

1. Introduction

Automotive coatings are functional multi-layer thin films that can provide protection against corrosion, weather resistance and improved color appearance over time [1

1. P. A. Lewis, Pigment Handbook, Properties and Economics (John Willey & Sons, 1988).

,2

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

]. The physical mechanisms of color appearance are a central issue and depend on the pigments deposited in the basecoat [1

1. P. A. Lewis, Pigment Handbook, Properties and Economics (John Willey & Sons, 1988).

3

3. G. A. Klein, Industrial Color Physics (Springer Science + Business Media LLC, 2010).

]. Two main categories of pigments can be considered: conventional chemical pigments and effect pigments [1

1. P. A. Lewis, Pigment Handbook, Properties and Economics (John Willey & Sons, 1988).

3

3. G. A. Klein, Industrial Color Physics (Springer Science + Business Media LLC, 2010).

]. Chemical pigments can be organic and inorganic and have typical particle sizes less than microns. They can absorb light and produce diffuse scattering [1

1. P. A. Lewis, Pigment Handbook, Properties and Economics (John Willey & Sons, 1988).

3

3. G. A. Klein, Industrial Color Physics (Springer Science + Business Media LLC, 2010).

]. However, effect pigments are manufactured with particle sizes of several microns and they modulate the flow of light by specular reflection (e.g., metal flakes), multi-layer interference (e.g., mica-based pigments), and diffraction [1

1. P. A. Lewis, Pigment Handbook, Properties and Economics (John Willey & Sons, 1988).

,3

3. G. A. Klein, Industrial Color Physics (Springer Science + Business Media LLC, 2010).

], by producing angle-dependent color effects or “goniochromism” [2

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

4

4. C. S. McCamy, “Observation and measurement of the appearance of metallic materials. Part I. Macro appearance,” Color Res. Appl. 21(4), 292–304 (1996). [CrossRef]

]. Those colored coatings containing only conventional chemical pigments are often called “solid colors” whereas those coatings containing metal pigments, “metallic colors” [2

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

,3

3. G. A. Klein, Industrial Color Physics (Springer Science + Business Media LLC, 2010).

]. Figure 1(a)
Fig. 1 (a) Optical microscopy image of a metallic-green paint (50x, dark field illumination). Yellow squares labeled as “1” and “2” indicate an example of an aluminum flake and a mica-based interference pigment, respectively. (b) Schematic representation of the illumination and detection positions for metallic colors at the aspecular angle γ of 15°, 25°, 45°, 75° and 110°.
shows an optical microscopy image of a metallic-green paint. Yellow squares labeled as “1” and “2” indicate an example of an aluminum flake and a mica-based interference pigment, respectively.

Color matching among assembly parts is a complex issue that depends on a considerable number of errors from different paint application processes, manufacturing parameters, measurement errors as well as human factors. A classic example in the automobile industry is the final color appearance of the vehicle body that must be the same for add-on parts such as bumpers, fenders, spoilers, etc. (usually called “color harmony”) [2

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

]. For each color design, color tolerances are a set of thresholds that aid for the visual acceptance of car parts and they are usually defined relative to a reference or “master” panel at each viewing angle [2

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

,3

3. G. A. Klein, Industrial Color Physics (Springer Science + Business Media LLC, 2010).

]. However, the use of color tolerances ignores texture effects [2

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

,3

3. G. A. Klein, Industrial Color Physics (Springer Science + Business Media LLC, 2010).

] and does not relate the intrinsic trial-to-trial color variations with the deposition of different effect pigments. In the present study, we describe a novel method of examining color harmony in metallic colors. We measured the reflectance spectra of car pieces painted in the production line in serial order following the current standards of gonioappearance [5

5. Deutsches Institut für Normung e.V., “Tolerances for automotive paint—Part 2: Goniochromatic paints,” DIN 6175–2 (2001).

7

7. American Society for Testing and Materials, “Standard practice for multiangle color measurement of metal flake pigmented materials,” ASTM E 2194–12 (2012).

]. Reflectance spectra were transformed to color coordinates [2

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

4

4. C. S. McCamy, “Observation and measurement of the appearance of metallic materials. Part I. Macro appearance,” Color Res. Appl. 21(4), 292–304 (1996). [CrossRef]

] and color coordinate variations were referred to the corresponding master panel. Each painted sample is therefore represented by its color variation and the entire batch production is mapped as color fluctuations in the time domain. These temporal color series are treated as stochastic time signals that can be transformed to the Fourier domain and the power spectral density can be estimated using a low-variance method [8

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

]. A common type of correlations in many stochastic signals follows 1/fα Fourier power spectrum, where f is the frequency and α is the scaling exponent [9

9. W. H. Press, “Flicker noises in astronomy and elsewhere,” Comments Mod. Phys., Part C 7, 103–119 (1978).

11

11. J. M. Medina and J. A. Díaz, “1/f noise in human color vision: the role of S-cone signals,” J. Opt. Soc. Am. A 29(2), A82–A95 (2012). [CrossRef] [PubMed]

]. When there is no correlation in the color coordinate variations at different time scales, α = 0, the Fourier power spectrum will be flat and all the frequencies have equal probability, i.e., the power spectrum will resemble “white noise”. If α = 2, there exits strong long-term correlations and the Fourier power spectrum resembles “Brown noise”, i.e., similar to a random walker that follows a traditional one-dimensional Brownian motion over time [10

10. B. J. West and M. Shlesinger, “The noise in natural phenomena,” Am. Sci. 78, 40–45 (1990).

,11

11. J. M. Medina and J. A. Díaz, “1/f noise in human color vision: the role of S-cone signals,” J. Opt. Soc. Am. A 29(2), A82–A95 (2012). [CrossRef] [PubMed]

]. However, a wide range of phenomena and many mathematical models can obey to a scaling exponent α close to unity known as “flicker noise”, “pink noise”, “1/f noise” or “1/f scaling” [9

9. W. H. Press, “Flicker noises in astronomy and elsewhere,” Comments Mod. Phys., Part C 7, 103–119 (1978).

11

11. J. M. Medina and J. A. Díaz, “1/f noise in human color vision: the role of S-cone signals,” J. Opt. Soc. Am. A 29(2), A82–A95 (2012). [CrossRef] [PubMed]

]. Here, we ascertain whether the trial-to-trial variability of color coordinates in metallic colors are correlated over time and follows 1/fα Fourier spectra. We also investigate the suitability of the exponent α to discern the contribution among different types of pigments by examining the power spectra at different aspecular angles [see Fig. 1(b)]. Finally, the color series of metallic colors are compared to those of solid colors as a control condition.

2. Methods

2.1 Data set and instrumentation

Two different color batch productions were examined. All panels were solvent-borne coatings and they were representative of original equipment manufacturer (OEM) paints of automobile suppliers in Europe. The outermost layer of typical solvent-borne coatings is a transparent lacquer that provides protection and a glossy finish. After that, the pigments are dispersed in a transparent basecoat providing the desired color appearance and opacity or hiding power [1

1. P. A. Lewis, Pigment Handbook, Properties and Economics (John Willey & Sons, 1988).

3

3. G. A. Klein, Industrial Color Physics (Springer Science + Business Media LLC, 2010).

]. The first color batch comprised of 159 plastic planar pieces. These were plastic pieces coated in serial order using a metallic-green paint. The color recipe contains lenticular aluminum flakes, mica-based interference pigments, conventional absorbing green and blue pigments and carbon black pigments [see Fig. 1(a)]. It corresponds to a typical metallic color that exhibits goniochromatic effects from a mixture of effect and chemical pigments [1

1. P. A. Lewis, Pigment Handbook, Properties and Economics (John Willey & Sons, 1988).

3

3. G. A. Klein, Industrial Color Physics (Springer Science + Business Media LLC, 2010).

]. Metal flakes are responsible for lightness changes and the interference flakes for chromaticity changes as a function of the aspecular angle γ. Flakes were oriented, on average, parallel to the substrate [1

1. P. A. Lewis, Pigment Handbook, Properties and Economics (John Willey & Sons, 1988).

3

3. G. A. Klein, Industrial Color Physics (Springer Science + Business Media LLC, 2010).

]. Color effects from aluminum and interference flakes dominate near-specular reflection whereas those color effects from absorption pigments are predominant far from the specular [see also Fig. 1(b)] [1

1. P. A. Lewis, Pigment Handbook, Properties and Economics (John Willey & Sons, 1988).

3

3. G. A. Klein, Industrial Color Physics (Springer Science + Business Media LLC, 2010).

]. The second color batch comprised of 181 plastic planar pieces coated with a white-red paint. The color recipe contains only titanium dioxide [1

1. P. A. Lewis, Pigment Handbook, Properties and Economics (John Willey & Sons, 1988).

] and opaque red pigments and corresponds to a typical solid color that shows poor goniochromatic effects. Both paints were uniformly spread using a painting robot [2

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

] in a production line following the automotive standards for plastic parts [2

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

].

Reflectance spectra were measured using an X-Rite MA68 II multi-angle spectrophotometer. This spectrophotometer is in agreement with the industry standards for metallic colors [2

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

,3

3. G. A. Klein, Industrial Color Physics (Springer Science + Business Media LLC, 2010).

,5

5. Deutsches Institut für Normung e.V., “Tolerances for automotive paint—Part 2: Goniochromatic paints,” DIN 6175–2 (2001).

7

7. American Society for Testing and Materials, “Standard practice for multiangle color measurement of metal flake pigmented materials,” ASTM E 2194–12 (2012).

] [see Fig. 1(b)]. A calibration procedure was done periodically to perform white and zero reflectance reference measurements by using a certified white ceramic tile and a black trap, respectively. For each painted sample, its reflectance at each aspecular angle was averaged from a minimum of 4 consecutive recordings. The spectral reflectance factor was measured in the visible range from 400 to 700 nm in 10-nm steps within the range of 0- 400% in accordance with the operator’s manual. The total number of reflectance measurements was 759 and 905 for the metallic-green and the white-red solid color, respectively.

2.2 Data analysis

2.2.1 Colorimetric analysis

The colorimetric methods employed are standard for the representation of pigmented coatings and they are described elsewhere [2

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

,3

3. G. A. Klein, Industrial Color Physics (Springer Science + Business Media LLC, 2010).

,12

12. G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (John Wiley & Sons, 1982).

]. The CIE (Commission Internationale de l’Éclairage, International Commission on Illumination) XYZ tristimulus values were calculated from reflectance spectra using the CIE 1964 10-deg color matching functions [12

12. G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (John Wiley & Sons, 1982).

]. The XYZ tristimulus values were converted to the CIE 1976 L*a*b* color space (CIELAB) [3

3. G. A. Klein, Industrial Color Physics (Springer Science + Business Media LLC, 2010).

,12

12. G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (John Wiley & Sons, 1982).

]. Color variations are defined as the difference between the test and the master panel and they have both positive and negative values. They are denoted by the lightness difference ΔL*, red-green, Δa* and the blue-yellow difference, Δb* or alternatively, in terms of ΔL*, chroma difference, ΔC*ab (related with the saturation or the reciprocal of white), and the hue difference, ΔH*ab [3

3. G. A. Klein, Industrial Color Physics (Springer Science + Business Media LLC, 2010).

,12

12. G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (John Wiley & Sons, 1982).

]. Color differences were examined under four different illuminants. These were the CIE standard illuminants D65 and A as well as the spectral power distributions of the fluorescent lamps FL2 and FL11. The illuminant spectra selected reproduce most of the common illumination sources used in industrial color testing [2

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

,3

3. G. A. Klein, Industrial Color Physics (Springer Science + Business Media LLC, 2010).

,12

12. G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (John Wiley & Sons, 1982).

].

2.2.2 Power spectra

3. Results and discussion

The results demonstrate the existence of 1/f scaling in all color coordinate variations. In some cases there is a low-frequency white noise plateau suggesting that the color series shows no correlation at very long time scales i.e., a short-range process. These data points were discarded from power law fits. In all cases, the coefficient R2 was between 0.89 and 0.99 and the standard error of the resulting exponent α varied between 0.01 and 0.2. In the metallic-green color, the power spectrum was higher at 15° in all color coordinates. Interestingly, the exponent α was close to zero at 15° (−0.25) for lightness variations, ΔL*, but it increases near to unity (−0.9) at 110°. This suggests low correlations in the deposition of aluminum flakes. Regarding hue variations, ΔH*ab, the exponent α varies slightly from −0.7 at 15° to −0.79 at 110° suggesting a possible contribution from interference pigments. In contrast, the magnitude of the power spectrum for the white-red solid color was very similar at different aspecular angles except for blue-yellow variations Δb*. The scaling exponent α remains invariant for lightness variations, ΔL*, but it does not neither for red-green, Δa* nor blue-yellow variations, Δb*. In the latter, the exponent varies from −0.7 at 15° to unity at 110° suggesting a possible origin from the deposition of chemical pigments, measurement errors as well as corrections of the final color recipe in the line. Table 1

Table 1. The exponent α of the Fourier power law spectra at different illuminants and aspecular angles

table-icon
View This Table
summarizes the values of the exponent α for different illuminants. Although there is some dependency with the illuminant spectra especially for ΔH*ab at 15°, ΔC*ab at 45° and for Δa*, the analysis in Fig. 3 is corroborated.

4. Conclusion

We have demonstrated that trial-to-trial variability of metallic and solid colors show 1/f-Fourier spectra at low frequencies and reflects anomalous diffusion in comparison to the classic Brownian motion (α = 2). Although we cannot exclude a potential source of variability from instrument noise, the evaluation of the exponent α at different aspecular angles suggests that power law correlations may be derived in part from the deposition of pigments. Those car plants and supplier painted parts having the same exponent α in the same color design will share the same type of correlations over time. This is interesting in order to select the right painted pieces and thus to control better color harmony. Although noise analysis has been restricted to automotive coatings, the methods employed based on the Fourier transform are general may be useful in different industrial paint processes.

Acknowledgments

Supported by the European Regional Development Fund – ERDF through Programa Operacional Factores de Competitividade – COMPETE (FCOMP-01-0124-FEDER-014588), by the National Portuguese funds through the Fundação para a Ciência e Tecnologia – FCT (PTDC/CTM-MET/113352/2009), and by the Center for Physics, University of Minho, Portugal.

References and links

1.

P. A. Lewis, Pigment Handbook, Properties and Economics (John Willey & Sons, 1988).

2.

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

3.

G. A. Klein, Industrial Color Physics (Springer Science + Business Media LLC, 2010).

4.

C. S. McCamy, “Observation and measurement of the appearance of metallic materials. Part I. Macro appearance,” Color Res. Appl. 21(4), 292–304 (1996). [CrossRef]

5.

Deutsches Institut für Normung e.V., “Tolerances for automotive paint—Part 2: Goniochromatic paints,” DIN 6175–2 (2001).

6.

American Society for Testing and Materials, “Standard practice for specifying the geometry of multiangle spectrophotometers,” ASTM E 2175–01 (2001).

7.

American Society for Testing and Materials, “Standard practice for multiangle color measurement of metal flake pigmented materials,” ASTM E 2194–12 (2012).

8.

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

9.

W. H. Press, “Flicker noises in astronomy and elsewhere,” Comments Mod. Phys., Part C 7, 103–119 (1978).

10.

B. J. West and M. Shlesinger, “The noise in natural phenomena,” Am. Sci. 78, 40–45 (1990).

11.

J. M. Medina and J. A. Díaz, “1/f noise in human color vision: the role of S-cone signals,” J. Opt. Soc. Am. A 29(2), A82–A95 (2012). [CrossRef] [PubMed]

12.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (John Wiley & Sons, 1982).

13.

B. Pilgram and D. T. Kaplan, “A comparison of estimators for 1/f noise,” Physica D 114(1-2), 108–122 (1998). [CrossRef]

OCIS Codes
(000.5490) General : Probability theory, stochastic processes, and statistics
(310.1620) Thin films : Interference coatings
(310.1860) Thin films : Deposition and fabrication
(330.1730) Vision, color, and visual optics : Colorimetry
(290.1483) Scattering : BSDF, BRDF, and BTDF
(310.3915) Thin films : Metallic, opaque, and absorbing coatings

ToC Category:
Thin Films

History
Original Manuscript: May 15, 2012
Revised Manuscript: June 24, 2012
Manuscript Accepted: June 25, 2012
Published: July 18, 2012

Virtual Issues
Vol. 7, Iss. 9 Virtual Journal for Biomedical Optics

Citation
José M. Medina and José A. Díaz, "Low-frequency correlations (1/fα type) in paint application of metallic colors," Opt. Express 20, 17560-17565 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-16-17560


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References

  1. P. A. Lewis, Pigment Handbook, Properties and Economics (John Willey & Sons, 1988).
  2. H. J. Streitberger and K. F. Dössel, Automotive Paints and Coatings (Wiley-VCH, 2008).
  3. G. A. Klein, Industrial Color Physics (Springer Science + Business Media LLC, 2010).
  4. C. S. McCamy, “Observation and measurement of the appearance of metallic materials. Part I. Macro appearance,” Color Res. Appl.21(4), 292–304 (1996). [CrossRef]
  5. Deutsches Institut für Normung e.V., “Tolerances for automotive paint—Part 2: Goniochromatic paints,” DIN 6175–2 (2001).
  6. American Society for Testing and Materials, “Standard practice for specifying the geometry of multiangle spectrophotometers,” ASTM E 2175–01 (2001).
  7. American Society for Testing and Materials, “Standard practice for multiangle color measurement of metal flake pigmented materials,” ASTM E 2194–12 (2012).
  8. W. H. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes in C (Cambridge University Press, 1992).
  9. W. H. Press, “Flicker noises in astronomy and elsewhere,” Comments Mod. Phys., Part C7, 103–119 (1978).
  10. B. J. West and M. Shlesinger, “The noise in natural phenomena,” Am. Sci.78, 40–45 (1990).
  11. J. M. Medina and J. A. Díaz, “1/f noise in human color vision: the role of S-cone signals,” J. Opt. Soc. Am. A29(2), A82–A95 (2012). [CrossRef] [PubMed]
  12. G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (John Wiley & Sons, 1982).
  13. B. Pilgram and D. T. Kaplan, “A comparison of estimators for 1/f noise,” Physica D114(1-2), 108–122 (1998). [CrossRef]

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