Abstract

Flakes in effect coatings, which are responsible for its color shift, are not perfectly horizontally oriented, producing a non uniform texture when observed from a distance of around one meter or less. If the coating is illuminated by a diffuse source, a granular appearance is observed, called graininess. But when the coating is illuminated by unidirectional light, some luminous spots on a dark background appear, effect that is known as sparkle. The characterization of these two textures is getting more important for automotive industry because of the high percentage of cars with effect coatings and because improvements in imaging technology allows this effect to be measured by, for instance, commercial instruments as BYK-mac. A single analytical model to understand and radiometrically characterize both sparkle and graininess in effect coatings is presented and studied in this work. It allows both patterns to be explained and, despite its simplicity, includes variables related to the optical system (Point Spread Function (PSF) and size of the entrance pupil), its distance to the coating, the diffusion grade of the illumination, the illumination and observation directions, and coating parameters.

© 2013 OSA

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References

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  1. F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments–past, present and future” Progress in Organic Coatings 54, 150–163 (2005).
    [Crossref]
  2. H. J. Streitberger and K. F. Dössel, Automotive Paints and Coatings (Wiley-VCH, Weinheim, 2008).
    [Crossref]
  3. G. Pfaff and P. Reynders, “Angle-Dependent Optical Effects Deriving from Submicron Structures of Films and Pigments,” Chem Rev. 99, 1963–1982 (1999).
    [Crossref]
  4. C. C. Esposito, “Metallic pigments: New finishes on the rise,” Coat World 8, 21–23 (2003).
  5. E. Kirchner, G. J. van den Kieboom, L. Njo, R. Sùper, and R. Gottenbos, “Observation of visual texture of metallic and pearlescent materials,” Col. Res. Appl. 32, 256–266 (2007).
    [Crossref]
  6. I. van der Lans, E. Kirchner, and A. Half, “Accurate appearance-based visualization of car paints,” Proceedings of the CGIV conference (Amsterdam, May 2012) 17–23.
  7. E. Kirchner and J. Ravi, “Predicting and measuring the perceived texture of car paints,” Proceedings of the 3rd International Conference on Appearance “Predicting Perceptions” (Edinburgh, April 2012) 17–19.
  8. S. Ershov, A. Khodulev, and K. Kolchin, “Simulation of sparkles in metallic paints,” Proceeding of Graphicon (August, 1999) 121–128.
  9. F. E. Nicodemus, J. C. Richmond, and J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. Monogr. 160, (1977).

2007 (1)

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

2005 (1)

F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments–past, present and future” Progress in Organic Coatings 54, 150–163 (2005).
[Crossref]

2003 (1)

C. C. Esposito, “Metallic pigments: New finishes on the rise,” Coat World 8, 21–23 (2003).

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]

1977 (1)

F. E. Nicodemus, J. C. Richmond, and J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. Monogr. 160, (1977).

Dössel, K. F.

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

Ershov, S.

S. Ershov, A. Khodulev, and K. Kolchin, “Simulation of sparkles in metallic paints,” Proceeding of Graphicon (August, 1999) 121–128.

Esposito, C. C.

C. C. Esposito, “Metallic pigments: New finishes on the rise,” Coat World 8, 21–23 (2003).

Gottenbos, R.

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

Half, A.

I. van der Lans, E. Kirchner, and A. Half, “Accurate appearance-based visualization of car paints,” Proceedings of the CGIV conference (Amsterdam, May 2012) 17–23.

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, and J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. Monogr. 160, (1977).

Khodulev, A.

S. Ershov, A. Khodulev, and K. Kolchin, “Simulation of sparkles in metallic paints,” Proceeding of Graphicon (August, 1999) 121–128.

Kirchner, E.

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

I. van der Lans, E. Kirchner, and A. Half, “Accurate appearance-based visualization of car paints,” Proceedings of the CGIV conference (Amsterdam, May 2012) 17–23.

E. Kirchner and J. Ravi, “Predicting and measuring the perceived texture of car paints,” Proceedings of the 3rd International Conference on Appearance “Predicting Perceptions” (Edinburgh, April 2012) 17–19.

Kolchin, K.

S. Ershov, A. Khodulev, and K. Kolchin, “Simulation of sparkles in metallic paints,” Proceeding of Graphicon (August, 1999) 121–128.

Maile, F. J.

F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments–past, present and future” Progress in Organic Coatings 54, 150–163 (2005).
[Crossref]

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, and J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. Monogr. 160, (1977).

Njo, L.

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

Pfaff, G.

F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments–past, present and future” Progress in Organic Coatings 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]

Ravi, J.

E. Kirchner and J. Ravi, “Predicting and measuring the perceived texture of car paints,” Proceedings of the 3rd International Conference on Appearance “Predicting Perceptions” (Edinburgh, April 2012) 17–19.

Reynders, P.

F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments–past, present and future” Progress in Organic Coatings 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,” Natl. Bur. Stand. Monogr. 160, (1977).

Streitberger, H. J.

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

Sùper, R.

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

van den Kieboom, G. J.

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

van der Lans, I.

I. van der Lans, E. Kirchner, and A. Half, “Accurate appearance-based visualization of car paints,” Proceedings of the CGIV conference (Amsterdam, May 2012) 17–23.

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]

Coat World (1)

C. C. Esposito, “Metallic pigments: New finishes on the rise,” Coat World 8, 21–23 (2003).

Col. Res. Appl. (1)

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

Natl. Bur. Stand. Monogr. (1)

F. E. Nicodemus, J. C. Richmond, and J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. Monogr. 160, (1977).

Progress in Organic Coatings (1)

F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments–past, present and future” Progress in Organic Coatings 54, 150–163 (2005).
[Crossref]

Other (4)

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

I. van der Lans, E. Kirchner, and A. Half, “Accurate appearance-based visualization of car paints,” Proceedings of the CGIV conference (Amsterdam, May 2012) 17–23.

E. Kirchner and J. Ravi, “Predicting and measuring the perceived texture of car paints,” Proceedings of the 3rd International Conference on Appearance “Predicting Perceptions” (Edinburgh, April 2012) 17–19.

S. Ershov, A. Khodulev, and K. Kolchin, “Simulation of sparkles in metallic paints,” Proceeding of Graphicon (August, 1999) 121–128.

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Figures (3)

Fig. 1
Fig. 1

Geometrical and radiometric variables involved in the calculation of the collected luminous flux from a single flake.

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Fig. 2
Fig. 2

Sparkle/graininess patterns as a result of applying Eq. (10) to a surface with flakes oriented at different directions. αS increases from top-left to bottom-right, whereas the other variables are kept constant.

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Fig. 3
Fig. 3

Density of sparkle spots calculated by the model for values of αS between 0° and 30°.

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Equations (11)

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

α sp = f α S
cos δ = r O ⋅ r sp
r S ′ + r sp ′ = ( 2 N F ⋅ r S ′ ) N F
ϑ S ′ = arcsin ( sin ϑ S n )
ϑ sp = arcsin ( n sin ϑ sp ′ )
A cs ( R , h ) = R 2 arccos | h | R − | h | R 2 − h 2
h 1 = D 2 + R 1 2 − R 2 2 2 D ;                               h 2 = D 2 − R 1 2 − R 2 2 2 D
I ( R 1 , R 2 , D ) = { 1 π R 2 2 [ A cs ( R 1 , h 1 ) + A cs ( R 2 , h 2 ) ] if   h 2 ≥ 0 1 π R 2 2 [ A cs ( R 1 , h 1 ) + π R 2 2 − A cs ( R 2 , h 2 ) ] otherwise
Φ ep , sp = { I ( f α S , α O , δ ) Φ sp if     f α S ≥ α O I ( α O , f α S , δ ) Φ sp otherwise
Φ ep = Φ ep , dif + Φ ep , sp = Φ i [ ρ dif + ρ sp I ( f α S , α O , δ ) ]
C = max ( Φ ep ) − Φ ep , dif Φ ep , dif = max ( Φ ep , sp ) Φ ep , dif = ρ sp ρ dif

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