# Angular and Spectral Bandwidth Considerations in BRDF Measurements of Interference- and Diffraction-Based Coatings

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials

_{2}-substrate, coated with a TiO

_{2}-layer.

## 3. Methodology

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Nicodemus, F.E.; Richmond, J.C.; Hsia, J.J.; Ginsberg, I.W.; Limperis, T. Geometrical Considerations and Nomenclature for Reflectance; US Department of Commerce, National Bureau of Standards: Washington, DC, USA, 1977; Volume 160.
- Klein, G.A. Industrial Color Physics; Springer: Berlin, Germany, 2010; Volume 154. [Google Scholar]
- Maile, F.J.; Pfaff, G.; Reynders, P. Effect pigments—Past, present and future. Prog. Org. Coat.
**2005**, 54, 150–163. [Google Scholar] [CrossRef] - Faulkner, E.B.; Schwartz, R.J. High Performance Pigments; John Wiley & Sons: Hoboken, NJ, USA, 2009. [Google Scholar]
- Streitberger, H.J.; Dossel, K.F. Automotive Paints and Coatings; Wiley-Vch: Weinheim, Germany, 2008. [Google Scholar]
- Rösler, M.; Mezger, N.; Dietz, R.; Huber, A. Isoline concepts to find measurement geometries for effect coatings full gonio-color-characterization. Farby i Lakiery
**2013**, 1, 24–31. [Google Scholar] - Cramer, W.R.; Gabel, P.W. Measuring special effects. Eur. Coat. J.
**2001**, 7–8, 34–39. [Google Scholar] - Kirchner, E.; Cramer, W. Making sense of measurement geometries for multi-angle spectrophotometers. Color Res. Appl.
**2012**, 37, 186–198. [Google Scholar] [CrossRef] - Ferrero, A.; Perales, E.; Rabal, A.M.; Campos, J.; Martínez-Verdú, F.M.; Chorro, E.; Pons, A. Color representation and interpretation of special effect coatings. J. Opt. Soc. Am. A
**2014**, 31, 436–447. [Google Scholar] [CrossRef] [Green Version] - Kirchner, E.; Ferrero, A. Isochromatic lines as extension of the Helmholtz reciprocity principle for effect paints. J. Opt. Soc. Am. A
**2014**, 31, 1861–1867. [Google Scholar] [CrossRef] [Green Version] - Ferrero, A.; Rabal, A.M.; Campos, J.; Pons, A.; Hernanz, M.L. Variables separation of the spectral BRDF for better understanding color variation in special effect pigment coatings. J. Opt. Soc. Am. A
**2012**, 29, 842–847. [Google Scholar] [CrossRef] [Green Version] - Ferrero, A.; Rabal, A.M.; Campos, J.; Martínez-Verdú, F.; Chorro, E.; Perales, E.; Pons, A.; Hernanz, M.L. Spectral BRDF-based determination of proper measurement geometries to characterize color shift of special effect coatings. J. Opt. Soc. Am. A
**2013**, 30, 206–214. [Google Scholar] [CrossRef] [Green Version] - Ferrero, A.; Bernad, B.; Campos, J.; Martínez-Verdú, F.M.; Perales, E.; van der Lans, I.; Kirchner, E. Towards a better understanding of the color shift of effect coatings by densely sampled spectral BRDF measurement. In Measuring, Modeling, and Reproducing Material Appearance; International Society for Optics and Photonics: Bellingham, WA, USA, 2014; Volume 9018, p. 90180K. [Google Scholar]
- Ferrero, A.; Campos, J.; Perales, E.; Martínez-Verdú, F.M.; van der Lans, I.; Kirchner, E. Global color estimation of special-effect coatings from measurements by commercially available portable multiangle spectrophotometers. J. Opt. Soc. Am. A
**2015**, 32, 1–11. [Google Scholar] [CrossRef] [Green Version] - Ferrero, A.; Bernad, B.; Campos, J.; Perales, E.; Velázquez, J.L.; Martínez-Verdú, F.M. Color characterization of coatings with diffraction pigments. JOSA A
**2016**, 33, 1978–1988. [Google Scholar] [CrossRef] [Green Version] - Rogelj, N.; Poberaj, I.; Gunde, M.K. Goniospectrophotometric space curves of diffraction gratings and their applicability as appearance fingerprints. Appl. Opt.
**2013**, 52, 8355–8362. [Google Scholar] [CrossRef] - Cramer, W.R.; Maile, F.J. Rainbows made to order. Eur. Coat. J.
**2016**, 16, 52–56. [Google Scholar] - Kettler, W.H.; Sôrmaz, M.; Ehbets, P. Apparatus and Method for Effect Pigment Identification. WO 2018041727A1. 2017. Available online: https://data.epo.org/gpi/EP3500830A1-APPARATUS-AND-METHOD-FOR-EFFECT-PIGMENT-IDENTIFICATION (accessed on 13 October 2020).
- Sperling, U.; Schwarz, P. Device for a Goniometric Examination of the Optical Properties of Surfaces. U.S. Patent 7,276,719, 10 February 2007. [Google Scholar]
- Hünerhoff, D.; Grusemann, U.; Höpe, A. New robot-based gonioreflectometer for measuring spectral diffuse reflection. Metrologia
**2006**, 43, S11–S16. [Google Scholar] [CrossRef] [Green Version] - Leloup, F.B.; Forment, S.; Dutré, P.; Pointer, M.R.; Hanselaer, P. Design of an instrument for measuring the spectral bidirectional scatter distribution function. Appl. Opt.
**2008**, 47, 5454–5467. [Google Scholar] [CrossRef] - Rabal, A.M.; Ferrero, A.; Campos, J.; Fontecha, J.L.; Pons, A.; Rubiño, A.M.; Corróns, A. Automatic gonio-spectrophotometer for the absolute measurement of the spectral BRDF at in-and out-of-plane and retroreflection geometries. Metrologia
**2012**, 49, 213–223. [Google Scholar] [CrossRef] - Obein, G.; Bousquet, R.; Nadal, M.E. New NIST reference goniospectrometer. Proc. SPIE
**2005**, 5880, 241–250. [Google Scholar] - Germer, T.A.; Asmail, C.C. Goniometric optical scatter instrument for out-of-plane ellipsometry measurements. Rev. Sci. Instrum.
**1999**, 70, 3688–3695. [Google Scholar] [CrossRef] - Baribeau, R.; Neil, W.S.; Côté, E. Development of a robot-based gonioreflectometer for spectral BRDF measurement. J. Mod. Opt.
**2009**, 56, 1497–1503. [Google Scholar] [CrossRef] - Nevas, S.; Manoocheri, F.; Ikonen, E. Gonioreflectometer for measuring spectral diffuse reflectance. Appl. Opt.
**2004**, 43, 6391–6399. [Google Scholar] [CrossRef] [Green Version] - Ouarets, S.; Ged, G.; Razet, A.; Obein, G. A new gonioreflectometer for the measurement of the bidirectional reflectance distribution function (brdf) at LNE-CNAM. In Proceedings of the CIE 2012 Lighting Quality and energy efficiency, Hangzhou, China, 19–21 September 2012; Volume 5880, pp. 687–691. [Google Scholar]
- Matsapey, N.; Faucheu, J.; Flury, M.; Delafosse, D. Design of a gonio-spectrophotometer for optical characterization of gonio–apparent materials. Meas. Sci. Technol.
**2013**, 24, 065901. [Google Scholar] [CrossRef] - Patrick, H.J.; Zarobila, C.J.; Germer, T.A. The NIST Robotic Optical Scatter Instrument (ROSI) and its application to BRDF measurements of diffuse reflectance standards for remote sensing. In Proceedings of the 2013, SPIE Optical Engineering+Applications; International Society for Optics and Photonics: Bellingham, WA, USA, 2013; Volume 8866, p. 886615-12. [Google Scholar]
- Schanda, J. Colorimetry: Understanding the CIE System; John Wiley & Sons: Hoboken, NJ, USA, 2007. [Google Scholar]
- Filip, J.; Vávra, R.; Maile, F.J. Optical analysis of coatings including diffractive pigments using a high-resolution gonioreflectometer. J. Coat. Technol. Res.
**2019**, 16, 555–572. [Google Scholar] [CrossRef] - Campos, J.; Corróns, A.; Pons, A.; Corredera, P.; Fontecha, J.L.; Jiménez, J.R. Spectral responsivity uncertainty of silicon photodiodes due to calibration spectral bandwidth. Measure. Sci. Technol.
**2001**, 12, 1926. [Google Scholar] [CrossRef] [Green Version] - SO/CIE Standard. ISO/CIE 11664-6:2014(E). Colorimetry—Part 6: CIEDE2000 Colour-Difference Formula; International Commission on Illumination (CIE): Vienna, Austria, 2014. [Google Scholar]
- CIE. CIE 15.3:2004: Colorimetry; CIE Central Bureau: Vienna, Austria, 2004. [Google Scholar]

**Figure 1.**Color shift of a highly goniochromatic interference-based special effect coating (reprinted with permission from [9] © The Optical Society).

**Figure 2.**Color shift of a highly goniochromatic diffraction-based special effect coating (reprinted with permission from [15] © The Optical Society). Solid lines represent Bidirectional Reflectance Distribution Function (BRDF) measurements on the incidence plane, whereas dots represent out-of-plane measurements.

**Figure 3.**Interpolated spectral BRDF data for a highly goniochromatic (

**a**) interference- and (

**b**) diffraction-based special effect coating. The spectral BRDFs correspond to geometries with a fixed ${\theta}_{\mathrm{asp}}={10}^{\circ}$ and values of ${\theta}_{\mathrm{i}}$ from ${10}^{\circ}$ to ${70}^{\circ}$ (angular step of (1/3)°) in (

**a**), and to geometries with a fixed ${\theta}_{\mathrm{i}}={10}^{\circ}$ and values of ${\theta}_{\mathrm{asp}}$ from $-{60}^{\circ}$ to ${10}^{\circ}$ (angular step of (1/3)°) in (

**b**); (

**a**) Interference-based special effect coating (Colorstream® T20-04 WNT Lapis Sunlight); (

**b**) Diffraction-based special effect coating (SpectraFlair® Silver 1500-14).

**Figure 4.**Distribution of Spectral-BRDF-error for the smallest and largest values of spectral and angular bandwidths used in this work. (

**a**) Interference-based special effect coating; (

**b**) Diffraction-based special effect coating.

**Figure 5.**Spectral-BRDF-error descriptors, ${P}_{95}\left({\u03f5}_{\mathrm{r}}\right)$, obtained in this study for (

**a**) Interference-based special effect coatings (Colorstream® T20-04 WNT Lapis Sunlight (solid line) and Colorstream® T20-02 WNT Arctic Fire (dash line)) (

**b**) Diffraction-based special effect coatings (SpectraFlair® Silver 1500-35 (solid line) and SpectraFlair® Plus 25 (dash line)). Two highly goniochromatic coatings of each type are represented, identified by solid and dashed lines.

**Figure 6.**Colour-difference descriptors, ${P}_{95}(\Delta {E}_{00})$, obtained in this study for (

**a**) interference- and (

**b**) diffraction-based special effect coatings. Two highly goniochromatic coatings of each type are represented, identified by solid and dashed line (

**a**) Interference-based special effect coatings (Colorstream® T20-04 WNT Lapis Sunlight (solid line) and Colorstream® T20-02 WNT Arctic Fire (dash line)); (

**b**) Diffraction-based special effect coatings (SpectraFlair® Silver 1500-35 (solid line) and SpectraFlair® Plus 25 (dash line)).

**Table 1.**Recommendations on spectral and angular bandwidths for measuring the spectral BRDF of goniochromatic coatings based on interference and diffraction pigments.

Recommended Angular/Spectral Bandwidths | Target Relative Uncertainty (k = 2) |
---|---|

Goniochromatism Based on Interference Pigments | |

≤4°/3 nm | <0.5% |

≤5°/7 nm | <1% |

≤6°/11 nm | <2% |

≤6${}^{\circ}$/17 nm | <3% |

Goniochromatism based on diffraction pigments | |

≤2${}^{\circ}$/3 nm | <1% |

≤3°/5 nm | <2% |

≤3°/11 nm | <3% |

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**MDPI and ACS Style**

Ferrero, A.; Campos, J.
Angular and Spectral Bandwidth Considerations in BRDF Measurements of Interference- and Diffraction-Based Coatings. *Coatings* **2020**, *10*, 1128.
https://doi.org/10.3390/coatings10111128

**AMA Style**

Ferrero A, Campos J.
Angular and Spectral Bandwidth Considerations in BRDF Measurements of Interference- and Diffraction-Based Coatings. *Coatings*. 2020; 10(11):1128.
https://doi.org/10.3390/coatings10111128

**Chicago/Turabian Style**

Ferrero, Alejandro, and Joaquín Campos.
2020. "Angular and Spectral Bandwidth Considerations in BRDF Measurements of Interference- and Diffraction-Based Coatings" *Coatings* 10, no. 11: 1128.
https://doi.org/10.3390/coatings10111128