# 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

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**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