# Texture Evaluation of Automotive Coatings by Means of a Gonio-Hyperspectral Imaging System Based on Light-Emitting Diodes

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{G}) was determined as the geometric mean of sparkle-intensity (I

_{S}) and sparkle-area (A

_{S}) for each measurement geometry as follows [2]:

^{®}from BYK Additives & Instruments. BYK Additives & Instruments also developed the cloud-runner

^{®}, an optical scanner to quantify mottling.

## 2. Experimental Setup

^{®}, and conduct valid comparisons of the results; the ROI for the IR camera was kept at 23 mm × 23 mm for further comparison among spectral ranges. For mottling, a larger ROI was set at 92 mm × 68 mm to capture the effect as a whole.

## 3. Methods

#### 3.1. Samples

#### 3.2. Measurements Settings

^{®}for further comparisons. At this stage of the study, this gonio-spectrophotometer was chosen as a reference because it has become one of the standards in the automotive industry for spectral, colorimetric, sparkle and graininess quantification. Since the BYK-mac

^{®}works in the VIS, only the results obtained in this range were compared. The input data for all the assessments were reflectance images as in reference [35].

#### 3.3. Sparkle Quantificacion

_{S}, and the sparkle-intensity, I

_{S}. The sparkle-area was estimated by means of a binary image that only considered the sparkling regions above the intensity threshold with dimensions of 4 by 20 pixels and a connectivity of 4 chosen according to experimental evaluations. Afterwards, this image was used for the estimation of sparkle-intensity. The A

_{S}index was calculated as the mean area of these regions.

_{S}, it was derived from the Weber’s contrast [36], which describes the contrast between bright spots and their surroundings. However, the indices used in this study replaced the luminance by reflectance values, r, with the purpose of expanding these evaluations beyond the VIS range and for spectral assessments:

_{s}accounted for the mean reflectance value of the bright spots, while r

_{b}referred to the mean reflectance value of the background.

_{G}. In order to weight this parameter by the number of sparkling spots, a quantification factor, Q

_{S}, was added to Equation (1), as shown in Equation (3). It represents the ratio between the amount of bright pixels and the total amount of pixels of the image.

#### 3.4. Graininess Quantificacion

#### 3.5. Mottling Quantificacion

_{St}, was computed as the difference of the maximum and minimum values of the subtraction profile D

_{St}and multiplied by 50 to obtain values within the same scale as sparkle and graininess.

## 4. Results and Discussion

^{®}. For this purpose, statistical analysis was performed using IBM SPSS

^{®}v25.0 software (IBM Corp.). To determine the correlation between the measurements of the two instruments, bivariate correlations were carried out and quantified using Pearson’s (r) or Spearman (ρ) coefficients for parametric or nonparametric variables, respectively. Bland and Altman analysis [47] was also used to analyze agreement between measurements. This method studies the degree of agreement between two sets of data by plotting the mean difference and the corresponding 95% confidence limits (CL), defined as 1.96 times the standard deviation of the mean difference, within which 95% of the differences measurements are expected to lie. Secondly, the proposed textural indices were implemented into the different spectral channels in the VIS and IR range. Mottling was also firstly analyzed considering the results for the white LED cluster, and afterwards, spectrally.

#### 4.1. General Assessment of Sparkle

^{®}is summarized in Table 1. The correlation analysis provided good results for those geometries closer to the specular reflection (−15°x: 0° and 45°x: 0°) with correlation coefficients above 0.870 and very similar outcomes for the sparkle grade (>0.930); all correlations found were statistically significant (p < 0.001). The 75°x: 0° configuration produced the results that differed the most from those provided by the BYK-mac

^{®}. As aforementioned, the settings for textural effects measurement with the GOHYLED system were adjusted according to the standards for multi-angle color measurements, and this, together with the mechanical and optical features of the device, led to a large illumination distance (≈600 mm). This fact caused less reflected light to reach the camera at the geometry further away from the specular reflection, and hence, the sparkle grades at this geometry were more sensitive to show larger differences when compared to the BYK-mac

^{®}.

_{G}mean) for solid samples is almost zero in all plots, since they do not contain goniochromatic pigments.

#### 4.2. Spectral Assessment of Sparkle

#### 4.3. General Assessment of Graininess

^{®}. By doing so, the pearlescent, metallic and solid samples in Figure 7 reached graininess values of 4.56, 6.47 and 2.06, respectively. The whole set of samples exhibited graininess values from 0.11 to 6.74.

^{®}led to a Pearson’s correlation coefficient of 0.820 (p < 0.001). The evaluation through the Bland and Altman method (Figure 8) led to a mean difference of −0.05, very close to zero, and narrow 95% CLs (−0.38, 0.29) with very few outliers, indicating good agreement between devices; these outliers were produced by a weak signal reaching the camera when measuring very dark coatings. Although the illumination is more uniform over the sample for graininess evaluations, the total amount of light decreases when compared with sparkle assessments close to the specular reflection. As mentioned in the general assessment of sparkle, this could be improved by increasing the signal-to-noise ratio of the system.

#### 4.4. Spectral Assessment of Graininess

#### 4.5. General Assessment of Mottling

_{St}index proposed, extracted from the GOHYLED system. Images taken at the 15°x: 0° geometry of the two samples affected by this effect and three without are shown in Figure 10, all of them when being illuminated by the white LED cluster; white arrows point to the vertical stripes. As anticipated, the two samples with stripes reached the highest values of this index for all geometries, which are shown in Table 2. The strongest mottling-striping effect was found at 15°x: 0° because the acquisition took place closer to the specular reflection. The largest acquisition distance especially affected the geometries further away from the specular reflection (15°x: 30° and 15°x: 45°).

#### 4.6. Spectral Assessment of Mottling

_{St}spectra for the two samples with striping. The spectra of samples without striping resulted in substantially smaller values.

_{St}grades for the spectral assessment, particularly at 15°x: 0°. The greatest response to mottling at longer wavelengths was observed for both samples with stripes, partly because of the diminished sparkle at the end of the VIS range. The better performance in the IR could also be caused by the thickness variations of the base coat, where the goniochromatic particles are immersed. In this case, the distance among particles increases, to the extent that regions where the deepest layers of the coating are more visible with IR light appear free from these particles. Consequently, the evaluation of mottling-striping beyond 750 nm, particularly from 900 to 1000 nm, is of great interest in addition to the VIS range. Moreover, the measurement of mottling in the IR range would simplify the mathematics behind this index because the removal of sparkle prior calculations by smoothing of the curves would not be critical.

_{St}values of the remaining geometries were lower than the 15°x: 0° values but still slightly above the geometries of samples without stripes. Finally, a connection between the spectral/colorimetric features and mottling-striping was observed, similarly to the spectral evaluation of graininess. It was therefore inferred that once the influence of sparkle is removed, textural effects in goniochromatic pigments are strongly related to the spectrum of the sample.

## 5. Conclusions

_{St}was found to be very useful, as it revealed a dissimilar behavior between samples with and without striping and geometries, particularly at that of 15°x:0°. Spectral differences were mainly observed between 900 and 1000 nm, as a consequence of sparkle removal and higher penetration of IR light. In fact, this IR analysis could be easily implemented in current devices by simply adding IR illumination, since most of them use sensors with sensitivities up to 1000 nm. The relationship between mottling-striping and spectral reflectance would not be critical in this case, because this effect is mainly caused by thickness variations of the coating.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Illustrations of sparkle (

**a**), graininess (

**b**) and mottling (

**c**) effects of goniochromatic automotive coatings.

**Figure 2.**Developed gonio-hyperspectral imaging system based on LEDs represented in (

**a**) a layout and in (

**b**) a picture: 1. UV–VIS camera, 2. sample holder, 3. 8MR191-30 rotation stage, 4. 8MR191-30-28 rotation stage, 5. rotation stages controller, 6. linear actuator, 7. lens, 8. LED clusters, 9. light source controller and power supply and 10. IR camera, which is not represented in (

**a**). θ refers to the illumination angle controlled by the 8MR151-30 rotation stage and α to the observation angle handled by the 8MR191-30-28 rotation stage. Figure adapted with permission from [35]. © The Optical Society.

**Figure 3.**(

**a**) Image of a sample with striping, and (

**b**) a plot with the averaged and smoothed image profile (blue line), the linearly fitted curve (red line) and the subtraction profile D

_{St}(black line).

**Figure 4.**GOHYLED sparkle images of (

**a**) a pearlescent, (

**b**) a metallic and (

**c**) a solid sample for the −15°x:0° geometry when illuminated with the white LED cluster.

**Figure 5.**Bland and Altman plots for the sparkle grade (S

_{G}) at the three sparkle geometries: (

**a**) −15°x: 0°, (

**b**) 45°x: 0° and (

**c**) 75°x: 0°. Dashed lines indicate the 95% limits of agreement and dotted lines denote the mean difference value.

**Figure 6.**GOHYLED sparkle spectra of (

**a**) a pearlescent, (

**b**) a metallic and (

**c**) a solid sample for the −15°x: 0°, 45°x: 0° and 75°x: 0° geometries of sparkle, and GOHYLED sparkle spectra of (

**d**) a pearlescent, (

**e**) a metallic and (

**f**) a solid sample for the geometries of spectral/colorimetric measurements 45°x: −60°, 45°x: −30°, 45°x: −20°, 45°x: 30°, 45°x: 65°, 15°x: −30° and 15°x: 0°. The sparkle grade related to the white LED cluster (W) is represented by diamond markers (−15°x: 0° in blue; 45°x: 0° in green; 75°x: 0° in purple).

**Figure 7.**GOHYLED graininess images of (

**a**) a pearlescent, (

**b**) a metallic and (

**c**) a solid sample for the −15°x: 0° geometry when illuminated with the white LED cluster.

**Figure 9.**GOHYLED graininess spectra of a pearlescent (orange), a metallic (blue) and a solid (green) sample for the geometry of d: 12.5°. The graininess value corresponding to the white LED cluster is represented in each graph with a diamond marker.

**Figure 10.**Images of (

**a**) the grey and (

**b**) the blue samples with stripes, and (

**c**) the grey metallic, (

**d**) the grey pearlescent and (

**e**) the grey solid samples without striping for the white LED cluster at the geometry of 15°x: 0°. The arrows indicate the stripes in samples with mottling-striping.

**Figure 11.**Mottling-striping spectra M

_{St}of (

**a**) the grey and (

**b**) the blue sample with striping. The M

_{St}related to the white LED cluster (W) is represented by diamond markers.

**Table 1.**Pearson

^{†}or Spearman

^{‡}correlation coefficients, and corresponding p-values; and Bland and Altman analysis (mean of the differences, MD, and the corresponding confidence limits, CL) between the sparkle-area (A

_{S}), sparkle-intensity (I

_{S}) and sparkle grade (S

_{G}) of the GOHYLED and the BYK-mac

^{®}.

Sparkle Parameters | Pearson ^{†} or Spearman ^{‡}Correlation Coefficient | p-Value | MD | CL |
---|---|---|---|---|

A_{S} -15°x:0° | 0.931 ^{†} | <0.001 ^{1} | −0.07 | −0.39 to 0.26 |

A_{S} 45°x:0° | 0.884 ^{†} | <0.001 ^{1} | −0.13 | −0.51 to 0.26 |

A_{S} 75°x:0° | 0.725 ^{†} | <0.001 ^{1} | −0.21 | −0.68 to 0.27 |

I_{S} -15°x:0° | 0.910 ^{‡} | <0.001 ^{1} | −0.24 | −0.48 to 0.01 |

I_{S} 45°x:0° | 0.872 ^{†} | <0.001 ^{1} | −0.14 | −0.46 to 0.17 |

I_{S} 75°x:0° | 0.788 ^{†} | <0.001 ^{1} | −0.26 | −0.61 to 0.08 |

S_{G} -15°x:0° | 0.963 ^{†} | <0.001 ^{1} | 0.05 | −0.13 to 0.24 |

S_{G} 45°x:0° | 0.933 ^{‡} | <0.001 ^{1} | 0.11 | −0.17 to 0.39 |

S_{G} 75°x:0° | 0.739 ^{‡} | <0.001 ^{1} | 0.13 | −0.41 to 0.67 |

^{1}Statistically significant correlations.

**Table 2.**Mottling-striping indices M

_{St}for the gray and blue samples with stripes; and the pearlescent, metallic and solid samples without striping at the geometries of 15°x:0°, 15°x:30° and 15°x:45°, and under white LED illumination.

Geometry | Grey Striping | Grey Pearlescent | Grey Metallic | Grey Solid |

15°x: 0° | 6.70 | 3.73 | 3.52 | 0.12 |

15°x: 30° | 1.13 | 0.17 | 0.41 | 0.15 |

15°x: 45° | 0.32 | 0.11 | 0.16 | 0.17 |

Geometry | Blue Striping | Blue Pearlescent | Blue Metallic | Blue Solid |

15°x: 0° | 4.33 | 3.21 | 3.43 | 0.34 |

15°x: 30° | 0.93 | 0.36 | 0.25 | 0.16 |

15°x: 45° | 0.40 | 0.06 | 0.09 | 0.09 |

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**MDPI and ACS Style**

Burgos-Fernández, F.J.; Pujol, J.; Perales, E.; Martínez-Verdú, F.M.; Vilaseca, M.
Texture Evaluation of Automotive Coatings by Means of a Gonio-Hyperspectral Imaging System Based on Light-Emitting Diodes. *Coatings* **2020**, *10*, 320.
https://doi.org/10.3390/coatings10040320

**AMA Style**

Burgos-Fernández FJ, Pujol J, Perales E, Martínez-Verdú FM, Vilaseca M.
Texture Evaluation of Automotive Coatings by Means of a Gonio-Hyperspectral Imaging System Based on Light-Emitting Diodes. *Coatings*. 2020; 10(4):320.
https://doi.org/10.3390/coatings10040320

**Chicago/Turabian Style**

Burgos-Fernández, Francisco J., Jaume Pujol, Esther Perales, Francisco M. Martínez-Verdú, and Meritxell Vilaseca.
2020. "Texture Evaluation of Automotive Coatings by Means of a Gonio-Hyperspectral Imaging System Based on Light-Emitting Diodes" *Coatings* 10, no. 4: 320.
https://doi.org/10.3390/coatings10040320