BRDF AND GLOSS MEASUREMENTS

Leloup, BRDF and gloss measurements

BRDF AND GLOSS MEASUREMENTS Leloup, Frédéric; Hanselaer, Peter; Versluys, Jorg; Forment, Stefaan KaHo St.-Lieven

ABSTRACT Gloss is an important aspect of our visual perception of objects. Many developments of gloss measurement have been carried out as part of the technical work of the ASTM, resulting in the ASTM method D523. Different application domains, manufacturers and gloss meters related to different standards can be found, and instruments from different manufacturers show wide variation in aperture size and beam geometry. The spectral Bidirectional Reflection Distribution Function (BRDF) is a fundamental quantity of the sample, and any other quantity can be calculated from the BRDF. In this paper, the relationship between BRDF characteristics and the standard gloss measurements on different NCS gloss scale samples is studied. Due to the limited dynamic range of the industrial instruments, it is rather difficult to characterize matt samples accurately. On the contrary, BRDF measurements provide much more information. Integration of the BRDF over the cone angle of the receptor correlates with standard gloss measurement results, but only at certain geometries. A full description and understanding of the complete optical design of a gloss meter seems to be necessary to improve this correlation. Keywords: Gloss, Bidirectional Reflection Distribution Function (BRDF) 1. INTRODUCTION Appearance can be described in terms of the ability of an observer to recognize an object, and this recognition is possible because of the interaction between light and the material of the object. It has been suggested that the characterization of the optical properties of materials can be divided into at least four groups: colour, gloss, translucency, and surface texture1.

lustrous, metallic appearance and is generally associated with the specular reflection of light from the surface of the object2. On the other hand, gloss may also be defined as the mode of appearance by which reflected highlights of objects are perceived as superimposed on the surface due to the directionally selective properties of that surface3. Hunter2 first defined specular gloss as the ratio of the light reflected from a surface at a specified angle to that incident on the surface at the same angle on the other side of the surface normal. However, after studying the characteristics of many materials he concluded that there were in fact six visual criteria for ranking or measuring gloss. Many developments of gloss measurement have been carried out as part of the technical work of the American Society for Testing and Materials (ASTM). The results were incorporated into a widely accepted standard ASTM Method4,5. It has become clear that visually scaled gloss data are not correlated with measured gloss data over the entire range6. In a survey of written measurement standards carried out by the National Physical Laboratory the word ‘gloss’ was identified in about 150 titles of standards, illustrating the complexity of the problem7. On the other hand, any gloss measurement can be related to the general Bidirectional Reflectance Distribution Function (BRDF) of the sample. Several empirical models were developed to fit the experimental BRDF data, some of them based on the assumption of a distribution of micro-facets at the surface8. In this paper, values obtained with an industrial gloss meter are compared to parameters deduced from experimental BRDF. Two black PU samples with a different texture and six grey NCS gloss scale samples are measured.

Gloss may be defined as the attribute of a surface that causes it to have a shiny or

1


2. INDUSTRIAL GLOSS MEASUREMENT Standard gloss measurements were executed on a tri-gloss Byk-Gardner meter (Serial number 638154, category number 82538) which complies with the ASTM Standard Method D523. This method designates three angles (20°, 60° and 85°) for measurement, depending on the gloss of the surface. Theoretically, measurements are made relative to a highly polished black glass standard with a refractive index of 1.567 at 589.3 nm. The gloss of the standard is assigned a value of 100 specular gloss units (SGU) for each geometry. Two main optical designs are possible: a parallel-ray configuration with a nearly parallel incident and reflected light beam and a converging-ray configuration which is easier to design and which is widely used. The geometry of a generic instrument is shown in Fig. 19. The angular requirements and tolerances are gathered in Table 1.

Figure 1. A generic specular reflection instrument Table 1. Angles of source and receptor compliant with ASTM D523 In plane measurement

of Perpendicular to plane of measurement

θ (°)

θ (°)

Source image

0.75 ±0.25

2.5 ±0.5

20° receptor

1.8 ±0.05

3.6 ±0.1

60° receptor

4.4 ±0.1

11.7 ±0.2

85° receptor

4.0 ±0.3

6.0 ±0.3

3. BRDF MEASUREMENT The spectral BSDF qe,λ can be defined as the differential spectral radiance dLe,λ of a

sample observed in a specific observation angle, characterized by spherical

coordinates (θs ,ϕ s ) , due to the scattering of incident radiation characterized by the differential spectral irradiance dEe,λ , received from a specific angle of incidence (θi ,ϕi ) : qe,λ =

dL e,λ dE e,λ

(1)

According to ASTM E139210 the practical formula used to determine the absolute BSDF under condition that the field of view of the receiver field stop is sufficiently large enough to include the entire illuminated area for all angles of interest, can be written as qe,λ =

Φe,λ,s Φe,λ,i .Ωs . cosθs

(2)

where Φe,λ,i and Φe,λ,s are the spectral distribution of radiant flux received by the sample and the detector respectively, and where Ωs is the solid angle subtended by the receiver aperture stop from the sample origin. Because the incident and scattered flux is measured with the same detector head, the flux ratio is equal to the ratio of the detector responses at each wavelength. In order to measure the spectral BSDF, a goniospectroradiometer was used. A 300W Xe light source is used for the illumination of the specimen. Having large emission intensities in the blue-violet region of the visual spectrum, good signal to noise ratios can be obtained over the whole visual spectrum. The detector head consists of a lens and a very small integrating sphere which is coupled to a spectrometer/CCD detection system with a quartz fiber. The diameter of the lens is 20 mm. The distance from the specimen to the detector head is 750 mm. The use of an automated filterwheel carrying three neutral density filters extends the dynamic range to 6 decades. While measuring the dark current, the incident light beam is directed to a Si photodiode. The response of this photodiode allows us to compensate for the fluctuations in the light source output. As we measure the incident power on the sample with the same detector head, absolute BSDF-values qe,λ can be calculated from both dark current corrected CCD readings (counts) according to Eq. (2). More details of the instrument are described in Ref. [11].

2


4. BLACK PU SAMPLES

We investigated two black PU samples produced by an important Belgian manufacturer of PU skins for dashboards. Both samples, having a different texture but the same pigmentation, were measured with the industrial gloss meter. The results for all three geometries can be found in Table 2. The values are very low and, although a difference in appearance is observed, gloss values of both samples are the same within the accuracy limits. Table 2. Specular gloss (SGU) of two PU samples for different measurement geometries. SAMPLE 1 (SGU)

SAMPLE 2 (SGU)

20°

0.1

0.1

60°

1.7

1.7

85°

2.6

2.5

In Fig. 2, BRDF-values at 589 nm for both samples are shown as a function of the observation angle. The incidence angle was taken at -8°, in accordance with the d:8 geometry for colour determination. Due to the wide dynamic range of our BRDF instrument, a clear distinction between the samples can be made. The lightness will be higher for sample 1 than for sample 2, in accordance with the perception. 0,030

qe at 589 nm (1/sr)

0,028 0,026

sample 1 sample 2

0,024 0,022 0,020 0,018 0,016 0,014 0,012

-5 0 5 10 15 20 25 30 35 40 45 50 55 60

Observation angle(°)

Figure 2. BRDF of two PU samples at 589 nm

The difference in appearance between both samples is confirmed by the analysis of the surface texture using laserscan. The roughness of sample 2 is indeed higher than for sample 1, resulting in a more efficient light trapping and absorption.

These measurements illustrate the rather low dynamic range of a gloss meter (only two decades). It is clear that when characterizing high gloss samples (e.g. the reference glass) as well as ultra matt samples, a higher dynamic range will be required. 5. NCS GLOSS SAMPLES 5.1 Experimental results

BRDF measurements were performed on six grey samples from the NCS gloss scale, ranging from ultra-matt to high-gloss. The samples are called NCS03, NCS07, NCS20, NCS40, NCS70 and NCS90, where the number refers to the nominal gloss value of the sample at 60° measurement geometry. The same samples were also measured with a Tri-gloss Byk-Gardner gloss meter and the results are expressed in standard gloss units (SGU). In order to be able to calculate gloss units from the BRDF, the BRDF of the black glass reference sample incorporated into the gloss meter was measured too. Measurements were only performed at an angle of incidence of 20° and 60°; at 85°, the influx region of our BRDF set-up was too large compared to the limited dimensions of the gloss reference. Due to the minor influence of the wavelength on the reflectance, any spectral dependencies will be neglected from now on. In Fig. 3 the reflectance of the purely specular reflecting reference glass is shown. Because the detector is underfilled, reflectance values are measured instead of BRDF values. The angular spread is the manifestation of the instrument signature. The peak values at 20° and 60° are equal to 4.3% and 9.4% respectively. Theoretical reflectance values of the gloss standard with an index of refraction of 1.567 at 589.3 nm and unpolarized incident light can be calculated according to Fresnel formulas, resulting in values of 4.9% and 10% respectively. These are significantly higher than our experimental results. However, the reference sample is not an absolute standard. This becomes obvious when we measure the gloss of the reference glass itself: values of 92 and 95 SGU at 20° and 60° geometry respectively are displayed. Using these values as a correction factor, the theoretical reflectance of the reference sample should be 4.5% and 9.5%

3


respectively, in close agreement with our results.

8 7 6 5

20°

4

NCS03 NCS07 NCS20 NCS40 NCS70 NCS90

0,8

60°

9

qe (normalised)

Reflectance at 589 nm (%)

10

1,0

0,6

0,4

0,2

3 2

0,0 14

1

18

20

22

24

56

58

60

62

64

66

Observation angle (°)

0 18

20

22

24

56

58

60

62


Figure 5. Normalised BRDF of six grey NCS samples

Figure 3. Reflectance of the reference glass at 589 nm for two angles of incidence.

BRDF measurements on six NCS samples are shown in Fig. 4. The peak value of the BRDF is clearly correlated to the gloss value of the sample. The peak values are higher at 60° incidence, which is in accordance with the Fresnel equations for external reflection. In Fig. 5, normalized BRDF values are presented. The FWHM of the near-specular BRDF is also correlated to the gloss value, but – as expected- rather insensitive to the angle of incidence. For high gloss samples, the FWHM is limited by the value of the instrument function. For very low gloss samples, the FWHM becomes irrelevant.

In a gloss meter, the detector signal will be proportional to the reflected light intensity, integrated over the finite aperture of the optical system of the receiver. In order to reproduce gloss values from the BRDF, an integration of the BRDF over the cone angles of the receptor compliant with Table 1 (and ASTM D523) could be considered. The results are summarized in Table 3. However, due to the lack of detailed measurements in the plane perpendicular to the plane of incidence, the integration was performed using a solid angle based on the in-plane receiver aperture angle. Table 3. Calculated gloss values from peak height ratio and from integrated BRDF ratio of six NCS samples compared to the measured specular gloss units.

110 100

qe at 589 nm (1/sr)

16

NCS03 NCS07 NCS20 NCS40 NCS70 NCS90

90 80 70 60 50 40 30 20 10 0 14

16

18

20

22

24

54

56

58

60

62

64

Observation angle (°) Figure 4. BRDF of six grey NCS samples .

66

Peak Height Ratio

Integrated BRDF Ratio

Gloss value (SGU)

20°

60°

20°

60°

20°

60°

NCS 03

-

-

-

-

0.6

2.7

NCS 07

0.62

0.55

0.77

1.17

1.0

6.9

NCS 20

2.21

2.94

2.74

5.92

3.2

22.0

NCS 40

6.94

10.0

8.43

18.1

9.2

41.4

NCS 70

26.9

35.0

30.9

49.6

32.9

71.9

NCS 90

55.5

52.5

60.8

70.5

66.7

91.2

4


illustrating the difficulty of the problem. Even in a recent publication6, only partial correlation between gloss meter measurements and the difference between luminance factors for specular-included and specular excluded spectrophotometer measurements was reported. Probably, the optical lay-out of the specific gloss meter (beam divergence, dimensions of the light patch on the sample, over- or underfilling of the detector) should be examined more in detail. As was already mentioned by Early9, a description of the optical design of a gloss meter in terms of only a cone half-angle of source and receiver is incomplete.

5.2 Discussion

The measured gloss values (in SGU) at 60° angle of incidence correspond well with the nominal values. At 20°, they are systematically much lower. At 20° we expect the external Fresnel reflectance on the sample to decrease, but the same is true for the reference glass. When Fresnel reflection is dominant, the value of the refractive index of the sample compared to the value of the reference glass (1.567) determines the variation of the gloss with incident angle. Only when the refractive index of the sample is smaller than 1.567, the gloss will increase with incident angle. However, additional to the Fresnel reflection, directional scattering from the samples will contribute to the light captured by the receiver. The angular variation of this contribution has to be considered too.

For very matt samples and small incident angles, the contribution of the diffuse reflection to the flux received by the detector can be substantial. This becomes clear when comparing SGU of ultra-matt black, grey and white samples, all having a nominal SGU value of three. Although the absence of any gloss at all, the “gloss value” is the highest for the white and the lowest for the black. This is confirmed by the BRDF of the same samples: the values are independent of the viewing angle and are ranged conform to the reflection factor (Fig. 6). Corrections for this diffuse contribution were proposed by other authors6,12.

Simulated gloss values obtained by dividing peak values of the sample by peak values measured on the reference glass are systematically lower than the SGU for both angles of incidence. The correspondence at 20° is better than at 60°. Probably, this can be related to the dimensions of the receiver aperture of the gloss meter, which are different for both geometries. BRDF peak values however are measured with the same aperture.

At 20° incident angle, the agreement between gloss values based on integrated BRDF values and results obtained with the industrial gloss meter is satisfactory, but the values are slightly too low. The partial integration (only the in-plane aperture angle) could be responsible for this difference. Although we expect the BRDF to be rather isotropic around the specular reflection, the receiver aperture of the gloss instrument is different in both planes (see Table 1). At 60°, the values are much too low. These discrepancies between gloss measurements and other characterization methods, either in an absolute or even in a relative way, were reported before13,

0,25

qe at 589 nm (1/sr)

The use of the FWHM of the nearspecular BRDF in combination with the peak value has been suggested to correlate with gloss appreciation12. In trying to simulate the situation which occurs in the gloss meter, integration of the BRDF over the receiver aperture was preferred.

0,30

Black Grey White

0,20

0,15

0,10

0,05

0,00 14

16

18

20

22

24

26


Figure 6. BRDF of a black, grey and white NCS03 sample 6. CONCLUSIONS

Gloss is an important aspect of the visual perception of objects. Several optical and analytical techniques are available, yielding a variety of answers. In this paper, results obtained with an industrial gloss meter are compared to

5


values obtained from the BRDF of both the sample and the gloss reference. The limited dynamic range of the gloss meter compromises an accurate characterization and for very matt samples, the diffusely reflected light dominates the read-out. The calculation of gloss values (expressed in SGU) from the BRDF or BRDF related parameters seems to be very difficult. Integration of the BRDF over the cone angles of the receptor compliant with ASTM D523 gives a rather good correlation at 20° but not at 60° incident angle. The lack of detailed information on the optical design of the industrial gloss meter (illuminated area, apertures, . . .) could be the reason. Before trying to correlate gloss meter values with visual assessments, a full knowledge and a complete standardization of the design of the meter should be required. Probably, it could be more relevant to look for correlations between visual gloss and parameters which can be deduced directly from the spectral BRDF.

[8] OBEIN, G., LEROUX, T., VIENOT, F., Bi-directional reflectance distribution factor and gloss scales, Proc. SPIE 4299, 279290, 2000 [9] EARLY, E.A., A systematic approach for describing the geometry of spectrophotometry, SPIE 4826, 87- 97, 2003. [10] ASTM E 1392- 1996, Standard Practice for Angle Resolved Optical Scatter Measurements on Specular or Diffuse Surfaces. [11] LELOUP, F., DE WAELE, T., VERSLUYS, J., HANSELAER, P., POINTER, M. R., Full 3D BSDF Spectroradiometer, Proc. of the ISCC/CIE Expert Symposium: 75 Years of the CIE Standard Colorimetric Observer, 2006. [12] TIGHE, B.J., Subjective and objective assessment of surfaces, Polymer surfaces, 1978. [13] CIE TC1-65 Technical Report, Draft D2, November 2005. A Framework for the Measurement of Visual Appearance.

REFERENCES

[1] HUTCHINGS, J. B., Food Color and Appearance, ed.: 2nd ed. Aspen, 1999. [2] HUNTER, R. S. and HAROLD, R. W., The Measurement of Appearance, ed.: John Wiley & Sons, New York, WileyInterscience, 1987. [3] CIE Publication 17.4 International Lighting Vocabular.

-

1987,

[4] ASTM D523 - 1999, Standard test method for specular gloss. [5] BS EN ISO 2813 - 2000, Paints and varnishes – Determination of specular gloss of non-metallic paint films at 20°, 60° and 85°. [6] WEI, J., POINTER, M. R., LUO, R. M., DAKIN, J., Gloss as an aspect of the measurement of appearance, J. Opt. Soc. Am. 23, 22-33, 2006.

ACKNOWLEDGEMENTS

The authors wish to thank the IWT and the Flemish Community for the financial support. Authors: Leloup Frédéric, Hanselaer Peter, Versluys Jorg, Forment Stefaan KaHo Sint-Lieven, Laboratorium voor Lichttechnologie Gebroeders Desmetstraat 1 B-9000 Gent Tel: 0032 9 265.87.13 Fax: 0032 9 225.62.69 [email protected] [email protected] [email protected]

[7]. HANSON, A. R, TAYLOR, J. A. F., BASU, M. A., WILLIAMS, D. C., ZWINKELS, J. and CZEPLUCH, W., Report on Project QR9816B1 Gloss Measurements at NPL, NPL, 2000.

6