Statistical parameters and analysis of local contrast gloss

Antti Oksman; Mikko Juuti; Kai-Erik Peiponen

doi:10.1364/OE.16.012415

1. Introduction

Gloss is one of the main elements of appearance beside texture, color, translucency and light distribution [1–3]. Hunter and Harold have made distinction between six types of gloss: specular gloss, contrast gloss, sheen, distinctness of image gloss, absence of bloom gloss, and surface uniformity gloss [1]. When the concept of gloss is discussed, it is generally associated with the specular gloss, which is the most used quality parameter among the six gloss types. For the measurement of the specular gloss several standards [4] have been defined, for example: ASTM D523 [5] and ISO 2813 [6]. There is not yet a standard for the measurement of the local specular gloss, but some measurement devices for this purpose have been presented previously, such as, a diffractive-optical-element (DOE)-based glossmeter (DOG) [4] has been developed. The DOE that is the main component of the DOG produces the measurement signal from the scattered light field. Other methods for the evaluation of the local specular gloss have been also presented [7–9]. The contrast gloss is also important, because it identifies two different surface that have the same specular gloss [10]. The contrast gloss is defined as a ratio of the diffusely reflected light to the specularly reflected light. The contrast gloss has been used, for example, in a research of dental fillers [11, 12], textile yarns [13], human hairs [14], and species of glass [15]. Recently, we introduced a sensor for the detection of local contrast gloss [16]. Two DOEs of this sensor produce signals for local specular gloss and local diffuse component in the normal direction, respectively. The value for the local contrast gloss can be calculated from these measured values of local specular gloss and local diffuse component in the normal direction.

In this paper, we introduce novel statistical parameters to the analysis of the contrast gloss. These statistical parameters for the diffuse component and contrast gloss are defined alike statistical parameters are defined for the surface roughness [17]. Statistical parameters for the specular gloss obtained by the DOG were already introduced in [18]. As an example, we applied these statistical parameters and measured specular gloss, diffuse-component, and contrast gloss maps in the assessment of five print samples. These prints included four printed line patterns sing four basic printing inks: black, magenta, yellow, and cyan, in each print. The fifth print represented an area from an image of a human cheek.

2. Methods

2.1. The main parameters

The contrast gloss is calculated using measured data for specularly and diffusely reflected light from an object, when the object is illuminated at an oblique angle of incidence. The detection direction for diffusely reflected light is usually the normal of the object, whereas the specular direction is the detection direction for specularly reflected light. The setup for local contrast gloss measurement is similar in our sensor, while the angle of the illumination is 45° (see Fig. 1).

We define contrast gloss G_c (or luster) like Hunter and Harold [1] as follows:

G_{c} = 100 (1 - \frac{D}{G}),

where D, diffuse component, is the parameter for diffusely reflected light and G, specular gloss, is the parameter for specularly reflected light. In the case of our sensor, the diffuse component in the normal direction D is defined as follows:

D = 100 \times \frac{I_{sample, diffuse}}{I_{reference}},

where I_{sample,diffuse} is the light intensity of image pattern recorded by a CCD camera detecting the diffusely reflected light and I_reference is intensity measured from the reference (black glass) at specular direction. The specular gloss G in turn is defined as follows:

G = 100 \times \frac{I_{sample, specular}}{I_{reference}},

where I_{sample,specular} is the light intensity of image pattern recorded by a CCD camera detecting the specularly reflected light and I_reference is intensity measured from the reference (black glass) at specular direction. The DOEs at both detection directions reconstruct regular arrays of 4×4 light-spot matrices on the chips of the CCD-cameras from the reflected light fields. Both the phases and the amplitudes of the reflected light fields affect these reconstructed image patterns that are illustrated in the bottom of Fig. 1. In Eqs. (2) and (3) the intensity is defined as follows:

I = \frac{1}{NM} \sum_{i = 1, j = 1}^{N, M} I_{i, j},

where I_i,j is the intensity detected by the (i,j)th element of the CCD camera array and N and M indicate the dimensions of the cell of the CCD camera. The calculation area in data analysis is illustrated by the grid at the left corner of Fig. 1.

In general, the measured values of the specular gloss, diffuse component, and contrast gloss depend on the used experimental setup. For example, the illumination angle, the detection direction of the diffuse component, and the wavelength of a light source can affect to the measured data. The used setup for the sensor for the detection of local contrast gloss is presented in Fig. 1 and explained in detail in the section 3.

A visibility parameter can be also defined for the signals produced by the DOEs of the sensor for the detection of local contrast gloss [16]. The visibility can be used, for example, in the estimation of the surface roughness of prints [19]. However, this parameter is not discussed in the following text.

2.2. Statistical parameters for the specular gloss, diffuse component and contrast gloss

We define statistical parameters for the specular gloss in the case of the sensor for the detection of local contrast gloss exactly the same way as they are defined for the specular gloss in [18]. Similarly, like in the case of the specular gloss, we define new statistical parameters for the diffuse component and contrast gloss. A parameter f represent either the specular gloss G, or the diffuse component D, or the contrast gloss G_c in the following equations. We define the mean value for the specular gloss, diffuse component, and contrast gloss as follows:

f_{mean} = 〈 f (x, y) 〉 = \frac{1}{A} \iint_{A} f (x, y) d x d y,

where f(x,y) is either the specular gloss G(x,y), or the diffuse component D(x,y), or the contrast gloss G_c(x,y) as a function of location in a cartesian coordinate system and A is the measured area. Average variation (f_a) and rms variation (f_q) for the specular gloss, diffuse component, and contrast gloss are defined as follows:

f_{a} = \frac{1}{A} \iint_{A} ∣ f (x, y) - 〈 f (x, y) 〉 ∣ d x d y

and

f_{q} = {\frac{1}{A} \iint_{A} {[f (x, y) - 〈 f (x, y) 〉]}^{2} d x d y}^{\frac{1}{2}} .

We define slope parameters for the specular gloss, diffuse component and contrast gloss at given direction in the cartesian coordinate system using partial derivatives as follows:

f_{a, x} = \frac{1}{A} \iint_{A} ∣ \frac{\partial f (x, y)}{\partial x} - \frac{\partial 〈 f (x, y) 〉}{\partial x} ∣ d x d y

and

f_{q, x} = {\frac{1}{A}, \iint_{A} {[\frac{∂f (x, y)}{\partial x} - \frac{\partial 〈 f (x, y) 〉}{\partial x}]}^{2} d x d y}^{\frac{1}{2}}

If a straight line is measured instead of an two-dimensional area A, Eqs. (5), (6), and (7) are simplified into one dimension.

3. Experimental and discussion

Maps from the prints describing the parameters G, D, and G_c were measured using the sensor presented in Fig. 1. The light source of the sensor is a HeNe laser that emits light at the wavelength 632.8 nm. The incidence angel of the laser beam is 45°, while the beam is focused onto the surface of the sample using lenses. The sample plane directions x and y are parallel and perpendicular to the plane of incidence, respectively. In addition, the sample plane direction x is tilted 45° compared with the incident light beam. A two-dimensional (x and y) translation table was used in the scanning of the sample during the measurement. The light reflected from the sample reaches the detection planes of the two DOEs that are located in fixed detection directions (specular and diffuse) at the far-field region. Two CCD cameras (CCD1 and CCD2 in Fig. 1) detect the signals reconstructed by the DOEs. The difference of the light sensitivities of the CCD cameras was considered in the data analysis. The specular and the diffuse reflections are detected at the angle of 45° and at the normal of the sample, respectively. The aperture size of the DOEs is 4 mm×4 mm, and the focal length of the DOEs is 100 mm. The DOEs were made using an electron beam writer [4]. A personal computer (PC) was utilize to control the measurement and to analyze the measured data.

The parameters G, D, and G_c were measured for five prints that were printed in a heatset-web-offset press on a light weight-coated paper. Four of the prints were line patterns printed using basic inks: black, magenta, yellow, and cyan. The fifth sample was a printed area representing an image of a human cheek.

Fig. 1. Schematic diagram of the sensor for the detection of local contrast gloss. C, collimating optics; L, lens; S, sample; WFR, speckle pattern incident on the DOE; and the image of the grating structure of the DOE is on the right-hand side of WFR. CCD1 and CCD2 are CCD cameras for recording specularly and diffusely propagating light, respectively. At the bottom are two images of 16 light spots recorded by the CCD cameras. The angle α is 45°. The schematic image of 16 light spots is presented in the left lower corner. A dashed square marks the area where the intensity [Eq. (4)] is calculated.

Download Full Size | PDF

All samples were measured in the first part of the measurement, while the calculated diameter (at the waist) of the Gaussian probe beam at the sample was about 14 μm in x direction and 10 μm in y direction. The distance between adjacent measurement points in the measured maps was 10 μm both in x and y direction. The size of the measured maps was 2 mm ×2 mm.

The specular gloss, diffuse-component and contrast gloss maps measured from the samples are presented in Fig. 2. The line pattern is horizontal for the black [Fig. 2(a)] and the yellow [Fig. 2(c)] prints, whereas the line pattern is vertical for the magenta [Fig. 2(b)] and the cyan [Fig. 2(d)] prints. The printed areas appear as high or low gloss areas in the specular gloss maps (the upper row of the Fig. 2), while the unprinted areas appear generally as semi-gloss areas. Thus, the line pattern of the prints and the raster pattern of the cheek print [Fig. 2(e)] can be observed from the specular gloss maps. The magenta and the yellow prints as well as the cheek print are more sensitive to reflect specularly red light than the black and the cyan print. Actually, the magenta ink causes the visible raster pattern in the specular gloss map of the cheek print.

In the case of the diffuse-component maps (the middle row of the Fig. 2), the line pattern can be clearly seen from the black and the cyan prints, whereas the line pattern is not observable for the magenta and the yellow prints. Red light reflects in diffuse direction as well from the printed area as from the unprinted area for the magenta and the yellow print. Instead, red light does not reflect in diffuse direction from the printed area of the black and the cyan print. Therefore, the printed area appears as a dark area in the diffuse-component maps of these prints, while the unprinted area appear as a bright area. This phenomenon was also detected for a black printed letter and a black printed raster pattern in [16]. If one uses a light source that emits light at different wavelength than the HeNe laser, it might be possible to detect the line patterns from the magenta and the yellow prints. The raster pattern can be observed for the diffuse-component map of the cheek print, but the visible pattern is different from the pattern in the specular gloss map of the cheek print. The cyan ink induces the visible raster pattern in the diffuse-component map despite of a presence of other inks, e.g. magenta.

The contrast gloss maps (the bottom row of the Fig. 2) are calculated based on Eq. (1), while the calculation is done separately for each measurement point using the values of the G and D maps. The line pattern of the ink prints and the raster pattern of the cheek print can also be observed from the contrast gloss maps, although there are clear differences between the magnitudes of the contrast gloss values of the samples. The contrast gloss appears to be highest for the black print, whereas the contrast gloss of the yellow print appears to be the smallest. In the case of the cyan print, the specular gloss and diffuse component from the printed areas are mostly smaller than the corresponding parameter values from the unprinted areas, whereas the magnitudes of the contrast gloss values obtained from the printed areas are higher than from unprinted areas. Thus, this contrast gloss map reveals that light is reflected stronger in the specular direction than in the diffuse direction from the printed area of the cyan print as from the unprinted area. The readings of the G_c [Eq. (1)] are dominated by the readings of the D in the case of the cheek print, because the angle of the raster patterns of the D and G_c maps are similar based on visual observations. The contrast gloss values are negative at some measurement points in the unprinted areas of the samples. Possibly, abnormal surface profile of these locations causes stronger light reflection in diffuse direction than in specular direction.

Fig. 2. Specular gloss maps G (upper row), diffuse-component maps D (middle row) and contrast gloss maps G_c (bottom row) measured from (a) black, (b) magenta, (c) yellow, (d) cyan, and (e) cheek prints. The scales of each parameter are in the sidebars. The maps covered the same region 2 mm × 2 mm on the surface of each sample.

Download Full Size | PDF

Calculated statistical parameters for the print samples are presented in the five left-hand columns of Table 1 [Eqs. (5)–(9) were used in calculation]. The calculated diameter of the beam in x and y direction at the surface of the prints and the size of the scanning step in x and y direction are also shown in the Table 1. The mean values of the parameters G, D, and G_c are consistent with the visual observations on the parameter maps presented in Fig. 2. It is worthwhile to notice that the values of the specular gloss for the yellow and the cheek prints are almost same, but the value of the contrast gloss distinguishes these samples, because the value of the diffuse component is different for the samples. Average and rms-variation of the specular gloss distinguishes also the yellow and cheek prints. Generally, increases of the average and rms-variation parameters of the specular gloss are in accordance with the increase of the mean specular gloss for the samples except for the yellow print. Instead, the values of the D_a parameters are almost constant for the samples and also the values of the D_q parameters are almost constant for the samples, although the values of the D_mean have different magnitudes for the samples, and although the visual appearances of the maps of D are also different according to the Fig. 2. Values of the G_c,a and G_c,q parameters are also quite similar for the samples, however the values of these parameters are lowest for the magenta print and highest for the black print. Thus, it is possible to detect differences between the prints using mean, average variation and rms-variation parameters for the specular gloss, diffuse component, and contrast gloss.

Table 1. Measurement parameters and statistical parameters from Eqs. (5)–(9) for the prints.

View Table

For the slope parameters of the G, D, and G_c, the values in x direction are smaller than the values in y direction in all cases, although there are differences in these parameters values between the samples. The directions of the line patterns do not affect clearly to the values of the slope parameters, although these patterns are horizontal for the black and yellow prints and vertical for the magenta and cyan prints. Instead, the size of the diameter of the probe beam affects clearly to the values of the parameters. The focus spots of the probe beam overlaps in adjacent measurement points in x direction, because the beam diameter is 14 μm and the scanning step is 10 μm. There does not exist overlapping in y direction, because the beam diameter and the scanning step have the same value (10 μm). Therefore, differences between the values of the adjacent measurement points are smaller in x direction than in y direction. Thus, this affects also the values of the slope parameters.

The black print was measured twice in the second part of the measurement, while the direction of the line pattern of the black print was horizontal in the first measured map and vertical in the second measured map. The sample was turned 90° clockwise between the measurements of these maps. The calculated diameter of the probe beam at the sample was about 42 μm in x direction and 30 μm in y direction. The intensity values obtained from the sample were recorded after every 40 μm in x and 30 μm in y direction. The size of the measured maps was 2.00 mm × 2.01 mm.

Calculated statistical parameters for the two measurements of the black print are presented in the two right-hand columns of Table 1. The values of mean, average variation, and rms-variation of the G, D, and G_c parameters are similar for both measurements of the black print as it can be assumed. Now, the slope parameters for the diffuse component and contrast gloss are smaller in the parallel direction with the printed lines than in the transversal direction of the printed lines for both measurements (horizontal and vertical). Thus, the direction of the line pattern affects clearly to the values of these parameters in the second part of the measurement not like the overlapping of the adjacent measurement points in x direction did in the first part of the measurement. The calculated overlapping area was only 1.6% of the size of the focus spot in the second part of the measurement, whereas it was 18% in the first part of the measurement. Therefore, this overlapping of the measurement points has to be considered in the assessment of the slope parameters. The parameters G_a,x and G_a,y have the same value for the vertical line pattern of the black print, because the line pattern is obviously not so observable in the case of the specular gloss than it is in the cases of the diffuse component and contrast gloss. This same phenomenon can be seen from Fig. 2(a) for the black print measured in the first part of the measurement.

It is possible to define other parameters such as skewness, kurtosis, autocorrelation and power spectral density function for the parameters G, D and G_c. The skewness is a measure of the symmetry of a parameter profile about the mean surface level, and the kurtosis is a measure of the sharpness of the height distribution function [17]. The autocorrelation can be used to determine similarities of a parameter map in a lateral direction. Instead, the power spectral density function indicates fluctuations of a parameter and their periodicity in the spatial frequency plane. The definitions of the autocorrelation and the power spectral density function for the specular gloss as well as images of the autocorrelation and the power spectral density function for specular gloss maps can be found from [18].

4. Conclusion

We have introduced statistical parameters for the evaluation of the local contrast gloss. The statistical parameters of the specular gloss and the novel statistical parameters for the diffuse component and contrast gloss are defined like they are defined for the characterization of the surface roughness. The mean, average variation, and rms-variation of the specular gloss, diffuse component, and contrast gloss as well as the measured specular gloss, diffuse-component, and contrast gloss maps are useful in quality assessment of prints. The defined slope parameters are also advantageous for the quality evaluation of prints, when the overlapping of the adjacent measurement points is considered in the measurement arrangements. The all defined statistical parameters and the sensor for the detection of local contrast gloss have also potential in the evaluation of any low or high gloss products.

References and links

1. R. S. Hunter and R. W. Harold, The Measurement of Appearance (Wiley, 1987).

2. M. Landy “Visual perception: A gloss on surface properties,” Nature (London) 447, 158–159 (2007). [CrossRef]

3. W. Ji, M. R. Pointer, R. M. Luo, and J. Dakin “Gloss as an aspect of the measurement of appearance,” J. Opt. Soc. Am. A 23, 22–33 (2006). [CrossRef]

4. R. Silvennoinen, K.-E. Peiponen, and K. Myller, Specular Gloss (Elsevier, 2008).

5. Standard Test Method for Specular Gloss D523–89(2008) (American Society for Testing and Materials, 2008).

6. Paints and varnishes - Determination of specular gloss of non-metallic paint films at 20, 60, and 85 degrees, ISO 2813:1994 (International Organization for Standardization, 1994). [PubMed]

7. N. Elton and J. Preston “Polarized light reflectometry for studies of paper coating structure II: Application to coating structure, gloss and porosity,” Tappi J. 5, 10–16 (2006).

8. M. Beland and J. M. Bennett “Effect of local microroughness on the gloss uniformity of printed paper surfaces,” Appl. Opt. 39, 2719–2726 (2000). [CrossRef]

9. M. MacGregor and P. Johansson “Submillimeter gloss variations in coated paper; Part I, The gloss imaging eguipment and analytical techniques,” Tappi J. 73, 161–168 (1990).

10. V. G. W. Harrison, Definition and Measurement of Gloss (Printing and Allied Trades Research Association, 1945).

11. W. J. O’Brien, W. M. Johnston, F. Fanian, and S. Lambert “The surface roughness and gloss of composites,” J. Dent. Res. 63, 685–688 (1984). [CrossRef] [PubMed]

12. P. M. Campbell, W. M. Johnston, and W. J. O’Brien “Light scattering and gloss of an experimental quartz-filled composite,” J. Dent. Res. 65, 892–894 (1986). [CrossRef] [PubMed]

13. A. Sugane and T. Gunji “Evaluation of the reflection properties of embroidery yarn by graphic image analysis,” Journal of the Textile Machinery Society of Japan 42, 16–22 (1996).

14. H. K. Bustard and R. W. Smith “Investigation into the scattering of light by human hair,” Appl. Opt. 30, 3485–3491 (1991). [CrossRef] [PubMed]

15. V. E. Gorbatenko, V. A. Guzii, A. A. Perminov, A. G. Tkachev, A. Ya. Kozyarskii, and V. S. Lukashov “Checking gloss factors on glassy surfaces,” Glass Ceram. 46, 153–155 (1989). [CrossRef]

16. A. Oksman, M. Juuti, and K.-E. Peiponen “Sensor for the detection of local contrast gloss of products,” Opt. Lett. 33, 654–656 (2008). [CrossRef] [PubMed]

17. J. M. Bennett and L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, 1989).

18. K.-E. Peiponen and M. Juuti, “Statistical parameters for gloss evaluation,” Appl. Phys. Lett. 88, 0711041–0711043 (2006). [CrossRef]

19. A. Oksman, M. Juuti, and K.-E. Peiponen “Visibility map for print quality assessment by means of a diffractive optical element based glossmeter,” Meas. Sci. Technol. 18, 2185–2188 (2007). [CrossRef]

	Black	Magenta	Yellow	Cyan	Cheek	Black horizontal	Black vertical
Beam diameter, x[μm]	14	14	14	14	14	42	42
Beam diameter, y[μm]	10	10	10	10	10	30	30
Scanning step, x[μm]	10	10	10	10	10	40	40
Scanning step, y[μm]	10	10	10	10	10	30	30
G_mean	8.30	12.51	10.16	6.56	10.14	2.85	2.87
G_a	1.95	2.47	1.75	1.29	2.04	0.50	0.54
G_q	2.87	3.45	2.43	1.78	2.83	0.79	0.82
G_a,x	1.47	1.90	1.44	1.01	1.62	0.56	0.62
G_q,x	2.20	2.68	1.97	1.46	2.27	0.89	1.00
G_a,y	1.78	2.30	1.81	1.25	1.99	0.60	0.62
G_q,y	2.64	3.24	2.46	1.78	2.75	0.96	0.99
D_mean	4.42	7.06	7.13	4.36	5.88	2.02	1.91
D_a	1.01	1.03	1.03	0.96	1.17	0.20	0.19
D_q	1.25	1.30	1.31	1.20	1.48	0.28	0.26
D_a,x	0.47	0.98	1.00	0.56	0.89	0.19	0.26
D_q,x	0.71	1.26	1.29	0.82	1.17	0.26	0.33
D_a,y	0.64	1.25	1.27	0.61	1.12	0.25	0.18
D_q,y	0.97	1.60	1.62	0.92	1.47	0.34	0.25
G_c,mean	42.04	40.01	26.50	30.62	38.68	25.42	29.57
G_c,a	16.82	13.97	15.82	15.19	15.75	13.71	13.47
G_c,q	21.65	17.80	20.19	20.43	20.18	17.79	17.31
G_c,a,x	11.06	11.96	14.34	12.76	12.92	14.43	16.77
G_c,q,x	14.69	15.52	18.54	17.00	16.98	18.28	21.18
G_c,a,y	13.95	14.72	18.00	15.44	16.03	16.52	14.66
G_c,q,y	18.55	18.89	23.05	20.55	20.93	21.07	18.49

Statistical parameters and analysis of local contrast gloss

Abstract

1. Introduction

2. Methods

2.1. The main parameters

2.2. Statistical parameters for the specular gloss, diffuse component and contrast gloss

3. Experimental and discussion

4. Conclusion

References and links

Cited By

Figures (2)

Tables (1)

Equations (11)

Optics Express