Effect of gloss and texture on the color of injection-molded pigmented plastics.
The interior of a car has undergone significant changes in design during recent years as a consequence of customer demands. Today, the interior is thought of as a "living space," which should offer the highest level of convenience for drivers and passengers, rather than being merely a place to sit in during driving. The variety of functions provided calls for a number of different materials including, of course, plastics.
Appearance demands are constantly increasing since quality is nowadays related not only to good performance and long duration of industrial products but also to aesthetic functions which are considered important, such as part size, shape, function, material selection, and processing method. In the particular case of car interiors, appearance must be considered whenever any new component is designed, with an emphasis on the three basic descriptors: color, gloss, and texture.
In color specifications and measurements, the illumination conditions, the reflectance of the object, and the position and nature of the observer are of fundamental importance. Light sources and observers have been standardized by the Commission Internationale de l' Eclairage (CIE) . The light source is represented by a standard illuminant with a defined spectral power distribution D([lambda]) where [lambda] denotes the wavelength of light. Commonly used illuminants are A (incandescent), D65 (average north sky daylight), and F2 (cool white fluorescent).
The CIE standard observer is described by the color matching functions [~.x]([lambda]), [~.y]([lambda]), and [~.z]([lambda]), which are related to the sensitivity curves in the region of the spectrum. These correspond to the three types of cone cells in the human eye responsible for color vision [2, 3].
The optical properties of an opaque and surface rough object are described by its spectral reflectance R([lambda]) . When light strikes a surface, some of this light is reflected from the surface. The reflected light which leaves the surface at the opposite angle (the specular angle) from the incoming light and is of the same color as the incident light gives rise to an appearance of gloss. Some part of the light is reflected from the surface in a diffuse (or scattered) manner due to the existence of protuberances in the rough surface. The rest of the light penetrates into the object and is either absorbed or reflected back towards the surface. The reflected light interacts with the material and is scattered in all directions before it leaves the surface of the object. The reflected contributions (surface and bulk) constitute the total diffuse reflection. The color of the diffuse reflection depends on the particular characteristics of the absorbing chromophores present in the object, and this determines the perceived color of the object for a given light source and given observer.
In many situations, it is necessary to describe a color stimulus in a simple manner, such as by a set of coordinates in a color space as in the CIE XYZ color system. The tristimulus values X, Y, Z are calculated by combining the spectral power distribution D([lambda]) of the illuminant, the reflectance R([lambda]) of the object and the observer color matching functions [~.x]([lambda]), [~.y]([lambda]), and [~.z]([lambda]), in the following way [3, 4]:
X = [summation] D([lambda]) * R([lambda]) * [~.x]([lambda]) * [100/[[summation] D([lambda]) * [~.y]([lambda])]] * d[lambda] (1)
Y = [summation] D([lambda]) * R([lambda]) * [~.y]([lambda]) * [100/[[summation] D([lambda]) * [~.y]([lambda])]] * d[lambda] (2)
Z = [summation] D([lambda]) * R([lambda]) * [~.z]([lambda]) * [100/[[summation] D([lambda]) * [~.y]([lambda])]] * d[lambda] (3)
According to Grassmann's law, the color sensation F registered by the eye can be described as F = X X + Y Y + Z Z, where X, Y, Z are the reference stimuli or primaries (red, green, and blue) and X, Y, Z are the tristimulus values for a given color . Therefore, the X, Y, Z represent the relative amounts of the primaries needed to match a certain color stimulus. However, these tristimulus values, X, Y, and Z, are of limited value as color specifications because they correlate poorly with any arrangement of visual attributes . In 1976, the CIE proposed a new color system named CIELAB which introduced new coordinates based on transformations of the tristimulus values: L* being the lightness of the color, a* the value on the red-green axis and b* the value on the yellow-blue axis [1, 3, 5, 6]. They are calculated using the 10[degrees] observer, the X, Y, Z tristimulus values for the given color, and the [X.sub.n], [Y.sub.n], [Z.sub.n] tristimulus values for an ideal reference white as:
L* = 116 * (Y/[Y.sub.n])[.sup.3] - 16 (4)
a* = 500 * [(X/[X.sub.n])[.sup.1/3] - (Y/[Y.sub.n])[.sup.1/3]] (5)
b* = 200 * [(Y/[Y.sub.n])[.sup.1/3] - (Z/[Z.sub.n])[.sup.1/3]]. (6)
In addition to the color, two other descriptors are needed to describe the appearance of an object, gloss and topography. Gloss is defined by the American Society for Testing and Materials (ASTM) as "the angular selectivity of reflectance, involving surface-reflected light, responsible for the degree to which reflected highlights or images of objects may be seen as superimposed on a surface"  (cf. Arino et al. ). Gloss variations, in the case of nonsmooth surfaces and, more specifically, for the type of surface textures typically used for plastic parts in automotive applications, are mainly related to changes in surface topography (and therefore variations in both lateral and height directions) .
Even though these three appearance descriptors (color, gloss, and topography) are well specified individually, their interrelations need further attention. In particular, this applies to the relation between gloss (and texture) and color. Recent literature [9, 10] as well as practical experience indicate that gloss affects the perceived color. Matte (and therefore rougher) surfaces are indeed perceived to be less intensely colored (lower chroma and higher lightness) than the corresponding glossy ones, especially in the case of dark or highly chromatic colors, due to the "dilution" effect of the diffuse part of the reflected light . For example, if a piece of polished black glass has part of its surface finely ground, this finely ground spot will no longer appear black, but more grayish .
A model that describes the influence of the gloss on the measured (reflected) color of xerographic prints and accounts for the geometry of the color measuring device  has here been applied to colored injection-molded plastics used in the interior of a car. The model is shown to give reasonable and promising results for the material and for the different colors used. The gloss-dependence of the measured color has also been satisfactorily expressed in terms of surface topography descriptors.
Surface Texture Characterization
The surface topography is conventionally described in an integral manner using the P-parameters (obtained from the Primary profile) or the R-parameters (obtained from the Roughness profile, i.e., two-dimensional (2D)) . The rapid development with regard to computing capability during recent years and the development of scanning/imaging three-dimensional (3D) measuring microscopes has facilitated the use of roughness parameters obtained over an area rather than along a line profile . These parameters are not approved standards yet but are mainly extensions of the standardized P- and R-parameters. In particular, they add a feasibility of determining anisotropy of the surface structure. The most commonly used 3D-descriptors of surface roughness heights are the average roughness [S.sub.a] and the root-mean-square roughness [S.sub.q] (or RMS) which are evaluated over the area A as:
[S.sub.a] = 1/A [[integral].sub.A] |z(x, y)| * dx * dy (7)
[S.sub.q] = [square root of ([1/A] [[integral].sub.A] [z.sup.2](x, y) * dx * dy)] (8)
where z(x,y) is the surface height corresponding to the discrete points (x, y) within A.
Spatial wavelength-dependent analyses of surface textures can provide additional information. Some examples of such analyses include autocorrelation functions, power spectral densities, and fractional analysis . The latter is the only method considered here, since it can be applied in a rather straightforward manner. A height-to-height correlation function or a heights-difference function [C.sub.z]([[lambda].sub.s]) is then evaluated . [C.sub.z]([[lambda].sub.s]) is defined as the mean square height fluctuation of the surface as a function of the horizontal length scale (or spatial wavelength) [[lambda].sub.s]:
[C.sub.z]([[lambda].sub.s]) = <(z(x + [[lambda].sub.s]) - z(x))[.sup.2]>. (9)
Here, the 2D counterpart of Eq. 9 was used, i.e., considering z(x,y).
The height-to-height correlation function [C.sub.z]([[lambda].sub.s]) is typically a power law function of [[lambda].sub.s] (partly associated with a so-called fractional behavior) followed by a plateau which is related to the roughness value [S.sub.q]. The correlation function is characterized by two correlation lengths that define the maximum length scales below which the fractional behavior is observed. They can be determined from the coordinates of the transition point, or corner wavelength, of [C.sub.z]([[lambda].sub.s]). The first is a lateral correlation length, [[xi].sub.//], which is the wavelength at which [C.sub.z]([[lambda].sub.s]) deviates from the power law behavior. The second, [[xi].sub.[perpendicular to]], is amplitude-related (in the z-direction), and is calculated from the value at which [C.sub.z]([[lambda].sub.s]) attains a constant value corresponding to [[xi].sub.[perpendicular to].sup.2] for [[lambda].sub.s] > [[xi].sub.//] (see also Arino et al.  and Kluppel and Heinrich ).
Glossmeters whose construction follows the ASTM-D2457 standard measure the specular reflectance of the surface of the test specimen relative to that of a smooth standard surface, such as a glass or a ceramic tile, at a specified angle. The total gloss value [G.sup.[theta]] obtained with a standard glossmeter for a specific incident angle [theta] is, however, the sum of the contributions of a coherent and a diffuse (incoherent) component passing through the detector of the glossmeter [8, 9]. The contribution of the diffuse component to the measured gloss increases with increasing roughness of the surface and should thus be taken into account when considering textured plastic materials. In the particular case of the rough surfaces typically used in automotive interiors, the main (or, in most cases, the sole) contribution to the measured gloss was associated with the diffuse component , since the coherent contribution vanished at larger [S.sub.q]/[lambda] ratios.
The numerical gloss value [G.sup.[theta]] ranges normally from 0 (low gloss) to 100 (high gloss) gloss units (GU in percent), even though it is not unusual to get glossmeter readings greater than 100 GU for surfaces that reflect more light than the smooth standard. Metallic finishes of the automotive exterior type, for example, generally give glossmeter readings that exceed 100 GU.
Several geometries can be used for the optics of the color measuring device or spectrophotometer . The Ulbricht sphere, however, is often preferred since the position of both the light source and the detector are better in accordance with the illumination/viewing conditions to which many objects are subjected during their service lifetime. The diffuse illumination/0[degrees] viewing angle is often selected. The detector of the spectrophotometer, however, is often not placed at 0[degrees] from the normal, but instead at an angle of 8[degrees]. This enables a specular port or gloss trap to be introduced. Measurements performed in the specular component included (SCI) mode, i.e., with the gloss trap closed, take into account the total reflectance (specular and diffuse) and the results are said to be in better accordance with the perceived color when the surfaces are smooth . Measurements made in the specular component excluded (SCE) mode, with the gloss trap opened, include the diffuse reflectance, but seek to exclude the specular component, and the effect of topography can therefore be considered to be enhanced in this mode.
Modeling the Effect of Gloss on Color
Judd and Wyszecki  described a chromaticity shift in the direction of the illuminant used (D65) when a glossy surface was abraded, and thus became rougher and more matte. This phenomenon was further investigated by Dalal and Natale-Hoffman  in order to quantify such changes in chromaticity in terms of gloss. They developed a model that predicted the total reflectance factor measured by the spectrophotometer [R.sub.m]([lambda], [G.sup.[theta]]) as the sum of an intrinsic reflectance factor [R.sub.intrinsic]([lambda]) associated with the light reflected from within the specimen that reaches the detector (not to be confused with the term "internal" reflectance, which is generally used to describe the reflection back into a specimen at the surface), and that part of the total front surface reflectance factor [R.sub.[fs.sup.T]] (denoted r([G.sup.[theta]])) that is captured by the detector, [G.sup.[theta]] being the total gloss measured at the angle [theta]. Therefore,
[R.sub.m]([lambda], [G.sup.[theta]]) = [R.sub.intrinsic]([lambda]) + r([G.sup.[theta]]). (10)
An important assumption underlying the model  is that the total front surface reflectance [R.sub.fs.sup.T] is constant and therefore independent of the specimen gloss. It can be calculated from the Fresnel equations and is determined only by the refractive index n of the material and the angle of incidence [theta] of the incoming light beam. [R.sub.fs.sup.T] is considered to be the sum of a coherent [R.sub.fs.sup.C] and a diffuse component [R.sub.fs.sup.D]. Thus, even though the total front surface reflectance [R.sub.fs.sup.T] is assumed to be constant, the [R.sub.fs.sup.C] component increases, whereas [R.sub.fs.sup.D] decreases as the gloss of the specimen increases.
[FIGURE 1 OMITTED]
The portion of total front surface reflectance [R.sub.fs.sup.T] captured by the detector of the sphere of the spectrophotometer, i.e., r([G.sup.[theta]]), is the reflectance term associated with both the specular (coherent) and that portion of the diffuse component that results from surface scattering, and not bulk, and it will clearly differ with the measuring mode selected, i.e., SCI or SCE. The SCI mode captures virtually all the front surface reflected light, and thus r([G.sup.[theta]]) [approximately equal to] [R.sub.fs.sup.T]. In the SCE mode, however, a significant part of the coherent component is lost and the importance of the diffuse component [R.sub.fs.sup.D] will increase. A schematic illustration of the different contributions to [R.sub.m] ([lambda], [G.sup.[theta]]) is shown in Fig. 1.
Rather than performing the analysis in terms of the reflectance (for a large number of wavelengths), Dalal and Natale-Hoffman  suggested using the CIE tristimulus values X, Y, and Z since they are linear functions of the corresponding reflectance spectra (see Eqs. 1-3). Thus,
[X.sub.m]([G.sup.[theta]]) = [X.sub.intrinsic] + r([G.sup.[theta]]) * [X.sub.n] (11)
where [X.sub.n] is the X tristimulus value of the white reference. Equation 11 is equivalent to Eq. 10, the only difference being that the wavelength-dependence of the reflectance factor has been eliminated. Equations equivalent to Eq. 11 for the other tristimulus values are obtained by just replacing the X tristimulus value with the Y or Z value. The estimation of the different parameters in Eq. 11 is briefly described below and in the Results section.
The gloss-independent intrinsic tristimulus [X.sub.intrinsic] of a colored specimen cannot be measured directly, since some part of the front surface reflectance always reaches the detector. It can, however, be obtained from the low gloss limit of [X.sub.m] following the procedure outlined by Dalal and Natale-Hoffman . From Eq. 11 with [G.sup.[theta]] = 0:
[X.sub.intrinsic] = [X.sub.m](0) = r(0) * [X.sub.n] (12)
with [X.sub.m] (0) = [X.sub.m SCI] for the colored specimen, since the SCI mode captures all the light reflected from the surface regardless of gloss and in this mode r(0) = r([G.sup.[theta]]) for all gloss values. It can be calculated from the Fresnel equation for a perfectly smooth surface:
r(0) = 1/2 * [[[[cos [theta] - [square root of ([n.sup.2] - sin[.sup.2][theta])]]/[cos [theta] + [square root of ([n.sup.2] - sin[.sup.2][theta])]]]][.sup.2] + [[[[n.sup.2] * cos [theta] - [square root of ([n.sup.2] - sin[.sup.2][theta])]]/[[n.sup.2] * cos [theta] + [square root of ([n.sup.2] - sin[.sup.2][theta])]]]][.sup.2]] (13)
where n is the real part of the refractive index of the material and [theta] = 0, i.e., normal incidence.
The r([G.sup.[theta]]) component in Eq. 11 represents the portion of the front surface reflectance captured by the detector of the spectrophotometer and depends only on gloss and not color. It cannot be directly measured, but is here experimentally obtained from black specimens with different gloss values. The procedure is outlined in a later section.
Color Related to Material and Structural Characteristics
The relation between the color of the pigmented plastic (injection-molded plaques in the present case) and material properties/structural characteristics can be described by means of the two-flux radiation Kubelka-Munk equation for pigment/paste mixtures  based on the light absorption and scattering coefficients. The reflectance of an optically infinite thick layer or the reflectivity [R.sub.[infinity]]([lambda]) is then related to the ratio of the light absorption coefficient K([lambda]) to the light scattering coefficient S([lambda]) as:
[[K([lambda])]/[S([lambda])]] = [[1 - [R.sub.[infinity]]([lambda])][.sup.2]]/[2 * [R.sub.[infinity]]([lambda])]. (14)
[R.sub.[infinity]]([lambda]) is here associated with the total reflectance of the injection-molded plaques.
Values of K([lambda]) and S([lambda]) for the same materials as used here have been evaluated earlier  from diffuse reflectance values obtained from measurements on a thin and smooth translucent sheet placed over a nonreflecting black background and then over a white background [17, 18]. If K([lambda]) and the reflectivity are known, S([lambda]) can be calculated from Eq. 14 in a straightforward manner. The effect of the surface texture on the scattering coefficient is discussed in a later section.
The acrylonitrile-butadiene-styrene terpolymer (ABS) used was a commercial multipurpose injection-molding grade from GE Plastics, denoted natural color Cycolac G100. It had a density of 1.05 g/[cm.sup.3] (ISO 1183) and a melt viscosity MV (260[degrees]C/1500 [s.sup.-1]) of 111 Pas (ISO 11443). Here, 3% by weight (which corresponded to 1.07% by volume) of a light beige master batch (MB), in pellet form, was added to the ABS-grade in order to obtain the colored specimens. This master batch was supplied by GE Plastics and contained 50% by weight of pigments and 50% of a styrene-acrylonitrile (SAN) copolymer as a carrier. A mixture of red, yellow, white, and black pigments was used to produce the desired beige color of the master batch.
In addition to the injection-molded ABS-plaques with a light beige color, a set of specimens of four other colors was included in the investigation for purposes described later. These specimens were produced from black, brown, and two gray (denoted light gray and gray) colored ABS and their CIELAB-coordinates in the SCE and SCI modes are given in Table 1 (black specimens) and in Table 2 for the other colors.
The value of the real part of the refractive index n at 20[degrees]C for ABS was 1.515 .
The light beige ABS-specimens were prepared by injection molding. The procedures for blending the pigments and polymer as well as the injection molding of the plaques are given in Ref. 10 and are not repeated here. The injection-molded specimens were plaques with three fields having different surface textures: smooth (or glossy), fine, and coarse (or "leather-like"). Figure 2 shows a photomicrograph (obtained with a Leica MZ 125 optical microscope) of the latter two textures.
Injection-molded plaques in brown, light gray, and gray with similar textures to those shown in Fig. 2 (i.e., smooth, fine, and coarse) were also included. The series of black ABS-specimens had different surface textures (denoted A to H, with A, E, and H being equivalent to the smooth, fine, and coarse textures of the injection-molded plaques and the rest generally considered middle-sized textures) and they were included in order to evaluate r([G.sup.[theta]]). Further details of the fine and coarse textures (in the case of the light beige specimens), as well as of the middle textures F and G (black plaques) are given in Ref. 8.
Evaluation of the Surface Topography
The equipment used to assess the topographical characteristics of the visibly rough textures was a UBM Optac 2000, which allows 2D- and 3D-measurements of waviness and roughness. It consists of an autofocus sensor UBC14, allowing a maximum measurable height of [+ or -]500 [micro]m and a resolution of 0.12 [micro]m, and an air-bearing stage, which provides the movement along a profile. All measurements were performed at room temperature (21 [+ or -] 2[degrees]C). An area of 16 X 16 [mm.sup.2] was scanned at a speed of 0.50 mm/s. A total of 81 profiles at a distance of 0.2 mm from each other were recorded. The sampling interval within each profile was 0.01 mm. A more detailed account of the measurements can be found in Ref. 14.
The topography of the (visibly) smooth surfaces was evaluated by means of a Talystep mechanical profilometer with a spherical diamond tip of radius 15 [micro]m, which can measure [S.sub.q] values in the range 0.04 nm to 4.0 [micro]m (strictly [P.sub.q] values, since the stylus profile measurements in this particular case were performed along a line) (cf. also ).
The gloss values were measured at 23[degrees]C according to ASTM D2457 by means of a conventional portable gloss-meter BYK Gardner micro-TRI-gloss equipped with a black glass standard which was used for calibration. A total of three measurements were performed on different parts of each specimen and an average value was used. The instrument repeatability is 0.1 GU.
Different measuring angles (incident and thus reflected) are recommended , depending on the reflectance properties of the material. The 60[degrees] geometry, however, is preferred in the automotive industry when measuring plastic parts, since experience indicates that the numerical values in the range of interest correlate in a satisfactory way with the perceived gloss. Therefore, only the 60[degrees] geometry was used and the dimensions of the measured area were 9 X 18 [mm.sup.2] .
[FIGURE 2 OMITTED]
Color of the Specimens
A conventional portable Datacolor Microflash spectro-photometer was used for the reflectance measurements. It is a dual-beam instrument with a pulsed xenon light source and a 66 mm diameter Ulbricht sphere as the measuring unit with a d/8[degrees] illumination/viewing geometry. The illuminated area and the measured area were 22 mm and 18 mm in diameter, respectively. Spectral data were obtained at 10 nm intervals from 400-700 nm (visible spectrum). The instrument repeatability is 0.001 CIELAB units.
Measurements were performed in both the specular component excluded (SCE) and the specular included (SCI) modes. The CIE standard illuminant D65 and the CIE 10[degrees] observer were used. The tristimulus values [X.sub.n], [Y.sub.n], and [Z.sub.n] of the standard white (for the D65 illuminant of interest) used were 94.81, 100, and 107.34 , respectively.
RESULTS AND DISCUSSION
Surface Texture Characterization
The characteristics of the surface texture for the light beige injection-molded plaques are given in terms of the descriptors described in Table 3. The glossy regions were analyzed using the mechanical profilometer Talystep and the UBM optical profilometer was used for the other textures. The average roughness [S.sub.a], the root-mean-square deviation of the profile [S.sub.q], as well as the surface descriptors provided by the fractional approach (height-to height correlation function) are included in Table 3.
The smooth (glossy) region of the light beige plaques exhibited an [S.sub.q]-value of 0.032 [micro]m, and the roughness values for the fine and coarse regions were 5.6 and 35.0 [micro]m. The series of black ABS-specimens was essentially injection-molded plates with different imposed surface textures and they were included in order to cover a wide gloss range. Their roughness values ([S.sub.q]) ranged from 0.026-31.6 [micro]m and they also exhibited different correlation lengths [[xi].sub.//], as shown in Table 4.
Gloss of the Specimens
The measured gloss values at 60[degrees] ([G.sup.60]) of the injection-molded ABS-plaques in the different colors are given in Table 5 and the values for the black ABS specimens are given in Table 6. The texturing of the surface was clearly very effective in reducing the gloss level.
Calculation of the Intrinsic Tristimulus Values
Table 7 shows the measured tristimulus values in the SCI mode for the five colors considered, to be used with Eq. 12 since [X.sub.m](0) = [X.sub.m SCI] (equivalent for Y and Z). The front surface reflectance factor r(0) of the perfectly smooth ABS, evaluated from Eq. 13, was 0.0419 when using 1.515 as the refractive index of ABS  and a normal angle of incidence ([theta] = 0).
The intrinsic tristimulus values [X.sub.intrinsic], [Y.sub.intrinsic], and [Z.sub.intrinsic] of the ABS specimens for the different colors obtained from Eq. 12 are given in Table 8.
Evaluation of r([G.sup.[theta]]) From the Black Plaques
The front surface reflectance factor r([G.sup.60]) captured by the detector of the spectrophotometer at [theta] = 60[degrees] can be experimentally obtained from the gloss measurements on the black specimens with different gloss values by application of Eq. 11. The measured tristimulus values in SCI mode (Table 7) and the calculated intrinsic tristimulus values (Table 8) of the black ABS-specimens were used for this purpose.
Figure 3 shows this calculated r([G.sup.60]) as a function of the gloss of the black specimens. The relation can be described by a function of the form:
[G.sup.60] = [k.sub.1] * [e.sup.-[r([G.sup.60])/[k.sub.2]]] (15)
where [k.sub.1] and [k.sub.2] are constants.
Predicted Influence of Gloss on the Color
Figures 4 and 5 show the experimental tristimulus values [X.sub.m]([G.sup.60]), [Y.sub.m]([G.sup.60]), and [Z.sub.m]([G.sup.60]) in the SCE mode as a function of gloss as well as the prediction (full lines) of Eq. 11 for the light beige and brown ABS specimens, respectively. The prediction is made using the front surface reflectance factor r([G.sup.60]) evaluated for the black specimens, i.e., Eq. 15. The agreement between the experimental results and the model prediction is apparently satisfactory and it is evident that the tristimulus values decrease with increasing gloss. A similar result was also obtained for the light gray and gray specimens (not shown).
The CIELAB coordinates are calculated from the tristimulus values using Eqs. 4-6. Figures 6 and 7 illustrate the dependence of the L*, a*, and b* coordinates in SCE mode, on gloss, for the light beige and brown specimens, respectively. Both experimental and calculated results are included. It is evident that the gloss level had a clear influence on the color coordinates, which is illustrated both by the model and the experiments. For example, a higher gloss gave a lower L* value, i.e., a darker specimen. This is in agreement with the perceived impression and can be interpreted in terms of an increased proportion of diffuse reflection . The greatest change in color with increasing gloss occurred at lower gloss values, e.g., below 10 GU. A similar result was obtained for the other light gray and gray specimens.
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
It is evident in Fig. 6 that the method described can predict the variation in the CIELAB color coordinates with the gloss in a rather accurate manner. In the particular case of the light beige ABS specimens, for example, changes of [DELTA]L* = 3.50, [DELTA]a* = 0.27, and [DELTA]b* = 1.34 are predicted with an increase in gloss from 1 to 92 GU. Such differences can be visually distinguished, since the smallest differences perceived by the human eye are about [DELTA]L* = 0.2-0.3 in L* and [DELTA]a* = [DELTA]b* = 0.10-0.15, according to experience.
Note that if the color was measured in the SCI mode, the effect of the gloss would be marginal. This is evident from both the experiments and from the model prediction (cf. ).
[FIGURE 5 OMITTED]
[FIGURE 6 OMITTED]
Predicted Color as Surface Topography-Dependent
The difference in gloss between the specimens is here due to variations in the surface texture, which means that the surface topography affects the color. Physically, r([G.sup.[theta]]) represents the portion of the front surface reflected light that is captured by the detector of the spectrophotometer and it is to be expected that r([G.sup.[theta]]) is dependent on the surface characteristics. In fact, Dalal and Natale-Hoffman  stated that it represents the smoothness of the surface. It may thus be of interest to discuss the relation between r([G.sup.[theta]]) and the surface topography in more detail.
The relation between the surface topography of injection-molded plastic objects with imposed textures and their gloss at an incidence angle of 60[degrees] has been previously investigated  using a modification of the general scalar Kirchhoff approximation. The surface descriptors used were the surface roughness [S.sub.q] and the lateral correlation length [[xi].sub.//], obtained using the fractional approach (cf. Tables 3, 4). In fact, the relation between [G.sup.60] and the roughness characteristics often had a similar functional form as that between [G.sup.60] and r([G.sup.60]), Eq. 15, and this can be of interest (cf. ). Admittedly, it is not easy (or even possible) to extract the same description of the surface using one parameter (r([G.sup.[theta]])) instead of two ([S.sub.q], [[xi].sub.//]), but it is certainly of interest to estimate how the surface characteristics affect the front surface reflectance factor r([G.sup.[theta]]). This is outlined to some extent in the following. Figure 8 is a graphical representation of [G.sup.60] as a function of the topography descriptors ([S.sub.q] and [[xi].sub.//]) obtained with the Kirchhoff approximation . The calculated gloss level at different surface roughness values is here shown for a given correlation length. The calculated results shown are in good agreement with the experimental results for these specimens . If these results are combined with those given in Fig. 3 (or Eq. 15), the front surface reflectance factor r([G.sup.60]) can be expressed in terms of the surface texture descriptors [S.sub.q] and [[xi].sub.//], as shown in Fig. 9.
[FIGURE 7 OMITTED]
[FIGURE 8 OMITTED]
[FIGURE 9 OMITTED]
It is clear in Fig. 9 that the reflectance factor r([S.sub.q], [[xi].sub.//]) exhibits a stronger dependence on the surface roughness for textures with shorter correlation lengths [[xi].sub.//] than for surfaces characterized by a longer correlation length, and that, for a given correlation length, r([S.sub.q], [[xi].sub.//]) increases with increasing roughness. Note also that for very smooth surfaces, r([S.sub.q], [[xi].sub.//]) attains very small values, as it should when the color measurements are performed in SCE mode . A word of caution should be given here. The general Kirchhoff theory is here mainly used to describe the relation between the surface texture and the gloss. The surfaces of interest in this context are probably too rough in relation to the wavelength of light for the theory to be strictly valid (cf. also ).
It is obvious that all color characteristics such as (X, Y, Z) or (L*, a*, b*) can be formally expressed in terms of [S.sub.q] and [[xi].sub.//]. One value of such a procedure would be to assess how different combinations of [S.sub.q] and [[xi].sub.//] can yield a similar color perception. This would certainly be of interest for the design engineer when seeking to match the colors of different objects or components. Of course, this has to be balanced against the requirements set in the manufacture of the molds to be used for the products.
Evaluation of the Light Scattering and Light Absorption Coefficients
In order to relate the measured color to physical properties and structure of the material, such as the light absorption and light scattering coefficients, the measured reflectance [R.sub.m]([lambda], [G.sup.60]), as expressed in Eq. 10, can be considered. The same procedure as described above for the evaluation of [X.sub.m]([lambda], [G.sup.60]), including a combination of Eqs. 10-13, was used to obtain [R.sub.m]([lambda], [G.sup.60]) at some selected wavelengths (450, 500, 550, and 600 nm) (see Fig. 10).
[FIGURE 10 OMITTED]
The Kubelka-Munk ratio K([lambda])/S([lambda]) can then be calculated from the [R.sub.m]([lambda], [G.sup.60]) using Eq. 14 (considering [R.sub.m]([lambda], [G.sup.60]) and [R.sub.[infinity]]([lambda]) equivalent). The predicted ratio for light beige ABS specimens with different gloss levels is shown in Fig. 11 as a function of the wavelength of light. The reflectance factor r([G.sup.[theta]]) used was, as before, evaluated from measurements on the black ABS-specimens. Figure 11 includes the experimental results for the smooth area of the ABS-plaque and the agreement with the model at a gloss level of 90 GU is satisfactory. A similar agreement was noted for the rougher surfaces and, in accordance with experimental results, the predicted Kubelka-Munk ratio decreased with decreasing gloss.
It may be of interest to extend this analysis. The coefficients of absorption K([lambda]) and scattering S([lambda]) in Eq. 14 for the light beige ABS were individually determined in earlier work  from measurements of the diffuse reflectance of a thin translucent sheet of the material placed over a nonreflecting black background and over a white background. Assuming the same absorption coefficient K([lambda]) for the films and the injection-molded plaques , and knowing the reflectivity (i.e., the reflectance of the plaques [R.sub.m]([lambda], [G.sup.60]) predicted using Eq. 11), S([lambda]) can be calculated from Eq. 14. The values of K([lambda]) as well as the calculated values of S([lambda]) are summarized in Fig. 12, which shows the calculated S([lambda])-values together with experimental results for the smooth region of the light beige ABS specimen as a function of the wavelength. The similarity between the prediction at 90 GU and the experimental result is good and the scattering coefficient increased as the roughness of the plaques increased.
[FIGURE 11 OMITTED]
[FIGURE 12 OMITTED]
There was, however, a quantitative difference between the scattering coefficient evaluated for the injection-molded plaques and that measured for the thin films, as noted earlier , although the wavelength dependence appeared to be similar. The scattering coefficient of the thin film is also included in Fig. 12. Possible reasons for this difference may be the differences in surface topography and also in the bulk structure between compressed films and molded plaques. Such a dependence of the scattering coefficient on structural arrangements is expected . Other phenomena, however, may also be responsible for the discrepancy.
A model that describes the influence of gloss on the measured (reflected) color of xerographic prints and accounts for the geometry of the color measuring device  has here been applied to colored injection-molded plastics used in the interior of a car. The model was shown to give reasonable results for the material chosen (acrylonitrile-butadiene-styrene polymer) in four different colors. An important parameter in the model is the portion of the front surface reflectance captured by the detector of the spectrophotometer r([G.sup.[theta]]), which depends only on gloss (and therefore texture) and not on color. This parameter was determined from an independent set of black ABS specimens.
In general, the CIELAB color coordinates changed when the gloss increased when the spectrophotometer was set in the SCE mode. The CIELAB lightness L* was most affected, decreasing quite drastically with increasing gloss, which is in accordance with the visual perception.
The gloss-dependence of the measured color can formally be expressed in terms of suitable surface topography descriptors, in this case the root-mean-square roughness and the lateral correlation length. Surfaces with shorter correlation lengths [[xi].sub.//] exhibited a stronger dependence of the reflectance factor r([G.sup.[theta]]) on the surface roughness [S.sub.q] than surfaces characterized by a longer correlation length and, for a given correlation length, r([G.sup.[theta]]) increased with increasing roughness. In terms of the Kubelka-Munk theory, the results obtained clearly illustrate that a rougher surface is associated with a higher light scattering coefficient.
TABLE 1. CIELAB coordinates of the black specimens with different textures (A, D, and H corresponding to smooth, fine, and coarse textures, respectively, the others being considered "middle" textures), measured in SCI/SCE mode. Specimen CIE L* CIE a* CIE b* A 30.07/17.17 0.06/0.03 -1.00/-1.06 B 25.67/23.35 -0.04/-0.06 -1.00/-1.29 C 28.73/27.34 -0.25/-0.29 -1.97/-2.06 D 30.10/29.44 0.00/0.02 -1.15/-1.18 E 26.22/25.45 -0.01/-0.02 -1.00/-1.05 F 28.94/28.38 -0.24/-0.24 -1.92/-1.92 G 29.77/29.51 0.10/0.10 -1.00/-1.04 H 29.72/29.58 0.03/0.03 -1.00/-1.06 TABLE 2. CIELAB coordinates of the other colored specimens (light beige, brown, light gray, and gray) measured in SCI/SCE mode. Specimen CIE L* CIE a* CIE b* Light beige Glossy 64.42/60.85 3.14/3.44 10.35/11.5 Fine 64.35/63.95 3.13/3.17 10.22/10.18 Coarse 64.43/64.38 3.16/3.17 10.29/10.16 Brown Glossy 49.90/45.20 1.13/1.28 5.47/6.51 Fine 50.01/49.57 1.11/1.12 5.44/5.53 Middle 49.51/49.55 1.16/1.16 5.88/5.91 Coarse 50.04/49.95 1.11/1.13 5.51/5.54 Light gray Glossy 60.56/57.44 0.24/0.25 1.93/2.03 Fine 60.74/60.35 0.24/0.24 1.88/1.90 Middle 60.72/60.77 0.34/0.35 1.95/1.95 Coarse 60.64/60.53 0.24/0.24 1.92/1.92 Gray Glossy 46.50/40.84 0.20/0.19 0.83/1.12 Fine 46.52/45.93 0.19/0.20 0.73/0.74 Coarse 46.62/46.60 0.21/0.20 0.85/0.87 TABLE 3. Surface descriptors of the different textures in the case of the light beige ABS plaques (in [micro]m). Fractional analysis, Roughness [C.sub.z]([lambda]) Region [S.sub.a] [S.sub.q] [[xi].sub.||] Smooth -- 0.032 16 Fine 4.5 5.6 90 Coarse 31.1 35.0 450 Fractional analysis, [C.sub.z]([lambda]) Region [[xi].sub.[perpendicular to].sup.2] Smooth -- Fine 67 Coarse 2812 TABLE 4. Same as Table 3 but for the black specimens (A, D, and H corresponding to smooth, fine, and coarse textures, respectively, the others considered "middle" textures) (in [micro]m). Fractional analysis, Roughness [C.sub.z]([lambda]) Specimen [S.sub.a] [S.sub.q] [[xi].sub.||] A -- 0.026 4 B 2.5 3.2 65 C 3.6 4.6 67 D 4.1 5.5 68 E 4.8 6.0 65 F 8.5 10.4 100 G 16.8 20.6 145 H 27.6 31.6 386 Fractional analysis, [C.sub.z]([lambda]) Specimen [[xi].sub.[perpendicular to].sup.2] A B 20.7 C 44 D 54 E 73 F 226 G 795 H 2252 TABLE 5. Measured gloss ([G.sup.60]) of the specimens (except for the black) used in this study. Specimen Gloss, [G.sup.60] [GU] Light beige Glossy 92.8 Fine 6.5 Coarse 3.0 Brown Glossy 85.0 Fine 5.2 Coarse 2.4 Light gray Glossy 84.6 Fine 6.6 Coarse 3.4 Gray Glossy 88.7 Fine 4.9 Coarse 1.8 TABLE 6. The same as Table 5, but for the black specimens (A, D, and H corresponding to smooth, fine, and coarse textures, respectively, the others considered "middle" textures). Specimen Gloss, [G.sup.60] [GU] A 89.0 B 7.5 C 5.7 D 3.2 E 3.0 F 2.9 G 1.9 H 1.3 TABLE 7. Tristimulus values of the glossy light beige, brown, light gray, gray, and black specimens, in both SCI/SCE modes. Color [X.sub.m] [Y.sub.m] [Z.sub.m] Light beige 32.46/28.43 33.33/29.08 28.33/23.68 Brown 17.57/14.10 18.32/14.66 16.97/13.03 Light gray 27.19/23.94 28.63/25.20 29.39/25.52 Gray 14.83/11.20 15.62/11.78 16.37/12.22 Black 5.98/2.15 6.30/2.27 7.04/2.64 TABLE 8. Intrinsic tristimulus values for the light beige, brown, light gray, gray, and black specimens obtained from Eq. 12. Color [X.sub.intrinsic] [Y.sub.intrinsic] [Z.sub.intrinsic] Light beige 29.07 29.74 24.46 Brown 14.18 14.73 13.10 Light gray 23.80 25.04 25.52 Gray 11.44 12.03 12.50 Black 2.59 2.72 3.17
We thank General Electric Plastics (both in Enhorna, Sweden, and in Bergen op Zoom, The Netherlands) for supplying the material. The contributions of K.-M. Jager, in the form of critical and very constructive debates, and of J. A. Bristow for the linguistic revision of the manuscript are also acknowledged.
Contract grant sponsors: Swedish Agency for Innovation Systems (Vinnova), Volvo Car Corporation.
A CIE-Standard illuminant, incandescent ABS Acrylonitrile-butadiene-styrene terpolymer CIE Commission Internationale de l'Eclairage D65 CIE-Standard illuminant, average north sky daylight F2 Standard illuminant, cool white fluorescent GU Gloss units (%) MB Master batch MV Melt viscosity (Pas) SAN Styrene-acrylonitrile copolymer SCE Specular component excluded mode (spectrophotometer) SCI Specular component included mode (spectrophotometer) 2D Two-dimensional 3D Three-dimensional a* CIELAB redness-greenness b* CIELAB yellowness-blueness n Real part of the refractive index (/) r([G.sup.[theta]]) Front surface reflectance (factor) detected by the glossmeter x, y Lateral lengths (mm) [~.x]([lambda]), CIE color matching functions [~.y]([lambda]), [~.z]([lambda]) z, z(x, y) Height ([micro]m) <z> Mean (average) of heights ([micro]m) A Area ([micro][m.sup.2]) [C.sub.z]([[lambda].sub.s]) Height-to-height correlation function ([micro][m.sup.2]) D([lambda]) Spectral power distribution of an illuminant F Color sensation registered by the eye [G.sup.[theta]] Total gloss at the angle [theta] (GU) K([lambda]) Light absorption coefficient (l/m) L* CIELAB lightness [L*.sub.SCE] CIELAB lightness, measured in SCE mode [L*.sub.SCI] CIELAB lightness, measured in SCI mode R([lambda]) Reflectance (factor) (/) or (%) [R.sub.fs.sup.C] Coherent part of the total front surface reflectance (factor) [R.sub.fs.sup.D] Diffuse part of the total front surface reflectance (factor) [R.sub.fs.sup.T] Total front surface reflectance (factor) [R.sub.intrinsic]([lambda]) Intrinsic reflectance (factor) [R.sub.m]([lambda], Total reflectance (factor) measured by [G.sup.[theta]]) the spectrophotometer (/) [R.sub.m SCE]([lambda], Total reflectance (factor) measured in [G.sup.[theta]]) SCE mode (/) [R.sub.m SCI]([lambda], Total reflectance (factor) measured in [G.sup.[theta]]) SCI mode (/) [S.sub.a] Average roughness (3D) ([micro]m) [S.sub.q] Root-mean-square roughness (3D) ([micro]m) S([lambda]) Light scattering coefficient (l/m) X, Y, Z Reference stimuli or primaries X, Y, Z CIE tristimulus values [X.sub.intrinsic], Intrinsic tristimulus values [Y.sub.intrinsic], [Z.sub.intrinsic] [X.sub.m], [Y.sub.m], Measured CIE tristimulus values [Z.sub.m] [X.sub.m SCE], [Y.sub.m SCE], Measured CIE tristimulus values in SCE [Z.sub.m SCE] mode [X.sub.m SCI], [Y.sub.m SCI], Measured CIE tristimulus values in SCI [Z.sub.m SCI] mode [X.sub.n], [Y.sub.n], CIE tristimulus values of the ideal [Z.sub.n] perfect reflecting diffuser [theta] Angle of incidence angle relative to the surface normal ([degrees]) or (rad) [lambda] Wavelength of incident light (nm) [[lambda].sub.s] Spatial wavelength (mm) [[xi].sub.//] Lateral correlation length (mm) [[xi].sub.[perpendicular to]] Amplitude correlation length (mm)
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Ingrid Arino, Ulf Kleist
Department of Interior and Climate Engineering, Volvo Car Corporation, SE-405 31 Goteborg, Sweden
Department of Materials and Manufacturing Technology, Chalmers University of Technology, SE-412 96 Goteborg, Sweden
Correspondence to: Mikael Rigdahl; e-mail: firstname.lastname@example.org
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|Author:||Arino, Ingrid; Kleist, Ulf; Rigdahl, Mikael|
|Publication:||Polymer Engineering and Science|
|Date:||May 1, 2005|
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