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Abstract
In this paper, we numerically analyze the effect of light source distance on the appearance of gloss unevenness. It is important to measure gloss unevenness because it affects the texture and appearance of a product. We propose a more efficient technique for measuring gloss unevenness. The experimental results for the proposed apparatus in this study are in good agreement with our theoretical analysis. We show that the appearance of the captured gloss unevenness image changes depending on the effect of light source distance. As an application of this gloss unevenness observation technology, we also report on the detection of scratches and coating unevenness in industrial quality control.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Our impression of the texture and appearance of a product comes from its various attributes (i.e., color, clarity, sharpness, …). Gloss, an important property of materials, also affects product texture and thus appearance. Not only the intensity of gloss, but also the gloss unevenness has a strong influence on the texture and appearance. When glossy printing paper is observed under a light source, gloss on its surface is also observed (see Fig. 1). In a dichromatic reflection model, the intensity of the reflected light is the sum of the diffuse reflection and the specular reflection. Gloss is physically a specular reflection phenomenon. Specular reflection is the mirror-like reflection of the light source from a surface and is much more directional than diffuse reflection. In this paper, specular reflection is referred to as gloss and is also equivalent in meaning to the word “shine” and “luster”. It does not mean “gloss” as defined in ISO standards [1,2].
Fig. 1. Photograph showing gloss on printing paper (right) and a magnification of the gloss region (left). The gloss unevenness is observed in the gloss region(left).
A comprehensive visual evaluation of gloss unevenness is performed in many industries for quality control purposes. It is relatively easy for humans to observe and evaluate gloss unevenness, but it is difficult to evaluate it comprehensively and quantitatively. The gloss unevenness region is part of the gloss region, which is generally small. Human inspectors mentally reconstruct the entire gloss unevenness region while moving the gloss region across their visual field.
Numerous methods for quantitatively measuring gloss unevenness have been proposed [3–14]. Gloss unevenness is the deviation of the continuous measurement of the gloss in a small region. These methods do not show how gloss unevenness looks in the material. Gloss unevenness is only observed in a small part of the gloss region. Therefore, it is necessary to have a technique to evaluate the gloss unevenness by widening this gloss region. For the evaluation of texture, it is important for gloss unevenness to be visible to the human eye.
Gloss unevenness is observed in the specular reflection region. The distribution of specular reflection can be analyzed using the bidirectional reflectance distribution function or the spread function of specular reflection [15–20]. The authors have previously analyzed the spread function of specular reflection [16–20]. In particular, we have investigated a method for measuring the line spread function of specular reflection (SR-LSF) that uses a line light source allowing observation of specular reflection over a wide range (Fig. 2) [20]. In this measuring method, the specular reflection image is captured by a camera. We call the captured image the line light image of specular reflection (SR-LLI). From our results, it is assumed that the specular reflection distribution region is related to the light source distance when a point light source is used. Based on the theory, gloss unevenness analysis can be improved by controlling the light source distance. In this paper, we investigate the effect of light source distance on apparent gloss unevenness under conditions that allow human visual inspection. We develop an apparatus for gloss unevenness observation and evaluate its performance. We also demonstrate its application to the detection of scratches and coating unevenness in industrial quality control.
Fig. 2. Schematic diagram of a measuring method for the line spread function of specular reflection (SR-LSF). The input of line light reflects off the object surface. The reflected light is measured at various angles. The photograph in the circle is a captured image of specular reflection. Gloss unevenness can be observed in the specular reflection region of the photograph.
2. Theory
We first describe the visual inspection geometry for gloss unevenness. Using this geometry, the observed gloss unevenness image is analyzed based on the SR-LSF. We derive the relationship between the gloss unevenness region and the light source distance.
2.1 Visual inspection geometry for gloss unevenness evaluation
The light reflected by an object is evaluated by visual inspection. The measurement geometry is important because gloss depends on the angle of reflection. Methods for measuring gloss have been proposed [1,2]. Standardized methods for measuring gloss have been developed. ISO 2813 specifies a method for determining the gloss of coatings using angles of 20°, 60°, and 85° depending on the reflection strength of the object. ISO 8254-1 specifies a method for measuring the gloss of paper at an angle of 75° with respect to the normal of its surface. The Japanese industrial standard (JIS) Z 8741 specifies a method for determining the gloss of materials using angles of 20°, 45°, 60°, 75°, and 85°.
Gloss can be evaluated by reflecting a line light source onto the object surface. This visual observation method is similar to that for line spread function measurement. Figure 3 shows a schematic diagram of a line light observation method based on visual inspection. An observer notes the intensity of the regular reflection of the line light source, the spread of the line light source image, and the gloss unevenness around the reflected line light source image. When humans observe the appearance of the surface of a sample in detail, they see it at a position close to the sample within the focus range. The viewing distance is thus set to 250 mm, which is the near point of the human eye. When humans observe an image, they observe it in the normal direction of the sample (i.e., 0°); however, a non-zero angle is needed to observe specular reflection. The reflection angle of 60°, 75° or 85° increase specular reflection. On the other hand, as the lager the reflection angle, the larger the observation region within a certain viewing angle. This has the disadvantage of averaging gloss unevenness. When observing the printing paper under a light source, gloss unevenness on the surface can be also observed along with images. The typical observation angle for images is 45°. An angle of 45° was thus chosen as the reflection angle for this experiment.
Fig. 3. Schematic diagram of a line light observation method based on visual inspection. The incident light angle and reflection angle create combinations. In this case, the light source distance is set to 250 mm and the camera distance is set to 250 mm.
The line light source can be a fluorescent light. Because a narrow line width of the line light source is preferred, the proposed apparatus uses a narrow line light source. In most cases, the light source is considered to be a collection of point light sources, and the light spreads over a wide angle. The angle of incident light varies with the position on the surface of the observed object. Human eyes have an angle of view. Therefore, in the visual inspection, the incident light angle and the reflection angle at each position on the object surface create combinations.
2.2 Effect of light source distance
Gloss unevenness is observed in part of the specular reflection region. The authors previously analyzed the specular reflection region using the SR-LSF [20]. The observed specular reflection image, SR-LLI, has a distribution similar to that of a Gaussian function with the peak of regular reflection in the center. This is the gloss region. As shown in Fig. 4, the angle of the incident light with respect to the position on the sample bed changes as the light source moves and the light source distance changes. For this reason, the SR-LLI changes according to the distance of the light source.
Fig. 4. Schematic diagram of the effect of light source distance. The angle of the incident light with respect to the position on the sample bed changes as the light source moves and the light source distance changes. For this reason, the SR-LLI changes according to the distance of the light source.
The authors previously proposed a method for calculating the SR-LSF from the SR-LLI [20]. The relationship between the SR-LSF and the SR-LLI is as follows.
The SR-LSF is a transfer function that represents the characteristics of reflection. Therefore, the SR-LSF is constant for a given material. According to these equations, changes in the light source distance should change the appearance of the SR-LLI and therefore the apparent gloss unevenness.
Equations (1) and (2) are derived from the positional relationship between the camera and the light source. For example, the distance between the sample center and the camera position is set equal to the distance between the sample center and the light source position. The camera distance is equal to the light source distance in Fig. 4. In Eq. (2), α is 1/2. Δθ is a function of Δx. The SR-LSF can be calculated from the SR-LLI in Eq. (1). Because the SR-LSF is constant for the given material, it is assumed that when the light source distance changes, α and the SR-LLI (that is, the gloss region) change.
3. Experiments
3.1 Apparatus
We developed a measurement apparatus for gloss unevenness based on visual inspection. Figure 5 shows a schematic diagram of the experiment. The measurement apparatus and geometry in the present experiment are the same as those in the previous study [20] except for the light source distance, as shown in Fig. 5. Figure 6 shows a photograph of the apparatus. The line light source aperture was 0.4 mm. The aperture length was 120 mm. The light source and camera angles were set to 45°. The light reflected from the sample was focused and a two-dimensional charge-coupled device (CCD) camera captured a digital image of the intensity distribution of the reflected light. The distance from the camera to the center of the sample bed was 250 mm. The camera distance was adjusted to match the near point of the human eye during visual inspection. The distance from the light source to the center of the sample bed was 125, 250, or 500 mm.
Fig. 5. Schematic diagram of the experiment. The incident light angle and the camera angle are both 45°. The camera distance is 250 mm. The light source distance (Dlight) is 125, 250, or 500 mm.
The image resolution of the CCD camera was 1920×1200 pixels. The center 1200×1200 pixels were used. The output level was 12 bits per pixel. The pitch of a pixel corresponds to 0.037 mm on the object plane. The output values can be used as the light intensity because of the linearity between them, which was confirmed in advance. The sample material was set on the sample bed, and an image was captured in a dark room. We prepared and measured black glass, whose refractive index is 1.567, for calibration of the measured values. The focal length of the lens was 12.5 mm. The F-number of the lens was 1.2.
For the apparatus, both the camera and sample are fixed and the line light distance is varied. Because the camera and sample positions are fixed, the positional relationship of the captured images does not change. Images can thus be combined using a cut and paste process.
3.2 Samples and captured images
Six types of sample were measured. A black glass plate with a sample refractive index of 1.567 was used for calibration and reference (denoted as BG). Three types of photo-like inkjet paper, namely high gloss (denoted as IJ-HG), medium gloss (denoted as IJ-MG), and low gloss (denoted as IJ-LG), were used. Two types of glossy printing paper, namely high gloss (denoted as PP-HG) and medium gloss (denoted as PP-MG), were also used.
Images were captured by the camera on the apparatus. The results are shown in Fig. 7. As shown, the apparent gloss unevenness region increases with light source distance.
Fig. 7. Gloss unevenness images obtained using the proposed apparatus. The light source distances are shown in parentheses. (a1-a3) Black glass, (b1-b3) IJ-HG, (c1-c3) IJ-MG, (d1-d3) IJ-LG, (e1-e3) PP-HG, and (f1-f3) PP-MG.
3.3 Relationship between light source distance and apparent gloss unevenness
Equations (1) and (2) indicate that a longer light source distance leads to a wider specular reflection region when a point light source is used. In this experiment, the camera distance was fixed at 250 mm. As shown in Fig. 7, the specular reflection region in the captured image becomes wider with increasing light source distance. We investigated the relationship between α and this spread. The distribution of the observed specular reflection is the SR-LLI. The one-dimensional average of the SR-LLI was calculated. To quantify the magnitude of this region, the full width at half maximum (FWHM) is used. The ratio of the FWHM values was calculated. Figure 8 shows the profile for IJ-MG.
Figure 9 shows the theoretical relationship between the light source distance and the ratio α. The ratio α is 0.50 when the light source distance is 250 mm. According to Eq. (2), α is 0.33 when the light source distance is 125 mm and 0.66 when it is 500 mm.
Figure 10 shows the relationship between theoretical and measured ratio α for five samples. In each sample, the ratio α was calculated as the ratio of FWHM when the light source distance is 125 mm. The ratio α is 1.0 when the light source distance is 125 mm. For comparison with the theoretical value, the ratio α was converted to 0.5 when the light source distance is 250 mm. The experimental results are in good agreement with the theoretical values, as shown in Fig. 10.
4. Discussion
4.1 Improvement of visual inspection for gloss unevenness
We confirmed that there is a relationship between the observed specular reflection region and the light source distance. The gloss unevenness region becomes wider with increasing light source distance (Fig. 7), which facilitates the visual inspection of gloss unevenness. According to Eq. (2) and Fig. 9, the specular reflection region can be enlarged by increasing the light source distance, but the increase of α gradually levels off. Theoretically, α converges to 1.0 when the light source distance is infinite. At that case, the light-source light will be as close to parallel light as possible. However, the surface of the sample to be measured must be illuminated by the light. Decreasing the camera distance increases the specular reflection region. For a human observer, the shortest focus distance is about 250 mm, as set here. Equation (2) can be used to design the measurement device.
4.2 Simultaneous measurement of gloss unevenness and SR-LSF
In this paper, we proposed an apparatus for improving the visual inspection of gloss unevenness that uses an SR-LSF measurement device. Therefore, the SR-LSF and gloss unevenness can be measured at the same time. To improve the visual inspection of gloss unevenness, the light source distance should be longer than the camera distance.
4.3 Alternative technique for detecting gloss unevenness in large area
There is a limit to the range of gloss unevenness that can be measured by a camera or the human eye at one time. The conventional method for measuring gloss unevenness over a wide range of the sample is to measure several sections of the sample and then combine the measurement results. We propose a method that takes advantage of the features of the proposed apparatus. Images of several gloss unevenness regions are combined to reconstruct the image of the entire gloss unevenness region. When the light source is moved parallel to the sample surface, the measured region of gloss unevenness on the sample moves simultaneously. Because the gloss unevenness region that can be measured at one time is wide, the objective can be achieved by moving in several steps. The camera and sample are fixed, so it is easy to combine the captured images. The images of the gloss unevenness region are combined to reconstruct an image of the entire gloss unevenness region (Fig. 11).
Fig. 11. Schematic diagram of image processing for the reconstructed image of the entire gloss unevenness region. Images of several gloss unevenness regions are combined to reconstruct the image of the entire gloss unevenness region. The sample is IJ-MG.
4.4 Detection of scratches and coating unevenness
As an application of the proposed technology, we consider the detection of scratches and coating unevenness in industrial quality control. Under diffuse light, it is difficult to detect fine scratches and slight irregularities. There is a known technique for detecting in a gloss unevenness region such scratches and coating unevenness. In this technique, the size of the gloss unevenness region is important. Even if there are scratches or coating unevenness regions that can be confirmed by inspection over a large area, only a partial difference in gloss can be judged in a narrow range. The effect of light source distance can be used when considering the observation conditions for the visual inspection of gloss unevenness.
The measurement apparatus is shown in Fig. 12. A second light source with a diffuser was added to this apparatus. We can capture images obtained with two kinds of reflection, diffuse reflection and specular reflection. We tested inkjet paper (IJ-MG). As shown in Fig. 13, the sample had five levels of scratches caused by a cutter knife. Also, the sample had five levels of coating unevenness caused by an adhesive. Markers were attached above and below scratches and coating unevenness regions to indicate their positions. Figure 14 shows the captured images obtained with specular and diffuse reflection. It can be seen that detection with specular reflection is better.
Fig. 12. Photograph of the measurement apparatus for gloss unevenness based on visual inspection. A second light source with a diffuser is used to take an image of sample surface in normal conditions.
Fig. 13. Diagram of test sample. The sample has five levels of scratches and coating unevenness caused by a cutter knife and adhesive, respectively. Markers above and below the scratches and coating unevenness regions indicate their positions.
Fig. 14. Images obtained with specular reflection (right) or diffuse reflection (left). In right upper photograph, the scratches are clearly observable. In right lower photograph, the areas with coating unevenness are clearly observable.
5. Conclusion
The relationship between the light source distance and the apparent gloss region was quantified. It was found that when a point light source is used, it is possible to visually inspect gloss unevenness in a wider area if the distance of the light source is increased. Scratches and coating unevenness that can be detected in a wide region of inspection may not be detected in a narrow region. Being able to calculate the size of the region of uneven gloss is useful for the design of future measuring devices. The proposed measurement apparatus was originally proposed for SR-LSF measurement. Therefore, gloss unevenness and the SR-LSF can be measured at the same time, making the proposed apparatus useful for a comprehensive measurement of gloss.
Funding
Institute for Global Prominent Research, Chiba University.
Disclosures
The authors declare no conflicts of interest.
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