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Abstract
Gloss is evaluated based on not only the intensity of reflected light but also the sharpness of the light source image. In this paper, we discuss the line spread function of specular reflection (SR-LSF). We developed a measurement apparatus for the SR-LSF based on the visual inspection of gloss. The measurement results of six types of samples with different glossiness values are shown. These samples were measured using the point spread function of specular reflection reported previously by the authors to verify the SR-LSF. It is shown that the SR-LSF can be measured easily and efficiently from an image recorded for visual inspection.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Gloss, an important property of materials, affects product texture and thus appearance. Because gloss unevenness and surface appearance are easy to observe near regular reflections, a comprehensive visual evaluation based on gloss evaluation is performed in the paper industry. Because visual inspection images contain textures that are manually evaluated, the observation images are recorded as is. It is desirable to derive physical characteristics from such images.
When a printed image is observed under a light source, gloss on the surface is observed in addition to the printed image. In a dichromatic reflection model, the intensity of the reflected light is the sum of the diffuse reflection and the specular reflection. As shown in Fig. 1, part of the incident light is absorbed, scattered, and widely reflected in all directions. This is called diffuse reflection. The printed image is observed as a diffuse reflection phenomenon. Specular reflection is the mirror-like reflection of the light source from a surface. Specular reflection is a much more directional reflection. Gloss is a specular reflection phenomenon.
Gloss is evaluated based on not only the intensity of reflected light but also the sharpness of the light source image [1]. As shown in Fig. 2, a visual inspection of the sharpness of a specular reflection image on the surface of materials is often performed to estimate gloss. If the specular reflection image is sharp, we estimate that it has high gloss. This means that gloss can be estimated by measuring the sharpness of the specular reflection image. In this case, a line light source such as a fluorescent lamp is often used. We refer to this method as the line light source observation method.
Fig. 2. Photographs showing the visual inspection of paper gloss. The top, middle, and bottom photographs on the right respectively show high gloss paper, medium gloss paper, and matt paper.
The line spread function (LSF) has been used for sharpness analysis in image science [2]. LSF theory, which estimates the sharpness of an image, can be applied to analyze gloss. In this paper, we discuss the line spread function of specular reflection (SR-LSF), which is a transfer function that represents the characteristics of reflection, as discussed later. A similar transfer function, the point spread function of specular reflection (SR-PSF), has been previously analyzed by the authors [3–5]. The SR-LSF and the SR-PSF are reflection angle distributions of incident light. They are part of the bidirectional reflection function (BRDF). Research on BRDF measurement can thus be applied to SR-LSF measurement.
Reflectance at the deviation angle, called gonio-reflectance, can be measured using a goniophotometer [6]. As shown in Fig. 3, a goniophotometer has a movable detector for measuring the reflectance at various angles for a given angle of incident light. The SR-LSF is the gonio-reflectance distribution when the incident light is at a certain angle.
Gonio-reflectance measurements with a goniophotometer are difficult to perform, and thus many simpler BRDF measurement methods have been proposed. Measurement techniques for BRDFs, such as the SR-LSF, also called reflectometry, have been proposed for various lighting environments and observation conditions [7–10]. For example, Marschner et al. measured the BRDF from a single image, focusing on the wide range of reflection angles of convex samples [7]. The light source was not a line light source, but flash. Gardner et al. used a linear light source (width: 10 mm) to scan the sample surface at intervals of 1 mm to measure the reflectance of each part of the sample [8]. Although this technique efficiently measures the entire sample, it is not intended for measuring the fine characteristics of materials like the SR-LSF.
Becker measured the SR-LSF (referred to in the study as “LSF”) from the one-dimensional reflected light distribution on the sample surface with the light source and detector fixed under regular reflection conditions [9]. This technique is based on the same concept as that of the SR-LSF measurement method proposed in the present study. However, as described later, we further propose an SR-LSF measurement technique from visual inspection images and a simple simulation technique based on the visual inspection geometry.
The SR-LSF can be measured using any BRDF measurement technique. However, there are some limitations. The light source must be a line light source. To increase the angular resolution, the line width of the line light source must be narrow. The angular resolution of the detector must be high. There are few simple SR-LSF measurement techniques that meet these conditions. This paper proposes a method for easily measuring the SR-LSF, which is a physical quantity, from a specular reflection linear image captured for visual inspection.
We discuss the SR-LSF and apply it to analyze gloss. We developed a measurement apparatus for the SR-LSF based on the visual inspection of gloss. The image obtained by the apparatus is equivalent to that obtained for human visual inspection. We propose an SR-LSF measurement technique based on this image. The measurement results of six types of sample with different glossiness values are shown. The samples were measured using the SR-PSF previously reported by the authors to verify the SR-LSF. In addition, gloss unevenness was measured using the SR-LSF and the inspection image. We demonstrate that the appearance of the observed (measured) image can be simulated using the SR-LSF. We discuss the advantages of the proposed gloss analysis based on the SR-LSF.
2. Theory
2.1 Line spread function of specular reflection
The LSF is of importance in many measurements used to determine image quality [2]. The advantages of the LSF are that it is a one-dimensional function and that it is easy to use and measure, as shown in Fig. 4.
The spread of the measured line image is defined as the LSF, which is a one-dimensional integral of the point spread function, as follows:
where x and y are positions.Here, we discuss the SR-LSF. The authors previously reported the SR-PSF, which is a gonio-reflectance distribution [3]. The SR-PSF can be defined as the gonio-reflectance distribution of incident point light with a constant angle. The universal method for describing the physical gonio-reflectance properties is the BRDF. The SR-PSF is part of the BRDF. The SR-LSF is thus the gonio-reflectance distribution of incident line light with a constant angle. The SR-LSF is a one-dimensional integral of the SR-PSF, as follows:
where θ is the azimuth angle of the y axis and φ is the azimuth angle of the x axis. The SR-LSF can be measured from SR-PSF integration. As described later, we verify the proposed SR-LSF measurement technique by measuring the SR-PSF of the same sample.2.2 Reflection line light observation method
The light reflected by an object is evaluated by visual inspection. Gloss is a specular reflection phenomenon. The measurement geometry is important because gloss depends on the angle of reflection. Measurement methods for gloss have been studied [11,12], and a standardized method of measuring gloss has been developed [11,12]. ISO 2813 specifies a method for determining the gloss of coatings using the three geometries of 20°, 60°, and 85°. Difference angles used depending on the reflection strength of the object. ISO 8254-1 specifies a method for measuring the specular gloss of paper at an angle of 75° to the normal to the paper surface. Japanese Industrial Standard, JIS, Z 8741 specifies a method for determining the gloss of materials using the five geometries of 20°, 45°, 60°, 75°, and 85°.
Gloss is generally evaluated by reflecting a line light source onto the object surface. This visual observation method is similar to that for the SR-LSF measurement technique. Figure 5 shows a schematic diagram of a line light observation method based on visual inspection. An observer pays attention to 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 line light source image. When an individual observes the appearance of the surface of a sample in detail, he/she observes it at a position close to the sample within the focused range. For this reason, the geometry for this experiment was set to 250 mm, which is the near point of the human eye. When a human observes the image, he/she observes it in the normal direction of the sample, that is 0°, but an angle is needed to observe the specular reflection. For this reason, the geometry of 45° was chosen as the reflection angle for this experiment. According to the standard, the gross unit of measurement was the relative value of the amount of reflection of a black glass plate with a refractive index of 1.567.
Fig. 5. Schematic diagram of the line light observation method based on visual inspection. The incident light angle and viewing light angle (reflection angle) create combinations.
The line light source can be, for example, a fluorescent light. Since a narrower line width of the line light source is better, the equipment 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 is different at each position on the surface of the observed object. Human eyes have a viewing angle. Therefore, in this method, the incident angle and the observation angle at each position on the object surface create combinations. As mentioned above, the SR-LSF is the gonio-reflectance distribution when the incident light is at a certain angle. It does not meet the SR-LSF definition.
2.3 Measurement of SR-LSF by light shift method
The SR-LSF can be measured using the reflection line light source observation method. By shifting the line light source, different reflection angles can be obtained for a given incident light angle, as shown in Fig. 6. The image is measured at each line light source position. This image is here called the line light image of specular reflection (SR-LLI). The SR-LSF is calculated from the light intensity at the SR-LLI position corresponding to the desired angle.
Fig. 6. Schematic diagram of the light shift method. The incident light angle is 45° at measuring position.
The measurement process of SR-LSF using the light shift method is as follows: The line light source sets by shifting to the position corresponding to the desired reflection angle. The image is captured and averaged in the direction of the line image. Here, the pixel corresponds to the position of the sample. The SR-LSF value of the desired reflection angle is the SR-LLI value at the pixel of the desired reflection angle. In each image, there is only one position where the incident light is at 45°. Therefore, an image in which the line light position is shifted for each desired reflection angle is required.
2.4 Measurement of SR-LSF by SR-LLI conversion method
We now describe a technique for measuring the SR-LSF with a fixed line light source.
Because the shift of the light source, Δx, is parallel to the sample surface, the position where the light intensity for the SR-LSF is measured is shifted by the same amount, Δx, on the sample surface. The regular reflection position is also shifted according to the light shift. The regular reflection position can be calculated, and thus the position where the light intensity is measured for the SR-LSF, Δx, can be estimated from the position of the new regular reflection. The SR-LSF (Δx) can be obtained from images (SR-LLI) measured by shifting light by Δx. In each image (SR-LLI), the position of regular reflection is also shifting proportionally. The distance Δx from the origin can thus be estimated from the position of regular reflection in the image (SR-LLI). The deviation from the origin of the angle seen from the camera, Δθ, corresponds to the deviation position from the origin, Δx, as shown in Table 1. The relation between the SR-LSF and the SR-LLI is as follows:
Table 1. Reflected light angle at each light source position, Δx.
Equations (3) and (4) are derived from the positional relationship between the camera and the light. In this experiment, the distance between the sample center and the camera position was set equal to the distance between the sample center and the light position. For this reason, the height of the camera is equal to the height of the light in Fig. 7. In Equation (4), α is 1/2 in this geometry. Since the light has shifted from the origin by Δx, the position of the new specular reflection will be the midpoint of the Δx. This is the ratio of two triangles, camera and light, as geometry. One is the triangle of camera height, camera position, and the regular reflection point on the sample. The other is the triangle of light height, light position, and the regular reflection point on the sample. The ratio is constant because the light height does not change as the light shifts. Δθ is a function of Δx. The SR-LSF can be calculated from the SR-LLI in Equation (3).
3. Experiments
3.1 Apparatus for measuring SR-LSF
We developed a measurement apparatus for the SR-LSF based on the visual inspection of gloss. Figures 7 and 8 show the apparatus. The light reflected from the sample is focused, and a two-dimensional charge-coupled device (CCD) camera captures a digital image of the intensity distribution of the reflected light. The line light source aperture is 0.5 mm. The aperture length is 120 mm. The light source and the camera angles are set to 45°. The distance from the light source to the center of the sample bed is 250 mm. The distance from the camera to the center of the sample bed is also 250 mm. The camera distance was adjusted to match the near point of the human eye during visual inspection.
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 darkroom. We prepared and measured black glass, whose refractive index is 1.567, for calibration of the measured values. The focal length of the lens is 12.5 mm. The F-number of the lens is 1.2.
The line light source was on a one-dimensional slide stage that moved from -20 mm to + 20 mm. This mechanism can be used for measuring SR-LSFs by the light shift method. In the apparatus, the camera is fixed and the sample is fixed. The line light is mounted on a precision one-dimensional slide stage, which is fixed in the default position. For this reason, after accurate assembly, measurement can be performed with high accuracy. In addition, verification was performed based on the movement amount of the slide stage and the measurement position of the specular reflection position of the black glass plate.
The developed device is similar to a goniophotometer. There are two important differences. The light source is a one-dimensional point light source. A point light source emits light in all directions from a specified point. The incident light angle thus depends on the position on the sample bed. The incident light in a goniophotometer is parallel light. Therefore, the incident light angle is constant in a goniophotometer. The optical system of the camera is a normal lens system and has an angle of view. The measured reflection angle thus depends on the position on the sample bed. The measured reflection angle in a goniophotometer is a value of each position of the detector. There are different combinations of illumination and measurement angles depending on the position on the sample bed in this apparatus. In other functions, the positions of the camera and sample are fixed, so the position of the image does not change as the light source shifts. The captured images can be easily processed.
Table 1 shows the relation between the position on the sample and the reflection angle in the apparatus. The line light source is on a sliding stage. This mechanism can be used for changing the position of the line light source. By shifting the line light source, the incident light angle can be 45° at the desired measurement position.
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.
The image was captured by the camera on the apparatus. The results are shown in Fig. 9. Figure 10 shows the profile of the light intensity averaged in the direction of the line. Here, the vertical axis is the relative intensity and the horizontal axis is the deviation of the reflection angle at each position of the image viewed from the camera.
Fig. 9. Reflection line images obtained using the proposed apparatus. The relative magnification at the time of measurement is shown in parentheses. (a) Black glass, (b) IJ-HG, (c) IJ-MG, (d) IJ-LG, (e) PP-HG, and (f) PP-MG.
3.3 Measurement of SR-LSFs by light shift method
The SR-LSFs of the samples were measured by the light shift method. Different reflection angles were obtained for a given incident angle, as shown in Table 1. The light source was shifted by 0.5° and measured in a range of ± 2.5°. Figure 11 shows the profile of the measured SR-LFSs. Here, the vertical axis is the relative intensity and the horizontal axis is the deviation of the reflection angle at each position of the image viewed from the camera. In this measurement, the IJ-HG sample with a small SR-LSF spread could not be measured well.
3.4 Measurement of SR-LSFs by SR-LLI conversion method
The SR-LSFs of the samples were measured by the SR-LLI conversion method. With this method, the SR-LSF can be measured with the camera, sample, and line light source all fixed. In addition, the SR-LSF can be measured from a single reflection image (SR-LLI) captured by the camera. The images (SR-LLIs) in Figs. 9 and 10 were used. The camera height and the light source height were the same in this experiment, and thus α = 1/2. This indicates that the spread of the SR-LSF is two times that of the SR-LLI. The results are shown in Fig. 12.
3.5 Measurement of SR-LSFs by SR-PSF integration method
We measured the SR-PSFs of the samples using the collimator method previously reported by the authors [3]. The SR-LSFs were calculated from the SR-PSFs using Eq. (2) to verify the measured SR-LSFs.
Figure 13 shows the profile of the SR-PSFs. The vertical axis (z) is the relative intensity and the horizontal axes (x and y) are the pixel values from the camera in the SR-PSF measurement apparatus. Figure 14 shows the SR-LSF profile calculated from the SR-PSF. The vertical axis is the relative intensity and the horizontal axis is the deviation of the reflection angle at the apparatus.
Fig. 13. Raw data of SR-PSFs measured by collimator method. The light source angle is 45°. The vertical axis (z) is the relative intensity and the horizontal axes (x and y) are the pixel values from the camera in the SR-PSF measurement apparatus. The relative magnification at the time of measurement is shown in parentheses. (a) Black glass, (b) IJ-HG, (c) IJ-MG, (d) IJ-LG, (e) PP-HG, and (f) PP-MG.
3.6 Comparison of SR-LSFs measured by three methods
We compared the SR-LSFs measured by the light shift method, SR-LLI conversion method, and SR-PSF integration method. Figure 15 shows the SR-LSFs obtained using these methods for each sample. The vertical axis is the relative intensity and the horizontal axis is the deviation of the reflection angle at the apparatus.
Fig. 15. Comparison of SR-LSFs measured by three methods. (a) IJ-MG, (b) IJ-LG, (c) PP-HG, and (d) PP-MG.
The SR-LSFs obtained using the three methods show the same trend for each sample, and have only slight differences. The SR-LSF obtained by the SR-PSF integration method has a slightly smaller spread. The SR-LSFs obtained by the light shift method and the SR-LLI conversion method are similar results. Although there are differences in the accuracy of the measurement methods, all measured SR-LSFs are considered to be practical.
4. Discussion
4.1 Advantage of measurement of SR-LSFs by SR-LLI conversion method
We introduced two measurement methods for the SR-LSF using an image, namely the light shift method and the SR-LLI conversion method. The results show that they are similar. This is achieved when the SR-LSF is similar as that of the SR-LSF within several degrees of regular reflection. In this case, the SR-LLI conversion method is easy and efficient. The SR-LSF can be measured easily and efficiently from an image recorded for visual inspection.
The SR-LSF measurement by the SR-LLI conversion method has two steps. In the first step, the profile of the reflected linear light source image (SR-LLI) under the set experimental environment is measured. In the second step, the SR-LSF is converted from the SR-LLI using Eqs. (3) and (4). The equation used for conversion is also simple. It is the ratio of the light source position to the camera position. When visual inspection is considered, the visual distance is constant at the near point (about 250 mm). If the position of the light source changes in the visual evaluation environment, the appearance will change. Thus, it is important to evaluate appearance based on physical quantities such as the SR-LSF.
4.2 Visual simulation by SR-LSF
The advantage of SR-LSF measurement is that it allows visual simulation. Three simulation approaches can be used. The first approach is computer graphics (CG). The characteristics of specular reflection have been modeled in CG [13–19]. Physics-based CG has been developed, and it uses the BRDF of materials [18]. Assuming isotropy and homogeneity, the SR-PSF can be estimated from the SR-LSF [2,3]. The SR-PSF is part of the BRDF and is a gonio-reflectance distribution of specular reflection. In addition, the authors previously investigated Perlin noise, which was proposed as a CG drawing technique, and reported an attempt to apply the SR-PSF as a mathematical model of paper surface shape [15,18].
The second approach is simulation by image processing. The gloss of an image can be simulated using a transfer function such as the SR-PSF [2]. The authors previously reported the simulation of gloss on curved paper using the SR-PSF [19].
The third approach is simulation using the SR-LLI conversion method proposed in this paper. The SR-LSF and the SR-LLI are related. If the SR-LSF is known, the SR-LLI can be calculated based on a simple ratio. This makes it very easy to simulate a visual change when the distance to the light source changes.
4.3 Application of captured image for appearance analysis
Appearance is generally evaluated by reflecting a light source onto the object surface. The image obtained by the apparatus developed in this study can be used for appearance analysis. For example, gloss unevenness can be seen near the regular reflection position in the image. It can be seen that the images measured with this apparatus show gloss unevenness and texture as shown in Fig. 9. These analyzes also require a psychological assessment. In relation to psychological evaluation, many studies have been conducted using gloss values as specular reflection characteristics [11,12]. It has been reported that gloss and appearance are affected by light intensity and geometry [20–22]. In recent years, research using BRDF has been advanced [23]. Nishida and Shinya studied surface-reflection properties using image-based information by using CG [24]. Wang and Luo studied the glint impression as a special surface effect [25]. Appearance analysis will be investigated by captured image using this apparatus in future research.
5. Conclusion
We discussed the SR-LSF and applied it to analyze gloss. We developed a measurement apparatus for the SR-LSF based on the visual inspection of gloss. The image obtained by the apparatus is equivalent to that obtained for human visual inspection. We proposed two SR-LSF measurement techniques based on this image. The measurement results of six types of sample with different glossiness values were verified using the SR-PSF. It was shown that the SR-LSF can be measured easily and efficiently from images recorded for visual inspection. The SR-LSF can be used to simulate the appearance of images. The obtained image can be used for appearance analysis. Gloss unevenness appeared near the regular reflection position in the image. In future research, the SR-LSF and image processing will be combined to analyze texture.
Disclosures
The authors declare no conflicts of interest.
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