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Bull. Soc. Photogr. Imag. Japan. (2015) Vol. 25 No. 2: 25–30

Original Paper

Simulating Gloss of Curved Paper by Using the Point Spread Function of Specular
Reflection
Norimichi Tsumura*, Kaori Baba*, and Shinichi Inoue**

Abstract:

 e propose a method that uses the point spread function of specular reflection (SR-PSF) to simulate paper gloss. The SR-PSF isW
defined as the impulse response of specular reflection, which is the distribution of light intensity reflected from microscopic facets on
the surface of the paper. In this study, we used a flat sample holder and measured the SR-PSFs of six paper samples, each of which
had a different level of specular gloss. We then used two different methods based on the measured SR-PSFs to simulate the gloss ofcurved paper. The results show that the gloss of curved paper can be adequately simulated by using the measured SR-PSF of that paper.

Key words:

paper gloss, specular reflection, point spread function, reproduction

1. Introduction
Gloss is an important quality of printing paper, and during the
manufacturing process, the gloss (i.e., the sharpness of a reflected
light source on the surface) of the curved paper is tested visually.
Gloss is a specular reflection phenomenon in the field of optics.
Hunter and Harold summarize the results of many different materials and their glossiness rankings, and showed the six different criteria by which glossiness rankings are made 1). Their types of gloss are
specular gloss, sheen, contrast gloss, absence of bloom gloss, distinctness of image gloss and surface uniformity gloss. In this paper, we
focus on the specular gloss and distinctness of image gloss since thegloss of paper is mainly dominated by these two attributes.
Many reflection models have been proposed and are used in computer graphics software to simulate gloss 2-7). Technologies that canmeasure and characterize gloss based on the measured bidirectionalreflectance distribution function have been developed and used in
evaluations 6-16). However, most of them require long measurement
times and many images of the surface of the target object. We therefore assessed technologies for measuring gloss, particularly on paper,
as a point spread function of specular reflection (SR-PSF) 14-16). The
SR-PSF can be measured from a single image of the spread of specular reflection on the target paper.
In this paper, we propose a new method, which is not based onconventional reflection models, that uses the SR-PSF to simulate
the gloss on the surface of a curved paper. The SR-PSF is defined as
the impulse response of specular reflection. The conventional PSF is
used as a transfer function in image science 17), and it can be calculated from the modulation transfer function (MTF). There have beensome studies of the MTFs of diffuse reflections 18, 19), including one
Received: 19th, June 2015; Accepted: 15st, September 2015

*Department of Information and Image Sciences, Chiba University, CHIBA, JAPAN**Mitsubishi Paper Mills Limited, TOKYO, JAPAN

Figure 1 The apparatus for measuring the SR-PSF

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Bull. Soc. Photogr. Imag. Japan. Vol. 25 No. 2 (2015)

by the authors of this paper 18). The SR-PSF is an expansion of theconventional PSF for diffuse reflections into the specular reflection
on the surface of paper 14-16).
In the next section, we introduce a method for measuring the SRPSF of paper. In Section 3, we present the measurements that weused for the simulations. Two methods to simulate paper gloss areproposed, and the results of the simulations are shown and discussed.
We present our conclusions in Section 4.

2. Experiment
Point spread function of specular reflection (SR-PSF) 14-16) can bemeasured from a single image of the spread of specular reflection on
the target paper. This PSF is different from conventional PSF of
optical system. Conventional PSF is measured on the imagining
plane as the spread of point, but SR-PSF is defined in the following
collimator lens system. Figure 1 shows the apparatus that we used tomeasure the SR-PSF for the study presented in this paper. It wasdeveloped by one of the authors 14-16). Light from a pinhole lightsource is projected onto a sample paper through a collimator lenssystem. The light reflected from the sample paper is focused, and a
two-dimensional charge-coupled device (CCD) camera captures adigital image of the intensity distribution of the reflected light. The
captured image of the intensity distribution shows the SR-PSF of
the paper sample because it is an impulse response to the pinhole
light. The lighting and viewing angles were both set to be 75°, according to the standard method (as defined by the ISO 21)) for measuring the specular gloss of paper. In this apparatus, the pinhole ismade of a metal plate, and its diameter is 100 µm. The CCD camera
has 512×512 pixels, and it has an output level of 16 bits per pixel. In
the captured image, each pixel corresponds to 0.029 mm on thesample. The output values could be used as a measure of the lightintensity because we confirmed in advance that there was a linear
relationship between them. Each paper sample was set on the sample bed, and the SR-PSF was measured in a darkroom. We can ignore the diffuse reflection component in this geometry since thevalue of reflected specular reflection is strongly higher than diffuse
reflection. We also prepared and measured a sample of black glasswith a refractive index of 1.567, which was used to perform thealignment of the optical system by setting the SR-PSF for the blackglass is similar to the delta function.
To define the SR-PSF, we considered both macroscopic and microscopic facets, as shown in Figure 2. The macroscopic facets produce the visible curvature of the surface, and the microscopic facets
produce the lobe of the specular reflection. In this system for measuring the SR-PSF, since the angle of the macroscopic facet is fixed
and the paper is attached to a flat bed, the directions of the reflected
lights are determined by the angles of the microscopic facets of thepaper. Therefore, the distribution of the reflected light intensity results in the gloss on the paper, as measured by the SR-PSF that is an
impulse response to the pinhole light. In Figure 2, we define theangles of the macroscopic and microscopic facets as (θx,θy) and(θx’,θy’), respectively. In the actual measurements, the angle of themacroscopic facet was set to (0°, 0°), since the paper was placed on aflat bed.
Six types of samples, each with a different level of specular gloss,
were prepared from the same type of paper. Figure 3 shows the specular gloss, as measured by a gloss meter (GM-26PRO, Murakami
Color Research Laboratory), following a standardized procedure(ISO 8254-1:2009) 20). Figure 4 shows the SR-PSF values that were
measured by using the apparatus shown in Figure 1. The x’ and y’axes indicate the position of the pixel on image from the CCD camera. The z’ axis indicates the value output by the CCD camera. As
the specular gloss of the sample paper decreases, the measured SRPSF has a broader distribution, and the peak value of the SR-PSF

Figure 3

Figure 2 chematic diagram showing the macroscopic and microscopic
S
facets on a flat paper surface

Specular gloss of the sample papers used in this study

Figure 4 Measurements of the SR-PSFs.
The maximum value on the z’-axis was (a) 2000, (b) 600, (c) 400, (d) 150, (e)60, and (f ) 20.

Norimichi Tsumura, Kaori Baba, and Shinichi Inoue

Simulating Gloss of Curved Paper by Using the Point Spread Function of Specular Reflection

27

Table 1. Specifications of the imaging device used in this study

CameraNikon D3X

Polarizing filter

Nikon 62 SPL 2 62mm

Lens

Nikon AF MICRO NIKKOR 60mm 1:2.8 D

Shutter speed (sec) 1.6
F-number

ISO speed (sec)

32

200

decreases with decreasing specular gloss. It is difficult to estimate theshape of SR-PSF for the measured specular gloss. Then, it is required to measure the SR-PSF or propose the shape of SR-PSF togive expected gloss on paper for printing industries as is mentioned
in beginning of the next section.

3. Simulating the gloss on curved paper
3.1 Method
In the paper and printing industries, the gloss of paper is usuallyobserved by the curved paper. Therefore, it is expected to develop thesimulator for reproducing the appearance of gloss on the curved paper for acceleration of product development. Figure 5 shows a diagram of the methodology for simulating gloss on paper. First, afluorescent light was projected onto a cylindrically curved specular
object (of diameter 260 mm) in order to obtain an initial image. The
image function fmirror(x’, y’) was used to express the image of the object. Since the fluorescent light is not the pinhole, fmirror(x’, y’) is different from the SR-PSF of black glass. The size of fmirror(x’, y’) was
1512×1008 pixels, and at the center of the image, each pixel corresponds to 0.029 mm on the object; this resolution matches that of
the SR-PSF. Table 1 summarizes the specifications of the photographing device used in this study.
In this section, we discuss the two methods used to simulate thegloss on paper. In Section 3.2 (i), we introduce the convolution
method, and in Section 3.2 (ii), we introduce the kernel method. We
note that, for both methods, we normalized the measured SR-PSFs(shown in Figure 4) according to the specular gloss, so that the valueof the pixel for each SR-PSF corresponded to the reflectance.
( i ) Convolution method
In the first method, we performed a convolution between the SRPSF fSR-PSF(x’, y’) and the original image fmirror(x’, y’), as follows.

Figure 5

Methodology used to simulate gloss on paper

the paper fdiffuse(x’, y’). This diffuse image was captured by setting thepolarizing filter in front of the light source and camera with thecrossed Nicols arrangement, so that the gloss component was removed. We note that the paper sample was attached to a cylindrically curved object. The final process required to obtain the simulated
gloss for the curved sample paper is shown in Eq. (2).
fpaper(x’, y’)=fspecular(x’, y’)+fdiffuse(x’, y’) …(2)In Eq. (2), we assumed that the imaging system for observation
has enough length of depth of focus to ignore the PSF of the imaging system toward the light source in the experiment. We also assumed that the reflection model can be described by dichromaticreflection model.

fspecular(x’, y’)=∫∫ fmirror(x’’, y’’)fSR-PSF(x’-x’’, y’-y’’)dx’’dy’’ …(1)The SR-PSF fSR-PSF(x’, y’) was measured by the method shown in
the previous section. As was mentioned above, the image function
fmirror(x’, y’) was an image of mirror –like cylindrically curved object
as is shown in the top of Fig. 5. Then, the convolution between an
image of mirror-like object and SR-PSF will give us the simulated
gloss appearance. Here, it is noted that fmirror(x’, y’) and SR-PSF
fSR-PSF(x’, y’) are known function, and fspecular is the estimated functionused as the predicted appearance. It is also noted that convolution
operation is shift invariant operation, then SR-PSF fSR-PSF (x’, y’) issame at each position even if the curved area.
Next, we added the calculated fspecular(x’, y’) to the diffuse image of

Figure 6

Coordinate system of the apparatus used to measure the SR-PSF

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Bull. Soc. Photogr. Imag. Japan. Vol. 25 No. 2 (2015)( ii ) Kernel method
In the second method, we performed a kernel operation between
the transformed SR-PSF f ’SR-PSF(x’, y’, x, y) and the original image
fmirror(x’, y’), as follows.
fspecular(x’, y’)=∫∫ fmirror(x’’, y’’)f ’SR-PSF(x’,y’, x’’, y’’)dx’’dy’’ …(3)Here, f ’SR-PSF(x’,y’, x’’, y’’) is obtained by transforming the original
SR-PSF fSR-PSF(x’, y’) as a function of the angle of the cylindricallycurved specular object. It is noted that the Kernel operation can beused for shift variant operation, then f ’SR-PSF(x’, y’, x’’, y’’) can be varied with the change of angle of the curved specular object. In thefollowing paragraph, we will explain this transformation process.
In the measurement apparatus (Figure 1), the collimator lens system focuses the incoming parallel light rays onto a single point on
the CCD. Even though the light rays are parallel when they enter
the measurement apparatus, they reach different points on the CCD.
This is because, as shown in Figure 2, the angles of the microscopic
facets (θx’,θy’) vary, and so the angles of the light rays are changed
when they are reflected from the paper. Figure 6 shows the three-dimensional coordinate system of the measurement apparatus, where
the angle of the macroscopic facet (θx,θy) is set to (0°, 0°). The anglesof (θx,θy) are used to indicate the slope of curved paper. A light rayreflected from a microscopic facet with an angle of (θx’,θy’) is observed at the position (x, y, z), where y is the optical axis, x is perpendicular to y and lies in the plane of the sample bed, and z is normal
to the plane of the sample bed. The position (x, y, z) is calculated asshown here.

() (xsin(2(θx,θx’))cos(75°+2(θy+θy’))zcos(2(θx+θx’))cos(75°+2(θy+θy’))y =dsin(75°+2(θy+θy’))

)

…(4)

Here, d is the distance between the center of ample and center of
CCD. The CCD camera angle was fixed at 75 degrees. In this equation, position O is only considered on the sample. It can be said thatthe ray from different position of sample also give the same results
since the sample is illuminated collimated parallel light and reflected
light is observed by the focused point. The new coordinate systemcorresponding to the CCD camera is defined by (x’, y’, z’). The position (x’, y’) of the pixel in the image of the CCD camera was calculated by rotating the original position vector, as follows.

()(

x’
1
0
0
y’ = 0 cos(75°) sin(75°)
z’
0 -sin(75°) cos(75°)){( ) ( )}x0y -d sin(75°)
zcos(75°)…(5)

In this equation, rotated axis is x-axis in the Figure 6 to give thesensor image coordinate. When the angles of the macroscopic facets(θx,θy) are changed, the pixel positions that correspond to each angle of the microscopic facets (θx’,θy’) can be calculated by using Eqs.
(4) and (5). Therefore, with Eqs. (4) and (5), we can transform the
SR-PSF measured at (θx,θy) = (0°, 0°) to that measured at (θx,θy) =(Δθx, Δθy). In this paper, we will only consider a rotation of Δθx,since, with a cylindrically curved object, the paper is only bent in theθx direction. This geometry is the form most commonly used toevaluate the gloss of paper.

Figure 7 The transformed SR-PSFs for sample No. 5.
The values of angle Δθx were (a) 0°, (b) -2°, (c) +2°, (d) -4°, and (e) +4°.

As an example of the transformed SR-PSF, Figure 7 shows theresults for sample No. 5 in Figure 4(e). Figure 7(a) shows the measured SR-PSF for (θx,θy) = (0°, 0°). Figures 7(b) to 7(e) show thetransformed SR-PSFs as a function of Δθx, where (θx,θy) = (Δθx, 0°),for -4° ≤ Δθx ≤ +4°, at intervals of 2°. The white dots in Figure 7 showthe (x’, y’) that corresponds to the angle of the microscopic facets(θx’,θy’), where -4° ≤θx’,θy’ ≤ +4°, at intervals of 2°. This transformation can be considered as rotation for y-axis in 3 dimensional space.
These are examples of the transformed SR-PSF, practical application will be given in the next section by comparing the captured
images.
3.2 Results of gloss simulation
As was mentioned before, in the paper and printing industries,
the gloss of paper is usually observed by the curved paper. Therefore,
it is expected to develop the simulator for reproducing the appearance of gloss on the curved paper for acceleration of product development. In this sub-section, we will compare between the results ofgloss simulation and real appearance. Figure 8 shows the images that
resulted from simulating the gloss for six kinds of paper. In thesefigures, a logarithmic conversion was applied to the values of fpaper(x’,y’) because they were too dark to observe with a low-dynamic-range

Norimichi Tsumura, Kaori Baba, and Shinichi Inoue

Simulating Gloss of Curved Paper by Using the Point Spread Function of Specular Reflection

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Figure 9 The values of the pixels in the x’ direction for each image in Figure 8

Figure 8 Simulations of gloss on paper.
From left to right, the figures show the captured images, the images simulated by using the convolution method, and the images simulated by using thekernel method.

display. The figures on the left side, center, and right side show, respectively, the images of the real gloss, as captured by the camera,
and the simulated gloss from the convolution and kernel methods.
Figure 9 shows the pixel values for the x’ direction for each image in
Figure 8. These pixel values were obtained by averaging the pixel
values for the y’ direction; the values shown are the initial values
before the logarithmic conversion. By comparing the distributionsof the captured images to those of the simulated images, it can beseen that the gloss on the curved paper was simulated adequately formost of the samples. In all cases, the kernel method simulated thecaptured image better than did the convolution method. Figure 10
shows the half width at half maximum (HWHM) for each distribution of the pixel values shown in Figure 9. It is noted that the advantages of the kernel method can be seen particularly in Samples No.
4, No. 5, and No. 6, where the surface gloss is lower than it is in theother samples. We also performed the subjective evaluation for 6
subject. All subjects answered that the all images by Kernel method
is similar to the captured images compared with the images by convolution method. These results indicate that the transformation of
SR-PSF fSR-PSF(x’, y’) into f ’SR-PSF(x’, y’, x’’, y’’) is effective for simulating gloss.

Figure 10 Th e half width at half maximum (HWHM) for each distributionof pixel values shown in Figure 9

4. Conclusion
We measured the SR-PSFs of six paper samples, each of which
had a different level of specular gloss, and we then simulated thegloss intensity distribution by using the convolution and kernel
methods, both of which were based on the SR-PSF for an original
image of a cylindrically curved object with mirror-like reflection.
From the simulated results, we found that both methods are able toadequately simulate the gloss on paper, and that the kernel method
better simulates paper with low gloss.
In the micro facets, the shadowing and masking of facets cause
off-specular phenomena as in Torrance and Sparrow model2. In thispaper we ignore this phenomena. We need to consider this phenomena when the incident angle increases. We also need to consider toapply SR-PSF to other materials such as plastic and metal in future
works.

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Bull. Soc. Photogr. Imag. Japan. Vol. 25 No. 2 (2015)

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