The 19th Korea -Japan Joint Workshop on Frontiers of Computer Vision

A Simulation of Multilayer Thin-film Interference
for Pearl Material Preproduction
Kensuke Tobitani

School of Science and Technology
Kwansei Gakuin University
Hyogo, Japan
Email:tobitani@kwansei.ac.jp

Atsushi Ishida

School of Science and Technology
Kwansei Gakuin University
Hyogo, Japan
Email: atsushi.ishida@kwansei.ac.jp

Akihiro Okada

Naris Cosmetics Co.,Ltd.
Research & Development Department
Osaka, Japan
Email: a_okada@naris.co.jp

Lisa Park

School of Science and Technology
Kwansei Gakuin University
Hyogo, Japan
Email: lpark@kwansei.ac.jp

Abstract-Visual simulation using computer graphics and virtual reality has come to be used recently in the production process
to enhance the quality of materials and products. In this paper,
we propose a simulation of multilayer thin-film interference
for pearl material preproduction such as cosmetic development.
Pearls manifest a very specific optical phenomenon caused by themultilayer thin-film structure, and most people have a common
sense that pearls have a own beauty. Therefore, the expected
merits of the simulation are not negligible. The author of thispaper have reported a method of modeling and visualizing perfectsphere pearls. For a construction of the simulation system fora preproduction, it is necessary to apply the visualizing method
to free-form surface, and consider the changes of blurring andinterference color due to view angle which was not mentioned
in the earlier research. As the results, we implemented the pearl
visual simulation method as a plug-ins material shader of 3D
computer graphics software MAYA and generated high-quality
pearl and free-form surface 3D images with optical properties
similar to pearl.

I. INTRODUCTION
In the area of materials development, preproduction using
visual simulation has come to be considered essential[ 1]. In
this paper, we propose a simulation of multilayer thin-film
interference for pearl material preproduction such as cosmetic
development. The author of this paper began research using
machine vision technology in 1992[2][3] for the evaluationof pearl quality requiring intuitive expertise, even during
inspection in the production process. Pearls, widely known
as jewelry items, have a multilayer thin-film structure anddisplay a unique rainbow color and a lustrous iridescence
due to the diverse behavior of light, such as refraction,interference, diffraction, multiple reflection, etc.[4]. Therefore,
the modeling and visualization of a pearl with specific opticaland structural features is an interesting theme. The study of avisualization of optical phenomenon in multi-layered structure
has previously been reported[5][6], however, no research has
yet been performed on a visualization of multilayer thinfilm interference as typified by pearls. Nagata and coworkers

978-1 -4673 -5621 -3/13/$31.00 02013 IEEE

Kumiko Nishiyama

Naris Cosmetics Co.,Ltd.
Research & Development Department
Osaka, Japan
Email: kumiko_nishiyama@naris.co.jp

Noriko Nagata

School of Science and Technology
Kwansei Gakuin University
Hyogo, Japan
Email:nagata@kwansei.ac.jp

succeeded in [7] in achieving a realistic representation of apearl ("pearl-like quality") by means of three principal factors,
namely, the interference component, mirroring component, andtexture component using physics-based modeling. Dobashi
and coworkers indicated the importance of the blurring oflight, as a fourth factor, to improve the representation of adelicate appearance, and proposed its computational model andcalculation algorithm[8]. Further, a new model named "partial
coherent model"was also proposed, including coherent light,
in addition to the incoherent light so far considered in thevisualization of the interference phenomenon in [7]. In theseresearches[7] [8], they succeeded in generating high-quality
perfect sphere pearl CG image. It is, however, necessary for thesimulation to apply the visualizing method to free-form surface
from the view point of preproduction of material development.
This paper proposes a simulation of multilayer thin-film
interference for pearl material preproduction such as cosmetic development. Pearls manifest a very specific opticalphenomenon, and most people have a common sense which
pearls have a own beauty. Therefore, the expected merits ofthe simulation are not negligible. The author of this paper
have reported a method of modeling and visualizing perfectsphere pearls. For a construction of the simulation system fora preproduction, we apply the visualizing method to free-form
surface, and consider the changes of blurring and interferencecolor due to view angle which was not mentioned in the earlier
research.
II. COMPUTATIONAL MODEL OF A PEARL BASEDON PHYSICSThis section deals with the previously announced
model[7] [8] of multilayer thin-film interference of a pearl,blurring of light and the pearl image synthesis algorithm
required to explain the simulation method in this paper.

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The 19th Korea -Japan Joint Workshop on Frontiers of Computer Vision

A. Computational Model of Multilayer Thin-Films Interference Based on Physics
Pearls show a very specific optical phenomenon that is notseen in the normal thin-film interference. The color fringechanges concentrically from the center of the sphere and,also, can be observed even on the part where light does
not hit directly. In other words, the interference color of apearl depends solely on the viewing direction and not on the
direction of the light source.

Fig. 1.

C. Synthesis of a Pearl Image based on illuminant Model

The synthesis algorithm is based on three psychologicalfactors, namely, the sense of depth, brightness, and grain, usedpreviously by Nagata and coworkers in their psychologicalexperiments to evaluate the pearl[3]. In other words, theinterference component, mirroring component, and texture
component, corresponding to the psychological factors, aresynthesized on the diffuse reflection component image. The
components and a synthesized image are shown in Fig. 2. Using these methods, a pearl has been successfully represented.
However, some experts pointed out the lack of the sense ofbrightness in the synthesized images. The sense of brightnessof a pearl is a material feeling deeply related with not only
the intensity of specular light, but the senses of transparency
and of gloss. In the next subsection, the representation of thesense of brightness is explained.

A physical model of multilayer thin films of a pearl.

The optical model of multilayer thin films of a pearl shownin Fig. 1 can be used to explain this phenomenon. The incident
light is distributed to the whole pearl layer through repeatedreflection and refraction. As a result, it appears as if eachpoint in the layer had a point light source transmitting rays inall directions (called an "illuminant model"). Each ray causes
local interference, and interference lights are propagated inall directions outside the pearl. Taking account of only theinterference light waves propagated in the viewing direction
and in Fig. 1, the light from each point on the concentric
circle is the interference light propagated with the same angleof refraction, so that the phase difference, i.e., the spectrum
distribution, must be equivalent. This accounts for the factthat the hue of the interference light does not depend on the
direction of the light source and shows concentric circularchange.

B. Calculation Algorithm of Interference Light Spectrum
The power spectrum of interference light is calculated in
the following manner. First, rays are cast from the viewpoint,
and, for all rays intersecting rays with the pearl surface, theincident angle, reflectance, and transmittance are calculated.
Next, interference calculations are made from the outer layer tothe inner layer of the nacreous layer for all visible wavelength
bands, in order to obtain the spectral power. By converting thespectrum obtained into an RGB image, an interference lightcomponent described in the next subsection, is generated.

Fig. 2.

Components of a synthesized image.

D. Blurring Model of Pearl Due to Subsurface Reflection
The blurring in a pearl can be explained as follows. The
quite high transmittance of the nacreous layer causes the light
to be repeatedly reflected and transmitted inside the layer. As
a result, the spread of light inside the layer tends to have theproperty of reflection and transmission rather than scattering.
The blurring of light in the nacreous layer is attributed to the
spread of light due to the deviation of light from the directionof the regular reflection. In order to represent the blurring
caused by the subsurface reflection, two models, based on
the Monte Carlo method and on the reflection distribution,
were proposed and compared in [8]. An example of theblurring component image synthesized based on the reflection
distribution is given in Fig. 3, showing clearly the light source
image at the center and the blurring around it.

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The 19th Korea -Japan Joint Workshop on Frontiers of Computer Visionand blurring gives a synergistic effect to further improve thesense of brightness, proving that blurring is an important factor
in the visualization of a pearl.

Fig. 3.

An image showing blurring.

E. Partial Coherent Interference Model
In Subsection A, the interference phenomenon independentof the direction of light source was taken into consideration to visualize the characteristic of the pearl interference
phenomenon. However, even this model failed to describe
fully the pearl interference phenomenon. Interference light,
the hue of which changes as the light source is moved, isfound inside the shell of a pearl oyster, the mother shell ofpearl, with a flat nacreous layer like that of a pearl. This
indicates that the general thin-film interference also occurs in
the nacreous layer, and a careful observation of the pearl showsthat the highlight does get slightly colored, which contributes
to the improvement in pearl-like quality, especially in the senseof brightness. In other words, the interference phenomenon
observed in a pearl is the mixture of the interference ofhighlight (spatial coherent light), dependent on the directionof the light source, and the interference of multiple reflectionof light (spatial incoherent light), so that it is necessary to takeaccount of both elements in order to carry out modeling of theinterference seen in a pearl and to synthesize the pearl images.
This model was called as the "partial coherent model"in [8]since both coherent and incoherent light are taken into account.

F Synthesis of a Pearl Image based on Partial Coherent
Model
Examples of synthesized images obtained through the partial coherent model and the blurring model mentioned in theabove subsection are given in Fig. 4, with Fig. 4(a) showing animage of diffuse component, Fig. 4(b) showing the interferencecomponent of incoherent light obtained through the illuminantmodel, Fig. 4(c) showing mirroring component and blurring
component with the interference component of coherent lightobtained through the partial coherent interference model andFig.4( d) showing synthesized pearl image containing all four
components. Both the concentric hue distribution of interference light and the coloring of highlight are visualized with nosense of incompatibility, providing an additional feel of pearllike quality, and slightly contributing to the improvement in
the sense of brightness. Further, the contrast between highlight

Fig. 4.

Images of each components and synthesized pearl.

G. Implementation to the Simulator

A visual pearl-quality evaluation simulator was built using
the visualization technique[5], in order to synthesize the virtual
pearl images. Virtual sample images of various qualities canbe synthesized by manipulating the following parameters:
1) sense of depth (intensity of interference component anddiffuse reflection component);2) sense of brightness (directivity of the specular reflection
and distribution of blurring);
3) sense of grain (texture strength);4) object color (hue of diffuse reflection component);5) interference color (hue of interference component);6) direction of light source.
High-quality pearl CG images can be generated with thesimulator. The generable images are, however, limited tohaving a spherical shape. Further, the light source is limited toa parallel light. In the next section, we propose a generalizationof the pearl visual simulator for a pearl material preproduction
by expansion of the blurring model and applying the methodof visualizing pearls to general-purpose 3D computer graphics
software MAYA as plug-in material shader for free-form
surface modeling.

III. GENERALIZATION OF THE PEARL VISUALSIMULATOR
In this section, we describe a method to generalize the pearl
visual simulator mentioned above.

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The 19th Korea -Japan Joint Workshop on Frontiers of Computer Vision

A. Expansion of Blurring Model
The pearl visual simulator described in Section II cangenerate only perfect sphere. Consequently, the generated
image depends on only light angle regardless of view angle.
For the generalization, It is necessary to expand the blurringmodel by considering view angle. Therefore, we review thesimulation using Monte Carlo method to represent the blurringof light considering view angle.
1) Simulation Using Monte Carlo Method: The Monte
Carlo method, which is also applied to the calculation of lightscattering. The stochastic process of tracing the reflection andtransmission is repeated for the light entering the nacreous
layer with a certain incident angle, and the intensity of thelight finally leaving the surface is integrated for each outgoingdirection to obtain the whole reflection distribution for acertain incident angle. The same process is carried out foreach incident direction to calculate the bidirectional reflectance
distribution function(BRDF), i.e., the reflectance distributionfunction with the incident direction and reflection direction
as variables. We describe the BRDF in the form of a lookup
table(LUT). The calculation procedure is illustrated in Fig. 5.

layer or the intensity of the light falls below the thresholdvalue.
Through repetition of the process of adding the intensity of
the light to the solid angle containing the exit direction Bout,
we can obtain the reflection distribution for a certain incident
angle. By carrying out the same process for all incident angles,
we can obtain the BRDF. We simulated the method underconditions which the number of aragonite crystal layer andconchiolin layer is 500, the refraction index of aragonite
crystal layer is 1.53, the refraction index of conchiolin layeris 1.43 and the slope of the microfacet is distributed normally.
Fig. 6 shows the BRDF for an incident angle of 30 degrees
using the aforesaid method. The BRDF shows asymmetricity
distribution of light with the direction of regular reflection as
the center, indicating that the blurring phenomenon is properly
simulated.

Fig. 6.

Fig. 5.

Simulation using Monte Carlo algorithm.

First, it is supposed that a light ray enters the layer with
the incident angle Bin, and is reflected or transmitted by amicrofacet with normal vector and with a slope Bn or m against
the normal vector of the layer. The slope of the microfacet
is stochastically determined in the following manner by using
the microfacet distribution function.

Bn or m == f(R)(1)

Here, R are uniform random numbers, and function f is
the probability density function of the normal distribution.
Whether to trace the reflection or the transmission of lightis determined stochastically. The incident angle is obtained
from the normal direction of the microfacet, and the reflection/transmission direction is calculated by using Snell's law.
The light energy after the reflection/transmission is obtainedby multiplying the current energy with the reflectance/ transmittance calculated by using Fresnel's formula. The processof tracing the light is repeated until the ray exits the nacreous

An example of BRDF by Monte Carlo algorithm.

Fig.7 shows a transition of the BRDF by changing theincident angle from 0 degree to 90 degrees at intervals of 10
degrees. As shown in Fig. 7, the asymmetricity shifts left side
to right side of the distribution with increase the incident angle,
and the BRDF finally has a large peak value by influence ofFresnel reflection. Actually, we measured BRDF of the underside of pearl oyster shell as shown in Fig. 8. Although the pearl
shell was not perfect flat surface, measured BRDF indicatesa similar tendency of the BRDF simulation. Therefore, it isreasonable to support that the blurring phenomenon is properly
simulated by the method.
2) Designing of Look-up Table: The BRDF with Monte
Carlo method described in foregoing section is determined byincident and outgoing elevation angle. For the application to
free-form surface, it is necessary to consider the alterationon the BRDF due to outgoing azimuth angle. We postulatethat the BRDF decay with increasing the difference between
incident azimuth angle and outgoing azimuth angle ¢ as shownin Fig. 9. Fig.l0 shows the BRDF for an incident angle of 30
degrees considering the decay due to difference of the azimuth
angle. We implement the BRDF considering azimuth angle as
LUT in plug-in material shader of 3DCG software MAYA for
application the blurring model to free-form surface.
3) Implementation of Partial Coherent Model: We implement the partial coherent model described in Section II in plug-

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The 19th Korea-Japan Joint Workshop on Frontiers of Computer Vision

Fig. 9.

Fig. 7.

BRDF decaying model.

Transition of BRDF.

Fig. 10.

BRDF considering azimuth angle

component and coherent light interference component. These
images represent texture component with bump mapping.
As shown in Fig.II and Fig.I2, we succeed to generalize
the pearl visual simulator by application to free-form surface.
IV. CONCLUSION

Fig. 8.

BRDF of pearl oyster shell.

in material shader of 3DCG software MAYA without major
modification.

B. Generation of Pearl and Free-form Surface CG Image
We generate 3D images of pearl and free-form surface
applied the pearl optical model on MAYA. Fig.II shows 3D
pearl image and Fig. 12 shows free-form surface with diffuse
component, interference component, blurring and mirroring

We have proposed a simulation method for pearl material preproduction by generalization of image synthesis algorithm and optical models of interference and blurring for
pearl visualization based on physics-based modeling. In orderto represent the blurring model considering view angle, amodel, based on the Monte Carlo method, were reviewed.
As for the representation of pearl interference, we adopted
the interference model for both coherent light and incoherent
light to visualize the physical phenomena more exactly. We
implemented these functions on 3DCG software MAYA as
plug-in material shader for application to free-form surface,and confirmed that this implementation was succeeded.
In the future, we plan to introduce natural fluctuations
and irregularities to build a model much closer to the actual
phenomena of a pearl. Further, we are determined to study
information compression and speeding up the calculation.

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The 19th Korea -Japan Joint Workshop on Frontiers of Computer Vision

Fig. 11.

Fig. 12.

Synthesized peal image with four components

Synthesized free-form surface with four components

REFERENCES[1] Maxfield, J., Dew, P. M., Zhao, J., Juster, N. P., Taylor, S., Fitchie,
M., Ion, W. J., and Thompson, M.,"Predicting Product Cosmetic Quality
using Virtual Environment,".
in Proceedings of 2000 ASME Design
Engineering Technical Conferences and Computers and Information in
Engineering Conference, Baltimore, Maryland, USA, 2000.
[2] N. Nagata, M. Kamei, M. Akane, and H. Nakajima, "Development of apearl quality evaluation system based on an instrumentation of eKanseif,".
in Trans. Inst. Elect. Eng. Jpn. C, vol. 112-C, no. 2, pp. 111-116, 1992.
[3] N. Nagata, M. Kamei, and T. Usami, "Factors identification using
sensitivity of layered neural networks and its application to pearl color
evaluation,".
Trans. Inst. Elect. Eng. Jpn. C, vol. 116-C, no. 5, pp.
556-562, 1996.
[4] K. Wada, "Pearl ". Tokyo, Japan: National Jewelry Association, 1982.
[5] J. S. Gondek, G. W. Meyer, and J. G. Newman, "Wavelength dependent
reflectance functions,". in Proc. Computer Graphics Annu. Conf. Series,
1994, pp. 213-220.
[6] Craig Donner, and Henrik Wann Jensen, "Light diffusion in multi-layeredtranslucent materials,". in ACM Transactions on Graphics, vol. 24, no.
3, pp. 1032-1039, July. 2005.
[7] N. Nagata, T. Dobashi, Y. Manabe, T. Usami, and S. Inokuchi, "Modelingand visualization for a pearl-quality evaluation simulator,". IEEE Trans.
Visual. Comput. Graphics, vol. 3, pp. 307-315, Oct./Dec. 1997.
[8] T. Dobashi, N. Nagata, Y. Manabe, and S. Inokuchi, "Implementationof a Pearl Visual Simulator Based on Blurring and Interference,".

IEEE/ASME Transactions on Mechatronics, vol. 3, no. 2, pp. 106-112,
June. 1998.

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