A NEW AUTOMATED MEASURING INSTRUMENT FOR MINUTE
PHOTOELASTICITY
Kenji Gomi, Kensuke Ichinose and Yasushi Niitsu
Department of Mechanical Engineering,
Tokyo Denki University,
2-2 Kanda Nishiki-cho, Chiyoda-ku, Tokyo, 101-8457, JAPAN
ABSTRACT
This paper introduces the principles and execution of a new automated technique for minute birefringence measurements with
high spatial resolution, which requires only three phase-stepping images. To verify the new technique experimentally, a
precise crystal wave plate of having 10.0±4.7 nanometers in retardation with tolerance was used as a specimen. The
measurements of the retardation with standard deviation were found to be 10.6±1.06 nanometers, which agreed well and
narrowed deviation in spite of minute amount of retardation. To estimate the measurements accuracy of the angular orientation
of the birefringence, the angular position of the rotation stage for the specimen was rotated intermittently 10.0 degrees at a
time during the experiment. As a result, the measured offsets of the angular orientation were found to be 9.99±1.73 degrees
with standard deviation. It is concluded that the new automated technique with high spatial resolution is effective for minute
birefringence measurements.
INTRODUCTION
Recently, the production technology of precision devices, such as ultra large-scale integrated circuits (ULSIs) and sensor
devices have advanced significantly. These devices have been widely employed in mechanical and electrical apparatuses.
They consist of many components bonded or molded with resins. These complex systems sometimes break due to thermal
stress induced by a mismatch of thermal expansions. Therefore, the development of evaluation technology for minute stressstrain states in electrical devices is required in various fields. On the other hand, the production technology of optoelectronic
devices, for example, flat-panels and semiconductor laser modules has also advanced. For these optoelectronic devices, the
development of evaluation technology for minute stress-strain states is also required in various fields. For example, glasses of
flat-panels sometimes crack in production processes such as dicing process due to the residual stress induced by insufficient
heat treatments. Another example is the laser caps for semiconductor laser modules which may reduce data transmission
efficiency due to the thermal stress during operation of the laser modules.
Compared with other stress-strain measurement techniques photoelasticity has the distinct advantages of being nondestructive, convenient, real time, precise, and quantitative. A number of different techniques have been developed for
photoelastic stress-strain measurement. Kowa and Umeda [1] have developed Zeeman Laser technique; Clayton et al. [2],
Yamada et al. [3] and Liang et al. [4] developed an improved linearly polariscope; and Niitsu et al. [5-7] and Oakberg et al.
[8,9] developed phase-modulation technique. However, all of these techniques are influenced by environmental factors such
as room temperature due to the complication of them.
One technique that has become more widespread in recent years is phase-stepping for which Hecker and Morche [10] first
suggested the adoption of ptotoelasticity. Subsequently, developed and improved by Kihara [11], Patterson et al. [12-17],
Sarma et al. [18], Asundi [19], Umezaki et al. [20-21], Otani et al. [22], and Lesniak [23]. In order to obtain both optical
retardation (isochromatic data) and angular orientation of birefringence (isoclinic angle), all the phase-stepping techniques
require at least four multiple images or rotation of specimen or optical elements which will become a bottleneck of high-speed
measurement. In addition, the objectives of all the studies are not precision measurements of minute retardation but good
measurements of widespread orders of retardation.
The aim of this study is to introduce the principle and automated execution of a new technique for minute birefringence
measurement with high spatial resolution, which requires only three phase-stepping images, with no rotation of specimens or
optical elements. The new technique will be referred to as the “simplified-phase-stepping technique” in this paper.
INSTRUMENT AND PRINCIPLE
Instrument
Figure 1 and 2 show the arrangement of the automated instrument for minute birefringence measuring with high spatial
resolution. This instrument enables the simultaneous measurement of the optical retardation and its angular orientation of the
birefringence in a specimen without rotation of the specimen or optical elements using the simplified-phase-stepping technique.
A Helium-Neon (He-Ne) laser whose wave length is 632.8 nanometer and quarter-wave plate are used to provide
monochromatic and circularly polarized light input for the specimen that is set in the instrument.
In the case of measuring the state of stress-strain in semiconductors, this instrument will obtain the capability by only changing
the wavelength of the He-Ne laser and the quarter-wave plate to infrared one. A set of a beam expander and lens focuses the
laser beam in the specimen to obtain high spatial resolution in a small area.
After the circularly polarized light passes through the specimen, the light is elliptically polarized. The elliptically polarized light is
then split into three lights of intensity that pass through analyzers and lenses before being measured by a conventional CCD
(charge-coupled device) chip. The analyzers are arranged so that each light generates a different phase-stepped image. One
possible set of orientations for the analyzers is given in Table 1. The notations i1, i2 and i3 denote the intensities of each light.
The resulting images of the intensities can be used to generate a contour map of the optical retardation and the angular
orientation of the birefringence of the specimen. The lenses after the analyzers convert the emerging lights from the analyzers
into parallel lights to direct the different phase-stepping images.
Principle of the Simplified-Phase-Stepping Technique [24]
The simplified-phase-stepping technique, which sets out the exact measurements of minute retardations and its orientations,
requires only three light intensities and three analyzers but does not require any output quarter-wave plates. On the other hand,
the conventional phase-stepping technique, which is set out on wide-spread orders of retardation measurements, requires four
lights of identical intensity that pass through four output quarter-wave plates and four analyzers.
0.1m
Figure 2. Photograph of the instrument as shown in Figure 1
The three light intensities; i1, i2 and i3; given in Table 1 which pass through the analyzers can be expressed according to Jones’
matrix as follows:
2
i0
(1 − cos 2φ sin γ )
2
2
i
i 2 = 0 (1 + sin 2φ sin γ )
2
2
i
i3 = 0 (1 − sin 2φ sin γ )
2
i1 =
(1a)
(1b)
(1c)
where the notation i0 denotes the amplitude of the light emerging from the polarizer, γ and φ are the optical retardation and its
angular orientation of the birefringence of the specimen. These equations can be combined to solve for the angular orientation,
φ, and the related retardation,γ, by using the following equations:
φ=
⎛
i 2 − i3
1
tan −1 ⎜⎜
2
⎝ − 2i1 + i 2 + i3
⎞
⎟
⎟
⎠
(2)
⎛ − 2i1 + i 2 + i3 ⎞
⎟
⎟
⎝ (i 2 + i3 ) cos 2φ ⎠
(3a)
⎞
i 2 − i3
⎟.
⎟
⎝ (i 2 + i3 ) sin 2φ ⎠
(3b)
γ = sin −1 ⎜⎜
⎛
γ = sin −1 ⎜⎜
SPECIMEN AND EXPERIMENTAL
Specimen
To verify the simplified-phase-stepping technique experimentally, a crystal wave plate (Figure 3(a)) and synthetic sapphire disk
(Figure 3(b))were used as a specimen. The amount of the retardation with tolerance of the wave plate was 10.0±4.7
nanometers; the retardation was controlled by the thickness of the specimen by its provider. The surface of the synthetic
sapphire disk was (0001) crystal surface as shown in Figure 3(b),
(a) Wave plate with metal packaging
(0001) surface
t=0.28 mm
(b) Synthetic sapphire whose peripheral is metallized
Figure 3. Photographs of the specimens: (a) wave plate, (b) synthetic sapphire disk
Experimental Procedure with the Wave Plate
This experimental procedure consisted of three steps as follows. First, the wave plate as the specimen was mounted in the
instrument between its input quarter-wave plate and beam splitters as shown in Figures 1 and 2. Second, the intensities of the
three different phase-stepped lights were measured simultaneously. Third, to demonstrate the use of equation (2) to indicate
the angular orientation of the birefringence of the specimen, the specimen was rotated intermittently 10 degrees at a time.
Then, the second and the third procedures were repeated through 360 degrees.
Experimental Procedure with the Synthetic Sapphire Disk
Sapphire crystal generates its retardation as a function of the angle, θ, between the incoming ray and [0001] direction of the
crystal. Figure 4(a) shows a part of the experimental setup and the tilted sapphire as a specimen. This setup is the same one
in Figure 1 expects some focusing parts. Figure 4(b) shows the theoretical retardation of the sapphire as a function of the
tilting angle, θ. To measure the retardation in the sapphire precisely; the angle, θ, was controlled by using an optical lever as
shown in Figure 4(a).
Retardation, nm
This experiment was carried out as follows. Firstly, the crossed nicols were retuned after remove a beam expander and four
lenses from the instrument as shown in Figure 1. Secondly, the sapphire as a specimen was set in the instrument as shown in
Figure 4(a). Thirdly, the intensities of the three different phase-stepped lights were measured simultaneously. Finally, the
sapphire was tilted one degree and this final and the third processes were repeated until θ =10 degrees.
RESULTS AND DISCUSSION
With the Wave Plate
The validity of the simplified-phase-stepping technique is shown in Table 2. The first and second row in Table 2 that consists of
four rows shows the comparison of the retardation amount in the specimen with the precise estimation by the specimen
provider by thickness and the measurements with standard deviation using the simplified-phase-stepping technique. They
agree well in spite of the low-level of retardation.
The third row in Table 2 shows the measured birefringent angle of specimen for the measurement sequence (the specimen
was rotated intermittently 10 degrees at a time). The measured angles agree well with the 10 degrees rotation.
Therefore, the simplified-phase-stepping technique with automated execution was verified experimentally and shown to be
valid for measurements of low-level retardation such as 10nm and its orientation.
With the Synthetic Sapphire Disk
Figure 5 shows the results of the retardation measurement of the tilting sapphire disk. The square plots in the figure denote the
measured values and the solid curve near the plots shows its approximation. The approximation agrees well qualitatively with
the theoretical curve that is shown in Figure 4(b). Although it could not find the cause of difference between approximated and
theoretical curves, it is found that the instrument has a capability of qualitative measurement
25
20
15
10
5
0
2
4
6
8
, deg
Figure 5. Experimental results and its approximation
CONCLUSIONS
The principle and automated execution of the simplified-phase-stepping technique that requires only three light intensities of
phase-stepped image and is set out on the precision measurement of low-level amounts of retardation has been described
and discussed. The major findings are as follows:
(1) Using simplified-phase-stepping technique, the retardation of 10 nanometers is measured within the standard deviation of
approximately ±1 nanometers.
(2) It is found that the instrument has a capability of qualitative measurement by using a synthetic sapphire disk as a specimen
to generate an arbitrary minute birefringence.
Acknowledgments
This research was partly sponsored by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports,
Science and Technology; Tokyo Denki University Science Promotion Fund Q06M-03; and Funai Foundation for Information
Technology. The authors would like to acknowledge the experimental working of Suzuki, H. (a student of the Graduate school
of Tokyo Denki University), Tsukahara, Y., and Suzuki, T. (students of the school of Tokyo Denki University).
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
Kowa, H. and Umeda, N., “Automated Birefringence Measurement Using Infrared Transverse Zeeman Laser,” Japanese
Journal of Optics, Vol.19, No.7 (1990), pp. 464-471.
Clayton, R. D. et al., “Scanning Birefringence Mapping of Semi-insulating GaAs Wafers,” Proceedings of Semi-insulating
III-V Materials, 1992, pp. 211-216.
Yamada, M., “High-sensitivity Computer-Controlled Infrared Polariscope,” Review of Scientific Instrument, Vol. 64, No.7
(1993), pp. 1815-1821.
Liang, H. et al., “A New Method of Determining the Stress State in Microelectronic Materials,” Measurement Scientific
Technology, Vol. 7 (1996), pp. 102-105.
Niitsu, Y et al., “Stress Measurement of Transparent Materials by Polarized Laser,” Transactions of the Japan Society of
Mechanical Engineers, Series A, Vol. 59, No.559 (1993), pp. 600-605.
Ichinose, K. and Niitsu, Y., “Scanning Stress Measurement Method by Laser Photoelasticity (1st Report, Stress
Measurement by Synthesis Method),” Transactions of the Japan Society of Mechanical Engineers, Series A, Vol. 60,
No.572 (1994), pp. 1114-1119.
Niitsu, Y. et al., “Development of Scanning Stress Measurement Method Using Laser Photoelasticity,” JSME International
Journal, Series A, Vol. 40, No. 2 (1997), pp.143-148.
Oakberg, T. C., “Measurement of Low-level Strain Birefringence in Optical Elements using a Photoelastic Modulator,”
Proceedings of International Symposium on Polarization Analysis and Applications to Device Technology, SPIE Vol. 2873
(1996), pp. 17-20.
Oakberg, T. C., “Measurement of Low-level Strain Retardation in Optical Materials,” Proceedings of International
Symposium on Polarization: Measurement, Analysis, and Remote Sensing, SPIE Vol. 3121 (1997), pp. 23-27.
Hecker, F. W. and Morche, B., “Computer Measurement of Relative Retardations in Plane Photoelasticity,” Experimental
Stress Analysis, Weringa, H., editor, Martinuus Nijhoff, Dordrecht, (1986), pp. 532-542.
Kihara, T., “Automatic Whole-Field Measurement of Photoelasticity Using Linear Polarized Incident Light,” Proceedings of
9th International Conference on Experimental Mechanics, Copenhagen, Denmark, Vol. 2 (1990), pp. 821-827.
Patterson, E. A. and Wang, Z. F., “Towards Full-Field Automated Photoelastic Analysis of Complex Components,” Strain,
Vol. 27, No. 2 (1991), pp. 49-56.
Wang, Z. F. and Patterson, E. A., “Use of Phase-Stepping With Demodulation and Fuzzy Sets for Birefringence
Measurement,” Optics and Lasers in Engineering, Vol. 22 (1995), pp. 91-104.
Patterson, E. A. and Wang, Z. F., “Simultaneous Observation of Phase-Stepped Images for Automated Photoelasticity,”
Journal of Strain Analysis, Vol. 33, No. 1 (1998), pp. 1-15.
Ji, W. and Patterson, E. A., “Simulation of Errors in Automated Photoelasticity,” Experimental Mechanics, Vol. 38, No. 2
(1998), pp. 132-139.
Hobbs, J. W., Greene, R. J. and Patterson, E. A., “A Novel Instrument for Transient Photoelasticity,” Experimental
Mechanics, Vol. 43, No. 4 (2003), pp. 403-409.
Zhao, F. M., Martin, R. D. S., Hayes, S. A., Patterson, E. A., Young, R. J. and Jones, F. R., “Photoelastic Analysis of
Matrix Stress around a High Modulus Sapphire Fiber by means of Phase-Stepping Automated Polariscope,” Composites
Part A: applied science and manufacturing, Vol. 36 (2005), pp. 229-244.
Sarma, A. V. S. S. R., Pillai, S. A., Subramanian, G. and Varadan, T. K., “Computerized Image Processing for Whole-Filed
Determination of Isoclinics and Isochromatics,” Experimental Mechanics, Vol. 31, No. 1 (1992), pp. 24-29.
Asundi, A., “Phase-Shifting in Photoelasticity,” Experimental Techniques, Vol. 17, No. 1 (1993), pp.19-23.
20. Umezaki, E., Pinit, P. and Ogasawara, T., “Full-Field Automated Determination of Isoclinic Angles in Linearly Polarized
th
RGB Lights,” Proceedings of 12 Inter national conference on Experimental Mechanics (Bari, Italy), on CD-ROM, Paper
No. 198 (2004).
21. Umezaki, E., Ogasawara, T. and Pinit, P., “Principal-Stress Directions Determined from Gaussian-Blurred Color
Photoelastic Fringes, Proceedings of 2004 SEM X International Congress on Experimental and Applied Mechanics (Costa
Mesa, USA), on CD-ROM (2004), Paper No. 170.
22. Otani, Y., Shimada, T., Yoshizawa, T. and Umeda, N., “Two-dimensional birefringence measurement using the phase
shifting technique,” Optical Engineering, Vol. 33, No. 5 (1994), pp. 1604-1609.
23. Lesniac, J. R., “Status Report on Grey-Field Photoelasticity,” Proceedings of SEM Annual Conference, Portland (2001),
pp. 836-838.
24. Gomi, K. et al., “A New Measurement Technique of Low-Level Strain Retardation in Optoelectronic Materials,”
Proceedings of Electronics Systemintegration Technology Conference, Dresden (2006), pp. 257-262.