A NEW AUTOMATED MEASURING INSTRUMENT FOR MINUTE PHOTOELASTICITY Kenji Gomi, Kensuke Ichinose and Yasushi Niitsu Department of Mechanical Engineering, Tokyo Denki University, - 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. [], 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. [1-17], Sarma et al. [18], Asundi [19], Umezaki et al. [0-1], Otani et al. [], and Lesniak [3]. 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 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 63.8 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 i 1, i and i 3 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 [4] 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. Photograph of the instrument as shown in Figure 1
The three light intensities; i 1, i and i 3 ; given in Table 1 which pass through the analyzers can be expressed according to Jones matrix as follows: 0 i 1 = i ( 1 cos φ sin γ ) (1a) 0 i = i ( 1 + sin φ sin γ ) (1b) 0 i 3 = i ( 1 sin φ sin γ ) (1c) where the notation i 0 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: 1 1 i i3 φ = tan () i1 + i + i3 1 i1 + i γ = sin γ = sin 1 + i ( i + ) cos φ i3 i ( i + ) sin φ i3 i 3 3 (3a). (3b) 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=0.8 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. Second, the intensities of the three different phase-stepped lights were measured simultaneously. Third, to demonstrate the use of equation () 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). 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. Retardation, nm
RESULTS AND DISCUSSION With the Wave Plate The validity of the simplified-phase-stepping technique is shown in Table. The first and second row in Table 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 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 5 0 15 10 5 0 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. () 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. 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, 199, pp. 11-16. 3. Yamada, M., High-sensitivity Computer-Controlled Infrared Polariscope, Review of Scientific Instrument, Vol. 64, No.7 (1993), pp. 1815-181. 4. Liang, H. et al., A New Method of Determining the Stress State in Microelectronic Materials, Measurement Scientific Technology, Vol. 7 (1996), pp. 10-105. 5. 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. 6. 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.57 (1994), pp. 1114-1119. 7. Niitsu, Y. et al., Development of Scanning Stress Measurement Method Using Laser Photoelasticity, JSME International Journal, Series A, Vol. 40, No. (1997), pp.143-148. 8. 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. 873 (1996), pp. 17-0. 9. 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. 311 (1997), pp. 3-7. 10. 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. 53-54. 11. Kihara, T., Automatic Whole-Field Measurement of Photoelasticity Using Linear Polarized Incident Light, Proceedings of 9th International Conference on Experimental Mechanics, Copenhagen, Denmark, Vol. (1990), pp. 81-87. 1. Patterson, E. A. and Wang, Z. F., Towards Full-Field Automated Photoelastic Analysis of Complex Components, Strain, Vol. 7, No. (1991), pp. 49-56. 13. 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. (1995), pp. 91-104. 14. 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. 15. Ji, W. and Patterson, E. A., Simulation of Errors in Automated Photoelasticity, Experimental Mechanics, Vol. 38, No. (1998), pp. 13-139. 16. Hobbs, J. W., Greene, R. J. and Patterson, E. A., A Novel Instrument for Transient Photoelasticity, Experimental Mechanics, Vol. 43, No. 4 (003), pp. 403-409. 17. 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 (005), pp. 9-44. 18. 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 (199), pp. 4-9. 19. Asundi, A., Phase-Shifting in Photoelasticity, Experimental Techniques, Vol. 17, No. 1 (1993), pp.19-3.
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