s70 Prototype of a Handheld Displacement Measurement System Using Multiple Imaging Sensors

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1 Journal of JSEM, Vol.15, Special Issue (2015) s70-s74 Copyright C 2015 JSEM Prototype of a Handheld Displacement Measurement System Using Multiple Imaging Sensors Motoharu FUJIGAKI 1, Hiroki MIAMIO 2, oboru IKOMA 3, Hiroki TAMAI 3 and Yorinobu MURATA 1 1 Faculty of Systems Engineering, Wakayama University, Wakayama, Japan 2 Graduate School of Systems Engineering, Wakayama University, Wakayama, Japan 3 JR WEST JAPA COSULTATS COMPAY, Osaka, Japan (Received 22 January 2015; received in revised form 1 June 2015; accepted 6 June 2015) Abstract Compact and conventional strain distribution measurement equipment is required to monitor the health and the lifelengthening characteristics of infrastructures, such as steel bridges. Digital holography is a convenient method that can be used to measure the displacement and the strain distributions on the surface of an object. Compact and handheld equipment is required for practical use on a field site. Simplification of the optical setup is required to produce more compact equipment. An imaging head with multiple imaging devices was developed by the authors to produce more compact equipment. In this paper, a prototype of a handheld displacement distribution measurement system using eight imaging devices was developed. The evaluation of the displacement measurement using the prototype was shown. Key words Handheld Displacement Measurement System, Health Monitoring of Railway Bridges, Digital Holographic Interferometry, Multiple Imaging Devices 1. Introduction The development of compact and conventional strain distribution measurement equipment for practical use is required to monitor the health and the life-lengthening characteristics of infrastructures, such as steel bridges. Specifically, in the case of a railway bridge, it is important to measure the strain distribution to inspect for defects. Phase-shifting digital holography is a convenient method that can be used to measure displacement and strain distributions on the surface of an object [1]. Many researchers are studying this method, and several compact equipment types are being developed [2-8]. Authors have also developed compact types of equipment for strain distribution measurements [9-11]. However, several object waves are necessary to measure the in-plane displacement and the strain distributions when using conventional equipment. Simplifying the optical setup is required to produce more compact equipment. An imaging head with multiple imaging devices was developed to produce more compact equipment by authors [12, 13]. A simple mechanism to generate a reference wave with a shifting phase to each imaging sensor using a glass plate is also proposed. The optical axis of each imaging sensor was directed to the object. Each imaging device could detect the phase difference distribution on the surface of the specimen. The multiple phase differences result in three directional displacement distributions. A simple mechanism to generate a reference wave with a shifting phase to each imaging sensor is required to realize compact equipment for strain distribution measurements using multiple cameras. In this paper, we report the development of a prototype of a handheld displacement measurement system using eight imaging devices. An evaluation of the displacement measurement using the prototype is shown. 2. Principle of Displacement Measurement Figure 1 shows a positional relationship between a light source, the imaging devices and the sensitivity vectors [14]. The angle between an incident wave onto an object and the scattered waves in the direction of the image sensor i is shown as θ i in this figure. The direction of the sensitivity vector e i is the direction of the angle that bisects the angle θ i [14]. The vector d is the displacement vector at the point P, as shown in Fig. 1, when a point P on an object is displaced into the point P'. The phase difference Δφ i obtained using digital holographic interferometry is expressed as follows: Δφ i = e i d (1) The phase difference Δφ i can be obtained as the phase difference of the incident wave before and after the deformation at a point on the object. The displacement vector and the sensitivity vector have components in the x, y, and z directions. Therefore, these values are expressed as follows: Δφ i = ( e ix e iy e iz ) d z = e ix + e iy + e iz d z, (2) where e i = (e ix, e iy, e iz ) and d = (,, d z ). When image sensors 1, 2,... are locations in the independent positions, sensitivity vectors are obtained. In this case, Eq. (2) can be rewritten as Eq. (3): Δφ 1 Δφ 2 = S : Δφ d z, (3) where subscripts 1, 2,... represent each imaging device. The matrix S, which is called a sensitivity matrix, is defined as Eq. (4). s70

2 Journal of JSEM, Vol.15, Special Issue (2015) e 1x e 1y e 1z e S = 2x e 2y e 2z : : : e x e y e z (4) 3. Prototype of a Handheld Displacement and Strain Measurement System Figure 2 shows a developed prototype of the handheld displacement and strain measurement system. Figure 2(a) shows a schematic design. The measurement head and the (a) Schematic design Fig. 1 Positional relationship between the light source, the imaging devices and the sensitivity vectors The sensitivity matrix S is obtained at each point on the object because the phase differences Δφ 1, Δφ 2,... Δφ change according to the angle between the incident wave and the direction of the image sensors. Each element of the matrix S is a constant number provided by the positional relationship between the light source and the corresponding imaging device. When the pseudo inverse matrix S + of the sensitivity matrix S is defined, as in Eq. (5), Eq. (3) can be rewritten as Eq. (6). (b) Photograph of the control unit f 1x f 2x f x S + = (S T S) 1 S T = f 1y f 2y f y f 1z f 2z f z = S + d z Δφ 1 Δφ 2 : Δφ (5) (6) (c) Photograph of the measurement head Equation (6) defines the displacement components, and d z as the phase differences Δφ 1, Δφ 2,... Δφ that are obtained by each image sensor. Displacement components, and d z for directions x, y and z, respectively, are expressed as follows: = f kx Δφ k, = f ky Δφ k, d z = f kz Δφ k. (7) That is, the displacement distributions can be derived from the phase difference distributions obtained from the imaging sensors 1, 2,.... (d) Photograph of the inside of the measurement head Fig. 2 Prototype of the handheld strain measurement system control unit are separated. A light source, a phase-shifting s71

3 M. FUJIGAKI, H. MIAMIO,. IKOMA, H. TAMAI and Y. MURATA device, a control circuit with a microcomputer, and batteries are located in the control unit, as shown in Fig. 2(b). A DDS laser (Diode Direct Second harmonic generation laser) (GP-9000, Photon R&D, Inc., Japan) with 100 mw of power at a wavelength of 532 nm is used as a light source. The phase-shifting device generates a camera trigger signal according to an interference signal produced in the phase shifting device using divided light from the light source. The appearance of the measurement head is shown in Fig. 2(c). Photographs of the inside of the measurement head are shown in Fig. 2(d). The measurement head has 8 imaging devices. Each imaging device has a concave lens to expand the measurement area. A glass plate is placed between an imaging head and an object, as shown in Fig. 2(d). A part of an incident wave is reflected from the surface of the glass plate, and the reflected wave arrives at the respective imaging sensors as a reference wave. This glass plate is attached to the PZT devices. The phase of the reference wave shifts as a variable voltage is applied to the PZT devices. The voltage is also applied to the other 4 PZT devices connected in series and placed within the control unit. A mirror that is attached to the PZT devices is placed in an interferometer, as shown in Fig. 2(b). This interferometer signals the imaging trigger. During one reference wave phase-shift period, four imaging trigger signals appear. 4. Experiment An experiment using the prototype shown in Fig. 2 to measure a displacement is performed to verify the performance of the prototype. Figure 3 shows the experimental setup. An aluminum plate was placed on a 3-axis PZT stage, as shown in Fig. 4, and was used as both a reference plate and as an object. In this experiment, to evaluate the accuracy of the 3D displacement measurement, the reference plane was used as the specimen. The given displacement of the specimen can be known accurately. First, a sensitivity matrix S was produced using a reference plate. The reference plate that was attached on a 3-axis PZT stage was moved 8 times at intervals of 45 nm, 45 nm and 9 nm for the x-, y- and z-directions, respectively. Figure 5(a), (b) and (c) show relationships between displacements of a reference plate on a 3-axis PZT stage and phase differences obtained by each image sensor for the x-, y- and z-directions, respectively. The phase differences were calculated as the between two areas on a displaced part and a fixed part. Each gradient of the phase differences obtained with each image sensor gives the corresponding element of the sensitivity matrix as shown in Eq. (8). The gradients are calculated from the phase differences with a least-square technique. (a) x direction (b) y direction Fig. 3 Experimental setup Fig. 4 Reference plate placed on a 3-axis PZT stage (c) z direction Fig. 5 Relationship between displacement of a reference plate on a 3-axis PZT stage and phase difference obtained by each image sensor s72

4 Journal of JSEM, Vol.15, Special Issue (2015) S = Second, the reference plate was used as a specimen. The movable area can be shifted in any direction using the 3-axis PZT stage. In this experiment, the amount of movement was 100 nm, 100 nm and 60 nm in the x-, y- and z-directions, respectively. Figure 6 shows the results of displacement distributions. The area A and area B shown in Fig. 6(a), (b) and (c), are extracted as the fixed area and the displaced area, respectively. Table 1 shows the results of the displacement measurement. The errors in the x, y and z directions were - 5 nm, -3 nm and 1 nm, respectively. The standard deviations were less than 10 nm. This results shows that the prototype can measure the displacement accurately. In general, the sensitivity matrix should be obtained at each point because the angle between the incident wave and the direction of each image sensor is changed at each point. However, in this experiment, the phase differences were calculated as the between two areas on a displaced part and a fixed part. Therefore, the sensitivity matrix shown in Eq. (8) is available for only the reference plate used as an specimen. (a) x direction (b) y direction (c) z direction Fig. 6 Results of the displacement distribution (8) Table 1 Result of the displacement measurement Given displacement Measured displace- Error (nm) Standard deviation (nm) (nm) ment (nm) Displaced part Fixed part Δx= Δy= Δz= Conclusions A prototype of a displacement measurement system using multiple imaging devices was developed. The experimental result of a displacement measurement using a flat plate moved using a 3-axis PZT stage was shown. The performance of the prototype system and the displacement measurement method using a multiple imaging device were evaluated. This prototype can be applied to measure the strain distribution. As the future work, the software will be improved to produce sensitivity matrices pixel by pixel and to measure the strain distribution. Acknowledgement This research is partially supported by the Japan Science and Technology Agency (JST) A-STEP program. References [1] Yamaguchi, I. and Zhang, T.: Phase-Shifting Digital Holography, Optics Letters, (1997), [2] Kolenovic, E., Osten, W., Klattenhoff, R., Lai, S., Von Kopylow, C. and Jüptner, W.: Miniaturized Digital Holography Sensor for Distal Three-Dimensional Endoscopy, Applied Optics, (2003), [3] Michalkiewicz, A. and Kujawinska, M.: Development of a Miniature Digital Holographic Interferometry System, Proc. SPIE, 5484 (2004), [4] Pedrini, G. and Alexeenko, I.: Miniaturized Optical System Based on Digital Holography, Proc. SPIE, 5503 (2004), [5] Kebbel, V., Kolenovic, E., Klattenhoff, R. and Jüptner, W.: Miniaturized Optical Sensor for Mechanical Testing in Industrial Environment, Proc. of the European Conference on Spacecraft Structures, Materials and Mechanical Testing 2005 (ESA SP-581) (2005), [6] Michalkiewicz, A., Kujawinska, M., Marc, P. and Jaroszewicz, L. R.: Miniaturized Low-Cost Digital Holographic Interferometer, Proc. SPIE, 6188 (2006), [7] Saucedo, A. T., Santoyo, F. M., Torre-Ibarra, M. De la, Pedrini, G. and Osten, W.: Endoscopic Pulsed Digital Holography for 3D Measurements, Opt. Express, 14-4 (2006), [8] Michalkiewicz, A., Kujawinska, M. and Stasiewicz, K.: Digital Holographic Cameras and Data Processing for Remote Monitoring and Measurements of Mechanical Parts, Opto-electronics Review, 16-1 (2008), [9] Fujigaki, M., Matui, T., Morimoto, Y., Kita, T., akatani, M. and Kitagawa, A.: Development of Real- Time Displacement Measurement System Using Phase- Shifting Digital Holography, Proc. of the 5th s73

5 M. FUJIGAKI, H. MIAMIO,. IKOMA, H. TAMAI and Y. MURATA International Conference on Mechanics of Time Dependent Materials (MTDM05), (2005), [10] Fujigaki, M., Kido, R., Shiotani, K. and Morimoto, Y.: High-Speed and Compact Strain Measurement System by Phase-Shifting Digital Holography, Proc. of the International Symposium to Commemorate the 60th Anniversary of the Invention of Holography, (2008), [11] Fujigaki, M., Shiotani, K., Kido, R. and Morimoto, Y.: Strain Distribution Measurement by Digital Holographic Interferometry Using Three Spherical Waves, Proc. SPIE 7063, 70630G(2008). [12] Fujigaki, M., Shiotani, K., ishitani, R., Masaya, A. and Morimoto, Y.: Off-axis Reconstruction Method for Displacement and Strain Distribution Measurement with Phase-Shifting Digital Holography, Fringe09, 6th International Workshop on Advanced Optical Metrology, Osten, W. and Kujawinska, M. eds., Springer, (2009). [13] Fujigaki, M., ishitani, R. and Morimoto, Y.: Strain Measurement Using Phase-shifting Digital Holography with Two Cameras, Proc. of ICEM 14, EPJ Web of Conferences 6, 30001(CD-ROM)(2010). [14] Schnars, U. and Jüptner, W.: Digital Holography, Springer (2005), s74