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Measurement of shock waves using phase shifting pulsed holographic interferometer
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Optics & Laser Technology 35 (2003) 323 – 329 www.elsevier.com/locate/optlastec
Measurement of shock waves using phase shifting pulsed holographic interferometer Young-June Kanga;∗ , Sung-Hoon Baikb , Weon-Jae Ryuc , Koung-Suk Kimd a School
of Mechanical Engineering, Mechatronics Research Center, Chonbuk National University, Duckjin-Dong 1 ga 664-14, Duckjin-Gu, Chonju, Chonbuk 561-756, South Korea b Laboratory for Quantum Optics, Korea Atomic Energy Research Institute, Dukjin-Dong 150, Yusong, Daejon 305-353, South Korea c Department of Mechanical Design, Graduate School, Chonbuk National University, Duckjin-Dong 1 ga 664-14, Duckjin-Gu, Chonju, Chonbuk 561-756, South Korea d Department of Mechanical Design Engineering, Laser Application Research Center, Chosun University, Kwangju 501-759, South Korea Received 17 December 2001; received in revised form 22 October 2002; accepted 27 October 2002
Abstract A phase shifting pulsed holographic interferometer was applied to the experimental study of the propagation of laser-induced shock waves over metal plates. A double-pulsed ruby laser was used to generate the shock waves and to make a holographic interferogram of the wave 6elds. The phase shifting method with a dual-reference beam solved the sign ambiguity problem in holographic fringe patterns and allowed a quantitative evaluation of the phase of the interference patterns. The transient surface pro6le and propagation behavior of the shock wave over plates were investigated from the holographic fringe patterns. ? 2002 Elsevier Science Ltd. All rights reserved. Keywords: Holographic interferometer; The phase shifting method; Laser-induced shock waves
1. Introduction Holographic interferometry is a widely used technique for measuring deformation, vibration of a structure and for visualization of :ow [1,2]. Holographic interferometry is so useful as a nondestructive testing tool that it has been used in many industries such as aircraft and automobiles. Especially, the pulsed holographic interferometer is a very useful tool for applications in investigation of a high-speed and transient events [3,4]. It is an important subject in engineering to investigate the propagation of shock waves. Especially, the visualization of shock waves are indispensable for the surface inspection in the aircraft and automobile industries [4]. However, it has an important problem known as “the sign ambiguity” for the analysis of fringe patterns. The sign ambiguity problem in pulsed holographic interferometry could be solved by the phase shifting method with a dual-reference beam [5,6]. In this paper, the experimental study of the visualization and the quantitative analysis of shock waves using a phase ∗ Corresponding author. Tel.: +82-63-270-2453; fax: +82-63270-2460. E-mail address: [email protected] (Y.-J. Kang).
shifting holographic interferometer with a dual-reference beam module, were described. In previous studies, a pendulum was used to generate the shock waves [1]. But there were two problems. One was the delay time of the sensors when a pendulum impacts the plate. It usually corresponds to several tens of micro-seconds. Jittering, which is another problem, appears because the impact time is quite long as compared with the propagation time of shock waves. In this study, the ruby laser pulse was used to generate the shock waves in order to remove the problems that are mentioned above [7,8]. 2. Phase shifting holographic interferometry Fig. 1 shows the optical arrangements of a phase shifting holographic interferometer with dual-reference beams. Fig. 1(a) is the diagram for recording a hologram. The object before object deformation is recorded with reference beam R1 and the deformed object is recorded with reference beam R2 on the same hologram plate. Fig. 1(b) is the diagram for reconstructing the hologram. When the hologram is illuminated by the two reference beams (R1 and R2 ) simultaneously, the hologram produces four images.
0030-3992/03/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 3 0 - 3 9 9 2 ( 0 2 ) 0 0 1 6 0 - 3
324
Y.-J. Kang et al. / Optics & Laser Technology 35 (2003) 323 – 329
BS
When the hologram which recorded the objects before and after deformation is reconstructed, the superposed local intensity I (x; y) is given by the following:
BS
Laser M
R1
M
E
I (x; y) = |U1 + U2 |2
R2
= Ia (x; y){1 + m(x; y) cos[(x; y) + ]};
M E
BS : Beamsplitter M : Mirror
E
E : Expander R1 : Reference Beam 1 R2: Reference Beam 2
(a)
Object
Hologram
BS
Laser R*1
M
E
M
where Ia (x; y) is the local mean intensity, m(x; y) the fringe visibility, (x; y) the phase diKerence, 2 (x; y) − 1 (x; y), and is the shifted phase by the phase shifter. In this study, the 4-buckets algorithm was used for the phase shifting. A phase shifter should be inserted on a path of the reference beam R1 or R2 in order to shift the phase of the interference patterns. The phase diKerence (x; y) from Eq. (2) can be obtained by the phase shifting method. Four interference fringe patterns (I1 ; I2 ; I3 ; I4 ) with = 0; =2; ; 3 =2 were obtained to calculate the phase of the deformation. From the four patterns, the resultant phase is calculated by following equation [9]: −1 I4 (x; y) − I2 (x; y) (x; y) = tan : (3) I1 (x; y) − I3 (x; y)
R*2
3. Experiments
M E
(b)
(2)
Hologram
Screen
Fig. 1. Arrangements of phase shifting holographic interferometer with dual-reference beams for (a) Recording hologram and (b) Reconstructing hologram.
Two of them give rise to the useful interference fringe patterns. The amplitudes of the diKused light from the object before and after the deformation, U1 (x; y) and U2 (x; y), can be represented by the following: U1 (x; y) = a1 (x; y) cos[1 (x; y)]; U2 (x; y) = a2 (x; y) cos[2 (x; y) + ];
(1)
where a1 (x; y) and a2 (x; y) are the beam intensities. 1 and 2 are phases of the beams, is the shifted phase by a phase shifter. For the quantitative analysis of the interference fringe pattern, a phase shifting method can be applied. Three or four (6ve) frames of phase shifted interference fringe patterns are needed to calculate the local phase of the interference fringe pattern in a phase shifting method. A phase shifter is needed to shift the phase of the interference patterns.
Fig. 2 shows the optical arrangements for generating and recording the shock waves. This holographic setup is sensitive to the out-of-plane displacement of the plate. A beam splitter divided the laser pulse into two beams. One of them was used to generate the shock waves and the other to record the propagation of the shock waves. The pulse energy used to generate the shock waves was about 0.4 –0:8 J with pulse width of 20 ns. Thus, the maximum power of the laser beam generating shock waves was approximately 20 –40 MW. The plates used for the experiments were made of an aluminum alloy and their size were 300 mm × 300 mm with various thicknesses, 1, 2, and 3 mm, as shown in Fig. 3. The plate was mounted vertically and its bottom was 6xed. In order to generate the shock waves in a plate, the beam from the ruby laser is focused on the back of the plate with a spot of 0:5 mm diameter by a plano-convex lens. The time diKerence between recording hologram and generating shock wave was so short that it could be ignored. At this time, the reference beam went along the path Ref 1 because no voltage was applied to the Pockels’ cell. After a delay of 10 –400 s, the second pulse from the ruby laser was 6red and was divided into two beams as was the 6rst one. One of them was used to record the shock waves that were generated by the 6rst pulse. And the other generated another shock waves that had no eKect on the interference patterns because the recording hologram and the generating shock waves occurred simultaneously. At this time, the reference beam went along the path Ref 2 because some voltage was applied to the Pockels cell so that the
Y.-J. Kang et al. / Optics & Laser Technology 35 (2003) 323 – 329 M
M
PCL : Plano-Convex Lens
PCL
NL : Negative Lens HF : Holographic Film
Plate M
NL BS M
NL
HF NL Ref 2
M
Amplifier
Ref 1
M M
BS 90R
M
PBS
90R : 90 Rotator PC : Pockels Cell M : Mirror
BS M
BS : Beamsplitter
Ruby Laser
Fig. 2. Arrangements for generating and recording the shock waves.
t
t =1mm
30 cm
t
30 cm
30 cm
30 cm
30 cm
30 cm
laser was used for reconstruction. The two reference beams were illuminating the hologram simultaneously so that the interference fringe pattern between the undeformed object and the deformed object could be seen. The interference fringe pattern was transferred into the PC image data by a CCD camera and the image processing system. For the quantitative analysis, a PZT actuator is inserted on the path of reference beam R1 as a phase shifter. As mentioned before, the 4-buckets phase shifting method was applied in this study. The quantitative deformation amount of the plate could be obtained by applying the unwrapping algorithm to the phase map. For these experiments, several cautions were required. One of them was that the interval of the fringe patterns produced by the two reference beam should remain within 1–2 mm. Secondly, the dual-reference beam in the reconstructing system should have almost the same optical path as the recording system.
PBS : Polarizing Beamsplitter
PC
M
325
t
t = 2mm
t = 3mm
Pulse impact Plate Fig. 3. Plates used for the experiments.
reference beam was polarized horizontally after the Pockels cell. The horizontally polarized beam became vertically polarized after the rotator. Fig. 4 shows the optical arrangements for reconstructing the holographic interferogram with a dual-reference beam. Having a similar wavelength with the ruby laser, a He–Ne
4. Experimental results and discussion In the 6rst experiment, a pulsed holographic interferometer with a single-reference beam was used to obtain typical double-exposure holographic interference fringes for the qualitative analysis of the propagation of shock waves. The results of the experiments show how the shock waves propagate in a plate with respect to the thickness of the plate (1, 2 and 3 mm) and the time interval (10, 60 and 100 s). The experimental results are shown in Fig. 5. They show that the shock waves propagate with a symmetric circular pattern due to the isotropy of the plate. From the 6gures, we can see that the propagation speed of the shock waves over the thin plate are faster than those over the thick one. The surface modulation amplitude due to the shock waves in the thin plate is much larger than that in the thick plates. Second experiments were performed for the quantitative analysis of the propagation of shock waves using a phase shifting holographic interferometer with a dual-reference beam. Fig. 6 shows the shock waves propagating over the plate whose thickness is 2 mm at 60 s after the pulse impact. Fig. 6(a) is the interferometric fringe pattern obtained by the phase shifting method with a dual-reference beam and Fig. 6(b) is the phase map obtained by the phase shifting method. Fig. 6(c) is the unwrapped image by applying the unwrapping algorithm and Fig. 6(d) is the three-dimensional image of the propagation of shock waves. The three-dimensional image shows the de6nite propagation shape of the shock waves over the plate. Fig. 7 is the three-dimensional images that show how the shock waves propagate in a plate with respect to the time interval. Except for the image at t = 10 s, all images have a hollow at the impact position. The hollows can be seen clearly in Fig. 8 that show the cross-sectional pro6les of the
326
Y.-J. Kang et al. / Optics & Laser Technology 35 (2003) 323 – 329
M
PZT
M
M BS
CCD Hologram Film
BS
E M
He-Ne LASER
Ref 1
Ref 2
M
M BS
PZT : Piezo-electric Transd BS : Beamsplitter M : Mirror Image Monitor Frame GrabberI BM PC
E : Expander
Fig. 4. Optical arrangements for reconstructing the hologram.
∆t =10 µs
∆t = 60 µs
∆t =100 µs
T= 1mm
T= 2mm
T= 3mm
Fig. 5. Interferograms showing bending waves propagation in 1, 2, 3 mm thick plate at 10, 60 and 100 s after the pulse impact. The header of the columns of the table show the delay times and that of the rows indicate the plate thickness.
Y.-J. Kang et al. / Optics & Laser Technology 35 (2003) 323 – 329
327
Fig. 6. Fringe evaluation process of shock wave propagation in a plate: (a) fringe pattern of the shock wave, (b) phase map of the shock wave, (c) unwrapping image of the shock wave, and (d) three-dimensional image of the shock wave.
surface deformation in 2 mm thick plate. And the hollow at the impact point grows as the shock waves propagate. It is the evidence that the shock waves by laser pulse are accompanied with thermal energy as well as mechanical energy. Finally, when t = 400 s, the deformation by the mechanical energy almost disappears, and only the deformation by the thermal energy exists. 5. Conclusions In this study, laser-induced shock waves were investigated experimentally using a phase shifting pulsed holographic interferometer. The propagating shock waves over metal plates were visualized and analyzed using the phase shifting method with dual-reference beam. The shock waves for these experiments were generated by the laser pulse itself. This method removed two problems; the long delay time and the jittering.
Only isotropic material was tested in this study, but it can be expanded to anisotropic material as a useful measuring tool for unknown material properties such as the elastic modulus and the Poisson’s ratio through evaluating the deformation of the material. And the material properties obtained by this study are expected to be used for the design of machines and structures that should overcome the dynamic load. In addition, this study can be applied to detect defects in plates and measure their shape and size as an NDT tool. Acknowledgements This research was supported by Mechantronics Research Center (MRC) in Chonbuk National University, Chonju, Korea. MRC is designated as a Regional Research Center appointed by the Korea Science and Engineering Foundation (KOSEF), Chollabukdo Provincial Government and Chonbuk National University.
328
Y.-J. Kang et al. / Optics & Laser Technology 35 (2003) 323 – 329
Fig. 7. Three-dimensional images of shock wave in a 2 mm thick plate with delay time of 10 –400 s: (a) 10 s, (b) 30 s, (c) 50 s, (d) 100 s, (e) 150 s, (f) 200 s, (g) 400 s.
Y.-J. Kang et al. / Optics & Laser Technology 35 (2003) 323 – 329
References
Profile of Shock Waves
0.4
0.2
Displacements
0
-0.2
-0.4
10 50 100 150 200 400
-0.6
-0.8
0
50
100
150
200
250
329
300
350
X
Fig. 8. Cross-sectional pro6les of the 2 mm thick plate with respect to the delay times.
[1] Dandliker R, Thalmann R. Heterodyne and quasi-heterodyne holographic interferometry. Opt Eng 1985;24:824–31. [2] Baik SH, Park SK, Kim CJ, Kim SY. Holographic visualization of laser-induced plume in pulsed laser welding. Opt Laser Technol 2001;33:67–70. [3] He:inger LO, Wuerker RF, Brooks RE. Holographic interferometry. J Appl Phys 1966;37:642–9. [4] Wang J, Grant I. Application of laser, holographic, nondestructive testing by impact loading. Appl Opt 1995;34:3603–6. [5] Stahl HP. Review of phase-measuring interferometry. Proc SPIE 1990;1332:704–19. [6] Mao TS, Zen LW. Digital phase shift holographic interferometry and its application in the experimental :ow study. Opt Quant Electron 1991;23:593–601. [7] Fallstrom K-E, Olofsson K, Saldner HO, Schedin S. Dynamic material parameters in an anisotropic plate estimated by phase-stepped holographic interferometry. Opt Lasers Eng 1996;24:429–54. [8] Duncan DD, Jacques SL, Johnson PC. Laser-induced retinal shock waves and bubbles and their dependencies on the thermo-mechanical properties of melanosomes. Proc SPIE 2001;4257:149–58. [9] Creath K. Comparison of phase-measurement algorithms. Proc SPIE 1986;680:19–28.
Optics & Laser Technology 35 (2003) 323 – 329 www.elsevier.com/locate/optlastec
Measurement of shock waves using phase shifting pulsed holographic interferometer Young-June Kanga;∗ , Sung-Hoon Baikb , Weon-Jae Ryuc , Koung-Suk Kimd a School
of Mechanical Engineering, Mechatronics Research Center, Chonbuk National University, Duckjin-Dong 1 ga 664-14, Duckjin-Gu, Chonju, Chonbuk 561-756, South Korea b Laboratory for Quantum Optics, Korea Atomic Energy Research Institute, Dukjin-Dong 150, Yusong, Daejon 305-353, South Korea c Department of Mechanical Design, Graduate School, Chonbuk National University, Duckjin-Dong 1 ga 664-14, Duckjin-Gu, Chonju, Chonbuk 561-756, South Korea d Department of Mechanical Design Engineering, Laser Application Research Center, Chosun University, Kwangju 501-759, South Korea Received 17 December 2001; received in revised form 22 October 2002; accepted 27 October 2002
Abstract A phase shifting pulsed holographic interferometer was applied to the experimental study of the propagation of laser-induced shock waves over metal plates. A double-pulsed ruby laser was used to generate the shock waves and to make a holographic interferogram of the wave 6elds. The phase shifting method with a dual-reference beam solved the sign ambiguity problem in holographic fringe patterns and allowed a quantitative evaluation of the phase of the interference patterns. The transient surface pro6le and propagation behavior of the shock wave over plates were investigated from the holographic fringe patterns. ? 2002 Elsevier Science Ltd. All rights reserved. Keywords: Holographic interferometer; The phase shifting method; Laser-induced shock waves
1. Introduction Holographic interferometry is a widely used technique for measuring deformation, vibration of a structure and for visualization of :ow [1,2]. Holographic interferometry is so useful as a nondestructive testing tool that it has been used in many industries such as aircraft and automobiles. Especially, the pulsed holographic interferometer is a very useful tool for applications in investigation of a high-speed and transient events [3,4]. It is an important subject in engineering to investigate the propagation of shock waves. Especially, the visualization of shock waves are indispensable for the surface inspection in the aircraft and automobile industries [4]. However, it has an important problem known as “the sign ambiguity” for the analysis of fringe patterns. The sign ambiguity problem in pulsed holographic interferometry could be solved by the phase shifting method with a dual-reference beam [5,6]. In this paper, the experimental study of the visualization and the quantitative analysis of shock waves using a phase ∗ Corresponding author. Tel.: +82-63-270-2453; fax: +82-63270-2460. E-mail address: [email protected] (Y.-J. Kang).
shifting holographic interferometer with a dual-reference beam module, were described. In previous studies, a pendulum was used to generate the shock waves [1]. But there were two problems. One was the delay time of the sensors when a pendulum impacts the plate. It usually corresponds to several tens of micro-seconds. Jittering, which is another problem, appears because the impact time is quite long as compared with the propagation time of shock waves. In this study, the ruby laser pulse was used to generate the shock waves in order to remove the problems that are mentioned above [7,8]. 2. Phase shifting holographic interferometry Fig. 1 shows the optical arrangements of a phase shifting holographic interferometer with dual-reference beams. Fig. 1(a) is the diagram for recording a hologram. The object before object deformation is recorded with reference beam R1 and the deformed object is recorded with reference beam R2 on the same hologram plate. Fig. 1(b) is the diagram for reconstructing the hologram. When the hologram is illuminated by the two reference beams (R1 and R2 ) simultaneously, the hologram produces four images.
0030-3992/03/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 3 0 - 3 9 9 2 ( 0 2 ) 0 0 1 6 0 - 3
324
Y.-J. Kang et al. / Optics & Laser Technology 35 (2003) 323 – 329
BS
When the hologram which recorded the objects before and after deformation is reconstructed, the superposed local intensity I (x; y) is given by the following:
BS
Laser M
R1
M
E
I (x; y) = |U1 + U2 |2
R2
= Ia (x; y){1 + m(x; y) cos[(x; y) + ]};
M E
BS : Beamsplitter M : Mirror
E
E : Expander R1 : Reference Beam 1 R2: Reference Beam 2
(a)
Object
Hologram
BS
Laser R*1
M
E
M
where Ia (x; y) is the local mean intensity, m(x; y) the fringe visibility, (x; y) the phase diKerence, 2 (x; y) − 1 (x; y), and is the shifted phase by the phase shifter. In this study, the 4-buckets algorithm was used for the phase shifting. A phase shifter should be inserted on a path of the reference beam R1 or R2 in order to shift the phase of the interference patterns. The phase diKerence (x; y) from Eq. (2) can be obtained by the phase shifting method. Four interference fringe patterns (I1 ; I2 ; I3 ; I4 ) with = 0; =2; ; 3 =2 were obtained to calculate the phase of the deformation. From the four patterns, the resultant phase is calculated by following equation [9]: −1 I4 (x; y) − I2 (x; y) (x; y) = tan : (3) I1 (x; y) − I3 (x; y)
R*2
3. Experiments
M E
(b)
(2)
Hologram
Screen
Fig. 1. Arrangements of phase shifting holographic interferometer with dual-reference beams for (a) Recording hologram and (b) Reconstructing hologram.
Two of them give rise to the useful interference fringe patterns. The amplitudes of the diKused light from the object before and after the deformation, U1 (x; y) and U2 (x; y), can be represented by the following: U1 (x; y) = a1 (x; y) cos[1 (x; y)]; U2 (x; y) = a2 (x; y) cos[2 (x; y) + ];
(1)
where a1 (x; y) and a2 (x; y) are the beam intensities. 1 and 2 are phases of the beams, is the shifted phase by a phase shifter. For the quantitative analysis of the interference fringe pattern, a phase shifting method can be applied. Three or four (6ve) frames of phase shifted interference fringe patterns are needed to calculate the local phase of the interference fringe pattern in a phase shifting method. A phase shifter is needed to shift the phase of the interference patterns.
Fig. 2 shows the optical arrangements for generating and recording the shock waves. This holographic setup is sensitive to the out-of-plane displacement of the plate. A beam splitter divided the laser pulse into two beams. One of them was used to generate the shock waves and the other to record the propagation of the shock waves. The pulse energy used to generate the shock waves was about 0.4 –0:8 J with pulse width of 20 ns. Thus, the maximum power of the laser beam generating shock waves was approximately 20 –40 MW. The plates used for the experiments were made of an aluminum alloy and their size were 300 mm × 300 mm with various thicknesses, 1, 2, and 3 mm, as shown in Fig. 3. The plate was mounted vertically and its bottom was 6xed. In order to generate the shock waves in a plate, the beam from the ruby laser is focused on the back of the plate with a spot of 0:5 mm diameter by a plano-convex lens. The time diKerence between recording hologram and generating shock wave was so short that it could be ignored. At this time, the reference beam went along the path Ref 1 because no voltage was applied to the Pockels’ cell. After a delay of 10 –400 s, the second pulse from the ruby laser was 6red and was divided into two beams as was the 6rst one. One of them was used to record the shock waves that were generated by the 6rst pulse. And the other generated another shock waves that had no eKect on the interference patterns because the recording hologram and the generating shock waves occurred simultaneously. At this time, the reference beam went along the path Ref 2 because some voltage was applied to the Pockels cell so that the
Y.-J. Kang et al. / Optics & Laser Technology 35 (2003) 323 – 329 M
M
PCL : Plano-Convex Lens
PCL
NL : Negative Lens HF : Holographic Film
Plate M
NL BS M
NL
HF NL Ref 2
M
Amplifier
Ref 1
M M
BS 90R
M
PBS
90R : 90 Rotator PC : Pockels Cell M : Mirror
BS M
BS : Beamsplitter
Ruby Laser
Fig. 2. Arrangements for generating and recording the shock waves.
t
t =1mm
30 cm
t
30 cm
30 cm
30 cm
30 cm
30 cm
laser was used for reconstruction. The two reference beams were illuminating the hologram simultaneously so that the interference fringe pattern between the undeformed object and the deformed object could be seen. The interference fringe pattern was transferred into the PC image data by a CCD camera and the image processing system. For the quantitative analysis, a PZT actuator is inserted on the path of reference beam R1 as a phase shifter. As mentioned before, the 4-buckets phase shifting method was applied in this study. The quantitative deformation amount of the plate could be obtained by applying the unwrapping algorithm to the phase map. For these experiments, several cautions were required. One of them was that the interval of the fringe patterns produced by the two reference beam should remain within 1–2 mm. Secondly, the dual-reference beam in the reconstructing system should have almost the same optical path as the recording system.
PBS : Polarizing Beamsplitter
PC
M
325
t
t = 2mm
t = 3mm
Pulse impact Plate Fig. 3. Plates used for the experiments.
reference beam was polarized horizontally after the Pockels cell. The horizontally polarized beam became vertically polarized after the rotator. Fig. 4 shows the optical arrangements for reconstructing the holographic interferogram with a dual-reference beam. Having a similar wavelength with the ruby laser, a He–Ne
4. Experimental results and discussion In the 6rst experiment, a pulsed holographic interferometer with a single-reference beam was used to obtain typical double-exposure holographic interference fringes for the qualitative analysis of the propagation of shock waves. The results of the experiments show how the shock waves propagate in a plate with respect to the thickness of the plate (1, 2 and 3 mm) and the time interval (10, 60 and 100 s). The experimental results are shown in Fig. 5. They show that the shock waves propagate with a symmetric circular pattern due to the isotropy of the plate. From the 6gures, we can see that the propagation speed of the shock waves over the thin plate are faster than those over the thick one. The surface modulation amplitude due to the shock waves in the thin plate is much larger than that in the thick plates. Second experiments were performed for the quantitative analysis of the propagation of shock waves using a phase shifting holographic interferometer with a dual-reference beam. Fig. 6 shows the shock waves propagating over the plate whose thickness is 2 mm at 60 s after the pulse impact. Fig. 6(a) is the interferometric fringe pattern obtained by the phase shifting method with a dual-reference beam and Fig. 6(b) is the phase map obtained by the phase shifting method. Fig. 6(c) is the unwrapped image by applying the unwrapping algorithm and Fig. 6(d) is the three-dimensional image of the propagation of shock waves. The three-dimensional image shows the de6nite propagation shape of the shock waves over the plate. Fig. 7 is the three-dimensional images that show how the shock waves propagate in a plate with respect to the time interval. Except for the image at t = 10 s, all images have a hollow at the impact position. The hollows can be seen clearly in Fig. 8 that show the cross-sectional pro6les of the
326
Y.-J. Kang et al. / Optics & Laser Technology 35 (2003) 323 – 329
M
PZT
M
M BS
CCD Hologram Film
BS
E M
He-Ne LASER
Ref 1
Ref 2
M
M BS
PZT : Piezo-electric Transd BS : Beamsplitter M : Mirror Image Monitor Frame GrabberI BM PC
E : Expander
Fig. 4. Optical arrangements for reconstructing the hologram.
∆t =10 µs
∆t = 60 µs
∆t =100 µs
T= 1mm
T= 2mm
T= 3mm
Fig. 5. Interferograms showing bending waves propagation in 1, 2, 3 mm thick plate at 10, 60 and 100 s after the pulse impact. The header of the columns of the table show the delay times and that of the rows indicate the plate thickness.
Y.-J. Kang et al. / Optics & Laser Technology 35 (2003) 323 – 329
327
Fig. 6. Fringe evaluation process of shock wave propagation in a plate: (a) fringe pattern of the shock wave, (b) phase map of the shock wave, (c) unwrapping image of the shock wave, and (d) three-dimensional image of the shock wave.
surface deformation in 2 mm thick plate. And the hollow at the impact point grows as the shock waves propagate. It is the evidence that the shock waves by laser pulse are accompanied with thermal energy as well as mechanical energy. Finally, when t = 400 s, the deformation by the mechanical energy almost disappears, and only the deformation by the thermal energy exists. 5. Conclusions In this study, laser-induced shock waves were investigated experimentally using a phase shifting pulsed holographic interferometer. The propagating shock waves over metal plates were visualized and analyzed using the phase shifting method with dual-reference beam. The shock waves for these experiments were generated by the laser pulse itself. This method removed two problems; the long delay time and the jittering.
Only isotropic material was tested in this study, but it can be expanded to anisotropic material as a useful measuring tool for unknown material properties such as the elastic modulus and the Poisson’s ratio through evaluating the deformation of the material. And the material properties obtained by this study are expected to be used for the design of machines and structures that should overcome the dynamic load. In addition, this study can be applied to detect defects in plates and measure their shape and size as an NDT tool. Acknowledgements This research was supported by Mechantronics Research Center (MRC) in Chonbuk National University, Chonju, Korea. MRC is designated as a Regional Research Center appointed by the Korea Science and Engineering Foundation (KOSEF), Chollabukdo Provincial Government and Chonbuk National University.
328
Y.-J. Kang et al. / Optics & Laser Technology 35 (2003) 323 – 329
Fig. 7. Three-dimensional images of shock wave in a 2 mm thick plate with delay time of 10 –400 s: (a) 10 s, (b) 30 s, (c) 50 s, (d) 100 s, (e) 150 s, (f) 200 s, (g) 400 s.
Y.-J. Kang et al. / Optics & Laser Technology 35 (2003) 323 – 329
References
Profile of Shock Waves
0.4
0.2
Displacements
0
-0.2
-0.4
10 50 100 150 200 400
-0.6
-0.8
0
50
100
150
200
250
329
300
350
X
Fig. 8. Cross-sectional pro6les of the 2 mm thick plate with respect to the delay times.
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