- Email: [email protected]
Influence of acoustic leakage at fluid–solid interface on interferometric detection of surface acoustic wave
Optik 125 (2014) 2458–2462
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Influence of acoustic leakage at fluid–solid interface on interferometric detection of surface acoustic wave Zhao Yan School of science, Nanjing University of Science and Technology, Nanjing 210094, PR China
a r t i c l e
i n f o
Article history: Received 27 May 2013 Accepted 24 October 2013 Keywords: Acoustic leakage Fluid–solid interface Laser ultrasonic Interferometric detection Surface acoustic wave Finite element method
a b s t r a c t When using laser interferometer to detect surface acoustic wave at fluid–solid interface, there are two factors which will cause the optical path length variation of the probe laser beam: interface deformation, and refractive index changes in fluid induced by acoustic leakage. Influence of acoustic leakage on laser interferometric detection for surface acoustic wave is researched here. A metal plate immersed in an infinite fluid is used as a physical model. Interface deformation due to laser-induced acoustic wave and pressure in fluid due to acoustic leakage are computed for select cases by finite element method. The optical path length variation caused by the two factors are calculated respectively and compared. The results show that the influence of acoustic leakage increases with the increasing acoustic impedance matching of fluid and solid, the peak-to-peak of influence degree increases linearly with the increasing acoustic impedance of fluid, and that decreasing the distance between the interferometer and interface can effectively reduce the influence of acoustic leakage. © 2014 Elsevier GmbH. All rights reserved.
1. Introduction There have been extensive studies on surface acoustic wave at fluid–solid interface due to its potential application in seismology, engineering, and non destructive test (NDT) [1–3]. However, its detection is still an urgent problem although there are many methods for measurement of surface acoustic wave. In fact, the most popular method for detection of surface acoustic waves is the transducer one, where the surface acoustic wave signal is detected by a piezoelectric transducer attached to the surface of the solid [4]. Unfortunately, it was pointed out that the acoustic connection between the sample and the transducer will influence the ultrasonic field. In this respects, noncontact measurements are desirable. One method is to employ interferometric detection which can detect without contact ultrasonic field and has a wide responsive bandwidth, so that it was extensively used to detect surface acoustic wave [5–11]. In this technique, the normal surface displacement is deduced from the optical path length variation of a laser beam reflected by the surface. Actually, it was pointed out recently that when surface acoustic wave propagates along fluid–solid interface, the energy of the wave “leaks” into the fluid [12], that will cause the refractive index changes in fluid as a function of both time and space, altering the
E-mail address: [email protected] 0030-4026/$ – see front matter © 2014 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2013.10.117
optical path length of laser beam which propagates in the fluid. As a result, expecting the surface displacement, there is the other factor which induced the optical path length variation of the laser probe beam in interferometric detection, that is refractive index change in fluid induced by acoustic leakage. In previous studies, the acoustic leakage factor is always ignored and the important subject, namely the influence of acoustic leakage on interferometric detection, did not arouse the researchers’ attention until now, which will directly influence the correctness of the results presented by laser interferometric sensor. In this paper, the influence of acoustic leakage in fluid on interferometric detection was researched. Laser-induced interface acoustic field is computed by finite element method due to its advantages and universal application of laser ultrasonic. Two optical path length variation of laser probe beam caused by these two factors are calculated respectively and compared. 2. Interferometric detection of surface acoustic wave Numerous optical interferometries have been developed for detecting surface acoustic wave, such as Michelson interferometry, Mach–Zender interferometry, heterodyne interferometry [7–10]. These devices use the mechanism that the displacement of a vibrating surface is obtained by measuring the optical path length variation of the probe beam due to the motion of the reflected surface. The schematic diagram of laser ultrasonic system is shown in Fig. 1. The optical probe beam from laser interferometer crosses a transparent fluid where the index of refraction is modulated by the
Z. Yan / Optik 125 (2014) 2458–2462
2459
Table 1 Parameter of steel solid. Density
Longitudinal velocity cL (m/s)
Shear velocity cs (m/s)
Acoustic impedance
7800
5980
3246
4.6644 × 107
Table 2 Fluid media.
Fig. 1. Schematic of laser ultrasonic system.
Designation
Density, f (kg/m3 )
Dilatational velocity, cf (m/s)
Acoustic impedance
Water Air F1 F2 F3 F4 F5 F6 F7
1000 1.21 1000 1000 1000 1000 76.5 1.21 76.5
1500 343 1250 1000 961 343 1500 1500 343
1.5 × 106 415.03 1.25 × 106 1 × 106 9.61 × 105 3.43 × 105 1.1475 × 105 1.815 × 103 2.62395 × 104
where M is the material parameter, is density, and c is the speed of sound in the fluid. To determine the influence of acoustic leakage on interferometric detection, it is necessary to firstly determine the acoustic variation in pressure in fluid caused by acoustic leakage and the normal displacement on solid surface. However, it is very difficult for experiment measurement, so numerical calculation is applied for acoustic field in fluid and solid. In this paper, finite element method was introduced to numerically simulate laser-induced ultrasonic wave on fluid–solid interface. Fig. 2. Absolute value of pressure (in water) and stress (in solid) field snapshot at t = 0.72 ms given by finite element analysis. The interface is subject to a transient 2 point load that varies with time as f (t) = sin (t/T ) with T = 200 s.
acoustic wave and is then reflected by a solid surface. The phasemodulated current measured by the laser interferometer is given as
i(t)∼ cos ı(t) + s − R
(1)
where R and s are the phase constants corresponding to the reference and the probe beams of the interferometer. ı(t) is the optical path length variation of probe laser due to the ultrasonic waves and includes two phase changes respectively induced by normal surface displacement (ıs ) and acoustic leakage modulated refraction index (ıR ) for fluid–solid interface case. ıS = −2Uy n0
(2)
L ıR = 2
ndy
(3)
0
where Uy is the normal displacement of the solid surface, n0 is the refractive index of the fluid when there is no acoustic wave present, L is the distance between the interferometer and the interface. Consider a traveling wave in fluid due to acoustic leakage, the variation in the index of refraction index (n) is proportional to the acoustic variation in pressure (p). For a liquid such as water, 1 n = 2
M p c
(4)
For a gas such as air, n =
(n0 − 1)p c 2
(5)
Fig. 3. Absolute value of pressure (in fluid) and displacement (in steel solid) field snapshot at t = 0.11 s given by finite element analysis.
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(a)
LR
0.2
due to normal displacement due to acoustic leakage caused refractive index change
S X=0.2mm
0.1
2
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0.6 X=0.4mm
0.6
X=0.6mm
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Time (us)
Fig. 4. Time history of pressure in water (a) and normal displacement in solid (b) near the interface at x = 0.2 mm, 0.4 mm, 0.6 mm for water–steel case. x is the distance between exciting laser and detecting point, LR represents leaky Rayleigh wave, and S represents Scholte wave.
The numerical analyses were performed to simulate the response for fluid–solid half-space cases. The detailed description of the employed finite element method could be found in our previous paper [13], so we did not discuss it comprehensively. 3. Results and discussions To verify the correctness of numerical simulations, a contrast calculation was performed according to Jinying Zhu’s study [14], and the acoustic field on water-concrete interface simulated by finite element method is shown in Fig. 2. It was in very good agreement with the numerical solution obtained by Jinying Zhu using the elastodynamic finite integration technique that indicated the correctness of our simulation method. Finite element simulations were performed for the case of a laser pulse load at a water–steel interface and air–steel interface. The physical parameters of air, water and steel used in calculations are available in Tables 1 and 2, respectively. The inserted energy of laser source is 13.3 mJ, its half-width and pulse widths are 50 m and 10 ns, respectively. To ensure the stability, efficiency and accuracy and finite element calculation, the size of spatial grid and time grids are 10 m and 2 ns, respectively. According to the numerical simulations, Fig. 3(a) and (b) shows the cross-sectional snapshot image of acoustic field at time t = 0.11 s for water–steel interface and air–steel interface case, respectively. In this figure, the half-circle in the upper half-plane represents the acoustic wave front in fluid, and the inclined lines represent the leaky Rayleigh wave fronts, which are tangent to the half circle at the leaky angle direction. Besides the leaky Rayleigh wave, there are also Scholte and fluid acoustic wave in fluid, longitude wave (L), head wave (HW) and transverse wave (S) in steel
(a) for water-steel case,
optical path length variation (*10^(-9))
Normal displacement (nm)
X=0.2mm
-2
-1
0.6
Time (us)
(b)
0 -1
due to normal displacement due to acoustic leakage caused refractive index change
1.5 1.0 0.5 0.0 -0.5 -1.0
X=0.2mm 0.0
0.1
0.2
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0.0
0.1
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X=0.4mm
1.5 1.0 0.5 0.0 -0.5 -1.0
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X=0.6mm 0.0
0.1
0.2
0.3
0.4
0.5
0.6
Time (us)
(b) for air-steel case Fig. 5. Optical path length variation due to acoustic leakage and surface displacement measured by laser interferometer position at x = 0.2 mm, 0.4 mm, 0.6 mm. x is the distance between exciting laser and detecting point.
solid. In this figure, the amplitudes of pressure in water and air are multiplied by 0.1 and 150 for clarity of expression. As we all known, when a surface acoustic wave propagates on a fluid–loaded solid surface, the energy of the wave leaks into the fluid and the acoustic leakage is stronger with the increasing acoustic impedance matching between the fluid and solid. So that, one can also easily find that the amplitude of acoustic wave in water are far greater than those in air due to their acoustic impedances. Besides, the velocity of leaky Rayleigh and Scholte wave approximately equal to the velocity of Rayleigh in solid and acoustic velocity in the fluid, respectively, but the waves in solid are identical for the two cases. Fig. 4 shows the time history of pressure in water and normal displacement in solid near the interface at x = 0.2 mm, 0.4 mm, 0.6 mm, respectively, where x is the distance between exciting laser and detecting point. From this figure, it can also be seen that most of Scholte wave energy is localized in the fluid, but leaky Rayleigh wave in solid, and that the two waves gradually separate from each other due to their different velocities. Based on the pressure in fluid and normal displacement on solid surface, the interferometric detected path variation due to refractive index change caused by acoustic leakage and surface displacement can be obtained by Eqs. (2) and (3), respectively, where M = 160 × 10−15 s3 kg−3 , = 1000 kg/m−3 for water, = 1.21 kg/m−3 for air, and c = 1500 ms−1 for water, and c = 343 ms−1 for air. The results are shown in Fig. 5. The influence of acoustic leakage for water–steel configuration is much greater than that for air–steel configuration. Detailed analysis was executed on the degree of influence, which is the ratio between those two path variation. As
Z. Yan / Optik 125 (2014) 2458–2462
Influence caused by leaky Rayleigh wave
2 1 0 -1 -2 -3
0.0
2 1 0 -1 -2 -3
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X=0.4mm 0.1
0.2
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3.5 3.0
Equation y = a + b*x Adj. R-Square 0.9985 0.99906 Value Standard Error Data1 Interce 0.0364 0.00237 Data1 Slope 9.98344 0.13693 Data2 Interce 0.4621 0.01977 Data2 Slope 105.333 1.1421
2.5 2.0
Original data1 Original data2 Linear Fit of data1 Linear Fit of data2
1.5 1.0 0.5 0.0 -0.005
X=0.6mm
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
Ratio of fluid and solid acoustic impedance 0.0
0.1
0.2
0.3
0.4
0.5
0.6
Fig. 8. Peak-to-Peak of influence degree for different fluid-steel configurations, data1 and data2 represent the influence caused by leaky Rayleigh wave and Scholte in fluid, respectively.
Time (us) Fig. 6. The degree of influence for water–steel case.
shown in Fig. 6 for water–steel configuration, there are two pulses: one is the influence caused by leaky Rayleigh wave, the other is the influence caused by Scholte wave. The former one is much smaller than the last one because most of leaky Rayleigh and Scholte wave are localized in solid and fluid, respectively. However, the influence caused by Scholte wave on the laser interferometric detection of surface acoustic wave on solid surface can be ignored due to its arrival time, but influence caused by leaky Rayleigh wave is much important due to its arrival time identical to that of surface acoustic wave. In order to be able to explore the influence of acoustic leakage on interferometric detection for surface acoustic wave, the finite element calculations are performed for different fluid–solid interface, and the degree of the influence for different cases are obtained. The parameters of fluid media were not restricted to those of known substances, and listed in Table 2. As shown in Fig. 7, when the acoustic impedance of the fluid approaches the acoustic impedance of the solid, the degree of influence due to acoustic leakage gradually increases, because the acoustic leakage and the amplitude of acoustic wave in fluid increase with the increasing acoustic impedance matching of two media. The peak-to-peak of influence degree is compared for different fluid-steel configurations. As shown in Fig. 8, the peak-to-peak of influence degree increases linearly with the increasing of acoustic impedance, and the slopes are 9.98344 and 105.333 for the influence due to leaky Rayleigh wave and Scholte wave in fluid, respectively.
1.5 1.0 0.5
6.0
data1 for L=10mm data2 for L=10mm data1 for L=15mm data2 for L=15mm
5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.005
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
Ratio of fluid and solid acoustic impedance
Fig. 9. Peak-to-peak of influence degree for different optical path, L represents the distance between the interferometer and interface.
Moreover, the same calculation is performed for changing the distance between laser interferometer and interface and the peakto-peak of influence degree is shown in Fig. 9. As shown in this figure, when the interferometer is placed closer to the interface, the influence of acoustic leakage will be smaller. That is to say decreasing the distance between the interferometer and interface can effectively reduce the influence of acoustic leakage. 4. Conclusion In summary, the influence of acoustic leakage on laser interferometric detection for surface acoustic wave on fluid–solid interface is investigated. We find that with the increasing acoustic impedance matching of fluid and solid, the leaky energy of Rayleigh wave and Scholte increases, and the optical path length variation due to acoustic leakage increases and then the influence of acoustic leakage increases. It is also found that the peak-to-peak of influence degree increases linearly with the increasing acoustic impedance of fluid up to that of solid, and that decreasing the distance between the interferometer and interface can effectively reduce the influence of acoustic leakage.
water-steel case F1-steel case F2-steel case F3-steel case F5-steel case F6-steel case
2.0
Degree of influence
Peak-to-peak of influence degree
X=0.2mm
Peak-to-peak of influence degree
degree of influence
4.0
Influence caused by Scholte wave
2 1 0 -1 -2 -3
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0.0 -0.5 -1.0 -1.5 -2.0
Acknowledgments
-2.5 0.0
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Fig. 7. The degree of influence for different fluid-steel configuration.
This work is supported by the Natural Science Foundation of Jiangsu Province (grant BK2010494), and the National Natural Science Foundation of China (grant 11204136).
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References [1] J.Y. Kim, V.A. Yakovlev, S.I. Rokhlin, Surface acoustic wave modulation on a partially closed fatigue crack, J. Acoust. Soc. Am. 115 (5) (2004) 1961–1972. [2] W. Li, S.D. Sharples, R.J. Smith, M. Clark, M.G. Somekh, Determination of crystallographic orientation of large grain metals with surface acoustic waves, J. Acoust. Soc. Am. 132 (2) (2012) 738–745. [3] C. Trillo, D. Cernadas, A.F. Doval, C. Lopez, B.V. Drrio, J.L. Fernandez, Detection of transient surface acoustic waves of naometric amplitude with double-pulsed TV holography, Appl. Opt. 42 (7) (2003) 1228–1235. [4] D. Royer, E. Dieulesaint, Optical probing of the mechanical impulse response of a transducer, Appl. Phys. Lett. 49 (17) (1986) 1056–1058. [5] C. Harvey Palmer, Ultrasonic surface wave detection by optical interferometry, J. Acoust. Soc. Am. 53 (1973) 948–949. [6] I. Suemune, H. Yamamoto, M. Yamanishi, Noncontact photoacoustic measurements of semiconductors with Michelson interferometry, J. Appl. Phys. 58 (1) (1985) 615–617.
[7] T. Nakata, T. Ninomiya, Real-time photodisplacement imaging using parallel excitation and parallel heterodyne interferometry, J. Appl. Phys. 97 (2005) 103110. [8] D. Clorennec, C. Prada, D. Royer, T.W. Murray, Laser impulse generation and interferometer detection of zero group velocity Lamb mode resonance, Appl. Phys. Lett. 89 (2006), 024101. [9] L. Lipiainen, K. Kokkonen, M. Kaivola, Phase sensitive absolute amplitude detection of surface vibrations using homodyne interferometry without active stabilization, J. Appl. Phys. 108 (2010) 114510. [10] P.H. Otsuka, O. Matsuda, M. Tomoda, O.B. Wright, Interferometric imaging of surface acoustic waves on a glass sphere, J. Appl. Phys. 108 (2010) 123508. [11] D.E. Chimenti, Energy leakage from Rayleigh waves on a fluid-loaded, layered half-space, Appl. Phys. Lett. 43 (1) (1983) 46–47. [12] Y. Zhao, Z. Shen, J. Lu, X. Ni, A finite element model for laser-induced leaky waves at fluid–solid interfaces, Phys. Lett. A 370 (2007) 104–109. [13] J. Zhu, J.S. Popovics, F. Schubert, Leaky Rayleigh and Scholte waves at the fluid–solid interface subjected to transient point loading, J. Acoust. Soc. Am. 116 (4) (2004) 2101–2110.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Influence of acoustic leakage at fluid–solid interface on interferometric detection of surface acoustic wave Zhao Yan School of science, Nanjing University of Science and Technology, Nanjing 210094, PR China
a r t i c l e
i n f o
Article history: Received 27 May 2013 Accepted 24 October 2013 Keywords: Acoustic leakage Fluid–solid interface Laser ultrasonic Interferometric detection Surface acoustic wave Finite element method
a b s t r a c t When using laser interferometer to detect surface acoustic wave at fluid–solid interface, there are two factors which will cause the optical path length variation of the probe laser beam: interface deformation, and refractive index changes in fluid induced by acoustic leakage. Influence of acoustic leakage on laser interferometric detection for surface acoustic wave is researched here. A metal plate immersed in an infinite fluid is used as a physical model. Interface deformation due to laser-induced acoustic wave and pressure in fluid due to acoustic leakage are computed for select cases by finite element method. The optical path length variation caused by the two factors are calculated respectively and compared. The results show that the influence of acoustic leakage increases with the increasing acoustic impedance matching of fluid and solid, the peak-to-peak of influence degree increases linearly with the increasing acoustic impedance of fluid, and that decreasing the distance between the interferometer and interface can effectively reduce the influence of acoustic leakage. © 2014 Elsevier GmbH. All rights reserved.
1. Introduction There have been extensive studies on surface acoustic wave at fluid–solid interface due to its potential application in seismology, engineering, and non destructive test (NDT) [1–3]. However, its detection is still an urgent problem although there are many methods for measurement of surface acoustic wave. In fact, the most popular method for detection of surface acoustic waves is the transducer one, where the surface acoustic wave signal is detected by a piezoelectric transducer attached to the surface of the solid [4]. Unfortunately, it was pointed out that the acoustic connection between the sample and the transducer will influence the ultrasonic field. In this respects, noncontact measurements are desirable. One method is to employ interferometric detection which can detect without contact ultrasonic field and has a wide responsive bandwidth, so that it was extensively used to detect surface acoustic wave [5–11]. In this technique, the normal surface displacement is deduced from the optical path length variation of a laser beam reflected by the surface. Actually, it was pointed out recently that when surface acoustic wave propagates along fluid–solid interface, the energy of the wave “leaks” into the fluid [12], that will cause the refractive index changes in fluid as a function of both time and space, altering the
E-mail address: [email protected] 0030-4026/$ – see front matter © 2014 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2013.10.117
optical path length of laser beam which propagates in the fluid. As a result, expecting the surface displacement, there is the other factor which induced the optical path length variation of the laser probe beam in interferometric detection, that is refractive index change in fluid induced by acoustic leakage. In previous studies, the acoustic leakage factor is always ignored and the important subject, namely the influence of acoustic leakage on interferometric detection, did not arouse the researchers’ attention until now, which will directly influence the correctness of the results presented by laser interferometric sensor. In this paper, the influence of acoustic leakage in fluid on interferometric detection was researched. Laser-induced interface acoustic field is computed by finite element method due to its advantages and universal application of laser ultrasonic. Two optical path length variation of laser probe beam caused by these two factors are calculated respectively and compared. 2. Interferometric detection of surface acoustic wave Numerous optical interferometries have been developed for detecting surface acoustic wave, such as Michelson interferometry, Mach–Zender interferometry, heterodyne interferometry [7–10]. These devices use the mechanism that the displacement of a vibrating surface is obtained by measuring the optical path length variation of the probe beam due to the motion of the reflected surface. The schematic diagram of laser ultrasonic system is shown in Fig. 1. The optical probe beam from laser interferometer crosses a transparent fluid where the index of refraction is modulated by the
Z. Yan / Optik 125 (2014) 2458–2462
2459
Table 1 Parameter of steel solid. Density
Longitudinal velocity cL (m/s)
Shear velocity cs (m/s)
Acoustic impedance
7800
5980
3246
4.6644 × 107
Table 2 Fluid media.
Fig. 1. Schematic of laser ultrasonic system.
Designation
Density, f (kg/m3 )
Dilatational velocity, cf (m/s)
Acoustic impedance
Water Air F1 F2 F3 F4 F5 F6 F7
1000 1.21 1000 1000 1000 1000 76.5 1.21 76.5
1500 343 1250 1000 961 343 1500 1500 343
1.5 × 106 415.03 1.25 × 106 1 × 106 9.61 × 105 3.43 × 105 1.1475 × 105 1.815 × 103 2.62395 × 104
where M is the material parameter, is density, and c is the speed of sound in the fluid. To determine the influence of acoustic leakage on interferometric detection, it is necessary to firstly determine the acoustic variation in pressure in fluid caused by acoustic leakage and the normal displacement on solid surface. However, it is very difficult for experiment measurement, so numerical calculation is applied for acoustic field in fluid and solid. In this paper, finite element method was introduced to numerically simulate laser-induced ultrasonic wave on fluid–solid interface. Fig. 2. Absolute value of pressure (in water) and stress (in solid) field snapshot at t = 0.72 ms given by finite element analysis. The interface is subject to a transient 2 point load that varies with time as f (t) = sin (t/T ) with T = 200 s.
acoustic wave and is then reflected by a solid surface. The phasemodulated current measured by the laser interferometer is given as
i(t)∼ cos ı(t) + s − R
(1)
where R and s are the phase constants corresponding to the reference and the probe beams of the interferometer. ı(t) is the optical path length variation of probe laser due to the ultrasonic waves and includes two phase changes respectively induced by normal surface displacement (ıs ) and acoustic leakage modulated refraction index (ıR ) for fluid–solid interface case. ıS = −2Uy n0
(2)
L ıR = 2
ndy
(3)
0
where Uy is the normal displacement of the solid surface, n0 is the refractive index of the fluid when there is no acoustic wave present, L is the distance between the interferometer and the interface. Consider a traveling wave in fluid due to acoustic leakage, the variation in the index of refraction index (n) is proportional to the acoustic variation in pressure (p). For a liquid such as water, 1 n = 2
M p c
(4)
For a gas such as air, n =
(n0 − 1)p c 2
(5)
Fig. 3. Absolute value of pressure (in fluid) and displacement (in steel solid) field snapshot at t = 0.11 s given by finite element analysis.
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Z. Yan / Optik 125 (2014) 2458–2462
(a)
LR
0.2
due to normal displacement due to acoustic leakage caused refractive index change
S X=0.2mm
0.1
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Fig. 4. Time history of pressure in water (a) and normal displacement in solid (b) near the interface at x = 0.2 mm, 0.4 mm, 0.6 mm for water–steel case. x is the distance between exciting laser and detecting point, LR represents leaky Rayleigh wave, and S represents Scholte wave.
The numerical analyses were performed to simulate the response for fluid–solid half-space cases. The detailed description of the employed finite element method could be found in our previous paper [13], so we did not discuss it comprehensively. 3. Results and discussions To verify the correctness of numerical simulations, a contrast calculation was performed according to Jinying Zhu’s study [14], and the acoustic field on water-concrete interface simulated by finite element method is shown in Fig. 2. It was in very good agreement with the numerical solution obtained by Jinying Zhu using the elastodynamic finite integration technique that indicated the correctness of our simulation method. Finite element simulations were performed for the case of a laser pulse load at a water–steel interface and air–steel interface. The physical parameters of air, water and steel used in calculations are available in Tables 1 and 2, respectively. The inserted energy of laser source is 13.3 mJ, its half-width and pulse widths are 50 m and 10 ns, respectively. To ensure the stability, efficiency and accuracy and finite element calculation, the size of spatial grid and time grids are 10 m and 2 ns, respectively. According to the numerical simulations, Fig. 3(a) and (b) shows the cross-sectional snapshot image of acoustic field at time t = 0.11 s for water–steel interface and air–steel interface case, respectively. In this figure, the half-circle in the upper half-plane represents the acoustic wave front in fluid, and the inclined lines represent the leaky Rayleigh wave fronts, which are tangent to the half circle at the leaky angle direction. Besides the leaky Rayleigh wave, there are also Scholte and fluid acoustic wave in fluid, longitude wave (L), head wave (HW) and transverse wave (S) in steel
(a) for water-steel case,
optical path length variation (*10^(-9))
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(b) for air-steel case Fig. 5. Optical path length variation due to acoustic leakage and surface displacement measured by laser interferometer position at x = 0.2 mm, 0.4 mm, 0.6 mm. x is the distance between exciting laser and detecting point.
solid. In this figure, the amplitudes of pressure in water and air are multiplied by 0.1 and 150 for clarity of expression. As we all known, when a surface acoustic wave propagates on a fluid–loaded solid surface, the energy of the wave leaks into the fluid and the acoustic leakage is stronger with the increasing acoustic impedance matching between the fluid and solid. So that, one can also easily find that the amplitude of acoustic wave in water are far greater than those in air due to their acoustic impedances. Besides, the velocity of leaky Rayleigh and Scholte wave approximately equal to the velocity of Rayleigh in solid and acoustic velocity in the fluid, respectively, but the waves in solid are identical for the two cases. Fig. 4 shows the time history of pressure in water and normal displacement in solid near the interface at x = 0.2 mm, 0.4 mm, 0.6 mm, respectively, where x is the distance between exciting laser and detecting point. From this figure, it can also be seen that most of Scholte wave energy is localized in the fluid, but leaky Rayleigh wave in solid, and that the two waves gradually separate from each other due to their different velocities. Based on the pressure in fluid and normal displacement on solid surface, the interferometric detected path variation due to refractive index change caused by acoustic leakage and surface displacement can be obtained by Eqs. (2) and (3), respectively, where M = 160 × 10−15 s3 kg−3 , = 1000 kg/m−3 for water, = 1.21 kg/m−3 for air, and c = 1500 ms−1 for water, and c = 343 ms−1 for air. The results are shown in Fig. 5. The influence of acoustic leakage for water–steel configuration is much greater than that for air–steel configuration. Detailed analysis was executed on the degree of influence, which is the ratio between those two path variation. As
Z. Yan / Optik 125 (2014) 2458–2462
Influence caused by leaky Rayleigh wave
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Equation y = a + b*x Adj. R-Square 0.9985 0.99906 Value Standard Error Data1 Interce 0.0364 0.00237 Data1 Slope 9.98344 0.13693 Data2 Interce 0.4621 0.01977 Data2 Slope 105.333 1.1421
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Time (us) Fig. 6. The degree of influence for water–steel case.
shown in Fig. 6 for water–steel configuration, there are two pulses: one is the influence caused by leaky Rayleigh wave, the other is the influence caused by Scholte wave. The former one is much smaller than the last one because most of leaky Rayleigh and Scholte wave are localized in solid and fluid, respectively. However, the influence caused by Scholte wave on the laser interferometric detection of surface acoustic wave on solid surface can be ignored due to its arrival time, but influence caused by leaky Rayleigh wave is much important due to its arrival time identical to that of surface acoustic wave. In order to be able to explore the influence of acoustic leakage on interferometric detection for surface acoustic wave, the finite element calculations are performed for different fluid–solid interface, and the degree of the influence for different cases are obtained. The parameters of fluid media were not restricted to those of known substances, and listed in Table 2. As shown in Fig. 7, when the acoustic impedance of the fluid approaches the acoustic impedance of the solid, the degree of influence due to acoustic leakage gradually increases, because the acoustic leakage and the amplitude of acoustic wave in fluid increase with the increasing acoustic impedance matching of two media. The peak-to-peak of influence degree is compared for different fluid-steel configurations. As shown in Fig. 8, the peak-to-peak of influence degree increases linearly with the increasing of acoustic impedance, and the slopes are 9.98344 and 105.333 for the influence due to leaky Rayleigh wave and Scholte wave in fluid, respectively.
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Fig. 9. Peak-to-peak of influence degree for different optical path, L represents the distance between the interferometer and interface.
Moreover, the same calculation is performed for changing the distance between laser interferometer and interface and the peakto-peak of influence degree is shown in Fig. 9. As shown in this figure, when the interferometer is placed closer to the interface, the influence of acoustic leakage will be smaller. That is to say decreasing the distance between the interferometer and interface can effectively reduce the influence of acoustic leakage. 4. Conclusion In summary, the influence of acoustic leakage on laser interferometric detection for surface acoustic wave on fluid–solid interface is investigated. We find that with the increasing acoustic impedance matching of fluid and solid, the leaky energy of Rayleigh wave and Scholte increases, and the optical path length variation due to acoustic leakage increases and then the influence of acoustic leakage increases. It is also found that the peak-to-peak of influence degree increases linearly with the increasing acoustic impedance of fluid up to that of solid, and that decreasing the distance between the interferometer and interface can effectively reduce the influence of acoustic leakage.
water-steel case F1-steel case F2-steel case F3-steel case F5-steel case F6-steel case
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Acknowledgments
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Fig. 7. The degree of influence for different fluid-steel configuration.
This work is supported by the Natural Science Foundation of Jiangsu Province (grant BK2010494), and the National Natural Science Foundation of China (grant 11204136).
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