Frequency dependence of laser ultrasonic SAW phase velocities measurements

Ultrasonics 53 (2013) 191–195

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Frequency dependence of laser ultrasonic SAW phase velocities measurements Chunhui Li a,b, Shaozhen Song a,b, Guangying Guan a,b, Ruikang K. Wang b, Zhihong Huang a,⇑ a b

School of Engineering, Physics and Mathematics, University of Dundee, Dundee DD1 4HN, Scotland, UK Department of Bioengineering, University of Washington, 3720 15th Ave. NE, Seattle, WA 98195, USA

a r t i c l e

i n f o

Article history: Received 1 September 2011 Received in revised form 29 May 2012 Accepted 29 May 2012 Available online 9 June 2012 Keywords: Laser ultrasonics Surface acoustic wave (SAW) Phase velocity Frequency content Young’s modulus

a b s t r a c t Advances in the field of laser ultrasonics have opened up new possibilities in applications in many areas. This paper verifies the relationship between phase velocities of different materials, including hard solid and soft solid, and the frequency range of SAW signal. We propose a novel approach that utilizes a low coherence interferometer to detect the laser-induced surface acoustic waves (SAWs). A Nd:YAG focused laser line-source is applied to steel, iron, plastic plates and a 3.5% agar–agar phantom. The generated SAW signals are detected by a time domain low coherence interferometry system. SAW phase velocity dispersion curves were calculated, from which the elasticity of the specimens was evaluated. The relationship between frequency content and phase velocities was analyzed. We show that the experimental results agreed well with those of the theoretical expectations. Crown Copyright Ó 2012 Published by Elsevier B.V. All rights reserved.

broad bandwidth. In general, the maximum frequency of a SAW signal is related to the phase velocity of material [9]:

1. Introduction Laser ultrasonics (LUS) is a remote, non-contact technique that uses a short pulsed laser to excite surface acoustic waves (SAWs) (dominated by Rayleigh waves) to characterize the mechanical properties of material by means of measuring the phase velocity dispersion curves of SAW. SAW-based technology has been used in industry applications such as analyzing the surface structure, compositions, geometry, roughness, plainness and elastic properties of metallic specimens [1–7]. When a material is illuminated with a short laser pulse, the absorption of laser energy results a rapid increase in temperature of the irradiated volume that in turn causes a rapid thermal expansion. The result is the generation of ultrasonic waves that propagate within the material, including SAW. The phase velocity of SAW at different frequency is dependent on the elastic and geometric properties of the material [8]. In isotropic homogeneous material, the surface wave velocity c can be approximated as [1]:

c¼

 12 0:87 þ 1:12v E 2qð1 þ v Þ 1þv

ð1Þ

where E is the Young’s modulus, v is the Poisson’s ratio, and q is the density of material. To detect the laser-induced SAW, the most common method is to employ contact ultrasound transducers. But the selection of proper operating frequency range for ultrasound probes is typically a problem in fabrication procedures, as a typical SAW signal has a ⇑ Corresponding author. E-mail address: [email protected] (Z. Huang).

fmax ¼

pffiffiffi 2 2c pr 0

ð2Þ

where r0 is the radius of laser pulse and c is the velocity of Rayleigh wave. However, no experimental data was found in literature in validating this equation. This paper verifies the relationship between laser-generated SAW frequency range and phase velocity, which could be greatly helpful for the development and fabrication of ultrasonic transducers employed as receivers of SAW in laser ultrasonics technology. A 532 nm Nd:YAG focused laser line-source was applied to three different kinds of hard solid materials including steel, iron, plastic plate. This paper also demonstrates that a laser-generated SAW phase velocity dispersion technique can be used to evaluate the mechanical properties of soft materials (tissue-mimicking phantom). The generated SAW signals from different materials were detected by a low coherence interferometry system, with different receiving points. Dispersion phase velocity curves and frequency mapping then were calculated to obtain the relationships as well as the elastic properties of different specimen. The relationship between Young’s modulus and frequency range of SAW signal were concluded. 2. System configuration The system set up for generation and detection of laser-induced SAW is shown in Fig. 1. Briefly, the system includes two main

0041-624X/$ - see front matter Crown Copyright Ó 2012 Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ultras.2012.05.009

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parts: the generation of laser-induced SAW and the detection of laser-induced SAW by a low coherence interferometry. 2.1. Generation of laser-induced SAW A solid state Nd:YAG laser (532 nm central wavelength) (Continuum Surelite Laser) was used as the high energy laser pulse source. The short laser pulse was set to the Q-switched mode with the single pulse duration of 6 ns FWHM (rise time 3 ns), average energy of 2.6–3 mJ and repetition rate of 0.5 Hz (2 s). The laser beam is in Gaussian profile. During the experiment, the laser irradiation on the test specimens was continuously monitored to make sure that there was no surface damage of the energy level used. Before laser pulses were applied to the sample, a cylindrical lens was employed to generate a line source with the line extent of 2– 2.5 mm with width of 1 mm. Compared with the focused laser pulse, the line source significantly reduced irradiated power density on the sample. Thus, the more affordable energy can be injected into the specimen, permitting an improved signal/noise ratio for measurement of surface wave-forms compared with that for a circularly symmetric source [10–13]. In order to record the dispersion of laser-induced surface waves, several detecting locations with known separation distances are required. Here, we propose a novel use of low coherence interferometry to record the laser-induced SAW from positions close to the excitation field to the far field. We mounted the reflection mirror and cylindrical lens (shown in Fig. 1) on a translation stage, so that the excitation laser beam was translated to the required distances for the measurement of generated SAW signals. In this way the stability of measured signals could be achieved without moving the interferometry detection arm. 2.2. Detection of laser-induced SAW by a low coherence interferometry Detection of the laser-induced SAW was performed by a low coherence interferometry system. There are several reasons to adopt the low coherence interferometry as the detection method in this project. Primarily compared with conventional interferometry, the low coherence interferometry is able to localize the targeted positions on the sample surface within a depth defined by axial resolution of the system (which is determined by the coherence length of the light source). This is advantageous because when the probe beam is aimed at the surface of the sample, only the surface wave signal is detected, which reduces noise from environment. The low coherence interferometry system consists of a 1310 ± 28 nm broadband superluminescent diode (Dense Light sled broad band source) as the light source, a 3-port optical fiber circulator, a 4-port 50/50 optical fiber coupler, a balanced amplified photo detector (PDB120C-75 MHz), a reference arm and a

sample arm. Briefly, light from low-coherence broadband light source is split into two paths in a 50/50 fiber based Michelson interferometry. One beam is coupled onto a stationary reference mirror and the second is focused onto the samples via an object lens. As mentioned before, the sample arm was fixed in order to maintain the stability of measured signals. The measured signal can be expressed as [5]:

pffiffiffiffiffiffiffiffiffiffiffi IðkÞ ¼ s I1  I2 cosðu þ 2kDz þ unoise Þ

ð3Þ

where k = 2p/k, Dz is the change of optical path caused by laser induced SAW signals, u is the initial phase difference due to the optical path length difference between the sample and reference arms, which was carefully adjusted to be p/2, and unoise is a random low frequency phase due to the optical system noise and environment vibration. The value of I(k) changed constantly and steadily due to the random noise unoise. I(k) was monitored by a digital oscilloscope (Tektronix TDS5104B Digital phosphor oscilloscope). We only recorded the SAW signals at the times that u + unoise = ±kp + p/2 when the system became most sensitive. This allowed the detection of SAW signals under similar conditions. The detection system shows a bandwidth of 75 MHz, with the sensitivity of 35 dB [14]. In order to avoid frequency aliasing, a 125 MHz sampling frequency was used for hard solid materials. Since the Young’s modulus for soft materials is much lower than that of the hard materials, the maximum frequency content of a SAW in soft solid can be lower than hard solid such as hard plastic plates [6,7,10]. The SAW signal generated in agar–agar phantom by the laser irradiation was recorded by the digital oscilloscope at 5 MHz. 2.3. Signal processing of SAW phase velocity dispersion curve The SAW signals were recorded on each sample surface at different temporal locations. For each temporal location on the sample surface, six measurements were made and their average was high-pass filtered to reduce the DC noise. Then the signal was denoised using Hilbert–Huang method to reduce the high-frequency random noise [15]. Most of the traditional de-noising methods are linear methods. But laser ultrasonic signal have sharp edges and very short duration, with a broadband frequency, so it is not appropriate to use linear de-noising methods. HHT uses empirical mode decomposition (EMD) method to decompose a signal into a collection of intrinsic mode functions (IMF) [15]. Similar with the wavelet method, each the decomposed IMF domains a frequency range, from high frequency to low frequency. To reduce the high frequency noise, we discard the high frequency domain IFM and add the rest of the IMF together to obtain a new de-noised signal. Then, the phase velocity dispersion of two measured signals, y1(t) and y2(t), at selected locations x1 and x2 were analyzed. The phase difference Du between y1(t) and y2(t) was calculated by the phase of the cross-power spectrum Y12(f):

Y 12 ðf Þ ¼ Y 1 ðf Þ  Y 2 ðf Þ ¼ A1 A2 eiðu2 u1 Þ

ð4Þ

where Y1(f) and Y2(f) are Fourier transforms of the measured signals y1(t) and y2(t), A1 and A2 are the amplitude of cross-power spectrum and Du = u1  u2 is the phase difference. When the propagation wave has a wavelength equal to the distance Dx (the distance between two measurement position, equal to x1  x2), the measured phase difference will be 2p. In general, the ratio between the phase difference and 2p equals to the ratio between the distance and the wavelength:

Du=2p ¼ ðx1  x2 Þ=k

ð5Þ

Also phase velocity and frequency are related by: Fig. 1. System set up of SAW generation and detection.

c ¼ ðx1  x2 Þ  2p  f =Du

ð6Þ

C. Li et al. / Ultrasonics 53 (2013) 191–195

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Fig. 2. Left column shows SAW signal of steel plate (a), iron (c) and plastic plate (e) with the distance of 1 mm (bottom) to 6 mm (top) to laser pulse, with 1 mm/step. Each SAW signal is purposely shifted vertically by equal distance in order to better illustrate the results captured from different positions; while right column shows power spectrum in the detected SAW of steel plate (b), iron (d) and plastic plate (f).

Here, both autocorrelation spectrum and phase velocity dispersion curves are the key functions in our analyses, as the former provides the available frequency range of the signals, while the latter provides important elastic and structural information of samples. Previously Wang et al. indicated that when signals dropped 20 dB

below the maximum of autocorrelation spectrum, uncertainty of dispersion curves increased [2]. Therefore, the frequency range of signals should be defined before analyzing phase velocity dispersion curves. The final phase velocity dispersion curve was measured by averaging the phase velocities of every two possible signals.

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4000

The specimen of mild steel, cast iron and Perspex plastic plates are utilized in the experiment, all the specimen plates have a thickness of 50–100 mm. Fig. 2a, c and e shows the typical SAW recorded from steel plate, iron and black plastic plate, respectively. The excitation laser beam was first located at a position 1 mm away from the detecting point (bottom), and then moved with 1 mm/step to 6 mm away (top). It is clear from these figures that the SAW is propagating away from the laser-excitation position. In addition, attenuations between the waveforms were clearly observed. Fig. 2b, d and f shows the normalized power spectrum of all six SAW signals of steel plate, iron and black plastic plate corresponding to the left column. Optimal cut-off frequency was selected based on the frequency content in the power spectrum. In this case, we chose the cut-off frequency at 5.5 MHz in the case of steel plate because at this frequency, the power spectrum dropped 20 dB below the maximum. While base on the same rule we could obtain that the maximum frequency content of a SAW

3500

Phase velocity (m/s)

3. Results and discussion

Phase velocity curve of steel Phase velocity curve of iron Phase velocity curve of plastic plate

3000 2500 2000 1500 1000 500

0

1

2

3

4

5

6

Frequency (MHz) Fig. 5. Phase velocity dispersion curve of steel, iron and plastic plate.

30

25

Phase velocity (m/s)

SAW Signal Strength (Arb.)

3mm to laser pulse 2.5mm to laser pulse 2mm to laser pulse 1.5mm to laser pulse

20

15

10

5

1mm to laser pulse 0.5mm to laser pulse

0

0

2

4

6

8

10

12

14

16

18

20

Frequency (kHz) 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

time (ms) Fig. 3. SAW signal of one layer 3.5% agar–agar phantom with the distance of 0.5 mm (top) to 3 mm (bottom) to laser pulse, with 0.5 mm/step. Each SAW signal is purposely shifted vertically by equal distance in order to better illustrate the results captured from different positions.

Fig. 4. Power spectrum of the detected SAW of one layer 3.5% agar–agar phantom.

Fig. 6. Phase velocity dispersion curve of 3.5% agar phantom.

signal in iron plate is approximately 3.5 MHz and that in plastic plate is approximately 2.0 MHz. Experiments are also carried on the tissue mimicking phantom, which was made of 3.5% solidified agar solution. All the phantoms were homogeneous, with a minimum thickness of 50 mm to make the treatment of our measurements under the semi-infinite conditions valid. Fig. 3 shows the typical SAW recorded from one layer 3.5% agar phantom. The excitation laser beam was first located at a position 0.5 mm away from the detecting point (bottom), and then moved in 0.5 mm steps to 3 mm away (top). Compared with the laser-induced SAW in the hard materials which shown in Fig. 2a, c and e the SAW in the soft material had a longer wavelength and traveled at a slower velocity with the amplitude of around 10 nm as estimated [10]. In addition, a clear attenuation between the waveforms was observed. The spikes observed in every signal at the time 0.08 ms is high frequency thermal expansion when laser pulse was given. Fig. 4 shows the power spectrum of all six SAW signals shown in Fig. 3. The cut-off frequency is at 20 kHz. Figs. 5 and 6 indicates the phase velocity dispersion curves of the SAWs in solid specimens and agar phantom. The phase velocity remains at a steady level in these homogeneous specimens as expected. Table 1 shows the relationship between Young’s modulus and maximum SAW frequency of steel, iron, plastic plate and 3.5% agar–agar phantom respectively. Combining Eq. (1), the Young’s moduli were evaluated by the mean phase velocity in each

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C. Li et al. / Ultrasonics 53 (2013) 191–195 Table 1 Relationship between Young’s modulus and maximum SAW frequency. Material

Steel Iron Plastic 3.5% Agar phantom

Material property

Experimental data 3

Poisson’s ratio

Density (g/cm )

Phase velocity (m/s)

Young’s modulus

0.29 0.27 0.39 0.495

7.9 7.2 1.18 1.05

3005.54 ± 137.95 2040.76 ± 157.31 1350 ± 170.87 13 ± 1.25

217.45 ± 0.46 GPa 87.38 ± 0.53 GPa 5.45 ± 0.69 GPa 592 ± 5.39 kPa

material phase velocity dispersion curves measured from Fig. 2a, c, and e and Fig. 3, the results were matched very well with literature. [1,2,10,16–18]. Note that the Poisson’s ratio and density of different materials are assumed from pervious study and literature [10,19–23]. From the table, as expected, with decreasing of Young’s modulus, the maximum SAW frequency reduces. In addition, the maximum of frequency content of SAW signal increases monotonically with the increase of the phase velocity of each sample, as expected. Thus, maximum of frequency content of SAW signal increased with the root of estimated Young’s modulus. Combining Eqs. (1) and (2), the maximum SAW frequency can be described by:

fmax

Max. SAW frequency

 12 2:46 þ 3:16v E ¼ 2qð1 þ v Þ ð1 þ v Þpr 0

ð7Þ

[3]

[4]

[5]

[6] [7] [8] [9]

Here, we employed r0 as 0.5 mm (equal to half of the line source width), it can be calculated from Eq. (2) that the expected maximum frequency contents of steel, iron, plastic plate and 3.5% agar phantom are 5.6 MHz, 3.6 MHz, 2.2 MHz and 23 kHz respectively. It can be observed that our experimental results agreed with the expectations. Eq. (6) could be employed to evaluate the maximum SAW frequency content, given the sample properties and generation setup. 4. Conclusion We have presented a technique that combines laser ultrasonics with a low coherence interferometry to characterize the mechanical properties of both hard materials and soft materials and find the relationship between the phase velocity and Young’s modulus of materials and the range of SAW frequency. We used a line lasersource to generate SAW in hard materials, such as steel, iron, plastic plate and 3.5% agar–agar phantom. From this study, the proper ultrasound transducer for SAW detection can be selected by calculating the available frequency range of SAW in a specific material. We have shown that the experimental results are in good agreement with that of the theoretical expectations.

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