LAMB WAVE DISPERSION CHARACTERIZATION USING
MULTIPLEXED TWO-WAVE MIXING INTERFEROMETRY
Yi Zhou, Feifei Zhang, and Sridhar Krishnaswamy
Center for Quality Engineering and Failure Prevention,
Northwestern University, Evanston, IL 60208-3020
ABSTRACT. In recent work at Northwestern University, Multiplexed Two-Wave Mixing
Interferometers (MTWM) have been developed. These systems are able to perform optical
detection of ultrasonic motion over an array of points simultaneously. Optical phase gratings are
used to create a detection-array of laser beams that are directed to the specimen. The detection
array can be arranged in several ways on the test object. The scattered beams from the detectionarray are collected and combined with a single reference beam in a photorefractive crystal to
form a multiplexed two-wave mixing configuration. Each of the output beams from the
photorefractive crystal is imaged on to a separate element of a photodetector array. The resulting
MTWM system is capable of providing simultaneous optical detection (with high spatial
resolution and sub-nanometer displacement sensitivities) at several points on a test object. The
MTWM system can be used in several modes for laser ultrasonic NDE of flaws and materials
characterization. In this paper we present recent advances and applications of this technology. An
application of the MTWM system for fast recovery of Lamb wave dispersion curves is presented.
We obtain the dispersive time-domain Lamb wave signals at multiple source-to-receiver
distances. Following the algorithm of Alleyne and Cawley, these time-position domain signals
are transformed to the frequency-wavenumber domain using a 2D FFT technique. The MTWM
system enables rapid characterization of Lamb wave dispersion.
INTRODUCTION
Laser ultrasonics has been demonstrated to be a promising technique in nondestructive
evaluation due to its noncontact, high spatial resolution nature, sub-nanometer sensitivities
and its ability to be used on complex shapes and at high temperature. Laser ultrasonic
systems, which perform both the generation and detection in a remote way, have been
proved to be good substitutes to conventional piezoelectric transducer systems. Several
applications of laser ultrasonic systems in crack locating, sizing, imaging and materials
characterization have been demonstrated. The most conventional setup in today's laser
ultrasonic system uses point source and point receiver configurations. This usually requires
scanning over the whole test area to get the desired result, which can be quite time
consuming. The array technique is a good candidate to solve this problem. The idea for
multiplexing in laser ultrasonic systems is to do parallel detection in one optical laser
CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti
© 2003 American Institute of Physics 0-7354-0117-9/03/$20.00
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ultrasonic system using an array of laser beams. With this configuration, we can
simultaneously detect the ultrasonic signal at a series of focused points on the test sample
surface. Recently at Northwestern, we have developed such a multiplexed two-wave
mixing (MTWM) interferometer system. This system is built using multiple laser beams
instead of a single laser beam in the conventional two-wave mixing setup. The noncontact
nature, ability to be used in complex shapes, parallel processing and dynamic focusing
ability make this system ideal for various laser ultrasonic applications.
Previously at Northwestern University, we have demonstrated several applications of
the MTWM system including for phased array imaging with surface waves and bulk waves
[1], and for anisotropic materials characterization [2]. In recent research on this MTWM
system, we have combined the MTWM receiver with the 2D-FFT technique to do fast
Lamb wave dispersion curve recovery. Alleyne and Cawley used the 2D-FFT technique to
obtain the dispersion curve for the two lowest modes of the Lamb wave [3] [4]. But their
work uses contact piezoelectric transducers, which can introduce frequency biases and is
also quite time consuming. Costley et al [5] used the laser ultrasonic technique and the
two-dimensional Fourier transform to develop the dispersion curve of the Lamb wave in a
limited frequency range. But they only used a laser in the generation part and used a PZT
transducer to detect the Lamb wave signal. Schumacher et al [6] used a complete laser
ultrasonic technique and FFT processing technique to obtain the phase velocity by
measuring the ultrasonic signal at two different points. But they could only identify three
modes because the two-points phase velocity extraction method requires that each of the
modes must be well separated from the others. Eisenhardt et al [7] used a complete laser
ultrasonic technique and two-dimensional Fourier transform to obtain the Lamb wave
dispersion. But their laser ultrasonic system used a single point source and a signal point
receiver scheme, with subsequent scanning to obtain data at multiple source-to-receiver
distances. Since several hundred data sets are needed to obtain high resolution and range in
the wavenumber domain, this is quite time consuming. In the technique discussed in this
paper, we use a fully laser ultrasonic technique, including optical generation and true
optical array detection. First we obtain the time trace signals at a set of discrete source-toreceiver distances using our MTWM system. These are then transferred from time-distance
domain to frequency-wavenumber domain using the 2D-FFT technique. Results are shown
for the Lamb wave dispersion curve on an aluminum plate. This application demonstrates
that the MTWM system enables rapid characterization of Lamb wave dispersion.
MULTIPLEXED TWO-WAVE MIXNG INTEFEROMETERY SYSTEM
Figure 1 shows a schematic of the multiplexed two-wave mixing (MTWM) system. The
multiplexed interferometer is a homodyne scheme based on two-wave mixing in a BSO
photorefractive crystal (PRC). This interferometer is similar to that described in detail in
the literature [8], but with the addition of a phase grating and imaging system making array
detection possible. The interferometer uses an argon laser source that is first sent to a
variable beamsplitter and divided into object and reference beams. The object beam is
passed through a phase grating which splits the beam, in the present case, into eight or nine
beams of approximately equal intensity that subsequently pass through a lens system to
illuminate the sample surface. The scattered light is collected by a lens, passed to a halfwave plate where the polarization is rotated 45 degrees, and directed to the PRC where the
object beams are mixed with a single reference beam. At the output of the PRC, the
diffracted pump beams (which are wavefront matched with the object beams) and the
transmitted object beams (which contain the signals of interest) are collected. The object
beams are then phase delayed with respect to the reference beam using a compensator. The
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to photodetectors
PRC, AC Field
6KV/cm, 3.2 KHz
FIGURE 1: Multiplexed Two-Wave Mixing (MTWM) interferometry system configuration. Optical
components are presented as follows: PG: Phase grating, PRC: Photorefractive crystal, BC: Berek
compensator, PBS: Polarizing beamsplitter.
phase shift is chosen such that interference occurs at quadrature in order to maximize the
detection sensitivity. The beams are then passed through another lens where they are
imaged to a series of points at the plane of the photodetector array. A half-wave plate and
polarized beam splitter combination allow for the combination of each of the polarization
components at balanced optical detectors. The BSO crystal was oriented with grating
vector along the [001] crystal axis and an electric field of 6kV/cm at 3200 Hz was applied
to enhance the diffraction efficiency. Note that PRC based systems are able to work off of
optically rough surfaces, and that they are adaptive and therefore do not require active
stabilization.
0.88
0.86
| 0.84
% 0.82
g 0.80
13 0.78
0.76
0.74
5
6
Time (jos)
7
FIGURE 2: Signals received by three adjacent elements in a nine-element array showing that cross-talk is
minimal.
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The MTWM system was first characterized to determine if the array elements were
operating independently and each array element was checked for cross-talk. A nine element
array was created with an array spacing of d = 0.5mm between elements. A focused laser
line source operating in the thermoelastic regime was used to generate surface waves
(SAWs) on an aluminum sample. The line source was perpendicular to the detection array
such there was a time delay of vd (where v is the SAW velocity) between the time that the
SAW arrived at adjacent elements. The total laser power was 400mW and the beam ratio
was adjusted using a variable beamsplitter to split the power into object and reference
beams while keeping the total laser power constant. It was observed that cross-talk is
minimal when the reference beam power is at least 10 times that of the object beams.
Figure 2 shows the signals detected by three adjacent elements. The amplitude SNR is -80
for the signals shown and it is clear that there is no detectable cross-talk.
LAMB WAVE DISPERSION CURVE CHARACTERIZATION USING 2D-FFT
As the literature [3-7] shows, the idea for Lamb wave dispersion characterization using
2D-FFT technique is very simple. In a broadband Lamb wave field, we detect the
ultrasonic signal at a set of different source to receiver distances at equal spacing, then
trasform the data set from the time and distance domain to the frequency and wavenumber
domain using two dimensional Fourier transform. The result is a direct map of the
dispersion of the Lamb waves in the structure.
Figure 3 shows the configuration for the dispersion curve characterization using 2D-FFT
technique. In this setup, we use a 0.44mm thick aluminum plate as the specimen. The plate
is large enough laterally that is can be treated as of infinite extent. A Nd: YAG laser is used
\
0.14J7,
:/
Aluminum plate
Scan direction
-12
8 element array
Line source
j
**——————
56 ——
cylindrical lens ^H p>
^
£L
1 Q
^
t
^
Nd:YAG laser source
Argon a ser (514nm)
(1064nm)
Start position
Stop position
Units: m
FIGURE 3: Experimental configuration of the dispersion curve characterization experiment using 2D-FFT
technique.
336
10
15
25
20
30
Time (us)
FIGURE 4: Typical detected Lamb wave signals with 0.97mm spacing.
as the generation laser source and is focused as a line source on to the specimen by a
cylindrical lens to generate broadband Lamb waves. An 8-element detection array with
spacing 0.14mm is used to detect the Lamb wave signals. In order to get 400 data sets at
different source to receiver distances, we move the line source 50 times by 1.12mm each
time. As we can see here, we save a lot of time by using an eight element array compared
to a single receiver setup where the generator will have to be moved 400 times.
Figure 4 shows the typical Lamb wave signals with 0.97mm spacing detected by the
MTWM system. From this figure it can be seen that the Lamb wave signal is highly
dispersive.
20000
1
2
3
4
Frequency-Thickness(MHz-mm)
FIGURE 5: The Lamb wave dispersion curve on an aluminum plate.
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20000 -
15000-
I
10000-
5000-
0
higher mode
1
2
3
_
4
Frequency-Thickness(MHz-mm)
FIGURE 6: The theoretical Lamb wave dispersion curve on an aluminum plate.
After all 400 sets of data were collected, they were trasformed from the time-distance
domain to the frequency-wave number domain by using the two-dimensional Fourier
transform:
H(k,f)=
(1)
where u(x,t) is the detected Lamb wave signal in time t and distance x domain, and H(k,f) is
its transform in the frequency/and wavenumber k domain.
The time-space domain data set u(x,t) is transformed using standard two dimensional
fast fourier trasform (2D-FFT) subroutine and the result is shown in figure 5. The x
coordinate in figure 5 is the frequency-thickness product which makes the result thickness
independent. The 3; coordinate is the wave number. From figure 5, we can see that four
modes appear. The strongest is the a0 mode which agrees with the fact that this mode
dominates the Lamb wave signal in the time domain trace, as shown in figure 4. Below the
ao mode one can see the first symmetric mode s0. In addition to the a0 and s0 modes, we can
also see that higher order modes such as the aj, sj modes appear. The experimental data
appear to agree well with the theoretical Lamb wave dispersional curve on aluminum
calculated in figure 6.
CONCLUSION
In this paper, fast characterization of the Lamb wave dispersion using a recently
developed MTWM system is reported. In this application, the MTWM system is used to
detect the time domain Lamb wave signal at different source to receiver distances
simultaneously. The collected data set, which is in time and distance domain, is
transformed into the frequency-wavenumber domain by using two-dimensional Fourier
transform. It is shown that the MTWM system enables rapid characterization of Lamb
wave dispersion.
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ACKNOWLEDGEMENTS
Support of the Air Force Office of Scientific Research through grant # F49620-98-10285 is gratefully acknowledged.
REFERENCES
1. T.W.Murry, Y. Zhou and S. Krishnaswamy, Review of Progress in Quantitative
Nondestructive Evaluation, Eds. D.O.Thompson and D.E.Chementi, Vol. 20,
pp236-243, (2000)
2. Y. Zhou, T.W. Murray, and S. Krishnaswamy, IEEE Trans. Ultrason., Ferroelect.,
Freq. Contr., Vol 49, No.8, ppl 118-1123 (2002)
3. D.Alleyne and P.Cawley, J.Acoust. Soc. Am. 89 (3) ppl 159-1168 (1991)
4. D.N.Alleyne and P. Cawley, IEEE Trans. Ultrason., Ferroelect., Freq. Contr.,
Vol. 39, No.3, pp381-397 (1992)
5. R.D.Costley, Y.H.Berthelot and L.JJacobs, Journal of Acoustic Emission, Vol.12,
No.l-2,pp.27-38
6. N.A.Schumacher, C.P.Burger and P.H.Gien, J.Acoust. Soc. Am. 93 (5) pp29812984(1993)
7. C.Eisenhardt, L.J.Jacobs and J.Qu, Journal of Applied Mechanics, Vol. 66,
pp!043-1045, (1999)
8. A.Blouin and J.P.Monchalin, Appl. Phys. Lett., 65(8) 1994
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