Laser Based Ultrasonic Generation and Detection of Zero Group Velocity
Lamb Waves in Thin Plates
Suraj Bramhavar1, Oluwaseyi Balogun2, Todd Murray2
1Boston University, Department of Electrical and Computer Engineering
2Boston University, Department of Aerospace and Mechanical Engineering
[email protected], [email protected]
This work was supported by CenSSIS, the Center for Subsurface Sensing and Imaging Systems,
under the Engineering Research Centers Program of the National Science Foundation (Award Number EEC-9986821)
Abstract:
A laser based ultrasonic technique for the inspection of thin plates and membranes is presented, in which Lamb waves are excited using a pulsed laser source. The dominant feature in the measured acoustic spectrum is a sharp resonance peak that occurs at the
minimum frequency of the first-order symmetric Lamb mode, where the group velocity of the Lamb wave goes to zero while the phase velocity remains finite. Experimental results with the laser source and receiver on epicenter demonstrate that the zero group velocity
resonance, generated thermoelastically, can be detected using a Michelson interferometer. The amplitude, resonance frequency, and quality factor of the zero group velocity resonance are studied as a function of plate thickness and mechanical properties. It is
proposed that the characteristics of the resonance peak may be used to map nanoscale thickness variations in thin plates, and for the detection and sizing of subsurface defects.
Introduction
Laser Generation of Ultrasound
Theoretical Formulation
Lamb Waves
Laser Detection of Ultrasound
• Dispersive guided waves
propagating in plate-like structures
Michelson Interferometer
Reference mirror
Obj.
Reference beam
= + (bright)
Quasi-Resonance (ZGVr)
• Propagate in the form of symmetric and
antisymmetric modes
Theoretical Spectrum (50 μm Tungsten)
• Resonance localized in space
Ref.
Beamsplitter
= - (dark)
Laser
Ref.
1.5
d
symmetric
Obj.
Amplitude
Specimen
Ref.
Rayleigh-Lamb Frequency Equations
for symmetric modes:
for antisymmetric modes:
tan(qh)
(q 2  k 2 ) 2

tan( ph)
4k 2 pq
tan(qh)
4k 2 pq
 2 2 2
tan( ph)
(q  k )
2
2
 
 
2
2
where: p     k and q     k 2
 cL 
 cT 
  angular frequency , cP = phase velocity
2
Applications / Advantages
• Allows for determination of thickness and mechanical properties of
materials
• Allows for high bandwidth generation and detection of ultrasound
(over GHz bandwidth possible)
• Develop a non-contact, non-destructive method to measure small-scale
thickness variations and mechanical properties in thin films
• Zero group velocity resonance is localized in space allowing for high
resolution material characterization
2.5
3.0
0
A2
15
80
100
350
ZGVr
10
300
5
250
1.0
1.5
2.0
2.5
3.0
• Q increases as
thickness decreases
3.5
• Allows for precise
thickness measurements
of very thin plates
200
150
100
• Arrows denote mode cutoff frequencies
(resonances)
50
0
• Phase velocity approaches infinity as
group velocity approaches zero
0
20
40
60
80
100
120
140
160
Plate Thickness (m)
Preliminary Experiments (50μm Tungsten)
Filtered Time-Domain Signal
Reference mirror on
piezoelectric mount
Pulsewidth = 610 ps
Amplitude Spectrum
0.0012
0.03
Rep. Rate = 5.6 kHz
ZGVr
0.0010
sample
lens
Amplitude (mV)
Generation
Laser: (1064nm)
Pulse Energy = 10.2 uJ
0.0008
0.00
0.0006
cL/2d
0.0004
3cL/2d
lens
0.0002
-0.03
0.0000
photodetector
0
2
Amplitude Spectrum Comparison
44.62MHz
23.87MHz
1.0
50m tungsten
Avg Q = 73.02
Amplitude (normalized)
100m tungsten
Avg Q = 48.58
0.8
• Waveforms were collected at
ten points separated by 1μm on
each sample
• Resonant frequency shifts as
sample thickness changes
0.4
4
6
0
20
Time (s)
40
60
80
100
• Agrees well with theoretical spectrum
Conclusions and Future Work
Conclusions
0.2
• Q increases as sample
thickness decreases
 Laser-based photoacoustic methods were used for in vivo imaging of rat
brains.[4]
10
20
30
40
50
Frequency (MHz)
60
Q vs. Spot Size
References:
1.0
2.
Hutchins, D.A., Lundgren, K., Palmer, S.B., “A laser study of transient Lamb waves in thin materials,”
J.Acoust. Soc. Am., 85(4), 1441-1448, (1989).
0.8
Amplitude (normalized)
1.
Murray, T.W., Balogun, O., “High-sensitivity laser-based acoustic microscopy using a modulated excitation
source,” Applied Physics Letters, 85(14), 2974-2976, (2004).
Spot Size
220m
170m
145m
120m
0.6
0.4
0.2
23.5
24.0
• Signal-to-Noise ratio increases
as spot size decreases
• Similar pattern was seen in
50μm tungsten sample
100m tungsten
23.0
• Results show that spot size has
negligible effect on Q
24.5
Frequency (MHz)
25.0
120
Frequency (MHz)
• High-pass filter at 25MHz was used
to eliminate large initial DC offset
0.6
0.0
4.
Wang, X., Pang, W., Ku, G., Xie, X., Stoica, G., Wang, L., “Non-invasive laser-induced photoacoustic
tomography for structural and functional in vivo imaging of the brain,” Nature Biotechnology, 21(7), 803-806, (2003).
60
Theoretical Model – Q vs.Thickness
20
Detection: 532nm
CW Laser
(120mW)
 A laser-based acoustic microscopy system was developed to generate
ultrasonic waves using a narrowband CW-modulated laser and detect these
waves using a Michelson interferometer. [1]
3.
Chimenti, D.E., Holland, S.D., “Air-coupled acoustic imaging with zero-group-velocity Lamb modes,”
Applied Physics Letters, 83(13), 2704-2706, (2003).
40
Frequency (MHz)
Experimental Setup
State of the Art
 A zero group velocity resonance was found that allowed for very efficient
transmission of sound waves through plates. [3]
• Changes in thickness of the
sample results in shift of
resonance peak
Experimental Results
• Research involves aspects of many fields including optics, acoustics, and
signal processing
 A method was developed using lasers to generate and detect Lamb waves in
thin materials in an effort to obtain thickness and elastic property measurements
simultaneously. [2]
20
S1
A1
25
Significance and Relation to CenSSIS
• High sensitivity and
high resolution may
create possibility for use
as small-scale chemical
or biological sensor
• Resonant frequency
dependent on thickness
0.0
Solutions to the Rayleigh-Lamb frequency
equations result in multiple modes shown above
• First order symmetric (S1) and
first and second order asymmetric
(A1, A2) modes shown
• Allows for small-scale
thickness mapping of
thin films
3cT/2d
3.5
Frequency*Thickness (MHz-mm)
• Dispersion curves are shown in the form
of phase velocity as a function of the
frequency-thickness product
Motivation
2.0
cT/2d
30

k=
; cL , cT  longitudinal,shear wave velocity
cP
• High spatial resolution
1.5
1.0
0.5
35
Phase Velocity (mm/us)
• Path length difference results in phase
change between reference and signal beams
which can be measured by a photodetector in
the form of intensity changes
1.0
• High quality factor (Q)
attainable
Amplitude
• Surface displacement creates path length
difference between object and reference
beams
Q
Photo-detector
• Thermal expansion results in thermoelastic
stresses which produce elastic waves
(ultrasound) propagating through the material
• Laser couples into ZGV
resonance very efficiently
antisymmetric
Obj.
• Localized heating occurs due to absorption of
electromagnetic radiation from the generation
laser
ZGVr
2.0
Object beam
• ZGV resonance is generated and detected successfully with high SNR
• Experimental spectrum shows agreement with theoretical spectrum
• Observed shift of ZGV resonance with thickness change
Future Work:
• Exploration of other factors that may affect Q (power density, surface roughness, grainboundary scattering)
• High resolution mapping of materials with varying thickness
• Measurement of resonant peaks at higher frequencies (up to 600MHz)
• Possible use for nanoscale biological or chemical sensor