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.

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 Engineering2Boston University, Department of Aerospace and Mechanical Engineering

suraj10@bu.edu, twmurray@bu.edu

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)

Introduction

Conclusions and Future Work

Significance and Relation to CenSSIS

Theoretical Formulation

Experimental Results

State of the Art

Motivation

Laser Generation of Ultrasound Laser Detection of Ultrasound

Reference mirror

Beamsplitter

Laser

Specimen

Ref.

Obj.

Ref.

Obj.= - (dark)

Ref.

Obj.

= + (bright)

Photo-detector

Reference beam

Object beam

• Localized heating occurs due to absorption of electromagnetic radiation from the generation laser

• Thermal expansion results in thermoelastic stresses which produce elastic waves (ultrasound) propagating through the material

• Surface displacement creates path length difference between object and reference beams

• 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

Michelson Interferometer

Lamb Waves

• Dispersive guided waves propagating in plate-like structures

• Propagate in the form of symmetric and antisymmetric modes

antisymmetric

symmetric

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)

• High spatial resolution

• 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

R1

R2

Overview of the Strategic Research PlanOverview of the Strategic Research Plan

FundamentalScienceFundamentalScience

ValidatingTestBEDsValidatingTestBEDs

L1L1

L2L2

L3L3

R3

S1 S4 S5S3S2

Bio-Med Enviro-Civil

• Allows for small-scale thickness mapping of thin films

• High sensitivity and high resolution may create possibility for use as small-scale chemical or biological sensor

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]

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]

A zero group velocity resonance was found that allowed for very efficient transmission of sound waves through plates. [3]

Laser-based photoacoustic methods were used for in vivo imaging of rat brains.[4]References:

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).

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).

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).

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).

Rayleigh-Lamb Frequency Equations

2 2 2 2

2 2 2 2

2 2

2 2 2 2

tan( ) 4 tan( ) ( )

tan( ) ( ) tan( ) 4

L T

for symmetric modes: for antisymmetric modes:

qh k pq qh q k

ph q k ph k pq

where: p k and q kc c

angular frequency

,

P

L TP

, c = phase velocity

k = ; c c longitudinal,shear wave velocity c

• Dispersion curves are shown in the form of phase velocity as a function of the frequency-thickness product

• First order symmetric (S1) and first and second order asymmetric (A1, A2) modes shown

• Arrows denote mode cutoff frequencies (resonances)

• Phase velocity approaches infinity as group velocity approaches zero

Solutions to the Rayleigh-Lamb frequency equations result in multiple modes shown above

Quasi-Resonance (ZGVr)

• Resonance localized in space

• Laser couples into ZGV resonance very efficiently

• High quality factor (Q) attainable

• Resonant frequency dependent on thickness

• Changes in thickness of the sample results in shift of resonance peak

Theoretical Spectrum (50 μm Tungsten)

Experimental Setup

Detection: 532nm CW Laser (120mW)

Reference mirror on piezoelectric mount

lens

photodetector

Generation

Laser: (1064nm

) sample

lens

Preliminary Experiments (50μm Tungsten)

Filtered Time-Domain Signal Amplitude Spectrum

Amplitude Spectrum Comparison

Conclusions

• 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, grain-boundary 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

Q vs. Spot Size

• High-pass filter at 25MHz was used to eliminate large initial DC offset

• Agrees well with theoretical spectrum

• Results show that spot size has negligible effect on Q

• Signal-to-Noise ratio increases as spot size decreases

• Similar pattern was seen in 50μm tungsten sample

• Waveforms were collected at ten points separated by 1μm on each sample

• Resonant frequency shifts as sample thickness changes

• Q increases as sample thickness decreases

Pulse Energy = 10.2 uJ

Pulsewidth = 610 ps

Rep. Rate = 5.6 kHz

• Research involves aspects of many fields including optics, acoustics, and signal processing

0 2 4 6

-0.03

0.00

0.03

Am

plit

ud

e (

mV

)

Time (s)

10 20 30 40 50 60

0.0

0.2

0.4

0.6

0.8

1.050m tungstenAvg Q = 73.02

Am

plit

ud

e (

no

rma

lize

d)

Frequency (MHz)

23.87MHz 44.62MHz

100m tungstenAvg Q = 48.58

0 20 40 60 80 100 120 140 160

0

50

100

150

200

250

300

350

Q

Plate Thickness (m)

Theoretical Model – Q vs.Thickness

• Q increases as thickness decreases

• Allows for precise thickness measurements of very thin plates

23.0 23.5 24.0 24.5 25.0

0.2

0.4

0.6

0.8

1.0

Am

plit

ud

e (

no

rma

lize

d)

Frequency (MHz)

220m 170m 145m 120m

Spot Size

100m tungsten