Experimental Measurement ofUltrasound Beam Profiles
Laura BlairN.A.H.K Rao, Maria Helguera, Daniel Phillips,
John K Schnieder*Chester F. Carlson Center for Imaging Science, RIT
*Ultra-Scan Corporation
May 12th 2003
Overview•Motivation
•Theory
•Experimental Setup
•Data Processing, Data Display and Filtering Noise
•FWHM and Misalignment Analysis
•Alternative Technique
•Theoretical Calculations
•Analysis of the Wire Target
•Modulation Transfer Function
•Conclusions and Future Studies
Motivation•Transducer beam characteristics important in resolution of overallimaging system. Finger
placedhere
Transducer
Container Filledwith Klearol Oilhouses thetransducer
System Components
Plastic Surface
Air gap or ContaminationFinger surface
Transducer
Goal –DetermineLSF and MTFfor transducerin FingerprintImagingSystem
Theory – Focused Transducer
E ABCD
Transducer
Focused Transducer Beam Profile
A, B = Near – Field
C = True Focus
D, E = Far - Field
Theory – Diffraction
Diffractiongoverns thevariation of
Beam Profilewith Z-
distance.
y
x
zzo
ρ
r
FocusedTransducer
Theory – LSF and MTF
MTF =Output ModulationInput Modulation
Reduction in contrast ofspectral components as theypass through the system
LSF Response of imaging system whenscanning the image plane with a linetarget of infinitesimally small width
Fourier Transform of LSFyields MTF
Theory
yx
z
FocusedTransducer
LommelDiffraction
Projection
FourierTransform
Line SpreadFunction
Short Pulse
Monochromatic
Modulation TransferFunction
1 Frequency
NumerousFrequencies foreach ρ and ZMeasurement
Experimental Setup
z
ρ
Transducer
Wire target
z
ρ
Transducer
Wire target
•Circular Disk Focused Transducer
•125 µm diameter nylon wire targetshown at 200X magnification
•Wire located in plasticcontainer filled with Klearol Oil
•Micrometers allow motion in Zand ρ direction
Defining the Experiment
0
5
10
15
20
25
-0.3 -0.2 -0.1 0 0.1 0.2 0.3
ρ -Distance from Nominal (mm)
Ampl
itude
of S
igna
l
0
5
10
15
20
25
-1.5 -1.25 -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 1.5
Z-Distance from Nominal (mm)
Ampl
itude
of S
igna
l
Identify location of maximumamplitude signal
Amplitude decreases as distancefrom nominal location increasesfor both ρ and Z
Experimental Plan
Label
Vertical Distance (z)
from nominal (µm)
Distance between ρ
measurements (µm)
Range of ρ measurements
(µm)
Number of Measurements
A -500 5 ±250 100B -250 5 ±245 98C 0 5 ±225 90D 250 5 ±213 85E 500 5 ±225 90
E ABCD
Transducer
Collect and Digitize Data for each Z, ρ position
Window Data
Calculate Fourier Transform
Calculate Magnitude
Forward Fourier Transform
Multiply by Gaussian of appropriate Width
Inverse Fourier Transform
Calculate Magnitude
Average Amplitude over SpecificFrequency Bins Resulting in one Value for
each ρ, Z and frequency.
Compile all ρ Results for a Particular Z andfrequency and Plot
CepstrumFiltering
Proc
essi
ng P
lan
Initial Results
Windowed DataEntire Digitized Signal
Data was windowed to the signal from the wire.
Appropriate windows required time-gating independently foreach Z position.
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
0 5 10 15 20
Time (microseconds)
Am
plitu
de
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
10 10.5 11 11.5 12
Time (microseconds)
Am
plitu
de
Data Processing
Fourier Transform and magnitude of time-gated signal.
Periodic noise observed.
FilteringNoise observed is possibly due to overlapping multiple reflectionsfrom the edges of the wire target.
3 Attempts to Remove the Noise• One dimensional convolution kernel
Ineffective: removed noise but also smoothed spectrum data
• Cepstrum Filtering
Useful if additive components in spectrum. Process involves takingFFT, applying a filter, and then inverse FFT.
• Homomorphic Filtering
Useful if spectrum composed of multiplicative components. Processinvolves calculating log, taking FFT, filtering, calculating inverseFFT, and calculating exponential.
Filtering
Forward FFT of Noisy Data
Filtered with Rect Filtered with Gaussian
Abrupt Cutoff Smooth Transition
Filtering
Spectrum after filtering with Rect ofwidth 150
Noise Remains
Spectrum after filtering with Rect ofwidth 100
No noise but slight decrease inamplitude
•Abrupt cutoff causes ringing in spectrum
•Must optimize width to eliminate noise but minimize reduction inamplitude
Filtering
Gaussian used to filterRinging not observed in
Spectrum
Data Processing
Average amplitude values over specificfrequency bins were calculated for 10frequency values.
Nominal, ±2MHz, ±4MHz, ±6MHz, -7MHz,+8MHz, +9MHz
Amplitude at each ρ for each Z location and aspecific frequency were plotted
Data Display
Tri-Level Display from –7MHz to +9MHz
ρ
Z
Data Display
Top Down View from –7MHz to +9MHz
ρ
Z
Data Display
-7 MHz +9 MHz
Nominal
Near-fieldDiffractionEffects
Broad beamprofile
Data Display
-7MHz
-4MHz
Nominal
+4MHz
+9MHz
Low Frequency = Broad Profile
High Frequency = Tight Profile
Near Field Diffraction Effects
0
2
4
6
8
10
12
14
16
18
-0.3 -0.2 -0.1 0 0.1 0.2 0.3
ρ -Distance (mm)
Ampl
itude
-7MHz-6MHz-4MHz-2MHzNominal+2MHz+4MHz+6MHz+8MHz+9MHz
0
5
10
15
20
25
30
35
40
-0.3 -0.2 -0.1 0 0.1 0.2 0.3
ρ-Distance (mm)
Am
plitu
de
-7MHz-6MHz-4MHz-2MHzNominal+2MHz+4MHz+6MHz+8MHz+9MHz
Near Field DiffractionEffects Apparent
Near Field Diffraction Effectsnot apparent for –7, -6 or –4MHz
Identification of near-field,true-focus or far-field must bebased on Z-position andFrequency.
Z position A
Z position B
E ABCD
00.10.20.30.40.50.60.70.80.9
1
-0.25 -0.15 -0.05 0.05 0.15 0.25
ρ -Distance (mm)
Norm
alize
d Am
plitu
de
-7MHz
-6MHz
-4MHz
-2MHz
Nominal
+2MHz
+4MHz
+6MHz
+8MHz
+9MHz
00.10.20.30.40.50.60.70.80.9
1
-0.1 -0.08 -0.06 -0.04 -0.02 0
ρ -Distance (mm)
Norm
alize
d Am
plitu
de
-7MHz
-6MHz
-4MHz
-2MHz
Nominal
+2MHz
+4MHz
+6MHz
+8MHz
+9MHz
Zoomin
00.10.20.30.40.50.60.70.80.9
1
-0.25 -0.15 -0.05 0.05 0.15 0.25
ρ -Distance (mm)
Norm
alize
d Am
plitu
de
-7MHz
-6MHz
-4MHz
-2MHz
Nominal
+2MHz
+4MHz
+6MHz
+8MHz
+9MHz
00.10.20.30.40.50.60.70.80.9
1
-0.2 -0.18 -0.16 -0.14 -0.12 -0.1
ρ -Distance (mm)
Norm
alize
d Am
plitu
de
-7MHz
-6MHz
-4MHz
-2MHz
Nominal
+2MHz
+4MHz
+6MHz
+8MHz
+9MHz
Zoomin
Beam ProfilesZ position C Z position E
E ABCD
Full-Width Half Maximum
0
0.05
0.1
0.15
0.2
0.25
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10Frequency from Nominal (MHz)
FWH
M (m
m)
EDC
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-0.3 -0.2 -0.1 0 0.1 0.2 0.3
ρ -Distance (mm)
Nor
mal
ized
Am
plitu
de
NominalFrequencyPosition CNominalFrequencyPosition D
NominalFrequencyPosition E
Position C = True Focus
Positions D,E = Far Field
Far Field = high FWHM
True Focus = low FWHM
E ABCD
Misalignment
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
Z Distance from Nominal
Max
imum
Loc
atio
n (m
m)
y = -0.085x - 0.0133R2 = 0.9988
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
Z Location
Max
imum
Loc
atio
n (m
m
The transducer and wire areslightly misaligned
Position A – Peak shifted Right
Position E – Peak shifted Left
Calculation indicatestransducer is 4.8 degrees
misaligned from wire.
Inconsequential
E ABCD
00.10.20.30.40.50.60.70.80.9
1
-0.25 -0.15 -0.05 0.05 0.15 0.25
ρ -Distance (mm)
Norm
alize
d Am
plitu
de
-7MHz
-6MHz
-4MHz
-2MHz
Nominal
+2MHz
+4MHz
+6MHz
+8MHz
+9MHz
Alternate Technique
Manufacturer uses envelope of signal in data processing
Collect and Digitize Data for each Z, ρ position
Window Data
Calculate Envelope of the Signal
Average Values Immediately SurroundingMaximum Amplitude
Compile all ρ Results for a Particular Z andPlot
Shift Phase ofSignal by 90
Degrees
CalculateMagnitude
CalculateMagnitude ofOriginal Data
SumMagnitudes
Identify Maximum Amplitude
Alternate Technique
Envelope of the Windowed Data
Compare Techniques
Position C
Position D Position E
E ABCD
00.10.20.30.40.50.60.70.80.9
1
-0.3 -0.2 -0.1 0 0.1 0.2 0.3
ρ -Distance (mm)
Norm
aliz
ed A
mpl
itude
Measurementof Envelope
NominalFrequency
00.10.20.30.40.50.60.70.80.9
1
-0.3 -0.2 -0.1 0 0.1 0.2 0.3ρ -Distance (mm)
Nor
mal
ized
Am
plitu
de
Measurementof Envelope
NominalFrequency
00.10.20.30.40.50.60.70.80.9
1
-0.3 -0.2 -0.1 0 0.1 0.2 0.3
ρ -Distance (mm)
Norm
aliz
ed A
mpl
itude
Measurementof EnvelopeNominalFrequency
Compare Techniques
Z LocationMeasurement of Envelope FWHM (mm)
Nominal Frequency
FWHM (mm)
+9MHz Frequency
FWHM (mm)
C 0.083 0.08 0.06D 0.135 0.13 0.105E 0.17 0.16 0.135
Nominal Frequency andMeasurement ofEnvelope may be
Statistically Equivalent
+9MHz is SignificantlyImproved
E ABCD
00.020.040.060.080.1
0.120.140.160.180.2
0 0.1 0.2 0.3 0.4 0.5 0.6Vertical Distance, Z (mm)
FWH
M (m
m)
NominalFrequencyMeasurementof Envelope+9 MHzFrequency
Theoretical Calculations
Z Position ANear Field Diffraction Effects
E ABCD
Theoretical Calculations
Z Position B
E ABCD
Theoretical Calculations
Z Position C
True Focus
E ABCD
Theoretical Calculations
Z Position D
Far Field
E ABCD
Theoretical Calculations
Z Position E
E ABCD
Theoretical Vs. ExperimentalAt Nominal Z
00.1
0.20.30.40.5
0.60.70.8
0.91
-0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25
ρ -Distance (mm)
Norm
alize
d Am
plitu
de•No Side-lobes in experimental results
•Transducer is apodized to reduce side-lobes but this increases the width.
•Apodization also would change ‘Effective Transducer Diameter’
• Apodization is an unknown parameter in the design
Wire Target AnalysisAnother possible cause of the larger FWHM is the
thickness of the wire target.
There may be overlapping multiple reflections from theedges of the wire!
Wire Target Analysis
Average of pixel profiles Zoom In
Measured Wire Diameter = 125 microns
Full Width Half Maximum of pixel profile = 75 microns
Effective width (where specular reflection takes place) = 20-30microns
Modulation Transfer Function
Higher Frequency or
Z closer to nominal =
Higher Cutoff Frequency
Nominal Z
Largest Z
Nominal Z = MTFs more spreadout as a function of frequency
Nominal Z
Z Position E
E ABCD
MTF = Fourier Transform {LSF}
Conclusions•Transducer Beam profile is Frequency and DepthDependent
•Measuring Signal from a thin wire target iseffective technique for focused high frequencytransducer
•Cepstrum filtering useful in removing periodicnoise
•MTF varies with frequency and Z-position
•+9MHz would be improvement over envelopemeasurement
Future Studies
•Repeat experiment with a 10-20 micron wire (not easy)
•Evaluate Edge Spread Function with glass slide andcalculate derivative to determine MTF
•Measure LSF and MTF for entire Fingerprint ImagingSystem and compare to results found for the transducer