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