ECSE4963 Introduction to Subsurface Sensing and Imaging Systems

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ECSE-4963Introduction to Subsurface Sensing and
Imaging Systems

• Lecture 16 Use of Phase in Coherent Imaging
• Kai Thomenius1 Badri Roysam2
• 1Chief Technologist, Imaging technologies,
• General Electric Global Research Center
• 2Professor, Rensselaer Polytechnic Institute

Center for Sub-Surface Imaging Sensing
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Recap

• We have reviewed the Big Picture w. Subsurface
  Imaging
• SSI Architectures for imaging in scattering media
• Time-Resolved Imaging
• New Examples
• DOT
• TOF-PET
• Next
• Use of phase in coherent imaging

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Ultrasound Imaging
Electrodes
Beam Sum
Piezoceramic
Transduction
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Cause Stress
Effect Strain
R0
Q
Cause Electric field
Beamformation
R1

R2
Effect Current
R3
-
Scan Conversion
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Acoustic Imaging SSI
Probes
Detectors
Surface
Medium
object
Medium
Object
Probe
Optical/IR
Electro- magnetic
Fluorescence
Absorption
X-ray
Acoustic
Absorption
Nonlinear Absorption
Dispersion
CW
Pulsed
Modulated
Nonlinear Scattering
Scattering
Scattering
Multi- Spectral
Partially Coherent
Coherent
Diffusion
Diffusive
Phase Object
Clutter
Quantum
Classical
Depolarizing
Inhomogeneous/ Layered
Outside
Inside
Auxiliary
Stationary
Moving
Rough Surface
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Use of Phase in Coherent Imaging

• With coherent radiation, we can keep track of
  amplitude phase.
• Often, phase info is more valuable than
  amplitude.
• We will use the Doppler effect to illustrate.

• Johan Christian Doppler
• born in 1803 in Salzburg, died in 1853 in Venice.
• A Professor of mathematics
• Modern astrophysics is based on his famous
  principle of 1842.

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What is the Doppler Principle ?

• Doppler described the theory of detecting motions
  of stars in his original paper in 1842
• On the colored light of the double stars and
  certain other stars of the heavens.
• Statement of the Doppler Principle
• any directional motion between a light source and
  an observer will produce a detectable frequency
  shift or color change

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Experiment on Doppler shift
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Analysis of Experiment

• As the train passed the observers
• the note being played by the musicians on the
  train increased and, after passing the listeners,
  decreased by 1/2 note.
• Observers on the train experienced the same
  effect from the horns at track side.
• Doppler's theory was now verified.

towards
away
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Moving this to ultrasound
Case 1 STATIONARY SOURCE (transducer)
MOVING LISTENER (red blood cell)
vcosq
Particle passes through approaching wavefronts
q
v
Stationary particle sees cT/l wavefronts in time T
Moving particle sees (cvcosq)T/l wavefronts in
time T
The frequency our particle sees is given by
where
Original xmit frequency
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Case 2 STATIONARY SOURCE (transducer)
MOVING LISTENER (red blood cell)
Particle scatters u/s energy back to transducer
vcosq
q
Probe sees wavefronts compressed as source moves
closer to xdcr
v
Frequency the transducer sees, ft, is
Plugging in for fs
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The Doppler Shift
cosq lt1 and c 1540 m/sec
Assume cgtgtv
Neglect value of q or have user input v
Measure -gt
lt- choose probe operating frequency
Assume average c for tissue
Plugging in some numbers assume blood
velocity 10cm/sec transmit frequency
2.5MHz
It is a nice coincidence that the Doppler signal
is in our audio range.
-gt fD around 325 Hz
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How do we measure fD, the Doppler frequency?
CW Doppler
Split the transducer in two halves
Xmit Rcv
One side constantly xmits pure tone at f0
Other side constantly receives frequency f0fD
Beam can be steered to give lateral spatial
resolution but no axial resolution

• scatterers along beam are continuously receiving
  and transmitting energy back to xdcr
• If they are in motion, the echoed signal will
  carry the velocity information.

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Doppler Signal Processing
Transmit signal cosw0t w0
2pf0 Receive signal S(t) Acos(w0wD)t
The Doppler processor is designed to pullout
the Doppler frequency from the echoes.
Beamformer
sinw0t
cosw0t
LPF
LPF
Q
I
Spectral Processor
Audio
Display
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Doppler Signal Processing
Using trigonometric identities
Low pass filters get rid of high frequency terms
Only depends on Doppler shift frequency
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A quick side comment
I and Q can be treated as a complex number
Real-gt
lt-Imaginary
With corresponding amplitude
and phase

• So how do we extract wD?
• FOURIER TRANSFORM one of the most common and
  most appropriate methods

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Spectral Processing for Doppler Information

• Fourier Processor Steps
• Get I/Q signals from beamformer
• Take FFT of the last N (say 64) samples.
• Display as time-frequency plot with brightness
  showingamount of energy in any give frequency
  bin.

This is the basic theory, we have neglected many
of the details
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• What we have discussed so far is CW Doppler
• Big drawback, no range resolution
• We can get this back by sending out a pulse, red
  signals below.
• Wait round trip traveling time to user positioned
  range gate before sampling data
• Just sample in small (user defined) region

-gt time depth/2c
Time PRF
Each pulse provides 1 point input to FFT
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Pulsed Doppler Sample Volume
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How do we do this Pulsed Doppler stuff?
Suppose the range gate length is 1cm
Length of data sample (time from latest
sample-time to earliest sample)sample rate

• 65 points _at_ 5MHz sample rate

Frequency resolution is 77KHz, not very useful
for clinical applications

• Solution
• send out multiple pulses
• look at change of I/Q phase from firing to
  firing
• stationary scatterer will return pulses with no
  phase change
• moving scatterers will have phase shift firing
  to firing

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Proof
v
L
Return echo is proportional to cos(w0tf)
Stationary particle L constant gt f constant
Moving particle position L-nvT n is
pulse number T is time between pulses
lt- phase rotation rate Doppler shift -gt
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Characteristic Doppler Spectral Waveforms of
different Vessels
The unique geometry, distance from the heart,
vessel wall properties, and interaction with
distal vasculature combine to produce a Doppler
signature that is specific to each vessel.
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Flow States
Laminar flow
Plug flow
Jet stream
Turbulence
(Spiraling flow in curved vessels)
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Example Carotid Artery Diagnosis
Turbulence gt Stenosis
Normal
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Going from PW Doppler to Color Doppler
Time PRF
But we cant display the spectrum for each pixel!
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Can we estimate the mean frequency for each pixel?
It turns out we can, and this is the basis of
color flow Doppler.
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Doppler shift is just the phase change between
firings...
Average over all firings in an ensemble.
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Other Doppler imaging modes
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Normal color flow of liver
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Summary

• We have reviewed the use of phase in coherent
  signal processing.
• A key application of this takes advantage of the
  Doppler effect.
• Blood flow detection in medical ultrasound has
  been used as an example.
• Basic equations governing Doppler processing were
  derived.

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Homework Lecture 12

• Assume you have a single red blood cell which is
  moving at various velocities axially wrt the
  transducer.
• You transmit a 2 MHz signal.
• Determine the Doppler frequency for the following
  red blood cell velocities
• Velocity 1 m/sec, velocity -1 m/sec
• Velocity 0.5 c ( 770 m/sec)
• Velocity -c, justify your answer

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Instructor Contact Information

• Badri Roysam
• Professor of Electrical, Computer, Systems
  Engineering
• Office JEC 7010
• Rensselaer Polytechnic Institute
• 110, 8th Street, Troy, New York 12180
• Phone [phone]
• Fax [phone]
• Email roysam_at_ecse.rpi.edu
• Website http//www.rpi.edu/roysab
• NetMeeting ID (for off-campus students)
  128.113.61.80
• Secretary TBD

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Instructor Contact Information

• Kai E Thomenius
• Chief Technologist, Ultrasound Biomedical
• Office KW-C300A
• GE Global Research
• Imaging Technologies
• Niskayuna, New York 12309
• Phone [phone]
• Fax [phone]
• Email thomeniu_at_crd.ge.com, thomenius_at_ecse.rpi.edu
  
• Secretary TBD