ECSE4962 Introduction to Subsurface Sensing and Imaging Systems

1
ECSE-4962Introduction to Subsurface Sensing and
Imaging Systems

• Lecture 12 Ultrasound Scanner as a Linear
  System
• Kai Thomenius1 Badri Roysam2
• 1Chief Technologist, Imaging Technologies,
• General Electric Global Research Center
• 2Professor, Rensselaer Polytechnic Institute

Center for Sub-Surface Imaging Sensing
2
Outline of Course Topics

• PULSE ECHO METHODS
• Examples
• MRI
• A different sensing modality from the others
• Basics of MRI
• MOLECULAR IMAGING
• What is it?
• PET Radionuclide Imaging
• IMAGE PROCESSING CAD

• THE BIG PICTURE
• What is subsurface sensing imaging?
• Why a course on this topic?
• EXAMPLES THROUGH TRANSMISSION SENSING
• X-Ray Imaging
• Computer Tomography
• Intro into Optical Imaging
• COMMON FUNDAMENTALS
• propagation of waves, ultrasound
• interaction of waves with targets of interest 

3
Recap

• We reviewed the major building blocks of an
  ultrasound scanner
• Transduction
• Beamformation
• Scanning modes
• Scan conversion
• Today we will discuss an ultrasound scanner as a
  linear system.
• We will work with Field II, a software package
  designed for analysis of pulse-echo systems.

4
Ultrasound Scanner as a Linear System

• Linear System
• Key characteristic
• Satisfies the principle of superposition
• Why is this important?
• Impulse response transfer function
• An ultrasound scanner can be modeled as a
  sequence of linear transfer functions.

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Scanner Block Diagram

• Let us see if we can describe this block diagram
  as a set of transfer functions.
• Key process steps
• Transmit beamformation pulsing
• Transduction electrical signal to particle
  velocity (or pressure)
• Propagation of field to scatterer
• Scattering
• Propagation of scattered field to transducer
• Transduction acoustic pressure to voltage
• Receive beamformation image formation

• All of these can be modeled conveniently as
  transfer functions within Field II.
• All we have to do is to determine all the
  transfer functions along the way.

6
Array Terminology, Geometry

• Schematic of a linear phased array
• Definition of azimuth, elevation
• Scanning angle shown, q, in negative scan
  direction.

7
Spatial Impulse Response Concept

• Spatial Impulse Response Method
• Assume a transducer undergoes a delta-function
  motion.
• What acoustic field arises from such a motion?
• Temporal response of this can be determined for
  all field points.
• This is the spatial impulse response.
• Once it is known, a field can be determined for
  any transducer driving function.
• All of Field II is based on this propagation
  model.

What is the spatial impulse response at the
focus of a circular aperture?
8
Field II coherent field simulation

• Set initial parameters
• R8/1000 Radius of transducer m
• Rfocus80/1000 Geometric focal point m
• ele_size1/1000 Size of mathematical elements
  m
• f03e6 Transducer center frequency Hz
• fs100e6 Sampling frequency Hz
• Define the transducer
• Th xdc_concave (R, Rfocus, ele_size)
• Set the impulse response and excitation of the
  transmit aperture
• impulse_responsesin(2pif0(01/fs2/f0))
• impulse_responseimpulse_response.hanning(max(siz
  e(impulse_response)))'
• xdc_impulse (Th, impulse_response)
• excitationsin(2pif0(01/fs2/f0))

• http//www.es.oersted.dtu.dk/staff/jaj/field/
• Matlab simulation of an ultrasound scanner
• Can be readily converted to any coherent probe.
• Homework assignments to be based on Field II
• We will go through a simulation to calculate the
  point spread function for a focused disk.
• Thus we wish to determine the pulse-echo response
  due to a point source.

9
Field II Code Review

• Transducer to be simulated
• Single circular element
• 8 mm radius
• Analysis grid 1 mm
• Center frequency 3 MHz
• Fields internal sampling frequency 100 MHz
• Xdc_concave is a routine supplied by Field II
• In Field, the transducer is modeled as small
  mathematical elements.

• Set initial parameters
• R8/1000 Radius of transducer
  m
• Rfocus80/1000 Geometric focus point m
• ele_size1/1000 Size of mathematical
  elements m
• f03e6 Transducer center
  frequency Hz
• fs100e6 Sampling frequency
  Hz
• Define the transducer
• Th xdc_concave (R, Rfocus, ele_size)
• Set the impulse response and excitation of the
  emit aperture
• impulse_responsesin(2pif0(01/fs2/f0))
• impulse_responseimpulse_response.hanning(max(siz
  e(impulse_response)))'
• xdc_impulse (Th, impulse_response)
• excitationsin(2pif0(01/fs2/f0))

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Field II Code Review

• Call to xdc_concave
• Purpose Procedure for creating a concave
  transducer
• Calling Th xdc concave (radius, focal radius,
  ele size)
• Input
• Radius Radius of physical elements.
• focal radius Focal radius.
• ele size Size of mathematical elements.
• Output Th -gt A pointer to this transducer
  aperture.

• Define the transducer
• Th xdc_concave (R, Rfocus, ele_size)
• Set the impulse response and excitation of the
  emit aperture
• impulse_responsesin(2pif0(01/fs2/f0))
• impulse_responseimpulse_response.hanning(max(siz
  e(impulse_response)))'
• xdc_impulse (Th, impulse_response)
• excitationsin(2pif0(01/fs2/f0))
• xdc_excitation (Th, excitation)
• Calculate the pulse echo field and display it
• xpoints(-100.210)
• RF_data, start_time calc_hhp (Th, Th,
  xpoints zeros(1,101) 30ones(1,101)'/1000)

11
Field II Code Review

• Field allows you to enter the transducer impulse
  response in any form you wish.
• We are talking about the response of the xdcr to
  an impulse.
• In the lab, we measure this transfer function w.
  a hydrophone.
• In this example, we use a Hanning-weighted sine
  wave as the impulse response.
• Note that we are asking for an impulse response
  with a duration of two cycles at the xdcr
  frequency.
• We tell Field this with the xdc_impulse command.
• The next step is to determine the waveform of the
  transmit pulse, or the excitation.

• Set impulse response and excitation of emit
  aperture
• impulse_responsesin(2pif0(01/fs2/f0))
• impulse_responseimpulse_response.hanning(max(siz
  e(impulse_response)))'
• xdc_impulse (Th, impulse_response)
• excitationsin(2pif0(01/fs2/f0))
• xdc_excitation (Th, excitation)
• Calculate the pulse echo field and display it
• xpoints(-100.210)
• RF_data, start_time calc_hhp (Th, Th,
  xpoints zeros(1,101) 30ones(1,101)'/1000)

12
Field II Code Review

• What waveshape do we use to energize the
  transducer?
• In this example, we use the same sine wave
  response as before.
• We tell Field this with the xdc_excitation
  command.
• In general, this input could be any temporal
  sequence such as a single pulse, a code,
  whatever.
• We have now given Field enough info to determine
  the acoustic response at the face of the
  transducer.
• The next step is to determine acoustic transfer
  function associated with transmit echo
  propagations.

• Set impulse response and excitation of emit
  aperture
• impulse_responsesin(2pif0(01/fs2/f0))
• impulse_responseimpulse_response.hanning(max(siz
  e(impulse_response)))'
• xdc_impulse (Th, impulse_response)
• excitationsin(2pif0(01/fs2/f0))
• xdc_excitation (Th, excitation)
• Calculate the pulse echo field and display it
• xpoints(-100.210)
• RF_data, start_time calc_hhp (Th, Th,
  xpoints zeros(1,101) 30ones(1,101)'/1000)

13
Field II Code Review

• Field gives us a number of different methods for
  determining acoustic fields.
• Our example uses calc_hhp which does the
  following
• Gives the pulse echo field along a given set of
  points
• In the code shown, this line is for x from -10 to
  10 mm at a depth of 30 mm.
• The figure shown gives the response at 50 mm.
• To determine this field (or point spread
  function), Field does the following
• Determines the spatial impulse response for the
  field points for the transmit operation
• Determines the spatial impulse response for those
  points for the receive operation.
• Combines those two spatial impulse responses for
  the total impulse response.
• Given the acoustic response at the transducer
  face (i.e. the forcing function), Field
  determines the echo responses along the line of
  interest.
• The figure shown gives the amplitude response
  (which requires a few more Field commands).

• Calculate the pulse echo field and display it
• xpoints(-100.210)
• RF_data, start_time calc_hhp (Th, Th,
  xpoints zeros(1,101) 30ones(1,101)'/1000)
• calc_hhp determines the round trip point
• spread function due to this aperture and
• excitation

14
Field II Code Review

• Call to calc_hhp
• Purpose Procedure for calculating the pulse echo
  field.
• Calling hhp, start time calc hhp(Th1, Th2,
  points)
• Input
• Th1 Pointer to transmit aperture.
• Th2 Pointer to receive aperture.
• points Field points. Vector with three columns
  (x,y,z) and one row for each field point.
• Output hhp - Received voltage trace (RF_data
  array).
• start time The time for the first sample in hhp.

• Calculate the pulse echo field and display it
• xpoints(-100.210)
• RF_data, start_time calc_hhp (Th, Th,
  xpoints zeros(1,101) 30ones(1,101)'/1000)
• calc_hhp determines the round trip point
• spread function due to this aperture and
• excitation

15
Field II Code Review

• Display of the envelope
• figure(1)
• envabs(hilbert(RF_data(15600,)))
• Hilbert transform is a nice way of doing
• envelope detection.
• env20log10(env/max(max(env)))
• N,Msize(env)
• env(env60).(envgt-60) - 60
• mesh(xpoints, ((0N-1)/fs start_time)1e6, env)
• ylabel('Time \mus')
• xlabel('Lateral distance mm')
• title('Pulse-echo field from 8 mm concave
  transducer at 30 mm')
• axis(-10 10 38.41 39.6 -60 0)
• view(-14 80)

• This set of statements creates the final display.
• RF_data array contains the RF pulse-echo
  responses from 30 mm
• env is the envelope of that RF data
• Matlabs hilbert m-file is used to determine
  this.
• env array is also converted to dB scale

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Selected Field Commands

• General Field II Commands
• Function name Purpose Page
• field debug Initialize debugging 13
• field end Terminate the Field II program system
  and release the storage 13
• field init Initialize the Field II program
  system 13
• set sampling Set the sampling frequency the
  system uses 14
• set field Set various parameters for the program
  14
• Transducer or array commands
• xdc apodization Create an apodization time line
  for an aperture. 16
• xdc baffle Set the baffle condition for the
  aperture. 16
• xdc center focus Set the origin for the dynamic
  focusing line. 17
• xdc concave Define a concave aperture. 17
• xdc convert Convert rectangular description to
  triangular description. 18
• xdc convex array Create a convex array
  transducer. 18
• xdc convex focused array Create an elevation
  focused convex array transducer. 19
• xdc convex focused multirow Create an elevation
  focused convex, multi-row transducer. 20

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Selected Field Commands

• Transducer or array commands
• xdc dynamic focus Use dynamic focusing for an
  aperture 22
• xdc excitation Set the excitation pulse of an
  aperture. 23
• xdc focus Create a focus time line for an
  aperture. 23
• xdc focused array Create an elevation focused
  linear array transducer. 23
• xdc focused multirow Create an elevation focused
  linear, multi-row transducer. 24
• xdc free Free storage occupied by an aperture.
  27
• xdc get Get information about an aperture. 27
• xdc impulse Set the impulse response of an
  aperture. 29
• xdc linear array Create a linear array
  transducer. 30
• xdc linear multirow Create a linear multi-row
  array transducer. 30
• Field Calculation Commands
• calc h Calculate the spatial impulse response.
  49
• calc hhp Calculate the pulse echo field. 50
• calc hp Calculate the emitted field. 51
• calc scat Calculate the received signal from a
  collection of scatterers. 52

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Pulse-echo Field from a Concave Source
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Homework

• Download Field II and the Users Guide to your
  computer.
• Execute the first example from http//www.es.oerst
  ed.dtu.dk/staff/jaj/field/examples.html, the
  point spread function logo case.
• You should get a strange looking impulse
  response.
• Dont forget to initialize Field with field_init
  command!
• Change the number of transmitted cycles to one
  cycle, three cycles. How does the point spread
  function change?
• Hand in your graphical matlab results.

20
Summary

• We have been introduced to the Field II
  simulation program and walked through some of the
  code.
• We have used this Field II example to demonstrate
  the role of linear system theory in the
  understanding of imagers.

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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 Laraine Michaelides, JEC 7012, (518)
  276 8525, michal_at_rpi.edu

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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 Laraine Michaelides, JEC 7012, (518)
  276 8525, michal_at_rpi.edu