Class 7 Arrays - Stanford University · 2019-11-13 · Rad225/Bioe225 Ultrasound Class 7: Arrays Fall 2019 1 Arrays Grating Lobes with Linear Arrays Phased Arrays and More Grating
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Rad225/Bioe225UltrasoundFall 2019Class 7: Arrays
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ArraysGrating Lobes with Linear ArraysPhased Arrays and More Grating LobesPulse-Echo or Transmit-Receive and Dynamic Receive Focusing
Rad225/Bioe225UltrasoundFall 2019Class 7
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ArraysGrating Lobes with Linear ArraysPhased Arrays and More Grating LobesPulse-Echo or Transmit-Receive and Dynamic Receive Focusing
Rad225/Bioe225UltrasoundFall 2019Definitions
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Transducers
• A transducer is a device which converts one form of energy to another. In ultrasound, a transducer or transducer array converts electrical energy to mechanical and vice versa.
width pitch kerf
height
aperture
Rad225/Bioe225UltrasoundFall 2019Most Common Transducers
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Transducer Arrays
http://sinaiem.us/tutorials/pneumothorax
Linear Curvilinear Phased
High Frequency~4cm field of view
Low Frequency-wide field of view
Low Frequency-small acoustic window-wide field of view at depthBeam Origins
• Linear – beam origins shift across field of view, beam direction (steering remains the same)
• Phased – beam origins stay the same, direction changes over the field of view.
• Curvilinear – both beam origins and direction changes over field of view
Beam Origins
• Linear – beam origins shift across field of view, beam direction (steering remains the same)
• Phased – beam origins stay the same, direction changes over the field of view.
• Curvilinear – both beam origins and direction changes over field of view
Transducer Arrays
http://sinaiem.us/tutorials/pneumothorax
Linear Curvilinear Phased
High Frequency~4cm field of view
Low Frequency-wide field of view
Low Frequency-small acoustic window-wide field of view at depth
Transducer Arrays
http://sinaiem.us/tutorials/pneumothorax
Linear Curvilinear Phased
High Frequency~4cm field of view
Low Frequency-wide field of view
Low Frequency-small acoustic window-wide field of view at depth
Rad225/Bioe225UltrasoundFall 2019Array Beamforming
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Transmit Beamforming
• Back to Huygen’s principle:
Translate which
elements are used
Image one line
at a time
Rad225/Bioe225UltrasoundFall 2019Beam From Subaperture
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Lens
Slice Thickness
Lateral res./Beam width
Axial/Depth (z)
Azimuth/Lateral (x)
Elevation/Slice Thickness (y)
θ
Rad225/Bioe225UltrasoundFall 2019Linear Array Imaging
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Array
Time-delayed electrical pulses for focusing
Focal Point
One focused ultrasound beam is used to form one image scan-line
Scanning Direction
Subaperture
FOV smaller than array
Wider beam, any one object goes into multiple lines, lower resolution
Picture Field of View
Choice of subaperture size presents a tradeoff between resolution and FOV
W = 1.22λFD
Rad225/Bioe225UltrasoundFall 2019Class 7
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ArraysGrating Lobes with Linear ArraysPhased Arrays and More Grating LobesPulse-Echo or Transmit-Receive and Dynamic Receive Focusing
Rad225/Bioe225UltrasoundFall 2019Single Element Rectangular Aperture
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Examples
Observation Plane
Rectangular Aperture:
sinc
Aperture Plane
rect
FTrect( x
Lx)⇔ sinc(Lx f )
u = f λrect
xLx
⎛
⎝⎜⎞
⎠⎟⇔ sinc
Lxuλ
⎛⎝⎜
⎞⎠⎟
Rad225/Bioe225UltrasoundFall 2019Ideal Array of point sources
grating lobes
Szabo
FT
combxp
⎛⎝⎜
⎞⎠⎟⇔ comb
uλ / p
⎛⎝⎜
⎞⎠⎟
Rad225/Bioe225UltrasoundFall 2019Subaperture Array of Point Sources
grating lobes
Szabo
FT
combxp
⎛⎝⎜
⎞⎠⎟rect
xLx
⎛
⎝⎜⎞
⎠⎟⇔ comb
uλ / p
⎛⎝⎜
⎞⎠⎟∗sinc
Lxuλ
⎛⎝⎜
⎞⎠⎟
Rad225/Bioe225UltrasoundFall 2019
Subaperture Array of Finite Width Sources
envelope on the grating lobesSzabo
FT
combxp
⎛⎝⎜
⎞⎠⎟*rect x
w⎛⎝⎜
⎞⎠⎟
⎛⎝⎜
⎞⎠⎟rect
xLx
⎛
⎝⎜⎞
⎠⎟⇔ comb
uλ / p
⎛⎝⎜
⎞⎠⎟sinc u
λ / w⎛⎝⎜
⎞⎠⎟
⎛⎝⎜
⎞⎠⎟∗sinc
Lxuλ
⎛⎝⎜
⎞⎠⎟
Rad225/Bioe225UltrasoundFall 2019Class 7
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ArraysGrating Lobes with Linear ArraysPhased Arrays and More Grating LobesPulse-Echo or Transmit-Receive and Dynamic Receive Focusing
Rad225/Bioe225UltrasoundFall 2019Steering
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Transmit Beamforming
• Back to Huygen’s principle:
Beam Steering
Utilizes the entire aperture for each scan line
θ
Scanning Direction
Electronic sector scanning is achieved through varying the steering angle θ
Rad225/Bioe225UltrasoundFall 2019Steered Subaperture Array of Finite Width
Sources
grating lobes modulated by the envelope
→ translationlinear phase
Szabo
combxp
⎛⎝⎜
⎞⎠⎟*rect x
w⎛⎝⎜
⎞⎠⎟
⎛⎝⎜
⎞⎠⎟rect
xLx
⎛
⎝⎜⎞
⎠⎟⇔ comb
uλ / p
⎛⎝⎜
⎞⎠⎟sinc u
λ / w⎛⎝⎜
⎞⎠⎟
⎛⎝⎜
⎞⎠⎟∗sinc
Lxuλ
⎛⎝⎜
⎞⎠⎟
Phase
Rad225/Bioe225UltrasoundFall 2019Beam pattern follows the envelope
Steered 15° to rightMain lobe intensity decreases
Grating lobe intensity increases
Grating lobes at 60°
Rad225/Bioe225UltrasoundFall 2019Grating Lobes
Energy goes into the near field from grating lobes
θg = sin−1 nλ
p⎛⎝⎜
⎞⎠⎟
p
Rad225/Bioe225UltrasoundFall 2019Correcting for Grating Lobes
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φg
Grating Lobe
Main Lobe
Side Lobe Intensity
Angle
Array
-90°
90°
d
θg
If the element spacing is less than λ, the grating lobe is greater than 90 degrees
sin(θg ) =λp
⎛⎝⎜
⎞⎠⎟
Rad225/Bioe225UltrasoundFall 2019
-80 -60 -40 -20 0 20 40 60 80-40
-35
-30
-25
-20
-15
-10
-5
0
Angle (degrees)
Am
plitu
de (d
B)
-80 -60 -40 -20 0 20 40 60 80-40
-35
-30
-25
-20
-15
-10
-5
0
Angle (degrees)
Am
plitu
de (d
B)
What is the pitch?
20d = 1.55λ
sin(90°) = λd
⎛⎝⎜
⎞⎠⎟
d = λ
sin(θg ) =λp
⎛⎝⎜
⎞⎠⎟
sin(40°) = λp
⎛⎝⎜
⎞⎠⎟
Rad225/Bioe225
Ultrasound
Fall 2019Grating Lobe Artifacts
Rad225/Bioe225UltrasoundFall 2019Class 7
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ArraysGrating Lobes with Linear ArraysPhased Arrays and More Grating LobesPulse-Echo or Transmit-Receive and Dynamic Receive Focusing
Rad225/Bioe225UltrasoundFall 2019Pulse - Echo
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Ultrasonic Imaging
• Because US is pulse-echo, we are concerned with both the transmitted pressure field (Tx) and the receiver sensitivity (Rx)– Rx sensitivity is the locations in the field where the
receiver is sensitive to incoming waves
• Rx can be determined using the principle of acoustic reciprocity
Rad225/Bioe225UltrasoundFall 2019Acoustic Reciprocity
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Acoustic Reciprocity
• The receiver sensitivity is equal to the transmit diffraction pattern of the receiver acting as a source
Rx = cos(SDfx)
D
Rad225/Bioe225UltrasoundFall 2019Pulse Echo Sensitivity
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The Radar Equation
• The pulse-echo beam pattern (i.e. the sensitivity of the ultrasound system) is equal to the product of the transmit diffraction pattern and the receive sensitivity pattern:
),(),(),( yxRxyxTxyxB
cos(SDfx)cos2(SDfx)=1+2cos(2SDfx)
Rad225/Bioe225UltrasoundFall 2019Transmit Beamforming: Plane Wave
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Transmit Beamforming
Rad225/Bioe225UltrasoundFall 2019
Transmit Beamforming: Focused Wave
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Transmit Beamforming
Rad225/Bioe225UltrasoundFall 2019Transmit Beam
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Fixed Focus Beamforming
Rad225/Bioe225UltrasoundFall 2019Receive Beamforming
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Receive Beamforming
• Transmit beamforming in reverse:
Use same equation as before to compute time delays for receiving!
Rad225/Bioe225UltrasoundFall 2019Transmit Focusing at Different Depths
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Dynamic Receive Focusing
Rad225/Bioe225UltrasoundFall 2019Dynamic Receive Focusing
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Dynamic Receive FocusingContinuously adjust the delays
Beam
form
ing
Unf
ocus
ed s
igna
l rec
eive
d fr
om
the
near
fiel
dFo
cuse
d sig
nal u
sing
time-
dela
ys:
Not
e ho
w w
avef
ront
sapp
ear a
s “p
lane
wav
es”
RF S
um
Chan
nels/
elem
ents
Depth/Time
Depth/Time
Raw (undelayed)
Dynamic Focusing on Receive
Rad225/Bioe225UltrasoundFall 2019Dynamic Receive Focusing
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Dynamic Receive FocusingContinuously adjust the delays
Beam
form
ing
Unf
ocus
ed s
igna
l rec
eive
d fr
om
the
near
fiel
dFo
cuse
d sig
nal u
sing
time-
dela
ys:
Not
e ho
w w
avef
ront
sapp
ear a
s “p
lane
wav
es”
RF S
um
Chan
nels/
elem
ents
Depth/Time
Depth/Time
delayed
Rad225/Bioe225UltrasoundFall 2019Receive Beamforming
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Beamforming
Unfocused signal received from the near field
Focused signal using time-delays: Note how wavefronts appear as “plane waves”
RF Sum
Channels/elements
Dept
h/Ti
me
Receive Beamforming
• Transmit beamforming in reverse:
Use same equation as before to compute time delays for receiving!
Rad225/Bioe225UltrasoundFall 2019Transmit Beamforming Only
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Fixed Focus Beamforming
Rad225/Bioe225UltrasoundFall 2019Dynamic Receive Beamforming
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Dynamic Receive Beamforming
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