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

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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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





Low Frequency-small acoustic window-wide field of view at depth

Transducer Arrays





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


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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

⎛⎝⎜

⎞⎠⎟


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Rad225/Bioe225UltrasoundFall 2019Steering

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• 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

⎛⎝⎜

⎞⎠⎟


-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


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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: Focused Wave

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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

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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