Chapter 6: Real-Time Image Formation

display

B, M, Doppler image

processingDoppler

processing

digital receive beamformer

beamformercontrol

digital transmit beamformer

high voltage

amplifierDAC

system controlkeyboard

ADCvariable

gain

T/R switch

arraybody

All digital

Generic Ultrasonic Imaging System

• Transmitter:– Arbitrary waveform.– Programmable transmit voltage.– Arbitrary firing sequence.– Programmable apodization, delay control and

frequency control.

Digital Waveform Generator

D/A HV Amp Transducer Array

Control

OR

Transmit Waveform• Characteristics of transmit waveforms.

0 2 4 6 8-6 0

-4 0

-2 0

0

-2 -1 0 1 2-1

0

1

MHz

dBN

orm

aliz

ed

Am

plitu

de

Spectra

Waveforms

µs

Generic Ultrasonic Imaging System

• Receiver:– Programmable apodization, delay control and

frequency control.– Arbitrary receive direction.

• Image processing:– Pre-detection filtering.– Post-detection filtering.

• Full gain correction: TGC, analog and digital.• Scan converter: various scan format.

Generic Receiver

beam former

filtering (pre-detection)

envelope detection

filtering(post-detection)

mapping and other processing

scan conversion

display

adaptive controls

A/D

Pre-detection Filtering

Z

t

X

Pre-detection Filtering• Pulse shaping. (Z)• Temporal filtering. (t)• Beam shaping. (X)

– Selection of frequency range. (Z X)

– Correction of focusing errors. (X X’)B xz T x z Rx z A d( ,) ( , ,)( , ,)()′ = ′ ′∫ ω ω ω ω

|C(x)|

|p(x’,z)|

-a a1

2a

λ/2ax'/z

F.T.

Pulse-echo effective apertures• The pulse-echo beam pattern is the multiplication of the

transmit beam and the receive beam• The pulse-echo effective aperture is the convolution of

transmit and receive apertures

−

= 0

2 112|)(|)( RR

jkx

exCxCFor C.W.

DynTx DynRx

0

0.5

1

0

0.5

1DynRx

1FixedRx

0510

0510

R=Ro

R≠Ro

Post-Detection Filtering

• Data re-sampling (Acoustic Display).• Speckle reduction (incoherent averaging).• Feature enhancement.• Aesthetics.• Post-processing:

– Re-mapping (gray scale and color).– Digital gain.

Envelope Detection

• Demodulation based:

{ }S t At ft Atej ft( ) ( )cos Re ()= =2 0

2 0π π

{ }A t LPFSt f( ) ( )cos= 2 0π

D t absAt( ) ( ())=rf signal

envelop

Envelope Detection

• Hilbert Transform

{ }{ }( )

S tjHT St Ate

D t absSt jHT St

j ft( ) .. ( ) ( )

( ) ( ) .. ( )/

+ ⋅ =

= + ⋅

2

2

2 0π

ff0-f0

ff0

-f0

ff0t

tht

fjfHT

π1)(

)sgn()(

−=

−=

H.T.

Beam Former Design

Implementaiton of Beam Formation

• Delay is simply based on geometry.• Weighting (a.k.a. apodization) strongly

depends on the specific approach.

Beam Formation - Delay

• Delay is based on geometry. For simplicity, a constant sound velocity and straight line propagation are assumed. Multiple reflection is also ignored.

• In diagnostic ultrasound, we are almost always in the near field. Therefore, range focusing is necessary.

Beam Formation - Delay

• Near field / far field crossover occurs when f#=aperture size/wavelength.

• The crossover also corresponds to the point where the phase error across the aperture becomes significant (destructive).

82

2 λ=

Ra

Phased Array Imaging

Rcx

cxRxt ii

irx 2cossin),,(

22 θθθ +−=

Transducer

Delay

Tx

Rx

θ

Rx

SymmetrySymmetry

Dynamic Focusing

• Dynamic-focusing obtains better image quality but implementation is more complicated.

Fix

DynamicDelay

R

Focusing Architecture

summ

ation

1

N

delay line

delay line

delay controller

transducer array

Delay Pattern

Delay

Timen0

k0

τθθ∆=+−= n

Rctx

ctxroundk

s

i

s

in )

2cossin(

22

• Delays are quantized by sampling-period ts.

Missing Samples

TimeTime

DelayDelay DelayDelay--Change Change

BeamformerBeamformer

t2

Human Human BodyBody

t1

Beam Formation ∆τ ∆τ∆τ

delay controller

input

output

n t n tx

c t ti( ) ( )cos

1 2

2 2

21 2

11 1

− = = −

θτ∆

n tx

c

x

c ti i( )sin cos

≈ − +θ

τθ

τ∆ ∆

2 2

2

Beam Formation - Delay

• The sampling frequency for fine focusing quality needs to be over 32*f0(>> Nyquist).

• Interpolation is essential in a digital system and can be done in RF, IF or BB.

∆∆τ θπ

= ≤2

1

320 0f f

2 32 1125π/ .≈ o

Delay Quantization

• The delay quantization error can be viewed as the phase error of the phasors.

∑−

=

=1

0)cos(

N

nnA φ

∑−

=

=

1

0

22

2N

nA nd

dAφσφ

σ

Delay Quantization

21sin2 =φ

12

222 φσσ φφ

∆==

n

NN

A241

24

22 <∆⇒<

∆⋅= φφσ

• N=128, 16 quantization steps per cycles are required.• In general, 32 and 64 times the center frequency is used.

Beam Formation - Delay

element i ADC interpolation digital delay summ

atio n

• RF beamformer requires either a clock well over 100MHz, or a large number of real-time computations.

• BB beamformer processes data at a low clock frequency at the price of complex signal processing.

Beam Formation - RF

• Interpolation by 2:

Z-1

Z-1

MU

X

1/2

Beam Formation - RF

• General filtering architecture (interpolation by m):

Delay

Filter 1

Filter 2

Filter m-1

MU

X

Fine delay control

FIFO

Coarse delay control

Autonomous Delay ControlAutonomous vs. Centralized

A=n0+1−φ∆n=1j=1

A<=0?

A=A+∆n+n0j=j+1

A=A+j−φ∆n=∆n+1 N bump

n0 n1

Beam Formation - BB

A(t-τ)cos2πf0(t-τ)

A(t-τ)cos2πf0(t-τ)e-j2πfdt

magnitude

ff0-fd-f0-fd

ff0-fd

LPF(A(t-τ)cos2πf0(t-τ)e-j2πfdt)

ff0-f0

rf

baseband

Beam Formation - BB

{ }

( )

I LPFAt f t ft

LPFA t

f ft f f f t f

A tf ft f

d

d d d d

d d

= − −

=−

− − − + + − +

=−

− − −

( )cos ( )cos

( )cos(( )( ) )cos(( )( ) )

( )cos(( )( ) )

τ π τ π

τ π τ τ π τ τ

τ π τ τ

2 2

22 2

22

0

0 0

0

{ }

( )

Q LPF At f t ft

LPFA t

f ft f f f t f

A tf ft f

d

d d d d

d d

= − − −

=−

− − − − + − +

=−

− − −

( )cos ( )sin

( )sin(( )( ) )sin(( )( ) )

( )sin(( )( ) )

τ π τ π

τ π τ τ π τ τ

τ π τ τ

2 2

22 2

22

0

0 0

0

Beam Formation - BBelement i A DC demod/

LPFtime delay/

phase rotation

I Q

I

Q

BBtA t

e ej ft j fd( )( ) ( )=− − −τ π τ π τ

22 2∆

O tA t

e ei i

i

Nj ft jfi i d i i( )

( ) ( ) ( )=− + ′

=

− + ′ − −∑τ τ π τ τ π τ θ

21

2 2∆

Beam Formation - BBelement i A DC demod/

LPFtime delay/

phase rotation

I Q

I

Q

∆∆∆ ∆

τ θπ

= ≤2

1

32f f

• The coarse time delay is applied at a low clock frequency, the fine phase needs to be rotated accurately (e.g., by CORDIC).

∆Σ-Based Beamformers

Why ∆Σ ?

• High Delay Resolution -- 32 f0 (requires interpolation)

• Multi-Bit Bus

Current ProblemsCurrent Problems

• High Sampling Rate -- No Interpolation Required

• Single-Bit Bus -- Suitable for Beamformers with Large Channel-Count

∆Σ∆Σ AdvantagesAdvantages

Conventional vs. ∆Σ

Advantages of Over-Sampling

• Noise averaging.• For every doubling of the sampling rate,

it is equivalent to an additional 0.5 bit quantization.

• Less requirements for delay interpolation.• Conventional A/D not ideal for single-bit

applications.

Advantages of ∆Σ Beamformers

• Noise shaping.• Single-bit vs. multi-bits.• Simple delay circuitry.• Integration with A/D and signal processing.• For hand-held or large channel count devices.

Block-Diagram of the ∆Σ ModulatorQuantizer

D/A

_yx Integrator

eLPF ↓ x*

Single-Bit

• Over-Sampling • Noise-Shaping

• Reconstruction

• The SNR of a 32 f0, 2nd-order, low-passed ∆Σ modulator is about 40dB.

Property of a ∆Σ Modulator

0 0.5-60

-40

-20

0

0 0.5-60

-40

-20

0

0 0.1 0.2 0.3 0.4 0.5-60

-40

-20

0dB

Frequency

1 1024-0.5

0

0.5

1 1024-1

0

1

1 256 512 768 1024-0.5

0

0.5

Sample

WaveformWaveform SpectrumSpectrum

xx

yy

x*x*

A Delta-Sigma Beamformer

Σ

Transducer TGC ∆Σ A/DShift-Register

Delay-Controller / MUX

Transducer TGC

Shift-Register

Delay-Controller / MUX

. . .

SingleSingle--BitBit

LPF

∆Σ A/D

• No Interpolation• Single-Bit Bus

A

-70

-60

-50

-40

-30

-20

-10

0B

D C

Results

A. RF

B. Repeat

C. Insert-Zero

D. Sym-Hold

Cross-Section-Views of Peak 3

-20 -10 0 10 20

-80

-60

-40

-20

0RF

dB

-20 -10 0 10 20

-80

-60

-40

-20

0Repeat

dB

-20 -10 0 10 20

-80

-60

-40

-20

0Insert-Zero

dB

Width (mm)-20 -10 0 10 20

-80

-60

-40

-20

0Symmetric-Hold

dB

Width (mm)

Scan Conversion

• Acquired data may not be on the display grid.

Acquired grid

Display grid

Scan Conversion

sinθ

R

x

y

acquired converted

Scan Conversion

original gridraster gridacquired data

display pixel

a(i,j)

a(i,j+1)

a(i+1,j)

a(i+1,j+1)

p

)1,1(

)1,(),1(),(),(

1,1,,

1,,,,1,,,,,

++

+++++=

++

++

jiac

jiacjiacjiacnmp

jinm

jinmjinmjinm

Moiré Pattern

Scan Conversion

original data buffer

interpolation display buffer

addresses and coefficients generation

display

Temporal Resolution (Frame Rate)

• Frame rate=1/Frame time.• Frame time=number of lines * line time.• Line time=(2*maximum depth)/sound

velocity.• Sound velocity is around 1540 m/s.• High frame rate is required for real-time

imaging.

Temporal Resolution

• Display standard: NTSC: 30 Hz. PAL: 25 Hz (2:1 interlace). 24 Hz for movie.

• The actual acoustic frame rate may be higher or lower. But should be high enough to have minimal flickering.

• Essence of real-time imaging: direct interaction.

Temporal Resolution

• For an actual frame rate lower than 30 Hz, interpolation is used.

• For an actual frame rate higher than 30 Hz, information can be displayed during playback.

• Even at 30 Hz, it is still possibly undersampling.

Temporal Resolution

• B-mode vs. Doppler.• Acoustic power: peak vs. average.• Increasing frame rate:

– Smaller depth and width.– Less flow samples.– Wider beam width.– Parallel beam formation.

Parallel Beamformation• Simultaneously receive multiple beams.• Correlation between beams, spatial ambiguity.• Require duplicate hardware (higher cost) or time

sharing (reduced processing time and axial resolution).

r1 r2t

t

r1 r2

Parallel Beamformation

• Simultaneously transmit multiple beams.• Interference between beams, spatial

ambiguity.

t1/r1 t2/r2

t1/r1t2/r2