Chapter 6: Real-Time Image Formation

display

B, M, Doppler image

processing

Doppler processing

digital receive beamformer

system controlkeyboard

beamformer control

digital transmit beamformer DAC

high voltage

amplifier

ADCvariable

gain

T/R switch

array

body

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 8-60

-40

-20

0

-2 -1 0 1 2-1

0

1

MHz

dBN

orm

aliz

ed

Am

plitu

de

Spectra

Waveforms

s

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. (ZX)

– Correction of focusing errors. (XX’)

B x z T x z R x z A d( , ) ( , , ) ( , , ) ( )

|C(x)|

|p(x’,z)|

-a a1

2a

/2ax'/z

F.T.

Pulse-echo effective apertures

0

2 11

2|)(|)( RR

jkx

exCxC DynTx DynRx

0

0.5

1

0

0.5

1DynRx

1FixedRx

0

5

10

0

5

10

• 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

For C.W.

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 A t f t A t ej f t( ) ( )cos Re ( ) 2 02 0

A t LPF S t f( ) ( )cos 2 0

D t abs A t( ) ( ( ))rf signal

envelop

Envelope Detection

• Hilbert Transform

S t j H T S t A t e

D t abs S t j H T S t

j f t( ) . . ( ) ( )

( ) ( ) . . ( ) /

2

2

2 0

ff0-f0

ff0

-f0

ff0H.T.

ttht

fjfHT

1

)(

)sgn()(

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

R

a

Phased Array Imaging

Rc

x

c

xRxt ii

irx 2

cossin),,(

22 SymmetrySymmetry

Transducer

Delay

Tx

Rx

Rx

Dynamic Focusing

Delay

R

Fix

Dynamic

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

Focusing Architecture

summ

ation

1

N

delay line

delay line

delay controller

transducer array

Delay Pattern

Delay

Timen0

k0

n

Rct

x

ct

xroundk

s

i

s

in )

2

cossin(

22

• Delays are quantized by sampling-period ts.

Missing Samples

TimeTime

DelayDelay Delay-Change Delay-Change

BeamformerBeamformerHuman Human BodyBody

t1t2

Beam Formation

n t n tx

c t ti( ) ( )cos

1 2

2 2

21 2

11 1

n tx

c

x

c ti i( )sin cos

2 2

2

delay controller

input

output

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.

2

1320 0f f

2 32 1125 / . o

Delay Quantization

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

1

0

)cos(N

nnA

1

0

2

2

2N

nA nd

dA

Delay Quantization

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

used.

2

1sin 2

12

222

n

N

NA

241

24

22

Beam Formation - Delay

• 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.

element i ADC interpolation digital delay summ

ation

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 Control

n0 n1

A=n0+1n=1j=1

A<=0?

A=A+n+n0

j=j+1

A=A+jn=n+1 N bump

Autonomous vs. Centralized

Beam Formation - BB

A(t-)cos2f0(t-)

A(t-)cos2f0(t-)e-j2fdt

magnitude

ff0-fd-f0-fd

ff0-fd

LPF(A(t-)cos2f0(t-)e-j2fdt)

ff0-f0

rf

baseband

Beam Formation - BB

I LPF A t f t f t

LPFA t

f f t f f f t f

A tf f t f

d

d d d d

d d

( )cos ( )cos

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

( )cos (( )( ) )

2 2

22 2

22

0

0 0

0

Q LPF A t f t f t

LPFA t

f f t f f f t f

A tf f t f

d

d d d d

d d

( )cos ( )sin

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

( )sin (( )( ) )

2 2

22 2

22

0

0 0

0

Beam Formation - BB

BB tA t

e ej f t j fd( )( ) ( )

22 2

element i A DC demod/LPF

time delay/phase rotation

I Q

I

Q

O tA t

e ei i

i

Nj f t j fi i d i i( )

( ) ( ) ( )

21

2 2

Beam Formation - BB

element i A DC demod/LPF

time delay/phase rotation

I Q

I

Q

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

2

132f f

-Based Beamformers

Why ?

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

• Multi-Bit Bus

• High Sampling Rate -- No Interpolation Required

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

AdvantagesAdvantages

Current ProblemsCurrent Problems

Conventional vs.

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 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 Modulator

Quantizer

D/A

_yx

Integrator

e

LPF x*

Single-Bit

• Over-Sampling • Noise-Shaping

• Reconstruction

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

Property of a 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

• No Interpolation

• Single-Bit Bus

Σ

Transducer TGC A/D

Shift-Register

Delay-Controller / MUX

Transducer TGC

Shift-Register

Delay-Controller / MUX

. . .

Single-BitSingle-Bit

LPF

A/D

A. RF

B. Repeat

C. Insert-Zero

D. Sym-Hold

A

-70

-60

-50

-40

-30

-20

-10

0B

D C

Results

-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)

Cross-Section-Views of Peak 3

Scan Conversion

• Acquired data may not be on the display grid.

Acquired grid

Display grid

Scan Conversion

sin

R

x

y

acquired converted

Scan Conversion

original grid

raster grid

acquired 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 vel

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

maging.

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/r1

t2/r2