Chapter 6: Real-Time Image Formation

display

B, M, Doppler image

processing

Doppler processing

digital receive beamformer

system control keyboard

beamformer control

digital transmit beamformer DAC

high voltage

amplifier

ADC variable

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

dB

Nor

mal

ized

A

mpl

itude

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. (ZàX’)

– Correction of focusing errors. (XàX’) |C(x)|

|p(x’,z)|

-a a 1

2a

λ/2a x'/z

F.T.

Pulse-echo effective apertures

DynTx DynRx"

0"

0.5"

1"

0"

0.5"

1"DynRx"

1"FixedRx"

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 à Display). •  Speckle reduction (incoherent averaging). •  Feature enhancement. •  Aesthetics. •  Post-processing:

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

Envelope Detection

•  Demodulation based:

rf signal"

envelop

Envelope Detection

•  Hilbert Transform

f f0 -f0

f f0

-f0

f f0 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).

Phased Array Imaging

Symmetry

Transducer

Delay

Tx

Rx

θ

R x

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

Time n0

k0

•  Delays are quantized by sampling-period ts.

Missing Samples

Time

Delay Delay-Change

Beamformer Human Body

t1 t2

Beam Formation Δτ Δτ Δτ

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.

Delay Quantization

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

Delay Quantization

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

used.

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.

e l e m e n t i A D C i n t e r p o l a t i o n d i g i t a l d e l a y s u m m

a t i o n

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+1−φ Δn=1 j=1

A<=0?

A=A+Δn+n0 j=j+1

A=A+j−φ Δn=Δn+1 N bump

Autonomous vs. Centralized

Beam Formation - BB

A(t-τ)cos2πf0(t-τ)

A(t-τ)cos2πf0(t-τ)e-j2πfdt

magnitude

f f0-fd -f0-fd

f f0-fd

LPF(A(t-τ)cos2πf0(t-τ)e-j2πfdt)

f f0 -f0

rf

baseband

Beam Formation - BB

Beam Formation - BB e l e m e n t i A D C d e m o d /

L P F t i m e d e l a y /

p h a s e r o t a t i o n

I Q

I

Q

Beam Formation - BB e l e m e n t i A D C d e m o d /

L P F t i m e d e l a y /

p h a s e r o t a t i o n

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).

ΔΣ-Based Beamformers

Why ΔΣ ?

•  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

ΔΣ Advantages

Current Problems

Conventional vs. ΔΣ

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 ΔΣ 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 ΔΣ Modulator Quantizer

D/A

_ y x Integrator

e LPF ↓ x*

Single-Bit

•  Over-Sampling •  Noise-Shaping

•  Reconstruction

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

Noise Shaped ΔΣ Modulator

Signal and Noise Transfer Function

Noise Shaping Transfer Functions •  For first order noise shaping, 1.5 bits (9 dB) is

gained when the sampling frequency is doubles. •  For second order noise shaping, 2.5 bits (15 dB) is

gained when the sampling frequency is doubles.

Property of a ΔΣ 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"

0"dB"

Frequency"

1" 1024"-0.5"

0"

0.5"

1" 1024"-1"

0"

1"

1" 256" 512" 768" 1024"-0.5"

0"

0.5"

Sample"

Waveform Spectrum

x

y

x*

A Delta-Sigma Beamformer

•  No Interpolation •  Single-Bit Bus

Transducer TGC ΔΣ A/D

Shift-Register

Delay-Controller / MUX

Transducer TGC

Shift-Register

Delay-Controller / MUX

. . .

Single-Bit

LPF

ΔΣ A/D

A. RF

B. Repeat

C. Insert-Zero

D. Sym-Hold

A "

-70"

-60"

-50"

-40"

-30"

-20"

-10"

0"B"

D "C"

Results

-20" -10" 0" 10" 20"

-80"

-60"

-40"

-20"

0"RF"

dB"

-20" -10" 0" 10" 20"

-80"

-60"

-40"

-20"

0"Repeat"

dB"

-20" -10" 0" 10" 20"

-80"

-60"

-40"

-20"

0"Insert-Zero"

dB"

Width (mm)"-20" -10" 0" 10" 20"

-80"

-60"

-40"

-20"

0"Symmetric-Hold"

dB"

Width (mm)"

Cross-Section-Views of Peak 3

Generic Receiver

beam former

filtering (pre-detection)

envelope detection

filtering(post-detection)

mapping and other processing

scan conversion

display

adaptive controls

A/D

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 grid raster grid acquired data

display pixel

a(i,j)

a(i,j+1)

a(i+1,j)

a(i+1,j+1)

p

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 r2 t

t

r1 r2

Parallel Beamformation

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

ambiguity.

t1/r1 t2/r2

t1/r1 t2/r2

Term Report

•  “The Applications of K-Space in Pulse-Echo Ultrasound”, W.F. Walker and G.E. Trahey, IEEE Trans. on UFFC, vol. 45-3, pp. 541-558, 1998.