Chapter 6: Real-Time Image Formation

Chapter 6: Real-Time Image Formation

digital transmit beamformer DAC high voltage amplifier keyboard system control beamformer control T/R switch array body display B, M, Doppler image processing digital receive beamformer ADC variable gain Doppler processing 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. 1 Waveforms Normalized Amplitude 0-1 0-2 -1 0 1 2 Spectra µs db -20-40 -60 0 2 4 6 8 MHz

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 A/D beam former envelope detection filtering (predetection) filtering(postdetection) adaptive controls display scan conversion mapping and other processing

Pre-detection Filtering t Z X

Pre-detection Filtering Pulse shaping. (Z) Temporal filtering. (t) Beam shaping. (X ) Selection of frequency range. (Zà X ) Correction of focusing errors. (Xà X ) C(x) F.T. 1 -a a p(x,z) 2a x'/z λ/2a

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 For C.W. R=Ro R Ro 1" 0.5" 0" 1" 0.5" 0" 1" DynTx DynRx" DynRx" FixedRx" 10" 5" 0" 10" 5" 0"

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 H.T. -f 0 f 0 f -f 0 f f 0 f f 0

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 Tx Transducer θ Rx Delay x R Symmetry

Dynamic Focusing Dynamic-focusing obtains better image quality but implementation is more complicated. Delay Dynamic Fix R

Focusing Architecture 1 delay line N transducer array delay controller delay line summation

Delay Pattern Delays are quantized by sampling-period t s. Delay k 0 n 0 Time

Missing Samples Human Body Beamformer Delay Delay-Change t 2 t 1 Time

Beam Formation input Δτ Δτ Δτ delay controller output

Beam Formation - Delay The sampling frequency for fine focusing quality needs to be over 32*f 0 (>> 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 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 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 MUX 1/2

Beam Formation - RF General filtering architecture (interpolation by m): Delay Filter 1 Filter 2 MUX FIFO Coarse delay control Filter m-1 Fine delay control

Autonomous Delay Control Autonomous vs. Centralized A=n 0 +1 φ Δn=1 j=1 A=A+j φ Δn=Δn+1 N A<=0? bump n 0 n 1 A=A+Δn+n 0 j=j+1

Beam Formation - BB magnitude A(t-τ)cos2πf 0 (t-τ) -f 0 f 0 rf f A(t-τ)cos2πf 0 (t-τ)e -j2πfdt -f 0 -f d f 0 -f d f LPF(A(t-τ)cos2πf 0 (t-τ)e -j2πfdt ) f 0 -f d baseband f

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 I Q t i m e d e l a y / p h a s e r o t a t i o n I Q

Beam Formation - BB e l e m e n t i A D C d e m o d / L P F I Q t i m e d e l a y / p h a s e r o t a t i o n 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

Current Problems Why ΔΣ? High Delay Resolution -- 32 f 0 (requires interpolation) Multi-Bit Bus ΔΣ Advantages High Sampling Rate -- No Interpolation Required Single-Bit Bus -- Suitable for Beamformers with Large Channel-Count

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 x _ Integrator e y LPF x* Single-Bit D/A Over-Sampling Noise-Shaping Reconstruction The SNR of a 32 f 0, 2nd-order, lowpassed 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 Waveform Spectrum x y x* 0.5" 0" -0.5" 1" 1024" 1" 0" -1" 1" 1024" 0.5" 0" -0.5" 1" 256" 512" 768" 1024" Sample" db" 0" -20" -40" -60" 0" 0.5" 0" -20" -40" -60" 0" 0.5" 0" -20" -40" -60" 0" 0.1" 0.2" 0.3" 0.4" 0.5" Frequency"

A Delta-Sigma Beamformer Transducer TGC ΔΣ A/D Single-Bit Shift-Register Transducer TGC... ΔΣ A/D Delay-Controller / MUX Shift-Register LPF No Interpolation Single-Bit Bus Delay-Controller / MUX

Results A " B" 0" -10" -20" -30" C" D " -40" A. RF -50" B. Repeat C. Insert-Zero -60" D. Sym-Hold -70"

Cross-Section-Views of Peak 3 0" RF" 0" Repeat" -20" -20" db" -40" db" -40" -60" -60" -80" -80" -20" -10" 0" 10" 20" -20" -10" 0" 10" 20" 0" Insert-Zero" 0" Symmetric-Hold" -20" -20" db" -40" db" -40" -60" -60" -80" -80" -20" -10" 0" 10" 20" Width (mm)" -20" -10" 0" 10" 20" Width (mm)"

Generic Receiver A/D beam former envelope detection filtering (predetection) filtering(postdetection) adaptive controls display scan conversion mapping and other processing

Scan Conversion Acquired data may not be on the display grid. Acquired grid Display grid

Scan Conversion sinθ x R y acquired converted

Scan Conversion a(i,j) a(i,j+1) p a(i+1,j) a(i+1,j+1) original grid raster grid acquired data display pixel

Moiré Pattern

Scan Conversion original data buffer interpolation display buffer display addresses and coefficients generation

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). t r1 t r2 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.