Digital Beamforming

1. Digital Beamforming

2. Beamforming • Manipulation of transmit and receive apertures. • Trade-off performance/cost to achieve: • Steer and focus the transmit beam. • Dynamically steer and focus the receive beam. • Provide accurate delay and apodization. • Provide dynamic receive control.

3. beam formation propagation object Beam Formation as Spatial Filtering • Propagation can be viewed as a process • of linear filtering (convolution). • Beam formation can be viewed as an inverse • filter (or others, such as a matched filter).

4. Implementaiton of Beam Formation • Delay is simply based on geometry. • Weighting (a.k.a. apodization) strongly depends on the specific approach.

5. 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, focusing is necessary.

6. 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).

7. Beam Formation - Delay • In practice, ideal delays are quantized, i.e., received signals are temporally sampled. • 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.

8. Delay Quantization • The delay quanitzation error can be viewed as the phase error of the phasors.

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

10. Beam Formation - Delay • RF beamformer requires either a clock frequency 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.

11. R q Beam Formation - Delay

12. 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 e l e m e n t i s u m m a t i o n Beam Formation - RF

13. MUX Z-1 Z-1 1/2 Beam Formation - RF • Interpolation by 2:

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

15. I t i m e d e l a y / A D C d e m o d / e l e m e n t i p h a s e r o t a t i o n L P F Q I Q Beam Formation - BB • The coarse time delay is applied at a low clock frequency, the • fine phase needs to be rotated accurately (e.g., by CORDIC).

16. A=n0+1-f Dn=1 j=1 A=A+j-f Dn=Dn+1 A<=0? N bump n0 n1 A=A+Dn+n0 j=j+1 Autonomous Delay Control

17. Beam Formation - Apodization • Aperture weighting is often simplified as a choice of apodization type (such as uniform, Hamming, Gaussian, ...etc.) • Apodization is used to control sidelobes, grating lobes and depth of field. • Apodization generally can use lower number of bits. • Often used on transmit, but not on receive.

18. 1/R R R R Range Dependence • Single channel (delay). • Single channel (apodization). • Aperture growth (delay and apodization). R

19. R Aperture Growth • Constant f-number for linear and sector formats. sector linear • Use angular response for convex formats. R

20. Aperture Growth • Use a threshold level (e.g., -6dB) of an individual element’s two-way response to control the aperture growth for convex arrays. element response sinq

21. R r r q’ q Aperture Growth

22. Aperture Growth • Use the threshold angle to control lens opening. • Channels far away from the center channel contribute little to the coherent sum. • F-number vs. threshold angle.

23. Apodization Issues • Mainlobe vs. sidelobes (contrast vs. detail). • Sensitivity (particularly for Doppler modes).

24. Apodization Issues • Grating lobes (near field and under-sampled apertures). • Clinical evaluation of grating lobe levels.

25. Apodization Issues • Near field resolution. Are more channels better ? • Depth of field : 2* f-number2*l (using the l/8 criterion).

26. Apodization Issues • Large depth of field - better image uniformity for single focus systems. • Large depth of field - higher frame rate for multiple focus systems. • Depth of field vs. beam spacing.

27. DS-Based Beamformers

28. 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.

29. Advantages of DS 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.

30. Beam Forming

31. Beam Forming: Conventional

32. Beam Forming: Delta Sigma

33. Dynamic Focusing Error • When relative delay is required, additional samples need to be inserted. • Reconstructed sample vs. direct representation. • The inserted samples must be cancelled out in the beam sum.

34. Dynamic Focusing Error Correction

35. Dynamic Focusing Error Correction • Using the delay symmetry:

36. Symthetic Aperture Imaging

37. Synthetic Aperture vs. Phased Array • Conventional phased array: all effective channels are excited to form a transmit beam. All effective channels contribute to receive beam forming. • Synthetic aperture: a large aperture is synthesized by moving, or multiplexing a small active aperture over a large array.

38. Applications in Medical Imaging • High frequency ultrasound: High frequency (>20MHz) arrays are difficult to construct. • Some applications: • Ophthalmology. • Dermatology. • Bio-microscopy.

39. Applications in Medical Imaging • Intra-vascular ultrasound: Majority of the imaging device needs to be integrated into a balloon angioplasty device, the number of connection is desired to be at a minimum. multiplexor imager T/R catheter

40. defocused beam focused beam scanning direction Applications in Medical Imaging • Hand-held scanners: multi-element synthetic aperture imaging can be used for optimal tradeoff between cost and image quality.

41. Applications in Medical Imaging • Large 1D arrays: For example, a 256 channel 1D array can be driven by a 64 channel system. • 1.5D and 2D arrays: Improve the image quality without increasing the system channel number.

42. Synthetic Aperture vs. Phased Array • Phased array has all N2 combinations. • Synthetic aperture has only N “diagonal” records. PA SA

43. Synthetic Aperture vs. Phased Array • Point spread function: weighting weighting aperture aperture d 2d

44. phased array synthetic aperture Synthetic Aperture vs. Phased Array • Spatial and contrast resolution:

45. Synthetic Aperture vs. Phased Array • Signal-to-noise ratio: SNR is determined by the transmitted acoustic power and receive electronic noise. Assuming the same driving voltage, the SNR loss for synthetic aperture is 1/N.

46. Synthetic Aperture vs. Phased Array • Frame rate: Frame rate is determined by the number of channels for synthetic aperture, it is not directly affected by the spatial Nyquist sampling criterion. Thus, there is a potential increase compared to phased array.

47. Synthetic Aperture vs. Phased Array • Motion artifacts: For synthetic aperture, a frame cannot be formed until all data are collected. Thus, any motion during data acquisition may produce severe artifacts. • The motion artifacts may be corrected, but it imposes further constraints on the imaging scheme.

48. Synthetic Aperture vs. Phased Array • Tissue harmonic imaging: Generation of tissue harmonics is determined by its nonlinearity and instantaneous acoustic pressure. Synthetic aperture is not ideal for such applications.

49. Synthetic Aperture vs. Phased Array • Speckle decorrelation: Based on van Cittert Zernike theorem, signals from non-overlapping apertures have no correlation. Therefore, such synthetic apertures cannot be used for correlation based processing such as aberration correction, speckle tracking and Doppler processing.

50. Filter Based Synthetic Focusing