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 as Spatial Filtering object propagation beam formation 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*f 0 (>> Nyquist). Interpolation is essential in a digital system and can be done in RF, IF or BB.

8. 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.

9. Beam Formation - Delay  R

10. Beam Formation - RF element i ADCinterpolationdigital delay s u m m a t i o n

11. Interpolation by 2: Z -1 MUX 1/2

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

13. Beam Formation - BB element i ADCdemod/ LPF time delay/ phase rotation IQ 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).

14. 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.

15. Range Dependence Single channel (delay). Single channel (apodization). Aperture growth (delay and apodization). 1/R R R RR

16. Aperture Growth Constant f-number for linear and sector formats. sector linear Use angular response for convex formats. RR

17. 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. sin  element response

18. Aperture Growth R r  ’’ 

19. 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.

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

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

22. Apodization Issues Near field resolution. Are more channels better ? Depth of field : 2* f-number 2 *  using the /8 criterion).

23. 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.

24. Synthetic Aperture Imaging

25. Synthetic Aperture vs. Phased Array Phased array has all N 2 combinations. Synthetic aperture has only N “diagonal” records. PASA

26. 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.

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

28. 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 T/R imager catheter

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

30. 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.

31. Synthetic Aperture vs. Phased Array Phased array has all N 2 combinations. Synthetic aperture has only N “diagonal” records. PASA

32. Full Data Set Transmit Receive Transmit Receive Phased Array Synthetic Aperture

33. Synthetic Aperture vs. Phased Array Point spread function: d weighting aperture 2d2d weighting

34. Synthetic Aperture vs. Phased Array Spatial and contrast resolution: phased arraysynthetic aperture

35. 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.

36. 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.

37. 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.

38. 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.

39. 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.

40. Filter Based Synthetic Focusing

41. Motivation Conventional ultrasonic array imaging system –Fixed transmit and dynamic receive focusing –Image quality degradation at depths away from the transmit focal zone Dynamic transmit focusing –Fully realize the image quality achievable by an array system –Not practical for real-time implementation

42. DynTx DynRxFixedTx DynRx beam pattern

43. Motivation Retrospective filtering technique –Treat dynamic transmit focusing as a deconvolution problem –Based on fixed transmit and dynamic receive focusing Synthetic transmit and receive focusing –Based on fixed transmit and fixed receive focusing –System complexity is greatly reduced

44. Retrospective Filtering Where s: scattering distribution function, bp oof : out of focused pulse-echo beam pattern, bp ideal : ideal pulse-echo beam pattern all are a function of (R, sinθ)

45. Inverse filter Spatial Fourier transform relationship –Beam pattern  aperture function The spectrum of the inverse/optimal filter is the ideal pulse-echo effective aperture divided by the out-of- focused pulse-echo aperture function Robust deconvolution –No singular point in the passband of spectrum –SNR is sufficiently high The number of taps equals to the number of beams –Not practical

46. Optimal filter Less sensitive to noise than inverse filter Filter length can be shorter the mean squared error(MSE) Minimize MSE where, b: the out-of-focused beam pattern, d: desired beam pattern f: filter coefficients Convolution matrix form

47. Pulse-echo effective apertures 0 5 10 0 DynTx DynRx 0 0.5 1 0 1 DynRx 0.5 1 FixedRx 0 5 10 0 5 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

48. Experimental Results DynTx DynRx FixedTx DynRx FixedTx FixedRx b filtered d filtered abcde

49. Experimental Results -0.15-0.1-0.0500.050.10.15 -40 -30 -20 -10 0 sinθ dB DynTx DynRx DynRx DynRx Filtered FixedRx Filtered

50. Experimental Results DynTx DynRx FixedTx DynRx FixedTx FixedRx

51. Homework Hint (Due 4/5 noon) Transmit Receive Phased Array Transmit Receive Synthetic Aperture