Pulse compression for finite amplitude distortion based harmonic imaging using coded waveforms

Coded Excitation for Ultrasonic Testing: A Review

Originating in the early 20th century, ultrasonic testing has found increasingly extensive applications in medicine, industry, and materials science. Achieving both a high signal-to-noise ratio and high efficiency is crucial in ultrasonic testing. The former means an increase in imaging clarity as well as the detection depth, while the latter facilitates a faster refresh of the image. It is difficult to balance these two indicators with a conventional short pulse to excite the probe, so in general handling methods, these two factors have a trade-off. To solve the above problems, coded excitation (CE) can increase the pulse duration and offers great potential to improve the signal-to-noise ratio with equivalent or even higher efficiency. In this paper, we first review the fundamentals of CE, including signal modulation, signal transmission, signal reception, pulse compression, and optimization methods. Then, we introduce the application of CE in different areas of ultrasonic testing, with a focus on industrial bulk wave single-probe detection, industrial guided wave detection, industrial bulk wave phased array detection, and medical phased array imaging. Finally, we point out the advantages as well as a few future directions of CE.

The feasibility of pulse compression by nonlinear effective bandwidth extension

Chirp-encoded excitation has been utilized for increased signal-to-noise ratio (SNR) in both linear and harmonic imaging. In either case, it is necessary to isolate the relevant frequency band to avoid artifacts. In contrast, the present study isolates and then combines the fundamental and the higher harmonics, treating them as a single, extended bandwidth. Pulse-inverted sum and difference signals are first used to isolate even and odd harmonics. Matched filters specific to the source geometry and the transmit signal are then separately applied to each harmonic band. Verification experiments are performed using up to the third harmonic resulting from an underwater chirp excitation. Analysis of signal peaks after scattering from a series of steel and nylon wires indicates increased compression using the extended bandwidth, as compared to well-established methods for fundamental and second harmonic chirp compression. Using third harmonic bands, a mean pulse width of 56% relative to fundamental compression and 48% relative to second harmonic compression was observed. Further optimization of the compression by altering the transmission indicated 17% additional reduction in the pulse width and a 47% increase in peak-to-sidelobe ratio. Overall, results establish the feasibility of extended bandwidth signal compression for simultaneously increasing SNR and signal resolution.

Third harmonic transmit phasing for SNR improvement in tissue harmonic imaging with Golay-encoded excitation

BACKGROUND

Ultrasound tissue harmonic signal generally provides superior image quality as compared to the linear signal. However, since the generation of the tissue harmonic signal is based on finite amplitude distortion of the propagating waveform, the penetration and the sensitivity in tissue harmonic imaging are markedly limited because of the low signal-to-noise ratio (SNR).

METHODS

The method of third harmonic (3f(0)) transmit phasing can improve the tissue harmonic SNR by transmitting at both the fundamental (2.25MHz) and the 3f(0) (6.75MHz) frequencies to achieve mutual enhancement between the frequency-sum and the frequency-difference components of the second harmonic signal. To further increase the SNR without excessive transmit pressure, coded excitation can be incorporated in 3f(0) transmit phasing to boost the tissue harmonic generation.

RESULTS

Our analyses indicate that the phase-encoded Golay excitation is suitable in 3f(0) transmit phasing due to its superior transmit bandwidth efficiency. The resultant frequency-sum and frequency-difference components of tissue harmonic signal can be simultaneously Golay-encoded for SNR improvement. The increase of the main-lobe signal with the Golay excitation in 3f(0) transmit phasing are consistent between the tissue harmonic measurements and the simulations. B-mode images of the speckle generating phantom also demonstrate the increases of tissue harmonic SNR for about 11dB without noticeable compression artifacts.

CONCLUSION

For tissue harmonic imaging in combination with the 3f(0) transmit phasing method, the Golay excitation can provide further SNR improvement. Meanwhile, the axial resolution can be effectively restored by pulse compression while the lateral resolution remains unchanged.

Coded tissue harmonic imaging with nonlinear chirp signals

Coded tissue harmonic imaging with pulse inversion (CTHI-PI) based on a linear chirp signal can improve the signal-to-noise ratio with minimizing the peak range sidelobe level (PRSL), which is the main advantage over CTHI with bandpass filtering (CTHI-BF). However, the CTHI-PI technique could suffer from motion artifacts due to decreasing frame rate caused by two firings of opposite phase signals for each scanline. In this paper, a new CTHI method based on a nonlinear chirp signal (CTHI-NC) is presented, which can improve the separation of fundamental and harmonic components without sacrificing frame rate. The nonlinear chirp signal is designed to minimize the PRSL value by optimizing its frequency sweep rate and time duration. The performance of the CTHI-NC method was evaluated by measuring the PRSL and mainlobe width after compression. From the in vitro experiments, the CTHI-NC provided the PRSL of -40.6 dB and the mainlobe width of 2.1 μs for the transmit quadratic nonlinear chirp signal with the center frequency of 2.1 MHz, the fractional bandwidth at -6 dB of 0.6 and the time duration of 15 μs. These results indicate that the proposed method could be used for improving frame rates in CTHI while providing comparable image quality to CTHI-PI.

Coded excitation for ultrasound tissue harmonic imaging

Coded excitation can improve the signal-to-noise ratio (SNR) in ultrasound tissue harmonic imaging (THI). However, it could suffer from the increased sidelobe artifact caused by incomplete pulse compression due to the spectral overlap between the fundamental and harmonic components of ultrasound signal after nonlinear propagation in tissues. In this paper, three coded tissue harmonic imaging (CTHI) techniques based on bandpass filtering, power modulation and pulse inversion (i.e., CTHI-BF, CTHI-PM, and CTHI-PI) were evaluated by measuring the peak range sidelobe level (PRSL) with varying frequency bandwidths. From simulation and in vitro studies, the CTHI-PI outperforms the CTHI-BF and CTHI-PM methods in terms of the PRSL, e.g., -43.5dB vs. -24.8dB and -23.0dB, respectively.

Design of chirp excitation waveform for dual-frequency harmonic contrast detection

Tissue background suppression is essential for harmonic detection of ultrasonic contrast microbubbles. To reduce the tissue harmonic amplitude for improvement of contrast-to-tissue ratio (CTR), the method of third harmonic (3f(0)) transmit phasing uses an additional 3f(0) transmit signal to provide mutual cancellation between the frequency-sum component and the frequency-difference component of tissue harmonic signal. Chirp excitation can further improve the SNR in harmonic imaging without requiring an excessive transmit pressure and thus reduce potential bubble destruction. However, for effective suppression of tissue harmonic background in 3f(0) transmit phasing, the 3f(0) chirp waveform has to be carefully designed for the generation of spectrally matched cancellation pairs over the entire second harmonic band. In this study, we proposed a chirp waveform suitable for the method of 3f(0) transmit phasing, the different-bandwidth chirp signal (DBCS). With the DBCS waveform, the frequency-difference component of tissue harmonic signal becomes a chirp signal similar to its frequency-sum counterpart. Thus, the combination of the DBCS waveform with the 3f(0) transmit phasing can markedly suppress the tissue harmonic amplitude for CTR improvement together with effective SNR increase of contrast harmonic signal. Our results indicate that, as compared with the conventional Gaussian pulse, the DBCS waveform can provide 6-dB improvement of SNR in 3f(0) transmit phasing with a CTR increase of 3 dB. Nevertheless, the limitation of available transmit bandwidth and the frequency-dependent attenuation can degrade the performance of the DBCS waveform in tissue suppression. The design of the DBCS waveform is also applicable to other dual-frequency imaging techniques that rely on the harmonic generation at the difference frequency.

Tissue harmonic depletion imaging

The inhomogeneous imaging advantages offered by finite amplitude distortion appear to be obtainable in an indirect fashion. Instead of acquiring images based on the accretion of amplitude in a higher harmonic bandwidth, comparable images could be obtained using the corresponding depletion of amplitude from a lower harmonic bandwidth. Such an approach offers some advantages over traditional harmonic imaging, including reduced bandwidth demands, and more generally could be a useful complement to the traditional approach.

Contrast harmonic detection with chirp excitation in 3f0 transmit phasing

The method of third harmonic (3f0 transmit phasing is capable of providing effective tissue background suppression for contrast-to-tissue ratio (CTR) improvement in harmonic imaging. With the additional 3f0 transmit signal to generate both the frequency-sum and the frequency-difference components of harmonic signal, the tissue suppression is achieved when the two components are opposite in phase and mutually cancel out. One major problem in 3f0 transmit phasing is the limited signal-to-noise ratio (SNR) due to the constraint on transmit amplitude. Chirp excitation can be applied in contrast harmonic imaging to enhance the SNR with minimal destruction of the microbubbles. In this paper, the effect of chirp waveform in combination with the 3f0 transmit phasing was studied using both in-vitro experiments and simulations. Our results indicate that, though the chirp transmit pulse can increase the SNR of harmonic imaging in 3f0 transmit phasing (3 dB, p < 0.001), it suffers from degraded tissue harmonic suppression and thus provides less CTR improvement as compared to a conventional pulse. The spectral mismatch between the frequency-sum and the frequency-difference components of tissue harmonic signal is particularly evident in the off-center region of second harmonic band, leading to significant residue tissue background. Consequently, with the chirp waveform, the improvement of CTR decreases from 9.5 dB to 5.9 dB (p < 0.0006) and thus a tradeoff exists between the SNR improvement and the CTR improvement in 3f0 transmit phasing.

Imaging parameters on third harmonic transmit phasing for tissue harmonic generation

In third harmonic (3f0) transmit phasing, transmit waveforms comprising fundamental (f0) signal and 3f0 signal are used to generate both frequency-sum and frequency-difference components for manipulation of tissue harmonic amplitude. Nevertheless, the acoustic propagation of 3f0 transmit signal suffers from more severe attenuation and phase aberration than the f0 signal and hence degrades the performance of 3f0 transmit phasing. Besides, 3f0 transmit parameters such as aperture size and signal bandwidth are also influential in 3f0 transmit phasing. In this study, extensive simulations were performed to investigate the effects of these imaging parameters. Results indicate that the harmonic enhancement and suppression in 3f0 transmit phasing are compromised when the magnitude of frequency-difference component decreases in the presence of tissue attenuation and phase aberration. To compensate for the reduced frequency-difference component, a higher 3f0 transmit amplitude can be used. When the transmit parameters are concerned, a smaller 3f0 transmit aperture can provide more axially uniform harmonic enhancement and more effective suppression of harmonic amplitude. In addition, the spectral leakage signal also interferes with tissue harmonics and degrades the efficacy of 3f0 transmit phasing. Our results suggest that, in the method of 3f0 transmit phasing, the transmit amplitude, phase and aperture size of 3f0 signal should remain adjustable for optimization of clinical performance. Besides, multipulse sequences such as pulse inversion are also favorable for leakage removal in 3f0 transmit phasing.

Third harmonic transmit phasing for tissue harmonic generation

Generation of tissue harmonic signals during acoustic propagation is based on the combined effect of two different spectral interactions of the transmit signal. One produces harmonic whose frequency is the sum of transmit frequencies. The other results in harmonic at difference frequency of the transmit signals. Both the frequency-sum component and the frequency-difference component are sensitive to the phase of their constitutive spectral signals. In this study, a novel approach for modifying the amplitude of tissue harmonic signal is proposed based on phasing these two components to achieve either harmonic enhancement or suppression. Both experiments and simulations were performed to investigate the effects of 3f0 transmit phasing on tissue harmonic generation. Results indicate that the relative phasing between the frequency-sum component and the frequency-difference component markedly changes the amplitude of the second harmonic signal. For harmonic enhancement, approximate 6 dB increase of second harmonic amplitude can be achieved while the lateral harmonic beam pattern also is improved as compared to conventional situations in which only the frequency-sum component is considered. For harmonic suppression, the second harmonic signal also could be significantly reduced by about 11 dB when the frequency-difference component is out of phase with the frequency-sum component. Hence, the method of 3f0 transmit phasing has potentials for both improving signal-to-noise ratio in tissue harmonic imaging and enhancing image contrast in contrast-agent imaging by suppression of tissue harmonic background.

Nonlinear pulse compression in pulse-inversion fundamental imaging

Coded excitation can be applied in ultrasound contrast agent imaging to enhance the signal-to-noise ratio with minimal destruction of the microbubbles. Although the axial resolution is usually compromised by the requirement for a long coded transmit waveforms, this can be restored by using a compression filter to compress the received echo. However, nonlinear responses from microbubbles may cause difficulties in pulse compression and result in severe range side-lobe artifacts, particularly in pulse-inversion-based (PI) fundamental imaging. The efficacy of pulse compression in nonlinear contrast imaging was evaluated by investigating several factors relevant to PI fundamental generation using both in-vitro experiments and simulations. The results indicate that the acoustic pressure and the bubble size can alter the nonlinear characteristics of microbubbles and change the performance of the compression filter. When nonlinear responses from contrast agents are enhanced by using a higher acoustic pressure or when more microbubbles are near the resonance size of the transmit frequency, higher range side lobes are produced in both linear imaging and PI fundamental imaging. On the other hand, contrast detection in PI fundamental imaging significantly depends on the magnitude of the nonlinear responses of the bubbles and thus the resultant contrast-to-tissue ratio (CTR) still increases with acoustic pressure and the nonlinear resonance of microbubbles. It should be noted, however, that the CTR in PI fundamental imaging after compression is consistently lower than that before compression due to obvious side-lobe artifacts. Therefore, the use of coded excitation is not beneficial in PI fundamental contrast detection.

Waveform design for ultrasonic pulse-inversion fundamental imaging

Pulse-inversion (PI) fundamental imaging exhibits significantly better contrast detection than linear and second-harmonic imaging. PI fundamental imaging involves two firings with inverted waveforms. When the returning echoes from the two firings are summed, the residual signal related to tissue is limited to even-order harmonics, whereas for microbubbles, the fundamental signal is not completely canceled due to the echo under compression differing from that under rarefaction. The efficacy of PI fundamental imaging has been reported previously. In this study, we investigated the performance of PI fundamental imaging using both simulations and in vitro experiments with various transmit waveforms, including coded excitation and asymmetrical waveforms (i.e., asymmetrical between compression and rarefaction). For coded excitation, a longer waveform was found to increase the similarity in the responses to positive and negative pulses, thus lowering the contrast between microbubbles and tissue. In addition, imperfect pulse compression also decreases the contrast because it increases the residue fundamental signal emanating from tissue. Using asymmetrical waveforms noticeably increased the residual microbubble signal in the fundamental band but the nonzero DC component that is inherent in such waveforms also increases the tissue fundamental signal. The combination of these two effects decreases the contrast. From these results, it is concluded that the use of coded excitation is undesirable in PI fundamental imaging and that the waveforms should contain no DC component. Furthermore, the transmit waveform needs to be appropriately windowed in order to reduce spectral leakage. Therefore, a Gaussian pulse with the pulse length determined by the signal-to-noise ratio of the imaging system is generally optimal for PI fundamental imaging.

Arbitrary waveform coded excitation using bipolar square wave pulsers in medical ultrasound

This paper presents a new coded excitation scheme that efficiently synthesizes codes for arbitrary waveforms using a bipolar square wave pulser. In a coded excitation system, pulse compression is performed to restore the axial resolution. In order to maintain low range sidelobes, the system needs to transmit signals that have smooth spectra. However, such a transmitter requires the generation of arbitrary waveforms and, therefore, is more expensive. In other words, a trade-off is necessary between the compression performance and the transmitter cost. Here we propose a method that preserves the low-cost advantage of a bipolar pulser while achieving approximately the same compression performance as an arbitrary waveform generator. The key idea of the proposed method is the conversion of a nonbinary code (i.e., requiring an arbitrary waveform generator) with good compression performance into a binary code (i.e., requiring only a bipolar pulser) by code translation and code tuning. The code translation is implemented by sending the nonbinary code into a virtual one-bit, sigma-delta modulator, and the code tuning involves minimizing the root-mean-square error between the resultant binary code and the original nonbinary code by sequential and iterative tuning while taking the transducer response into account. Tukey-windowed chirps are known to have good compression performance. Such chirps of different durations (16, 20, and 24 micros), all with a taper ratio of 0.15, a center frequency of 2.5 MHz, and an equivalent bandwidth of 1.5 MHz, were converted into binary Tukey-windowed chirps that were compared with pseudochirps (i.e., direct binary approximations of the original chirp) over the same spectral band. The bit rate was 40 MHz. Simulation results show that the use of binary Tukey-windowed chirps can reduce the code duration by 20.6% or the peak sidelobe level by 6 dB compared to the commonly used pseudochirps. Experimental results obtained under the same settings were in agreement with the simulations. Our results demonstrate that arbitrary waveform coded excitation can be realized using bipolar square wave pulsers for applications in medical ultrasound.

Coded excitation for diagnostic ultrasound: a system developer's perspective

Resolution and penetration are primary criteria for clinical image quality. Conventionally, high bandwidth for resolution was achieved with a short pulse, which results in a tradeoff between resolution and penetration. Coded excitation extends the bounds of this tradeoff by increasing signal-to-noise ratio (SNR) through appropriate coding on transmit and decoding on receive. Although used for about 50 years in radar, coded excitation was successfully introduced into commercial ultrasound scanners only within the last 5 years. This delay is at least partly due to practical implementation issues particular to diagnostic ultrasound, which are the focus of this paper. After reviewing the basics of biphase and chirp coding, we present simulation results to quantify tradeoffs between penetration and resolution under frequency-dependent attenuation, dynamic focusing, and nonlinear propagation. Next we compare chirp and Golay code performance with respect to image quality and system requirements, then we show clinical images that illustrate the current applications of coded excitation in B-mode, harmonic, and flow imaging.

Tissue harmonic image analysis based on spatial covariance

The van Cittert-Zernike theorem has been widely used to describe spatial covariance of the pressure field backscattered from a speckle object. Spatial covariance contains important information in the context of correlation-based correction of sound velocity inhomogeneities. Previous work was primarily based on spatial covariance analysis for linear imaging. In this paper, we extend the analysis to tissue harmonic imaging. Specifically, we investigate effects of the signal-to-noise ratio (SNR) and sound velocity inhomogeneities on spatial covariance. Results from tissue harmonic imaging are also compared with those from linear imaging. Both simulations and experiments are performed. At high SNRs, although both linear imaging and tissue harmonic imaging have spatial covariance functions close to theory, the spatial covariance of tissue harmonic imaging is consistently lower than that of linear imaging regardless of the presence of sound velocity inhomogeneities. At low SNRs, on the other hand, spatial covariance of tissue harmonic imaging is significantly affected. Because the tissue harmonic signal is much weaker than the linear counterpart, the low SNR reduces the accuracy of correlation-based estimation. It is concluded that the linear signal is more suitable for correlation-based correction of sound velocity inhomogeneities, despite the fact that tissue harmonic imaging generally has improved image quality over linear imaging.

Filter-based synthetic transmit and receive focusing

Most diagnostic ultrasonic imaging systems perform fixed focusing on transmit and dynamic focusing on receive. Such systems suffer from image quality degradation at depths away from the transmit focal zone. Several dynamic transmit focusing techniques have been previously investigated. Among them, a filter-based, retrospective focusing technique was proposed to increase the length of the transmit focal zone. In this paper, the filter-based technique is extended from dynamic receive focusing to fixed receive focusing. It is shown that the filtering technique with fixed receive focusing can achieve an image quality similar to that of dynamic receive focusing with filtering. The performance of the proposed approach is verified using real ultrasound data. It is shown that the proposed approach with fixed receive focusing requires a longer filter than that with dynamic receive focusing. Nonetheless, system complexity is greatly reduced with synthetic transmit and receive focusing because the dynamic receive focusing circuit is no longer needed.

Effects of transmit focusing on finite amplitude distortion based second harmonic generation

Generation of the second harmonic signal was studied for finite amplitude distortion based harmonic imaging. Acoustic field amplitudes along the range axis of a fixed focus transducer were measured using a PVDF needle hydrophone. Results indicated that on-axis amplitudes strongly depended on the f-number at both the fundamental and the second harmonic frequencies. Differences of the on-axis amplitudes between the two frequencies were also investigated. To explore the possibility of increasing harmonic generation by extending the depth of focus, a two-focus transducer was employed. Hydrophone measurements, pulse-echo imaging and simulations were performed. Although the increase in harmonic generation depended on specific imaging parameters, the effectiveness of improving the harmonic signal-to-noise ratio (SNR) by increasing the depth of field was clearly demonstrated. Degradation in contrast resolution associated with the two-focus transducer was also evaluated. It was found that the contrast resolution was still significantly better than that of the fundamental image at the same frequency. Results of the study using the two-focus transducers can be generalized to imaging systems with full dynamic transmit focusing capabilities. In other words, it is expected that dynamic transmit focusing can improve the SNR of finite amplitude distortion based second harmonic imaging while improving the contrast resolution over fundamental imaging.