David M. J. Cowell

Separation of overlapping linear frequency modulated (LFM) signals using the fractional fourier transform

Linear frequency modulated (LFM) excitation combined with pulse compression provides an increase in SNR at the receiver. LFM signals are of longer duration than pulsed signals of the same bandwidth; consequently, in many practical situations, maintaining temporal separation between echoes is not possible. Where analysis is performed on individual LFM signals, a separation technique is required. Time windowing is unable to separate signals overlapping in time. Frequency domain filtering is unable to separate signals with overlapping spectra. This paper describes a method to separate time-overlapping LFM signals through the application of the fractional Fourier transform (FrFT), a transform operating in both time and frequency domains. A short introduction to the FrFT and its operation and calculation are presented. The proposed signal separation method is illustrated by application to a simulated ultrasound signal, created by the summation of multiple time-overlapping LFM signals and the component signals recovered with ±0.6% spectral error. The results of an experimental investigation are presented in which the proposed separation method is applied to time-overlapping LFM signals created by the transmission of a LFM signal through a stainless steel plate and water-filled pipe.

Ultrasound array transmitter architecture with high timing resolution using embedded phase-locked loops

Coarse time quantization of delay profiles within ultrasound array systems can produce undesirable side lobes in the radiated beam profile. The severity of these side lobes is dependent upon the magnitude of phase quantization error¿ the deviation from ideal delay profiles to the achievable quantized case. This paper describes a method to improve interchannel delay accuracy without increasing system clock frequency by utilizing embedded phase-locked loop (PLL) components within commercial field-programmable gate arrays (FPGAs). Precise delays are achieved by shifting the relative phases of embedded PLL output clocks in 208-ps steps. The described architecture can achieve the necessary interelement timing resolution required for driving ultrasound arrays up to 50 MHz. The applicability of the proposed method at higher frequencies is demonstrated by extrapolating experimental results obtained using a 5-MHz array transducer. Results indicate an increase in transmit dynamic range (TDR) when using accurate delay profiles generated by the embedded-PLL method described, as opposed to using delay profiles quantized to the system clock.

Quinary excitation method for pulse compression ultrasound measurements

A novel switched excitation method for linear frequency modulated excitation of ultrasonic transducers in pulse compression systems is presented that is simple to realise, yet provides reduced signal sidelobes at the output of the matched filter compared to bipolar pseudo-chirp excitation. Pulse compression signal sidelobes are reduced through the use of simple amplitude tapering at the beginning and end of the excitation duration. Amplitude tapering using switched excitation is realised through the use of intermediate voltage switching levels, half that of the main excitation voltages. In total five excitation voltages are used creating a quinary excitation system. The absence of analogue signal generation and power amplifiers renders the excitation method attractive for applications with requirements such as a high channel count or low cost per channel. A systematic study of switched linear frequency modulated excitation methods with simulated and laboratory based experimental verification is presented for 2.25 MHz non-destructive testing immersion transducers. The signal to sidelobe noise level of compressed waveforms generated using quinary and bipolar pseudo-chirp excitation are investigated for transmission through a 0.5m water and kaolin slurry channel. Quinary linear frequency modulated excitation consistently reduces signal sidelobe power compared to bipolar excitation methods. Experimental results for transmission between two 2.25 MHz transducers separated by a 0.5m channel of water and 5% kaolin suspension shows improvements in signal to sidelobe noise power in the order of 7-8 dB. The reported quinary switched method for linear frequency modulated excitation provides improved performance compared to pseudo-chirp excitation without the need for high performance excitation amplifiers.

The effect of amplitude modulation on subharmonic imaging with chirp excitation

Subharmonic generation from ultrasound contrast agents depends on the spectral and temporal properties of the excitation signal. The subharmonic response can be improved by using wideband and long-duration signals. However, for sinusoidal tone-burst excitation, the effective bandwidth of the signal is inversely proportional to the signal duration. Linear frequency-modulated (LFM) and nonlinear frequencymodulated (NLFM) chirp excitations allow independent control over the signal bandwidth and duration; therefore, in this study LFM and NLFM signals were used for the insonation of microbubble populations. The amplitude modulation of the excitation waveform was achieved by applying different window functions. A customized window was designed for the NLFM chirp excitation by focusing on reducing the spectral leakage at the subharmonic frequency and increasing the subharmonic generation from microbubbles. Subharmonic scattering from a microbubble population was measured for various excitation signals and window functions. At a peak negative pressure of 600 kPa, the generated subharmonic energy by ultrasound contrast agents was 15.4 dB more for NLFM chirp excitation with 40% fractional bandwidth when compared with tone-burst excitation. For this reason, the NLFM chirp with a customized window was used as an excitation signal to perform subharmonic imaging in an ultrasound flow phantom. Results showed that the NLFM waveform with a customized window improved the subharmonic contrast by 4.35 ± 0.42 dB on average over a Hann-windowed LFM excitation.

Phase-inversion-based selective harmonic elimination (PI-SHE) in multi-level switched-mode tone- and frequency- modulated excitation

Switched-mode operation allows the miniaturization of excitation circuitry but suffers from high harmonic distortion. This paper presents a method of phase-inversion-based selective harmonic elimination (PI-SHE) and the use of multiple switching levels. PI-SHE is shown to enable multiples of any selected harmonic to be eliminated through controlled timing of the transition between different excitation voltage levels. Multiples of the third harmonic are shown to be eliminated in three-level tone waveforms. In addition, multiples of the fifth harmonic are shown to be eliminated using five-level tone waveforms. A method of calculating the expected amplitude of each harmonic is presented. The application of PI-SHE in linear frequency-modulated (LFM) excitation is proposed. A heuristic derivation of the spectral properties of multilevel switched LFM waveforms is presented. The performance of the proposed PI-SHE method is confirmed through experimental measurement of the harmonics present in an ultrasound wave using two, three, and five levels for both tone and LFM excitation. The proposed method of controlling harmonics through the use of multilevel switched excitation is especially suitable for applications in which portability, high channel counts, and precise harmonic control are required.

Width-modulated square-wave pulses for ultrasound applications

A method of output pressure control for ultrasound transducers using switched excitation is described. The method generates width-modulated square-wave pulse sequences that are suitable for driving ultrasound transducers using MOSFETs or similar devices. Sequences are encoded using an optimized level-shifted, carrier-comparison, pulse-width modulation (PWM) strategy derived from existing PWM theory, and modified specifically for ultrasound applications. The modifications are: a reduction in carrier frequency so that the smallest number of pulses are generated and minimal switching is necessary; alteration of a linear carrier form to follow a trigonometric relationship in accordance with the expected fundamental output; and application of frequency modulation to the carrier when generating frequency-modulated, amplitude- tapered signals. The PWM method permits control of output pressure for arbitrary waveform sequences at diagnostic frequencies (approximately 5 MHz) when sampled at 100 MHz, and is applicable to pulse shaping and array apodization. Arbitrary waveform generation capability is demonstrated in simulation using convolution with a transducer¿s impulse response, and experimentally with hydrophone measurement. Benefits in coded imaging are demonstrated when compared with fixedwidth square-wave (pseudo-chirp) excitation in coded imaging, including reduction in image artifacts and peak side-lobe levels for two cases, showing 10 and 8 dB reduction in peak side-lobe level experimentally, compared with 11 and 7 dB reduction in simulation. In all cases, the experimental observations correlate strongly with simulated data.

Superharmonic imaging with chirp coded excitation: filtering spectrally overlapped harmonics

Superharmonic imaging improves the spatial resolution by using the higher order harmonics generated in tissue. The superharmonic component is formed by combining the third, fourth, and fifth harmonics, which have low energy content and therefore poor SNR. This study uses coded excitation to increase the excitation energy. The SNR improvement is achieved on the receiver side by performing pulse compression with harmonic matched filters. The use of coded signals also introduces new filtering capabilities that are not possible with pulsed excitation. This is especially important when using wideband signals. For narrowband signals, the spectral boundaries of the harmonics are clearly separated and thus easy to filter; however, the available imaging bandwidth is underused. Wideband excitation is preferable for harmonic imaging applications to preserve axial resolution, but it generates spectrally overlapping harmonics that are not possible to filter in time and frequency domains. After pulse compression, this overlap increases the range side lobes, which appear as imaging artifacts and reduce the Bmode image quality. In this study, the isolation of higher order harmonics was achieved in another domain by using the fan chirp transform (FChT). To show the effect of excitation bandwidth in superharmonic imaging, measurements were performed by using linear frequency modulated chirp excitation with varying bandwidths of 10% to 50%. Superharmonic imaging was performed on a wire phantom using a wideband chirp excitation. Results were presented with and without applying the FChT filtering technique by comparing the spatial resolution and side lobe levels. Wideband excitation signals achieved a better resolution as expected, however range side lobes as high as -23 dB were observed for the superharmonic component of chirp excitation with 50% fractional bandwidth. The proposed filtering technique achieved >50 dB range side lobe suppression and improved the image quality without affecting the axial resolution.

Pulse Compression of Harmonic Chirp Signals Using the Fractional Fourier Transform

In ultrasound harmonic imaging with chirp-coded excitation, a harmonic matched filter (HMF) is typically used on the received signal to perform pulse compression of the second harmonic component (SHC) to recover signal axial resolution. Designing the HMF for the compression of the SHC is a problematic issue because it requires optimal window selection. In the compressed second harmonic signal, the sidelobe level may increase and the mainlobe width (MLW) widen under a mismatched condition, resulting in loss of axial resolution. We propose the use of the fractional Fourier transform (FrFT) as an alternative tool to perform compression of the chirp-coded SHC generated as a result of the nonlinear propagation of an ultrasound signal. Two methods are used to experimentally assess the performance benefits of the FrFT technique over the HMF techniques. The first method uses chirp excitation with central frequency of 2.25 MHz and bandwidth of 1 MHz. The second method uses chirp excitation with pulse inversion to increase the bandwidth to 2 MHz. In this study, experiments were performed in a water tank with a single-element transducer mounted coaxially with a hydrophone in a pitch-catch configuration. Results are presented that indicate that the FrFT can perform pulse compression of the second harmonic chirp component, with a 14% reduction in the MLW of the compressed signal when compared with the HMF. Also, the FrFT provides at least 23% reduction in the MLW of the compressed signal when compared with the harmonic mismatched filter (HMMF). The FrFT maintains comparable peak and integrated sidelobe levels when compared with the HMF and HMMF techniques.

The capture of flowing microbubbles with an ultrasonic tap using acoustic radiation force

The accumulation of 1–10 μm phospholipid-shelled microbubbles was demonstrated by creating an “ultrasonic tap” using acoustic travelling waves. Microbubbles were flowed through a 200 μm cellulose tube at rates ranging between 14–50 ml/h, in order to approximate the velocities and wall shear rates found throughout the human circulatory system. The generated acoustic radiation force directly opposing the flow direction was sufficient to hold microbubbles in a fluid flow up to 28 cm/s. Clusters of microbubbles subject to wall shear rates of up to 9000 s−1 were retained near a pressure null for several seconds.

Solving the inverse problem of magnetisation–stress resolution

Magnetostriction in various metals has been known since 1842, recently the focus has shifted away from ferrous metals, towards materials with a straightforward or exaggerated stress magnetostriction relationship. However, there is an increasing interest in understanding ferrous metal relationships, especially steels, because of its widespread use in building structures, transportation infrastructure, and pipelines. The aim of this paper is to solve the inverse problem of determining stress from an observed magnetic field which implies a given magnetic structure and to demonstrate that theoretical calculations using a multi-physics modeling technique agree with this experimental observation.