Spatial coherence of the nonlinearly generated second harmonic portion of backscatter for a clinical imaging system

Correlation-based approaches to phase aberration correction rely on the spatial coherence of backscattered signals. The spatial coherence of backscatter from speckle-producing targets is predicted by the auto correlation of the transmit apodization (Van Cittert-Zernike theorem). Work by others indicates that the second harmonic beam has a wider mainlobe with lower sidelobes than a beam transmitted at 2f. The purpose of this paper is to demonstrate that the spatial coherence of backscatter for the second harmonic is different from that of the fundamental, as would be anticipated from applying the Van Cittert-Zernike theorem to the reported measurements of the second harmonic field. Another objective of this work is to introduce the concept of the effective apodization and to verify that the effective apodization of the second harmonic is narrower than the transmit apodization. The spatial coherence of backscatter was measured using three clinical arrays with a modified clinical imaging system. The spatial coherence results were verified using a pseudo-array scan in a transverse plane of the transmitted field with a hydrophone. An effective apodization was determined by backpropagating these values using a linear angular spectrum approach. The spatial coherence for the harmonic portion of backscatter differed systematically and significantly from the auto correlation of the transmit apodization.     

Impact of propagation through an aberrating medium on the linear effective apodization of a nonlinearly generated second harmonic field

Techniques based on the nonlinearly generated second harmonic signal (tissue harmonic imaging) have rapidly supplanted linear (fundamental) imaging methods as the standard in two-dimensional echocardiography. Enhancements to the compactness of the nonlinearly generated second harmonic (2f) field component with respect to the fundamental (1f) field component are widely considered to be among the factors contributing to the observed image quality improvements. The objective of this study was to measure the impact of phase and amplitude aberrations resulting from propagation through an inhomogeneous tissue, on the beamwidths associated with: the fundamental (1f); the nonlinearly generated second harmonic (2f); and the linearly propagated, effective apodization signal at the same (21) frequency. Modifications to the transmit characteristics of a phased-array imaging system were validated with hydrophone measurements. Results demonstrate that the characteristics of the diffraction pattern associated with the linear-propagation effective apodization transmit case were found to be in good agreement with the detailed spatial characteristics of the nonlinearly generated second harmonic field. The effects of the abdominal wall tissue aberrators are apparent for all three of the beam profiles studied. Consistent with the improved image quality associated with harmonic imaging, the aberrated nonlinearly generated second harmonic beam was shown to remain more compact than the corresponding aberrated fundamental beam patterns in the presence of the interposed aberrator.     

Harmonic spatial coherence imaging: an ultrasonic imaging method based on backscatter coherence

We introduce a harmonic version of the short-lag spatial coherence (SLSC) imaging technique, called harmonic spatial coherence imaging (HSCI). The method is based on the coherence of the second-harmonic backscatter. Because the same signals that are used to construct harmonic B-mode images are also used to construct HSCI images, the benefits obtained with harmonic imaging are also obtained with HSCI. Harmonic imaging has been the primary tool for suppressing clutter in diagnostic ultrasound imaging, however secondharmonic echoes are not necessarily immune to the effects of clutter. HSCI and SLSC imaging are less sensitive to clutter because clutter has low spatial coherence. HSCI shows favorable imaging characteristics such as improved contrast-to-noise ratio (CNR), improved speckle SNR, and better delineation of borders and other structures compared with fundamental and harmonic B-mode imaging. CNRs of up to 1.9 were obtained from in vivo imaging of human cardiac tissue with HSCI, compared with 0.6, 0.9, and 1.5 in fundamental B-mode, harmonic B-mode, and SLSC imaging, respectively. In vivo experiments in human liver tissue demonstrated SNRs of up to 3.4 for HSCI compared with 1.9 for harmonic B-mode. Nonlinear simulations of a heart chamber model were consistent with the in vivo experiments.     

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.     

Optimal apodization design for medical ultrasound using constrained least squares part II: simulation results

In the first part of this work, we introduced a novel general ultrasound apodization design method using constrained least squares (CLS). The technique allows for the design of system spatial impulse responses with narrow mainlobes and low sidelobes. In the linear constrained least squares (LCLS) formulation, the energy of the point spread function (PSF) outside a certain mainlobe boundary was minimized while maintaining a peak gain at the focus. In the quadratic constrained least squares (QCLS) formulation, the energy of the PSF outside a certain boundary was minimized, and the energy of the PSF inside the boundary was held constant. In this paper, we present simulation results that demonstrate the application of the CLS methods to obtain optimal system responses. We investigate the stability of the CLS apodization design methods with respect to errors in the assumed wave propagation speed. We also present simulation results that implement the CLS design techniques to improve cystic resolution. According to novel performance metrics, our apodization profiles improve cystic resolution by 3 dB to 10 dB over conventional apodizations such as the flat, Hamming, and Nuttall windows. We also show results using the CLS techniques to improve conventional depth of field (DOF).     

Apodized distributed feedback fiber laser as an optical filter

The potential was investigated of using distributed feedback fiber lasers (DFB-FLs) with different apodizations for C-band optical filtering. Design optimizations were carried out, to mainly target ultra-dense wavelength division multiplexing (UDWDM) filtering specifications. Optimization led to choice of the positive-tanh apodization profile as being the most suitable for UDWDM filtering specifications.     

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 (3f₀) transmit phasing uses an additional 3f₀ 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 3f₀ transmit phasing, the 3f₀ 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 3f₀ 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 3f₀ 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 3f₀ 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.     

Precompensated excitation waveforms to suppress harmonic generation in MEMS electrostatic transducers

Microelectromechanical systems (MEMS) electrostatic-based transducers inherently produce harmonics as the electrostatic force generated in the transmit mode is approximately proportional to the square of the applied voltage signal. This characteristic precludes them from being effectively used for harmonic imaging (either with or without the addition of microbubble-based contrast agents). The harmonic signal that is nonlinearly generated by tissue (or contrast agent) cannot be distinguished from the inherent transmitted harmonic signal. We investigated two precompensation methods to cancel this inherent harmonic generation in electrostatic transducers. A combination of finite element analysis (FEA) and experimental results are presented. The first approach relies on a calculation, or measurement, of the transducer's linear transfer function, which is valid for small signal levels. Using this transfer function and a measurement of the undesired harmonic signal, a predistorted transmit signal was calculated to cancel the harmonic inherently generated by the transducer. Due to the lack of perfect linearity, the approach does hot work completely in a single iteration. However, with subsequent iterations, the problem becomes more linear and converges toward a very satisfactory result (a 18.6 dB harmonic reduction was achieved in FEA simulations and a 20.7 dB reduction was measured in a prototype experiment). The second approach tested involves defining a desired function [including a direct current (DC) offset], then taking the square root of this function to determine the shape of the required input function. A 5.5 dB reduction of transmitted harmonic was obtained in both FEA simulation and experimental prototypes test.     

Native tissue imaging at superharmonic frequencies

The second harmonic imaging mode has been adapted to image tissue and shown considerable improvements in image quality in several applications compared to the fundamental mode. The improvements were attributed to the effects of wave distortion due to nonlinear propagation in tissue. However, imaging tissue at the second harmonic frequency only has various drawbacks. Because the energy in the second harmonic frequency band is much lower than that in the fundamental frequency band, there must be excellent sensitivity and dynamic range in the receiving system to achieve an acceptable amount of signal-to-noise ratio. To increase the sensitivity, the spectral overlap between the fundamental and the second harmonic has to be diminished, which in return deteriorates the imaging resolution. Consequently, a trade-off is mandatory between resolution and sensitivity. Using simulations and measurements, we show that, at appropriate scanning acoustic settings, higher harmonics are generated in tissue. The higher harmonics represent additional, relevant information for tissue imaging and characterization. An elegant way to take advantage of the higher harmonics and to bring all the information together is to combine and incorporate all the multiple higher harmonics into a single component that we call the superharmonic component. Using a newly developed array transducer having a wide frequency band, B-mode images of a phantom were made in the superharmonic mode transmitting at 1.2 MHz. These images have exceptionally improved clarity and yield a dramatically cleaner and sharper contrast between the different structures being imaged. In addition to increased signal-to-noise ratio, superharmonic imaging shows better contrast and axial resolution as well as acceptable penetration depth.     

Intravascular ultrasound tissue harmonic imaging in vivo

Tissue harmonic imaging (THI) has been shown to increase image quality of medical ultrasound in the frequency range from 2 to 10 MHz and might, therefore, also be used to improve image quality in intravascular ultrasound (IVUS). In this study we constructed a prototype IVUS system that could operate in both fundamental frequency and second harmonic imaging modes. This system uses a conventional, continuously rotating, single-element IVUS catheter and was operated in fundamental 20 MHz, fundamental 40 MHz, and harmonic 40 MHz modes (transmit 20 MHz, receive 40 MHz). Hydrophone beam characterization measurements demonstrated the build-up of a second harmonic signal as a function of increasing pressure. Imaging experiments were conducted in both a tissue-mimicking phantom and in an atherosclerotic animal model in vivo. Acquisitions of fundamental 20 and 40 MHz and second harmonic acquisitions resulted in cross sections of the phantom and a rabbit aorta. The harmonic results of the imaging experiments showed the feasibility of intravascular THI with a conventional IVUS catheter both in a phantom and in vivo. The harmonic acquisitions also showed the potential of THI to reduce image artifacts compared to fundamental imaging.     

High frequency nonlinear B-scan imaging of microbubble contrast agents

It was previously shown that it is possible to produce nonlinear scattering from microbubble contrast agents using transmit frequencies in the 14-32 MHz range, suggesting the possibility of performing high-frequency, nonlinear microbubble imaging. In this study, we describe the development of nonlinear microbubble B-scan imaging instrumentation capable of operating at transmit center frequencies between 10 and 50 MHz. The system underwent validation experiments using transmit frequencies of 20 and 30 MHz. Agent characterization experiments demonstrate the presence of nonlinear scattering for the conditions used in this study. Using wall-less vessel phantoms, nonlinear B-scan imaging is performed using energy in one of the subharmonic, ultraharmonic, and second harmonic frequency regions for transmit frequencies of 20 and 30 MHz. Both subharmonic and ultraharmonic imaging modes achieved suppression of tissue signals to below the noise floor while achieving contrast to noise ratios of up to 26 and 17 dB, respectively. The performance of second harmonic imaging was compromised by nonlinear propagation and offered no significant contrast improvement over fundamental mode imaging. In vivo experiments using the subharmonic of a 20 MHz transmit pulse show the successful detection of microvessels in the rabbit ear and in the mouse heart. The results of this study demonstrate the feasibility of nonlinear microbubble imaging at high frequencies     

Phase-matched generation of highly coherent radiation in water window region

Highly coherent extreme ultraviolet radiation around the water window region (~4.4 nm) is generated in a semi-infinitive helium gas cell using infrared pulses of wavelength 1300 nm, energy 2.5 mJ, duration 40 fs, and repetition rate 1 kHz. The pressure-squared dependence of the intensity and the almost-perfect Gaussian profile and low divergence of the high harmonic source indicate a phase-matched generation process. The spatial coherence of the source is studied using Young's double-slit measurements.     

Multiple harmonic generators for improved efficiency of laser-pumped lasers

A multistage system of three second-harmonic-generating crystals has been used to improve the total conversion efficiency from the fundamental at 1.06 mum to the second harmonic at 532 nm. Demagnifying telescopes placed into the path of the residual fundamental light, after chromatic separation of the second harmonic, allow further second-harmonic crystals to be used. More than 97% conversion has been obtained from 207-mJ, Q -switched Nd:YAG laser pulses at 1.06 mum, producing more than 201 mJ at 532 nm. Good agreement is achieved between experiment and theory for the spatial and temporal evolution of the second-harmonic beams at each stage.     

Multiresonant broadband optical antennas as efficient tunable nanosources of second harmonic light

We report the experimental realization of efficient tunable nanosources of second harmonic light with individual multiresonant log-periodic optical antennas. By designing the nanoantenna with a bandwidth of several octaves, simultaneous enhancement of fundamental and harmonic fields is observed over a broad range of frequencies, leading to a high second harmonic conversion efficiency, together with an effective second order susceptibility within the range of values provided by widespread inorganic crystals. Moreover, the geometrical configuration of the nanoantenna makes the generated second harmonic signal independent from the polarization of the fundamental excitation. These results open new possibilities for the development of efficient integrated nonlinear nanodevices with high frequency tunability.     

Pulse inversion Doppler: a new method for detecting nonlinear echoes from microbubble contrast agents

A novel technique for the selective detection of ultrasound contrast agents, called pulse inversion Doppler, has been developed. In this technique, a conventional Doppler or color Doppler pulse sequence is modified by inverting every second transmit pulse. Either conventional or harmonic Doppler processing is then performed on the received echoes. In the resulting Doppler spectra, Doppler shifts from linear and nonlinear scattering are separated into two distinct regions that can be analyzed separately or combined to estimate the ratio of nonlinear to linear scattering from a region of tissue. The maximum Doppler shift that can be detected is 1/2 the normal Nyquist limit. This has the advantage over conventional harmonic Doppler that it can function over the entire bandwidth of the echo signal, thus achieving superior spatial resolution in the Doppler image. In vitro measurements comparing flowing agent and cellulose particles suggest that pulse inversion Doppler can provide 3 to 10 dB more agent to tissue contrast than harmonic imaging with similar pulses. Similar measurements suggest that broadband pulse inversion Doppler can provide up to 16 dB more contrast than broadband conventional Doppler. Nonlinear propagation effects limit the maximum contrast obtainable with both harmonic and pulse inversion Doppler techniques.     

Conductance measurements on a leaky SAW harmonic one-port resonator

Conductance measurements are reported on a leaky SAW (LSAW) harmonic one-port resonator on a 64 degrees Y-X LiNbO(3) substrate. This employed a short three-finger IDT for fundamental and second harmonic operation together with long reflection gratings. Conductances were measured with and without the end gratings. From an analysis of the measurements, it was deduced that, for optimum second harmonic performance, the grating stop-band frequency should be higher than the IDT unperturbed center frequency. This result is in contrast to fundamental frequency resonator designs in which the end grating stop-band frequency is placed below the IDT center frequency for optimum performance.     

Harmonic leakage and image quality degradation in tissue harmonic imaging

Image quality degradation caused by harmonic leakage was studied for finite amplitude distortion-based harmonic imaging. Various sources of harmonic leakage, including transmit waveform, signal bandwidth, and system nonlinearity, were investigated using both simulations and hydrophone measurements. Effects of harmonic leakage in the presence of sound velocity inhomogeneities were also considered. Results indicated that sidelobe levels of the harmonic beam pattern were directly affected by harmonic leakage when the harmonic signal was obtained by filtering out the fundamental signal. Because sidelobe levels also increase with the bandwidth of the transmitted signal, a trade-off exists between axial resolution and contrast resolution. It is concluded that accurate control of the frequency content of the waveform prior to propagation is necessary to optimize imaging performance of tissue harmonic imaging. The filtering technique was also compared with the pulse inversion technique. It was shown that the pulse inversion technique effectively suppresses harmonic leakage at the cost of imaging frame rate and potential motion artifacts     

Source prebiasing for improved second harmonic bubble-response imaging

The use of the second harmonic bandwidth in order to improve the contrast enhancement of vascular space provided by microbubble echo contrast is well established. A significant obstacle to improving on the contrast advantage of the second harmonic bandwidth arises from the linear response of tissue to the finite amplitude distortion produced second harmonic in the beam. A scheme in which the source wave contains a second harmonic component designed to cancel out the second harmonic produced by finite amplitude distortion in the focal region was computationally investigated. This prebiasing scheme was found to offer significant reductions in the amplitude of the second harmonic in the focal region. These reductions were found in both the homogeneous tissue path case and in the inhomogeneous tissue path case. The resulting clinical potential of source prebiasing is discussed. Also, it was observed that the inhomogeneous focusing of the finite amplitude distortion-produced second harmonic was significantly better than that of a same frequency fundamental with an identical homogeneous path focal profile.     

Analysis on the saturation of refractive index modulation in fiber Bragg gratings (FBGs) written by partially coherent UV beams

We present an analysis on the saturation of refractive index modulation of fiber Bragg gratings written in nonhydrogenated Ge-B co-doped single-mode photosensitive optical fiber by partially coherent pulsed UV beams. The UV beams of different spatial coherence properties were generated by second harmonic conversion of high repetition rate, high average power copper vapor laser (CVL) oscillators with different optical resonators. It is observed that for UV beams of higher spatial coherence, the fiber Bragg grating reflectivity growth was faster and saturation of refractive index modulation was higher. The experimental results are explained with the help of a physical model based on exponential decay of defect centers per unit volume on UV absorption in the fiber core. The subsequent increase in the refractive index was attributed to the structural modification and densification of the fiber core.