Orthogonalized Plane Wave Research Articles

Ultrafast 3-D Transcutaneous Super Resolution Ultrasound Using Row-Column Array Specific Coherence-Based Beamforming and Rolling Acoustic Sub-aperture Processing: In Vitro, in Rabbit and in Human Study

ObjectiveThis study aimed to realise 3-D super-resolution ultrasound imaging transcutaneously with a row-column array which has far fewer independent electronic channels and a wider field of view than typical fully addressed 2-D matrix arrays. The in vivo image quality of the row-column array is generally poor, particularly when imaging non-invasively. This study aimed to develop a suite of image formation and post-processing methods to improve image quality and demonstrate the feasibility of ultrasound localisation microscopy using a row-column array, transcutaneously on a rabbit model and in a human. MethodsTo achieve this, a processing pipeline was developed which included a new type of rolling window image reconstruction, which integrated a row-column array specific coherence-based beamforming technique with acoustic sub-aperture processing. This and other processing steps reduced the ‘secondary’ lobe artefacts, and noise and increased the effective frame rate, thereby enabling ultrasound localisation images to be produced. ResultsUsing an in vitro cross tube, it was found that the procedure reduced the percentage of ‘false’ locations from ∼26% to ∼15% compared to orthogonal plane wave compounding. Additionally, it was found that the noise could be reduced by ∼7 dB and the effective frame rate was increased to over 4000 fps. In vivo, ultrasound localisation microscopy was used to produce images non-invasively of a rabbit kidney and a human thyroid. ConclusionIt has been demonstrated that the proposed methods using a row-column array can produce large field of view super-resolution microvascular images in vivo and in a human non-invasively.

Coulomb effect in hybrid double quantum dot-metal nanoparticle systems considering the wetting layer

Many body effects in the wetting layer (WL)-double quantum dot (DQD)-metal nanoparticle (MNP) structure have been studied by modeling the Coulomb scattering rates in this structure. The strong coupling between WL-DQD-MNPs was considered. An orthogonalized plane wave (OPW) is assumed between WL-QD transitions. The transition momenta are calculated accordingly to specify the normalized Rabi frequency on this structure, considering the strong coupling between the WL-DQD-MNP structures. This approach is important for realizing scattering rates, including in-and-out capture and relaxation rates, which are essential for specifying the type of structure used depending on the optimum value of the scattering time required to fit the application. The QD hole capture rate is the highest, and the hole capture times are the shortest. The relaxation times are less than the electron capture times by one order, while they are half of the hole capture times. The capture rates increase with increasing distance R between the DQDs and the MNP. High tunneling increases hole-capture rates and changes the relaxation rates, showing the importance of tunneling in controlling the scattering rates.

Enhancing Row-column array (RCA)-based 3D ultrasound vascular imaging with spatial-temporal similarity weighting.

Ultrasound vascular imaging (UVI) is a valuable tool for monitoring the physiological states and evaluating the pathological diseases. Advancing from conventional two-dimensional (2D) to three-dimensional (3D) UVI would enhance the vasculature visualization, thereby improving its reliability. Row-column array (RCA) has emerged as a promising approach for cost-effective ultrafast 3D imaging with a low channel count. However, ultrafast RCA imaging is often hampered by high-level sidelobe artifacts and low signal-to-noise ratio (SNR), which makes RCA-based UVI challenging. In this study, we propose a spatial-temporal similarity weighting (St-SW) method to overcome these challenges by exploiting the incoherence of sidelobe artifacts and noise between datasets acquired using orthogonal transmissions. Simulation, in vitro blood flow phantom, and in vivo experiments were conducted to compare the proposed method with existing orthogonal plane wave imaging (OPW), row-column-specific frame-multiply-and-sum beamforming (RC-FMAS), and XDoppler techniques. Qualitative and quantitative results demonstrate the superior performance of the proposed method. In simulations, the proposed method reduced the sidelobe level by 31.3 dB, 20.8 dB, and 14.0 dB, compared to OPW, XDoppler, and RC-FMAS, respectively. In the blood flow phantom experiment, the proposed method significantly improved the contrast-to-noise ratio (CNR) of the tube by 26.8 dB, 25.5 dB, and 19.7 dB, compared to OPW, XDoppler, and RC-FMAS methods, respectively. In the human submandibular gland experiment, it not only reconstructed a more complete vasculature but also improved the CNR by more than 15 dB, compared to OPW, XDoppler, and RC-FMAS methods. In summary, the proposed method effectively suppresses the side-lobe artifacts and noise in images collected using an RCA under low SNR conditions, leading to improved visualization of 3D vasculatures.

Three-dimensional ultrafast ultrasound imaging of blood flow using row-column addressing array: A simulation study

Three-dimensional (3D) ultrafast imaging is important for ultrasound technology development. The traditional 3D imaging method based on fully sampled two-dimensional (2D) matrix often requires a large number of electronic channels with high density which limits the aperture size and imaging resolution in application. Recently developed row-column addressing (RCA) matrix effectively reduces the number of electronic channels from <i>N</i> × <i>N</i> to <i>N</i> + <i>N</i> by addressing the row and column elements. The beamforming strategy designed for 3D ultrasound imaging was based on the coherent compounding of orthogonal plane waves (OPW). Such a multi-angle OPW compounding strategy achieves virtual transmit focusing in both directions by transmitting a set of plane waves in one direction and receiving along the orthogonal direction, which finally leads to an isotropic point spread function (PSF). In this paper, multi-angle OPW method was investigated for 3D blood flow imaging using an RCA matrix with 128 rows and 128 columns, centered at 6 MHz. The delay and sum (DAS) beamforming was developed for coherent OPW compounding, and the singular value decomposition (SVD) filtering method was used for separating the dynamic blood flow signals from the static tissue signals and low-amplitude noise. The Doppler velocity was computed by the autocorrelation method, and finally the 3D power Doppler and color Doppler imaging of the blood flow were realized. To evaluate the imaging quality and investigate the effect of different OPW tilting angles, quantitative analysis was carried out using multiple parameters, including –6 dB resolution measurements of the PSF, SNR of the power Doppler images and velocity distribution of the color Doppler. The –6 dB resolution is improved from 0.986 mm to 0.493 mm with the number of angles increasing from 5 to 33. With 17 plane wave angles, the SNR of the power Doppler image reaches 30 dB, and the average deviation between the velocity distribution along the diameter of the blood flow phantom and the actual value is about 26.0%. In conclusion, results show that the ultrafast 3D imaging method based on RCA matrix can obtain 3D B-mode, power Doppler and color Doppler images. Increasing the number of tilting angles and enlarging the angle range can significantly improve the imaging quality. The proposed method can be helpful for developing 3D ultrafast ultrasound Doppler imaging and functional ultrasound imaging based on neuro-vascular coupling.

Heavy-fermion representation for twisted bilayer graphene systems

We construct a heavy fermion representation for twisted bilayer graphene (TBG) systems. Two local orbitals (per spin/valley) are analytically found, which are exactly the maximally localized zero modes of the continuum Hamiltonian near the AA-stacking center. They have similar properties to the Wannier functions found in a recent study, but also have a clear interpretation as the zeroth pseudo Landau levels (ZLL) of Dirac fermions under the uniform strain field created by twisting. The electronic states of TBG can be viewed as the hybridization between these ZLL orbitals and other itinerant states, which can be obtained following the standard procedure of orthogonalized plane wave method. The ``heavy fermion'' model for TBG separates the strongly correlated components from the itinerant components and provides a solid base for the comprehensive understanding of the exotic physics in TBG.

Energy absorbed from double quantum dot-metal nanoparticle hybrid system

This work proposes the double quantum dot (DQD)-metal nanoparticle (MNP) hybrid system for a high energy absorption rate. The structure is modeled using density matrix equations that consider the interaction between excitons and surface plasmons. The wetting layer (WL)-DQD transitions are considered, and the orthogonalized plane wave (OPW) between these transitions is considered. The DQD energy states and momentum calculations with OPW are the figure of merit recognizing this DQD-MNP work. The results show that at the high pump and probe application, the total absorption rate ({Q}_{tot}) of the DQD-MNP hybrid system is increased by reducing the distance between DQD-MNP. The high {Q}_{tot} obtained may relate to two reasons: first, the WL washes out modes other than the condensated main mode. Second, the high flexibility of manipulating DQD states compared to QD states results in more optical properties for DQD. The {Q}_{DQD} is increased at a small MNP radius on the contrary to the {Q}_{MNP} which is increased at a wider MNP radius. Under high tunneling, a broader blue shift in the {Q}_{tot} due to the destructive interference between fields is seen and the synchronization between {Q}_{MNP} and {Q}_{DQD} is destroyed. {Q}_{tot} for the DQD-MNP is increased by six orders while {Q}_{DQD} is by eight orders compared to the single QD-MNP hybrid system. The high absorption rate of the DQD-MNP hybrid system comes from the transition possibilities and flexibility of choosing the transitions in the DQD system, which strengthens the transitions and increases the linear and nonlinear optical properties. This will make the DQD-MNP hybrid systems preferable to QD-MNP systems.

Tunability of solar cell with double quantum dot structure

This work introduces a double quantum dot (QD) structure as an intermediate band for high-performance solar cells. The density matrix equations, coupled with the continuity-current equation, are solved numerically to address the interaction between all the states, which is impossible with the rate equation modeling. This modeling allowed us to obtain quantum efficiency (QE). Using the orthogonalized plane wave assumption for WL-QD, the momentum matrix elements of QD-QD, QD-wetting layer (WL), WL-barrier transitions are calculated. Results are simulated in both the excitonic and non-excitonic (electron-hole, eh) cases and exhibit the importance of adding the QD layer.The results confirm the importance of adding the intermediate band (QD layer). Both band-to-band recombination rates and relaxation rates in the DQD structure are modulated according to the energy difference between DQD states. Compared to the eh model, the excitonic model reduces the QD-QD relaxation rates and all band-to-band recombination rates. The quantum efficiency (QE) is attaining at longer recombination and relaxation times that are confirmed depending on the wider energy difference by manipulating the transitions of the DQD structure.

Ultrafast 3-D Ultrasound Imaging Using Row-Column Array-Specific Frame-Multiply-and-Sum Beamforming.

Row-column arrays have been shown to be able to generate 3-D ultrafast ultrasound images with an order of magnitude less independent electronic channels than traditional 2-D matrix arrays. Unfortunately, row-column array images suffer from major imaging artifacts due to high sidelobes, particularly when operating at high frame rates. This article proposes a row-column-specific beamforming technique, for orthogonal plane-wave transmissions, row-column-specific frame multiply and sum (RC-FMAS), that exploits the incoherent nature of certain row-column array artifacts. A series of volumetric images is produced using row or column transmissions of 3-D plane waves. The voxelwise geometric mean of the beamformed volumetric images from each row and column pair is taken prior to compounding, which drastically reduces the incoherent imaging artifacts in the resulting image compared to traditional coherent compounding. The effectiveness of this technique was demonstrated in silico and in vitro, and the results show a significant reduction in sidelobe level with over 16-dB improvement in sidelobe to main-lobe energy ratio. Significantly improved contrast was demonstrated with contrast ratio increased by ~10 dB and generalized contrast-to-noise ratio increased by 158% when using the proposed new method compared to the existing delay and sum during in vitro studies. The new technique allowed for higher quality 3-D imaging while maintaining high frame rate potential.

Recombination rates of the double quantum dot solar cell structure

This work proposes a double quantum dot structure as an intermediate-band layer to developing solar cell performance for the first time. The continuity-current equation is coupling with the density matrix equations, which are solved numerically to obtain the quantum efficiency. This modeling will calculate the momentum matrix elements of transitions, consider the orthogonalized plane wave for wetting layer- quantum dot transitions, and covers more characteristics than the rate equations by considering all the possible interactions between the states. The results simulate both the excitonic and nonexcitonic (electron-hole) cases. The work emphasizes adding the double quantum dot layer, which gives flexibility in choosing the energy difference between states controlling the recombination rates. The work refers to the importance of orthogonalized plane-wave in solar cell work. In both models, the band-band recombination is high for slight energy differences between the states, confirms the importance of the double quantum dot system to manipulate transitions between states and obtain higher rates. For the electron-hole model, the leakage is high due to the fast recombination of holes. The discrimination between occupations of states is increasing under the excitonic model due to growing hole occupation. In both models, reducing the quantum dot - quantum dot recombinations and increasing all other recombinations will increase the quantum efficiency. The high quantum dot band-to-band rate increases the quantum efficiency. In the excitonic model, lower rates than in the electron-hole model are enough for high quantum efficiency.

XDoppler: Cross-Correlation of Orthogonal Apertures for 3D Blood Flow Imaging.

Row column addressing (RCA) transducers have the potential to provide volumetric imaging at ultrafast frame rate using a low channel count over a large field of view. In previous works we have shown that vascular imaging of large arteries as well as functional neuroimaging of the rat brain were feasible using RCA orthogonal plane wave imaging (OPW), but these applications required to transmit many plane waves, significantly reducing the frame rate. In this study, we introduce XDoppler imaging, a novel method to increase the performances of RCA flow imaging by taking advantage of the blood spatial decorrelation statistics combined with the limited spatial overlap of the point spread functions (PSF) of the two orthogonal apertures of the RCA transducer. We provide at first a theoretical basis to understand how the correlation operation reduces the sidelobe level. Then, we demonstrate both in vitro and in vivo in the human carotid artery and in the rat brain that XDoppler provides a significant gain in contrast-to-noise ratio (CNR) (between 3 and 6 dB depending on the application) compared to OPW. This improvement also leads to a sensitivity increase in the rat brain as more blood vessels are detected by XDoppler imaging.

Negative refraction in the double quantum dot system

This work proposes a double quantum dot (DQD) system, with a wetting layer (WL) is included, to study the negative refractive index (NRI) under the application of the electric fields: pump, probe, and fields between WL-QD state, in addition to the magnetic field. The density matrix theory is used to write the equation of motion and an orthogonalized plane wave is used between WL-QD states. The results show that the DQD system exhibit NRI ordinarily until with pump and probe signals, only, due to the manipulation between states. A high NRI corresponding to neglected absorption is obtained under applied electric fields between QD-QD, the conduction (CB) and valence bands (VB) WL-QD fields. It is shown that the main requirement in increasing NRI is the high electric gain connected with a low magnetic one. This can be obtained under five applied electric fields in addition to a high VB WL-QD electric field. Neglecting WL reduces NRI by ~ 16 times. In single QD, the NRI is very small compared with DQD.

4D Functional Imaging of the Rat Brain Using a Large Aperture Row-Column Array.

Functional ultrasound imaging (fUS) recently emerged as a promising neuroimaging modality to image and monitor brain activity based on cerebral blood volume response (CBV) and neurovascular coupling. fUS offers very good spatial and temporal resolutions compared to fMRI gold standard as well as simplicity and portability. It was recently extended to 4D fUS imaging in preclinical settings although this approach remains limited and complex. Indeed 4D fUS requires a 2D matrix probe and specific hardware able to drive the N2 elements of the probe with thousands of electronic channels. Several under-sampling approaches are currently investigated to limit the channel count and spread ultrasound 4D modalities. Among them, the Row Column Addressing (RCA) approach combined with ultrafast imaging is a compelling alternative using only N + N channels. We present a large field of view RCA probe prototype of 128 + 128 channels and 15 MHz central frequency adapted for preclinical imaging. Based on the Orthogonal Plane Wave compounding scheme, we were able to perform 4D vascular brain acquisitions at high volume rate. Doppler volumes of the whole rat brain were obtained in vivo at high rates (23 dB CNR at 156 Hz and 19 dB CNR at 313 Hz). Visual and whiskers stimulations were performed and the corresponding CBV increases were reconstructed in 3D with successful functional activation detected in the superior colliculus and somato-sensorial cortex respectively. This proof of concept study demonstrates for the first time the use of a low-channel count RCA array for in vivo 4D fUS imaging in the whole rat brain.

Temperature dependence of the energy band gap of CuSi2P3 semiconductor using PSOPW method

Abstract Theoretical formalism based on the orthogonalized plane wave method supplemented by a potential scaling scheme was used to predict the temperature dependence of energy gap of CuSi2P3 semiconductor. A computer code in Pascal was used to perform the variation of fundamental energy gap with temperature in the range of 150 K to 800 K. The dependence of energy gap on temperature for lattice dilation contribution, lattice vibration contribution and total temperature effect were performed separately. The results revealed that, as temperature increases, the top of the valence band and the bottom of the conduction band increase, while the energy band gap decreases. Generally, at low temperatures, the energy gap varies slowly and exhibits a nonlinear dependence and approaches linearity as temperature increases. The calculated energy gap of CuSi2P3 at T = 300 K is 0.4155 eV. The temperature coefficients in the linear region due to lattice dilation contribution, lattice vibration contribution and total temperature effect were calculated as –1.101 × 10−5 eV/K, –1.637 × 10−4 eV/K and –1.7523 × 10−4 eV/K, respectively. Also, the ratio of temperature coefficient of the energy gap due to LV contribution to its value and LD contribution in the linear region is equal to 14.868. That ratio is compared to those of CuGe2P3 and III-V compounds, where those of the latter show a systematic change with Eg. Moreover, the Eg of all the compounds shows a quadratic dependence on the inverse of mean bond length.

A large aperture row column addressed probe for in vivo 4D ultrafast doppler ultrasound imaging

Four-dimensional (4D) Ultrafast ultrasound imaging was recently proposed to image and quantify blood flow with high sensitivity in 3D as well as anatomical, mechanical or functional information. In 4D Ultrafast imaging, coherent compounding of tilted planes waves emitted by a 2D matrix array were used to image the medium at high volume rate. 4D ultrafast imaging, however, requires a high channel count (>1000) to drive those probes. Alternative approaches have been proposed and investigated to efficiently reduce the density of elements, such as sparse or under-sampled arrays while maintaining a decent image quality and high volume rate. The row–columns configuration presents the advantage of keeping a large active surface with a low amount of elements and a simple geometry. In this study, we investigate the row and column addressed (RCA) approach with the orthogonal plane wave (OPW) compounding strategy using real hardware limitations. We designed and built a large 7 MHz 128 + 128 probe dedicated to vascular imaging and connected to a 256-channel scanner to implement the OPW imaging scheme. Using this strategy, we demonstrate that 4D ultrafast Power Doppler imaging of a large volume of up to depth, both in vitro on flow phantoms and in vivo on the carotid artery of a healthy volunteer at a volume rate of 834 Hz.

Double well potentials with a quantum moat barrier or a quantum wall barrier give rise to similar entangled wave functions

The solution to a problem in quantum mechanics is generally a linear superposition of states. The solutions for double well potentials epitomize this property, and go even further than this: they can often be described by an effective model whose low energy features can be described by two states—one in which the particle is on one side of the barrier, and a second where the particle is on the other side. Then the ground state remains a linear superposition of these two macroscopic-like states. In this paper, we illustrate that this property is achieved similarly with an attractive potential that separates two regions of space, as opposed to the traditionally repulsive one. In explaining how this comes about we revisit the concept of “orthogonalized plane waves,” first discussed in 1940 to understand electronic band structure in solids, along with the accompanying concept of a pseudopotential. We show how these ideas manifest themselves in a simple double well potential, whose “barrier” consists of a moat instead of the conventional wall.

A Dual-Polarized Cross-Slot Antenna Array on a Parallel-Plate Waveguide With Compact Structure and High Efficiency

A dual-polarized cross-slot antenna array based on the parallel-plate waveguide (PPW) is presented in this letter. A new compact 2 × 2-element subarray consisting of four radiating cross-slots, four out cavities, one coupling cross-slot, and one metallic-block-loaded resonant cavity is first proposed to achieve dual polarization and high efficiency. Two orthogonally arranged H-plane waveguide feed networks combined with the low-loss PPW are used to generate a pair of orthogonal plane waves to feed the subarray. To demonstrate the merits of the antenna, an 8 × 8 array prototype is designed and fabricated. The measured result shows that the aperture efficiency exceeding 60% is obtained throughout the band of 12–12.6 GHz. The isolation between two polarizations is higher than 25 dB over the bandwidth. Therefore, this antenna array can be a good alternative for satellite communications systems in airborne applications.

4D in vivo ultrafast ultrasound imaging using a row-column addressed matrix and coherently-compounded orthogonal plane waves

4D ultrafast ultrasound imaging was recently shown using a 2D matrix (i.e. fully populated) connected to a 1024-channel ultrafast ultrasound scanner. In this study, we investigate the row-column addressing (RCA) matrix approach, which allows a reduction of independent channels from N × N to N + N, with a dedicated beamforming strategy for ultrafast ultrasound imaging based on the coherent compounding of orthogonal plane wave (OPW). OPW is based on coherent compounding of plane wave transmissions in one direction with receive beamforming along the orthogonal direction and its orthogonal companion sequence. Such coherent recombination of complementary orthogonal sequences leads to the virtual transmit focusing in both directions which results into a final isotropic point spread function (PSF).In this study, a 32 × 32 2D matrix array probe (1024 channels), centered at 5 MHz was considered. An RCA array, of same footprint with 32 + 32 elements (64 channels), was emulated by summing the elements either along a line or a column in software prior to beamforming. This approach allowed for the direct comparison of the 32 + 32 RCA scheme to the optimal fully sampled 32 × 32 2D matrix configuration, which served as the gold standard.This approach was first studied through PSF simulations and then validated experimentally on a phantom consisting of anechoic cysts and echogenic wires. The contrast-to-noise ratio and the lateral resolution of the RCA approach were found to be approximately equal to half (in decibel) and twice the values, respectively, obtained when using the 2D matrix approach. Results in a Doppler phantom and the human humeral artery in vivo confirmed that ultrafast Doppler imaging can be achieved with reduced performances when compared against the equivalent 2D matrix. Volumetric anatomic Doppler rendering and voxel-based pulsed Doppler quantification are presented as well. OPW compound imaging using emulated RCA matrix can achieve a power Doppler with sufficient contrast to recover the vein shape and provides an accurate Doppler spectrum.

Second-order nonlinearity in ladder-plus-Y configuration in double quantum dot structure.

Second-order nonlinear susceptibility (SONS) in a ladder-plus-Y double quantum dot structure was modeled and then studied numerically under the application of an electric field. The density matrix theory was used to formulate the system while the orthogonalized plane waves for wetting layer-quantum dot (WL-QD) were considered to state the momentum matrix elements for this system. It is found that the momenta follow the smallest energy difference between states with an obvious overlap of the mediated states. Since WL-QD momenta are small, neglecting WL gives high SONS. Millimeter waves are predicted, and a huge SONS can be obtained by the application of more optical fields, which is important in medical and biological applications. The possibility of changing light speed between subluminal and superluminal was predicted here. This opens the way for many applications like multichannel waveguide-multichannel quantum information processing, real quality imaging, and temporal clock.

Fully nonlinear analysis of second-order sloshing resonance in a three-dimensional tank

The 3D boundary element method (BEM) based on the potential flow theory is developed to study the second-order resonance problems in rectangular sloshing tanks. Fully-nonlinear free-surface boundary conditions are considered. A local surface fitting method is used to calculate tangential derivatives. A shared-memory parallel procedure based on OpenMP is adopted for the efficiency improvement. Both 2D and 3D sloshing cases are studied. It is found that the second-order resonance may occur due to the interaction among natural frequencies and excitations frequencies. The second-order resonance becomes obvious after a sufficient long time length. After increasing the excitation amplitude, the second-order resonance emerges much earlier. For 3D situations, the second-order resonance in rectangular tanks with either equal or unequal length and width sides are investigated. The second-order resonances due to the interaction of two orthogonal plane waves in length and width directions are observed.

Impact of eigenvalues on the electron-phonon coupling strength of aluminium and its binary alloys

Aluminium is a third group element according to the periodic table. Chemically it is a reactive metal often forming complexes within its binary alloys. In the present work we have dealt with the impact of eigenvalues on the superconducting state parameter viz. the electron-phonon coupling strength of this metal. We have also dealt with the same for two binary alloys of it viz. aluminium-magnesium and aluminium-zinc. For this purpose we have computed the non-local screened form factor for each of them. Initially the orthogonalised plane wave parameter has been taken as unity. Thereafter Vashishta-Singwi form of exchange and correlation is employed. The core energy eigenvalues of Herman-Skillman have been used. Our results are quite satisfactory for the metal as well as its present alloys. Our computation reveals that the superconducting state parameter can be reasonably reproduced by Harrison’s first principle pseudopotential technique along with McMillan’s formalism provided a proper choice of the core energy eigenvalues is made.DOI: http://dx.doi.org/10.3126/bibechana.v12i0.11699BIBECHANA 12 (2015) 35-39