Lorentzian Fitting Research Articles

Phonon characteristics and dielectric properties of a phase pure CoWO4 ceramic

A phase pure CoWO4 ceramic was prepared using the conventional solid-state reaction method and sintering at 1150 °C for 2 h. The sintered sample exhibited a tetragonal wolframite structure (space group P2/c) without impurity phases according to X-ray diffraction analysis. The Raman and infrared spectra of the CoWO4 ceramic were studied based on Lorentz fitting, a first-principles calculation, the four-parameter semiquantum (4-P) model and the Kramers-Krönig (K-K) transformation to reveal the local structure and intrinsic properties. The infrared spectrum was fitted based on the 4-P model, which showed that the simulated properties are similar to the experimental results and that the largest contribution to the dielectric response comes from the Bu(1) mode, which is related to the stretching vibration of the WO6 octahedra.

Estimation of Error in Brillouin Frequency Shift in Distributed Fiber Sensor

Brillouin frequency shift (BFS) is the most frequently used quantity in the distributed fiber temperature and strain sensor. To estimate the error in the measured temperature and strain, the influences of signal-to-noise ratio, linewidth ( $\Delta {v}_{\text {B}}$ ), number of sweeps, and frequency sweep span (coefficient) on the BFS error are systematically investigated based on a large number of numerically generated Brillouin spectra and the Lorentzian profile-based fitting algorithm. The results reveal that they have a considerable impact on the BFS error. If the other factors remain unchanged, the influence of single factor on the BFS error is as follows: The BFS error varies as a power of the number of sweeps, the exponent is about −0.5. A threefold rise in average time or number of sweeps results in halving BFS error. If the frequency sweep span varies from $0.6\Delta {v}_{\text {B}}$ to $2\Delta {v}_{\text {B}}$ , it has no big influence on the error. The BFS error is proportional to linewidth. The BFS error reduces exponentially with increasing signal-to-noise ratio (in dB). A very large number of Brillouin spectra with the frequency sweep span from ${v}_{\text {B}}-\Delta {v}_{{\text {B}}}$ to ${v}_{{\text {B}}}+\Delta {v}_{{\text {B}}}$ , signal-to-noise ratio from 2 to 52 dB, $\Delta {v}_{{\text {B}}}$ from 0.03 to 0.15 GHz, number of sweeps from 11 to 601 are numerically generated and BFS is calculated. A formula for BFS error estimation is proposed according to the above results. The formula is fully validated through measured Brillouin spectra with different values of signal-to-noise ratio, linewidth, number of sweeps and frequency sweep span.

Accurate and ultra-fast estimation of Brillouin frequency shift for distributed fiber sensors

The original Lorentzian profile-based nonlinear least-squares problem for BFS estimation is converted to a linear least-squares one. Then, Brillouin frequency shift (BFS) can be readily calculated. The typical nonlinear least-squares Lorentzian, Gaussian, pseudo-Voigt and Voigt fits using Levenberg-Marquardt algorithm, the correlation-based algorithm and the proposed Lorentzian model-based linear least-squares fitting algorithm are used to estimate BFS of the measured Brillouin spectra with different values of SNR (signal-to-noise ratio) and frequency step. The results reveal that the proposed algorithm has similar accuracy with the nonlinear fits. However, the computation time of the typical nonlinear fits is 187.56–11481.67 times as long as the proposed algorithm. The proposed algorithm can estimate BFS with less computational burden and higher accuracy than the correlation-based algorithm. If SNR is low, the frequency step should be set to a low value.

In-situ quantification of alkali metals from biomass combustion by optical emission spectroscopy

In this study, an in-situ method was developed to quantify the alkali metal emissions and its speciation from the combustion of biomass in a 150 kWth furnace. An optical emission spectrometer was used to detect the spontaneous atomic emissions of the potassium and sodium in the flame. A calibration is performed to obtain the radiation intensities of potassium and sodium, which are precursive values needed to quantify each alkali metals’ relative ground state number densities. The results show that the spontaneous emissions of the alkali metals appear as doublet lines in the spectra. The calibrated radiation intensities for sodium were converted to relative values via Lorentzian fitting. The relative excited state number densities for sodium and potassium were within the range of 0.536 to 0.791 cm−3 and 23.468 and 30.320 cm−3 respectively. This shows that potassium vapours and its compounds were higher compared to sodium. These number densities will be compared to the sodium and content in the ash for further discussion and validation.

Added Value of Chemical Exchange-Dependent Saturation Transfer MRI for the Diagnosis of Dementia.

ObjectiveChemical exchange-dependent saturation transfer (CEST) MRI is sensitive for detecting solid-like proteins and may detect changes in the levels of mobile proteins and peptides in tissues. The objective of this study was to evaluate the characteristics of chemical exchange proton pools using the CEST MRI technique in patients with dementia.Materials and MethodsOur institutional review board approved this cross-sectional prospective study and informed consent was obtained from all participants. This study included 41 subjects (19 with dementia and 22 without dementia). Complete CEST data of the brain were obtained using a three-dimensional gradient and spin-echo sequence to map CEST indices, such as amide, amine, hydroxyl, and magnetization transfer ratio asymmetry (MTRasym) values, using six-pool Lorentzian fitting. Statistical analyses of CEST indices were performed to evaluate group comparisons, their correlations with gray matter volume (GMV) and Mini-Mental State Examination (MMSE) scores, and receiver operating characteristic (ROC) curves.ResultsAmine signals (0.029 for non-dementia, 0.046 for dementia, p = 0.011 at hippocampus) and MTRasym values at 3 ppm (0.748 for non-dementia, 1.138 for dementia, p = 0.022 at hippocampus), and 3.5 ppm (0.463 for non-dementia, 0.875 for dementia, p = 0.029 at hippocampus) were significantly higher in the dementia group than in the non-dementia group. Most CEST indices were not significantly correlated with GMV; however, except amide, most indices were significantly correlated with the MMSE scores. The classification power of most CEST indices was lower than that of GMV but adding one of the CEST indices in GMV improved the classification between the subject groups. The largest improvement was seen in the MTRasym values at 2 ppm in the anterior cingulate (area under the ROC curve = 0.981), with a sensitivity of 100 and a specificity of 90.91.ConclusionCEST MRI potentially allows noninvasive image alterations in the Alzheimer's disease brain without injecting isotopes for monitoring different disease states and may provide a new imaging biomarker in the future.

Analytic model of a compound thermal-field emitter and its performance

A methodology for implementing the recently developed reformulated general thermal-field equation describing simultaneous thermal and field emission contributions to electron emission is developed, with modifications directed to enhancing speed and accuracy of computation as demanded by emitter characterization and electron beam simulations. An accurate factor to correct both thermal-field (TF) and high field (Fowler-Nordheim or FN) predictions based on a rapid Lorentzian fit model is given. The analytic protrusion model is constructed from modifications to a point dipole model that allow surface elements and field enhancement factors to be rapidly evaluated. The model is applied to an analytical model of a protrusion on a bump in a diode configuration to characterize how current-voltage I(V) relations are affected by TF emission conditions. In addition, it is also shown (i) how aggressively Schottky’s conjecture is undermined as the protrusion dimensions become larger; (ii) how the total current in the TF regime can be substantially larger than predicted by canonical [FN and Richardson-Laue-Dushman (RLD)] formulations; (iii) how an optimal protrusion size may exist; and (iv) how the inference of field enhancement, notional emission area, and work function are poorly predicted using conventional methods relying on the canonical FN and RLD equations even outside the thermal-field regime, even though data can be linear on FN and RLD plots.

DeepCEST 3T: Robust MRI parameter determination and uncertainty quantification with neural networks-application to CEST imaging of the human brain at 3T.

Calculation of sophisticated MR contrasts often requires complex mathematical modeling. Data evaluation is computationally expensive, vulnerable to artifacts, and often sensitive to fit algorithm parameters. In this work, we investigate whether neural networks can provide not only fast model fitting results, but also a quality metric for the predicted values, so called uncertainty quantification, investigated here in the context of multi-pool Lorentzian fitting of CEST MRI spectra at 3T. A deep feed-forward neural network including a probabilistic output layer allowing for uncertainty quantification was set up to take uncorrected CEST-spectra as input and predict 3T Lorentzian parameters of a 4-pool model (water, semisolid MT, amide CEST, NOE CEST), including the B0 inhomogeneity. Networks were trained on data from 3 subjects with and without data augmentation, and applied to untrained data from 1 additional subject and 1 brain tumor patient. Comparison to conventional Lorentzian fitting was performed on different perturbations of input data. The deepCEST 3T networks provided fast and accurate predictions of all Lorentzian parameters and were robust to input perturbations because of noise or B0 artifacts. The uncertainty quantification detected fluctuations in input data by increase of the uncertainty intervals. The method generalized to unseen brain tumor patient CEST data. The deepCEST 3T neural network provides fast and robust estimation of CEST parameters, enabling online reconstruction of sophisticated CEST contrast images without the typical computational cost. Moreover, the uncertainty quantification indicates if the predictions are trustworthy, enabling confident interpretation of contrast changes.

Probing number of layers and quality assessment of mechanically exfoliated graphene via Raman fingerprint

To attain the expected outcomes of any measurement, probing the quality of graphene is a prerequisite among the various graphene samples. Herein, we investigate the identification of the number of layers in mechanically exfoliated graphene using Raman spectroscopy. The intensity ratio (I2D/IG) and peak width of the 2D peak have been used to distinguish the number of layers. The 2D peak consists of a single Lorentzian fit having peak width 24 cm−1 in single layer graphene (SLG) and splits into four, six and five components for bilayer, trilayer, and five layers respectively. Further, the quality of graphene has been analyzed by I2D/IG, Raman mapping and the charge carrier mobility. In addition, the high quality of graphene has been encapsulated in terms of two phonon scattering processes and the variation in I2D/IG of SLG as a result of crossover from electron-electron to electron-hole scattering. The maximum mobility of SLG has been obtained ∼11,931 cm2V−1s−1 when the peak width and I2D/IG are 23.88 cm−1 and 5.36 respectively. Hence, the present study sets a platform to use Raman scattering as a probe for quantification of graphene layers and Raman mapping with spatial resolution provides the solution for specific area selection to fabricate the next generation graphene based quantum devices.

Ferromagnetic resonance imbalance at high microwave power: Effect on the Gilbert damping parameter

Nowadays, electron spin resonance (ESR) systems are routinely used to measure the ferromagnetic resonance (FMR) in a wide range of experiments. However, the number of spins in ferromagnets far exceeds the small number of spins in paramagnetic systems that ESR systems were originally designed for. In this study, we show that high spin concentration and microwave input power—conditions routinely met in various FMR experiments—lead to the strong distortion of the FMR shape due to the sublinear operating regime of the microwave detector. We introduce the additional imbalance term in the FMR Lorentzian fitting function that allows extracting correct values of the Gilbert damping parameter under such conditions. Our results are crucial for the quantitative estimation of the Gilbert damping—the key parameter in many magnetic and spintronics measurements.

Functionalised microwave sensors for real-time monitoring of copper and zinc concentration in mining-impacted water

Microwave spectroscopy has been identified as a novel and inexpensive method for the monitoring of water pollutants. Integrating microwave sensors with developed coatings is a novel strategy to make the sensing system more specific for a target contaminant. This study describes the determination of copper and zinc concentration in water in both laboratory-prepared and acquired mine water samples from two abandoned mining areas in Wales, UK. Uncoated sensors immersed in samples spiked with 1.25 mg/L concentrations of copper and zinc, using the standard addition method, were able to quantify the concentration at 0.44 GHz with a strong linear correlation (R2 = 0.99) for the reflection coefficient magnitude (|S11|). Functionalised microwave sensors with l-cysteine, chitosan and bismuth zinc cobalt oxide-based coatings have shown improvement in the sensing performance. Specifically, the linear correlation at 0.91–1.00 GHz between |S11| and a polluted water sample spiked with Cu showed a higher (R2 = 0.98), sensitivity (1.65 ΔdB/mg/L) and quality factor (135) compared with uncoated sensors (R2 = 0.88, sensitivity of 0.82 ΔdB/mg/L and Q-factor 30.7). A Lorentzian peak fitting function was applied for performing advanced multiple peak analysis and identifying the changes in the resonant frequency peaks which are related to the change in metal ion content. This novel sensor platform offers the possibility of in situ monitoring of toxic metal concentrations in mining-impacted water, and multiple peak features, such as area, full width half maximum, centre and height of the peaks, have the possibility to offer higher specificity for similar toxic metals, as between copper and zinc ions.

A Faraday laser operating on Cs 852 nm transition

We demonstrate a Faraday laser at Cs-D2 resonance line 852 nm using a Cs Faraday optical filter as frequency-selecting element. In contrast to typical diode laser with high stability of the emission frequency by additional control systems, our Faraday laser offers stable output frequency exactly set by the peak transmission frequency of the Cs 852 nm Faraday optical filter. The system works stably over a range of laser diode (LD) current from 60 to 130 mA and the LD temperature from 14 to 35 ^{circ }C, as well as the 48-h wavelength fluctuation range of no more than ± 2 p.m. A most probable linewidth of 17 kHz with Lorentz fitting is obtained by beating between two identical laser systems. The wavelength of our system is stabilized within transmission frequency region of 852 nm Faraday optical filter, and the peak of the transmission is corresponding to Cs atomic Doppler broadened line at the cell temperature of 41 ^{circ }C and the magnetic field of 330 G, making it suitable for laser-pumped Cs gas-cell and atomic beam frequency standard, etc. Moreover, this scheme is firstly used on Cs atom, opening new doors in research of Faraday laser and its applications.

Outer hair cell electromotility is low-pass filtered relative to the molecular conformational changes that produce nonlinear capacitance.

The outer hair cell (OHC) of the organ of Corti underlies a process that enhances hearing, termed cochlear amplification. The cell possesses a unique voltage-sensing protein, prestin, that changes conformation to cause cell length changes, a process termed electromotility (eM). The prestin voltage sensor generates a capacitance that is both voltage- and frequency-dependent, peaking at a characteristic membrane voltage (Vh), which can be greater than the linear capacitance of the OHC. Accordingly, the OHC membrane time constant depends upon resting potential and the frequency of AC stimulation. The confounding influence of this multifarious time constant on eM frequency response has never been addressed. After correcting for this influence on the whole-cell voltage clamp time constant, we find that both guinea pig and mouse OHC eM is low pass, substantially attenuating in magnitude within the frequency bandwidth of human speech. The frequency response is slowest at Vh, with a cut-off, approximated by single Lorentzian fits within that bandwidth, near 1.5 kHz for the guinea pig OHC and near 4.3 kHz for the mouse OHC, each increasing in a U-shaped manner as holding voltage deviates from Vh Nonlinear capacitance (NLC) measurements follow this pattern, with cut-offs about double that for eM. Macro-patch experiments on OHC lateral membranes, where voltage delivery has high fidelity, confirms low pass roll-off for NLC. The U-shaped voltage dependence of the eM roll-off frequency is consistent with prestin's voltage-dependent transition rates. Modeling indicates that the disparity in frequency cut-offs between eM and NLC may be attributed to viscoelastic coupling between prestin's molecular conformations and nanoscale movements of the cell, possibly via the cytoskeleton, indicating that eM is limited by the OHC's internal environment, as well as the external environment. Our data suggest that the influence of OHC eM on cochlear amplification at higher frequencies needs reassessment.

High-resolution creatine mapping of mouse brain at 11.7 T using non-steady-state chemical exchange saturation transfer.

The current study aims to optimize the acquisition scheme for the creatine chemical exchange saturation transfer weighted (CrCESTw) signal on mouse brain at 11.7T, in which a strong magnetization transfer contrast (MTC) is present, and to further develop the polynomial and Lorentzian line-shape fitting (PLOF) method for quantifying CrCESTw signal with a non-steady-state (NSS) acquisition scheme. Studies on a Cr phantom with cross-linked bovine serum albumin (BSA) as well as on mouse brain demonstrated that the maximum CrCESTw signal was reached with a short saturation time determined by the rotating frame relaxation time of the MTC pool instead of the steady-state saturation. The saturation power for the maximal signal was around 1-1.5 μT for Cr with 20% cross-linked BSA and in vivo applications, but 2 μT was found to be most practical for signal stability. For the CrCEST acquisition with strong MTC interference, the optimal saturation power and length are completely different from those on Cr solution alone. This observation could be explained well using R1ρ theory by incorporating the strong MTC pool. Finally, a high-resolution Cr map was obtained on mouse brain using the PLOF method with the NSS CEST acquisition and a cryogenic coil. The Cr map obtained by CEST showed homogenous intensity across the mouse brain except for regions with cerebrospinal fluid.

Microstructures and mechanical properties of Al-Mg2Si-Si alloys resistance spot welded with Al-Si interlayers

This study investigates Al-Mg2Si-Si alloy joints produced via resistance spot welding (RSW) with and without the use of Al-Si interlayers. The joint microstructures produced both with and without Al-Si interlayers consist of three zones: the base material (BM), the heat affected zone (HAZ) and the weld nugget (WN). The WN is oval, and increases in the welding current increase the WN size in both welding methods. The joints produced via RSW with an Al-Si interlayer have larger WNs than those produced without an interlayer under the same welding current conditions. Relationships between the welding current and the WN size are established by Gaussian fitting and Lorentz fitting. A comparison of the two welding approaches shows that a successful weld can be obtained at a low welding current when an Al-Si interlayer is used, whereas a larger welding current is required to obtain the same result without the use of an Al-Si interlayer. The transition layer (interface between the HAZ and the WN) in the joints welded without an interlayer is a single eutectic phase structure; however, in the joints welded with an interlayer, the transition layer generates an equiaxed-columnar crystal zone. The formation of the equiaxed-columnar crystal zone and the change in composition of the WN (according to the results of differential scanning calorimetry tests) improve the tensile-shear loads (TSLs). The equations of the peak TSLs as a function of the welding current and WN size are established by Gaussian fitting.

A Novel Method of the Brillouin Gain Spectrum Recognition Using Enhanced Sobel Operators Based on BOTDA System

Enhanced Sobel operators were proposed to identify the scattering spectrum based on a Brillouin optical time-domain analysis (BOTDA) system and experimentally demonstrated. To the best of our knowledge, this is the first time to use the enhanced Sobel operators in the BOTDA system. The proposed approach regarded the Brillouin scattering spectrum as an image, where the Brillouin gain could be regarded as edges of the image, the Brillouin gain spectrum was sharpened more, and better denoising effect was achieved by the enhanced Sobel operators. Not only that, the novel method could omit the Lorentz fitting and make scattering spectrum recognition more intuitive and fast regardless of fitting multiple points caused by different temperatures or strain along the different positions of the fiber. We successfully realized the recognition method over a 14-km single-mode fiber with 10-m spatial resolution and obtained the temperature at 61.4°C of the heated water, compared with the consequence (61.4°C) of Lorentz curve fitting without much sacrifice of the sensing accuracy.

Frequency shift estimation technique near the hotspot in BOTDA sensor.

When studying the spatial resolution and Brillouin frequency shift (BFS) uncertainty in Brillouin optical time domain analysis (BOTDA) system with a hotspot, people usually focuses on the point with best performance in the hotspot and neglect the huge error around it. The error is caused by the Brillouin gain spectrum (BGS) contributed by both the hotspot and the ambient segment, which is distorted from standard Lorentzian curve. Due to the distortion of BGS, the estimated BFS near the hotspot is shifted from the actual value and results in BFS error along the fiber. The distorted BGS can be double-peak or single-peak curve that is dependent on both the length of the hotspot that contributes to BGS and the BFS difference between the hotspot and the ambient segment. A fitting technique considering the combined contributions of hotspot and ambient segment is proposed to recover the distorted BGS near the hotspot and evaluate BFS. It is demonstrated that BFS error around hotspot is greatly reduced compare to the conventional Lorentzian fitting and dual Lorentzian fitting schemes.

Back propagation neutral network based signal acquisition for Brillouin distributed optical fiber sensors.

This manuscript proposes a method based on back propagation (BP) neural network and the spectral subtraction method to quickly obtain sensing information in Brillouin fiber optics sensors. BP neural network's characteristics which can realize any complex nonlinear mapping help to determine the frequency shift section(s) information. The training function, transfer function and number of hidden layer nodes of BP neural network are determined with experimental data. The experimental results show that comparing with traditional Lorentz fitting algorithm and edge detection with Sobel operator, the BP neural network is about 1/12 in terms of time complexity with the Lorentz algorithm, about 1/9 with the edge detection based on Sobel operator; while the respective accuracy on determine the frequency shifted section(s) has improved by 79.4% and 27.9%.

Chemical exchange saturation transfer imaging of phosphocreatine in the muscle

To determine the exchange parameters for the CEST of phosphocreatine (PCrCEST) in phantoms and to characterize PCrCEST in vivo in the muscle at different saturation powers and magnetic fields. Exchange parameters were measured in PCr solutions using varying saturation power at 15.2 T. Z-spectra were analyzed using multipool Lorentzian fitting in the hindlimb using various powers at 2 different fields: 9.4 T and 15.2 T. Modulation of PCr signal in PCrCEST and phosphorus MRS was observed in the mouse hindlimb before and after euthanasia. The exchange rate of PCr at physiological pH in phantoms was confirmed to be in a much slower exchange regime compared with Cr: kex at pH 7.3 and below was less than 400 s-1 . There was insufficient signal for detection of PCrCEST in the brain, but PCrCEST in the hindlimb was measured to be 2.98% ± 0.43 at a B1 of 0.47 μT at 15.2 T, which is 29% higher than 9.4T values. The value of PCrCEST at a B1 of 0.71 μT was not significantly different than that measured at a B1 of 0.47 μT. After euthanasia, PCrCEST signal dropped by 82.3% compared with an 85% decrease in PCr in phosphorus MRS, whereas CrCEST signal increased by 90.6%. The PCrCEST technique has viable sensitivity in the muscle at high fields and shows promise for the study of metabolic dysfunction and cardiac systems.

A Selectable Single-Mode Erbium Laser With Power-Flattened Output Employing Dual-Sagnac-Ring

To achieve wavelength-selectable and stable erbium-doped fiber (EDF) laser, a dual-Sagnac-ring configuration is designed to reach single-longitudinal-mode (SLM) oscillation and power-flattened output simultaneously. The presented and experimentally demonstrated EDF laser can also obtain the output power of 7.5 to 11.8 dBm in the continuous-wave (CW) tunability of 1523.0 to 1571.0 nm. Here, the power variation of lasing wavelength can be below than 1.0 dB over a wide working range of 1525.0-1565.0 nm for power-flattened output. Moreover, the 3-dB spectrum linewidth of presented EDF-based laser is measured in the range of 16.4-22.2 kHz via the Lorentzian fitting.

Optimized Feedforward Neural Network Training for Efficient Brillouin Frequency Shift Retrieval in Fiber

Artificial neural networks (ANNs) can be used to replace traditional methods in various fields, making signal processing more efficient and meeting the real-time processing requirements of the Internet of Things (IoT). As a special type of ANN, recently the feedforward neural network (FNN) has been used to replace the time-consuming Lorentzian curve fitting (LCF) method in Brillouin optical time-domain analysis (BOTDA) to retrieve the Brillouin frequency shift (BFS), which could be used as the indicator in temperature/strain sensing, etc. However, FNN needs to be re-trained if the generalization ability is not satisfactory, or the frequency scanning step is changing in the experiment. This is a cumbersome and inefficient process. In this paper, FNN only needs to be trained once with the proposed method. 150.62 km BOTDA is built to verify the performance of the trained FNN. Simulation and experimental results show that the proposed method is promising in BOTDA because of its high computational efficiency and wide adaptability.