Frequency-domain Spectrum Research Articles

Frequency-domain interferometry for the determination of time delay between two extreme-ultraviolet wave packets generated by a tandem undulator

Synchrotron radiation, emitted by relativistic electrons traveling in a magnetic field, has poor temporal coherence. However, recent research has proved that time-domain interferometry experiments, which were thought to be enabled by only lasers of excellent temporal coherence, can be implemented with synchrotron radiation using a tandem undulator. The radiation generated by the tandem undulator comprises pairs of light wave packets, and the longitudinal coherence within a light wave packet pair is used to achieve time-domain interferometry. The time delay between two light wave packets, formed by a chicane for the electron trajectory, can be adjusted in the femtosecond range by a standard synchrotron technology. In this study, we show that frequency-domain spectra of the tandem undulator radiation exhibit fringe structures from which the time delay between a light wave packet pair can be determined with accuracy on the order of attoseconds. The feasibility and limitations of the frequency-domain interferometric determination of the time delay are examined.

Spectrum-optimized direct image reconstruction of super-resolution structured illumination microscopy

Super-resolution structured illumination microscopy (SR-SIM) has become a widely used nanoscopy technique for rapid, long-term, and multi-color imaging of live cells. Precise but troublesome determination of the illumination pattern parameters is a prerequisite for Wiener-deconvolution-based SR-SIM image reconstruction. Here, we present a direct reconstruction SIM algorithm (direct-SIM) with an initial spatial-domain reconstruction followed by frequency-domain spectrum optimization. Without any prior knowledge of illumination patterns and bypassing the artifact-sensitive Wiener deconvolution procedures, resolution-doubled SR images could be reconstructed by direct-SIM free of common artifacts, even for the raw images with large pattern variance in the field of view (FOV). Direct-SIM can be applied to previously difficult scenarios such as very sparse samples, periodic samples, very small FOV imaging, and stitched large FOV imaging.

Quantitative Assessment of Cold Injury in Tea Plants by Terahertz Spectroscopy Method

Cold injury (CI) causes irreversible damage to tea plants, which results in decline in the quality of famous teas and huge economic loss. A new, quick, non-destructive method is provided to assess the CI of tea leaf based on terahertz (THz) spectroscopy. Absorbance of the samples was measured with THz spectroscopy in frequency bands from 0.1 to 1.6 THz under low temperature treatments of 4.0, 0, −2.5, −5.0, −7.5, and −10.0 °C. Fast Fourier transformation was explored to decompose the endpoint signal to improve the ratio of signal to air and convert the time-domain spectra to the corresponding frequency-domain spectra. To improve the separation of overlap signals caused by substantial scattering of injured cells in the leaf, two-dimensional correlation spectroscopy (2DCOS) and average intensity (AI) were introduced into the partial least squares regression (PLSR) to build 2DCOS–PLSR and AI–PLSR models. Quantitative assessments of the 2DCOS–PLSR and AI–PLSR models were conducted to evaluate the three models. The assessment results showed that the correlation coefficients of the 2DCOS–PLSR model (R2D) were 0.7873, 0.8305, and 0.9103, respectively. The root mean square errors of the 2DCOS–PLSR model (RMSE2D) were 0.6032, 0.5763, and 0.5221, respectively. For the AI–PLSR model, RAI values were 0.7477, 0.7691, and 0.8974, respectively. RMSEAI values were 0.6038, 0.5962, and 0.5797. The combination of THz spectroscopy with the 2DCOS–PLSR model provided a better benchmark for the input interval selection and improved the accuracy of cold-injury detection results.

Generation of non-uniformly correlated sources with controllable beam profile by devising its statistics in the spatial frequency domain.

We introduce an efficient approach to simultaneously tailor the spatial profile and the degree of coherence (DOC) of partially coherent light by devising its statistical properties in the spatial frequency domain. The relationship between the beam profile and the DOC in the source plane and the correlation function and power spectrum in the spatial frequency domain is analyzed in detail. This approach enables us to generate partially coherent sources with spatially uniform or non-uniform coherence states, and the source profiles are controlled. The condition for switching two coherence states is given through two theoretical examples. Furthermore, we validate our approach in experiment through generating two kinds of spatially non-uniform correlated sources with controllable beam profiles. The experimental results agree well with our theoretical analysis.

Nonlinear response of the Kitaev honeycomb lattice model in a weak magnetic field

We investigate the nonlinear response of the Kitaev honeycomb lattice model in a weak magnetic field using the theory of two-dimensional (2D) coherent spectroscopy. We observe that at the isotropic point in the non-Abelian phase of this model, the nonlinear spectrum in the 2D frequency domain consists of sharp signals that originate from the flux excitations and Majorana bound states. Signatures of different flux excitations can be clearly observed in this spectrum, such that one can observe evidences of flux states with 4-adjacent, 2-nonadjacent, and 4-far-separated fluxes, which are not visible in linear response spectroscopy such as neutron scattering experiments. Moreover, in the Abelian phase we perceive that the spectrum in the frequency domain is composed of streak signals. These signals, as in the nonlinear response of the pure Kitaev model, represent a distinct signature of itinerant Majorana fermions. However, deep in the Abelian phase whenever a Kitaev exchange coupling is much stronger than the others, the streak signals are weakened and only single sharp spots are seen in the response, which resembles the dispersionless response of the conventional toric code.

Global Sensitivity Analysis for Impedance Spectrum Identification of Lithium-Ion Batteries Using Time-Domain Response

Accurate modeling is of great importance for describing battery dynamics under different working conditions. To achieve high accuracy and obtain insights into battery operations, it is critical to bridge the time-domain equivalent circuit model and frequency-domain electrochemical impedance spectroscopy. However, the practical battery running data are recorded at a very low sampling frequency, it is thus challenging to identify the frequency-domain impedance spectrum using time-domain response data. To solve this problem, this article proposes a systematic battery time-domain modeling approach considering impedance spectrum identification. First, a probabilistic approach for global sensitivity analysis is proposed to evaluate the impact of different parameters on model performance. The parameter sensitivity of both integer-order and fractional-order models are evaluated using the Sobol indices obtained by Monte Carlo simulations. Then, a Bayesian optimization algorithm is proposed to identify model parameters to reduce the evaluation times of the battery model. Finally, the experimental data conducted on LiFePO <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{4}$</tex-math></inline-formula> cells are employed to verify the proposed method. The results indicate that the total Sobol indices show a miscellaneous sensitivity of parameters on impedance spectra, which consolidates the understanding of impedance characteristics, and the higher order integer-order models with well-initialized low sensitive parameters are more suitable for predicting frequency-domain characteristics.

Thermal Aging-Based Degradation Parameters Determination for Grid-Aged Oil Paper Insulation

Elevated thermal stress-related aging is significant on the oil-impregnated paper (OIP) used as insulation in high-pressure gas cables (HPGCs). The aim of this article is to develop a cheap alternative for lab dielectric measuring and characterizing temperature-dependent parameters for OIP. First, this article derives the operating thermal conditions of the grid-aged cable based on IEC standards after analyzing the loading data using machine learning techniques to determine the elevated temperature levels for the experiments. Second, a novel lab-fabricated inexpensive electronics circuit is developed for polarization and depolarization current (PDC) measurements which can be adapted for such measurements over expensive commercial devices. From the measured parameters, an extended three-branch Debye model is optimized using a developed error function approach based on the Akaike information criterion (AIC) and goodness of fit. The model indicated a reduction in the branch resistance with temperature elevation and aging, whereas the branch capacitance revealed an increasing trend. The resultant relaxation time (RC) showed a decrease overall. Last, a short-duration frequency domain spectrum was analyzed and extrapolated to obtain parameters for a wide range of frequencies and fit in a Cole–Cole model, derived for oil-paper insulation. The time constants obtained from this model also confirmed a reducing trend across the temperature and aging variations and the model parameter, the alpha coefficient showed a decreasing trend. Last, the effect of the measured dielectric parameters is reflected with breakdown values to investigate the effect of temperature on the electrical life of insulation.

Non-destructive evaluation and fast conductivity calculation of various nanowire-based thin films with artificial neural network aided THz time-domain spectroscopy.

Terahertz time-domain spectroscopy (THz-TDS) has been utilized extensively to characterize materials in a non-destructive way. However, when materials are characterized with THz-TDS, there are many extensive steps for analyzing the acquired terahertz signals to extract the material information. In this work, we present a significantly effective, steady, and rapid solution to obtain the conductivity of nanowire-based conducting thin films by utilizing the power of artificial intelligence (AI) techniques with THz-TDS to minimize the analyzing steps by training neural networks with time domain waveform as an input data instead of a frequency domain spectrum. For this purpose, Al-doped and undoped ZnO nanowires (NWs) on sapphire substrates and silver nanowires (AgNWs) on polyethylene terephthalate (PET) and polyimide (PI) substrates have been measured for dataset creation via THz-TDS. After training and testing a shallow neural network (SSN) and a deep neural network (DNN) to obtain the optimum model, we calculated conductivity in a conventional way, and the prediction based on our models matched successfully. This study revealed that users could determine a sample's conductivity without fast Fourier transform and conventional conductivity calculation steps within seconds after obtaining its THz-TDS waveform, demonstrating that AI techniques have great potential in terahertz technology.

Terahertz-Based Insulation Delamination Defect Inspection of Vehicle Cable Terminals

Cable terminals of the high-speed electric multiple units (EMUs) are prone to undertake insulation delamination defects due to their special operating conditions. Such a defect is difficult to identify and it may pose a great threat to the safety of the EMUs. To achieve accurate detection of insulation delamination defects, this article proposes a terahertz (THz)-based approach that combines the spectrum of the THz wave and THz imaging techniques. Specifically, a synthetic multilayer composite insulation structure with an air gap is firstly built to simulate the internal delamination defect of the cable terminal. Then THz tests in both time and frequency domains are performed on the synthetic structure. Experimental results show that the delamination defect of the multilayer insulation structure can be quickly detected by observing the absorption spectrum in the THz frequency domain. The location and geometry of the defect can be preliminarily determined by the THz imaging and then further refined through image segmentation. In addition, the thickness of the delamination defect can be quickly calculated by the THz time-domain spectrum (TDS). By combining the THz spectrum and the THz imaging information, the delamination defects are quantitatively detected for the multilayer composite structure or even for the EMU’s cable terminals.

Low-complexity fast diffraction calculation for Bessel–Gauss beam generated by reflective off-axis axicon

A low-complexity fast diffraction calculation algorithm is proposed for theoretically studying the Bessel–Gauss beam generated by reflective off-axis axicon. By carefully exploiting the non-uniform inverse discrete Fourier transform (NU-IDFT), complicated interpolation algorithm is avoided when calculating the diffraction propagation between two tilted planes. Since only the central diffraction field is calculated, the computational complexity is dramatically reduced. By simply shifting the spectrum in frequency domain according to the tilted angle, the algorithm can suit to different tilted angles without increasing the sampling points. At last, three different kinds of imperfect fabricated reflective axicons are studied, simulation results validate the accuracy and high efficiency of the proposed method, implying it is promising in studying the feature of the Bessel–Gauss beam generated by reflective off-axis axicon.

Measurement Speed Improvement of OFDR Using Differential-Spectrum Dispersion Degree

Signal processing in optical frequency-domain reflectometry (OFDR) involves the cross correlation between the reference and the measured Rayleigh backscattering spectra (RBS), which is a time-consuming operation with a large data size. This work demonstrates a fast demodulation method to accelerate the data processing of OFDR in static strain measurement. The dispersion degree of the optical frequency-domain differential spectrum (OFDS) is analyzed to remove the strain-free RBS. Therefore, data demodulation can be accomplished based only on the local cross correlation (LCC) between the retained RBSs. The validity of the proposed method was verified by multiple sets of static strain experimental results. The time consumption of the proposed method is evaluated under the different sensing spatial resolutions and the number of padding zeros. Compared to the conventional method with the whole RBS, the proposed method decreases the time cost from 4575.7 to 637.1 ms when the fiber length is 40 m with 8-mm sensing spatial resolution and 6000 padding zeros.

Detection of biomarkers using terahertz metasurface sensors and machine learning.

To achieve classification and concentration detection of cancer biomarkers, we propose a method that combines terahertz (THz) spectroscopy, metasurface sensors, and machine learning. A metasurface sensor suitable for biomarker detection was designed and fabricated with five resonance frequencies in the range of 0.3-0.9THz. We collected biomarkers of five types and nine concentrations at 100 sets of time-domain spectra per concentration. The spectrum is processed by noise reduction and fast Fourier transform to obtain the frequency-domain spectrum. Five machine learning algorithms are used to analyze time- and frequency-domain spectra and ascertain which algorithm is more suitable for the classification of the biomarker THz spectrum. Experimental results show that random forest can better distinguish five biomarkers with an accuracy of 0.984 for the time-domain spectrum. For the frequency-domain spectrum, the support vector machine performs better, with an accuracy of 0.989. For biomarkers at different concentrations, we used linear regression to fit the relationship between biomarker concentration and frequency shift. Experimental results show that machine learning can distinguish different biomarker species and their concentrations by the THz spectrum. This work provides an idea and data processing method for the application of THz technology in biomedical detection.

Unsupervised Across Domain Consistency- Difference Network for Hyperspectral Image Super-Resolution

Without reducing the spectral resolution, hyperspectral image super-resolution has achieved remarkable progress thanks to the success of deep neural networks. However, existing methods can not fully excavate the latent high-frequency details only in the single spatial domain. Different from existing methods that only achieves the super-resolution task in spatial domain, we optimize the amplitude spectrum and phase spectrum in frequency domain to obtain high resolution hyperspectral image (HR-HSI). We propose a new unsupervised framework to reconstruct HR-HSI using only the observed low resolution HSI and HR multispectral image. Based on triple-level modeling, the encoder-decoder learns abundant features including contextual information from multiple scales. In addition, we propose iterative across domain consistency-difference (ADCD) module, which is embedded between encoder and decoder. In ADCD module, three parallel convolution streams, (amplitude spectrum adjustment branch, phase spectrum adjustment branch and spatial domain branch) are used to explore the consistency-difference between each other, which is preserved by memory units within the module. Particularly, we embed the dilated causal convolution in the frequency domain processing branch, which is convenient to flexibly adjust the receptive field and adapt to different domains. Extensive experiments are conducted on widely-used datasets in comparison with state-of-the-art models, demonstrating the advantage of the proposed method.

Short – Term Forecasting for Daily Stock Market Indices using Discrete Fourier Transforms

The stock market indices are used to gauge the financial movements in the stock markets. If the index rises, the market is growing, and if it falls, the market is declining. The only stock exchange in Sri Lanka is operated by the Colombo Stock Exchange (CSE). Its two primary stock market indices are All Share Price Index (ASPI) and Standard &amp; Poor’s Sri Lanka 20 (S&amp;P SL20). Market indices provide information to investors. So, they can predict the risks and returns of their investments. While ASPI forecasts assist investors in understanding the future direction of the entire market, S&amp;P SL20 forecasts help investors make investment decisions. Therefore, in order to make the correct investment decisions, it is crucial to identify appropriate forecasting methods for those two indices to meet investor expectations. The Discrete Fourier Transform (DFT) is a technique that can be used to convert a time-domain discrete signal into a frequency-domain discrete spectrum. In this study, the ASPI and S&amp;P SL20 indexes were modeled as the Fast Fourier Transform amplitude spectrum using the daily stock values. The daily index data from the years 2017 to 2022 were used to formulate this model. The study also examined the periodic deviations of both indices during the considered period. Additionally, this research predicts the near future of both indices by modeling the daily indices values. To further verify the accuracy of the model, data from the SET (Thailand Stock Index) were employed. According to the results, the ASPI and S&amp;P SL20 datasets show periodic patterns ranging from 4 days to 7 days and the SET datasets show periodic patterns between 5 and 6 days. The forecasting ability of the proposed Fourier model was assessed by using metrices such as Mean Squared Error (MSE), Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE). Finally, it is concluded that the proposed Fourier model is capable of forecasting the daily ASPI and S&amp;P SL20 indices for a short period of time equivalent to their periodicities.

Research on Vibration Data-Driven Fault Diagnosis for Iron Core Looseness of Saturable Reactor in UHVDC Thyristor Valve Based on CVAE-GAN and Multimodal Feature Integrated CNN

The imbalance of data samples and fluctuating operating conditions are the two main challenges faced by vibration data-driven fault diagnosis for the iron core looseness of saturable reactors in UHVDC thyristor valves. This paper proposes a vibration data-driven saturable reactor iron core looseness fault diagnosis strategy named CVG-MFICNN based on CVAE-GAN and MFICNN to overcome the two challenges. This strategy uses a novel 1-D CVAE-GAN model to produce generated samples and expand the training set based on imbalanced training samples. An MFICNN model structure is designed to allow the simultaneous processing of multimodal features such as the SST time-frequency spectrum, time-domain vibration sequence, frequency-domain power spectrum sequence, and time-domain statistics. Using these multimodal features and the MFICNN model, the hidden fault information in vibration data can be effectively mined. An experiment is conducted to collect vibration data of saturable reactors with different faults. Models based on the proposed strategy and other methods are trained and tested using the collected data. The comparison results show that the performance of the proposed CVG-MFICNN approach is significantly superior to that of single-feature CNNs, traditional machine learning methods, and classical image classification CNNs in the application of UHVDC thyristor valve saturable reactor iron core looseness fault diagnosis.

Fault Recognition for Mechanical Arm by Using Relative Margin SVM

Monitoring and detecting faults during the operation of the manipulator is the prerequisite for fault recognition and safe operation. Accurate classification of mechanical arm faults can support to effectively eliminate mechanical arm faults. In this paper, the authors utilize a relative margin support vector machine (RMSVM) to classify and monitor the faults for mechanical arm. First, the status of mechanical arm are represented a high dimensional vector which consists of the mean, variance, correlation coefficient of the residual momentum signal in time domain, and the wavelet packet energy spectrum in frequency domain. The collected feature vectors for mechanical arm status are used to train RMSVM. A virtual prototype of mechanical arm is used to analyze the changes in the features of the residual momentum caused by fault and evaluate the RMSVM model for future mechanical arm status. The simulation results show that RMSVM can effectively detect the faults during the operation of manipulator.

Terahertz spectroscopic detection of amino acid molecules under magnetic field

Terahertz (THz) waves can cover the characteristic spectra of substances such as plasma, organisms, and biomolecules, whereas THz photons have low energy and do not damage biological tissues. Therefore, its absorption characteristics in the THz region can be used to characterize the internal structure of biomolecules. In this study, we designed a microfluidic chip and combined it with THz technology. The spectral intensity in descending order was found to be deionized water, phenylalanine, histidine, glycine and glutamic acid by observing the THz wave transmission in the range of 0.1–1.0 THz, comparing the frequency domain spectra of four amino acid solutions with volume fraction of 2% and deionized water. It is inferred that different molecular structures of amino acids resulted in different numbers of hydrogen bonds formed between them and water molecules, leading to different degrees of absorption of THz waves. In addition, magnetic fields parallel to the THz wave transmission were used to study the variation of different amino acids with magnetic field intensity. It is found that increasing the magnetic field strength decrease the transmission of THz waves. This is because under the action of the magnetic field, on the one hand, the hydrogen bonds formed by water molecules are strengthened and the absorption of THz waves is enhanced; on the other hand, amino acid molecules aggregate and the radius of molecular clusters increases, thus blocking the transmission of THz waves. Finally, we also calculated the electric conductivity of the solutions to prove the accuracy of the experimental results from a theoretical point of view.

Study on the laser-induced damage of thin films by terahertz time-domain spectroscopy

The undamaged and damaged areas of the ITO thin film deposited on a silicon substrate induced by laser with different energies were tested with the transmission terahertz time-domain spectroscopy system. Their time-domain spectra and frequency-domain spectra of 0.4–1.0 THz were obtained, and the differences were analyzed between the undamaged and damaged areas in these two spectra. The results show that the peak-to-peak value in the time domain and the amplitude in the frequency domain of the damaged area evidently increased compared with those of the undamaged area, and with the increase in laser-induced energy, resulting in the larger damaged area and heavier surface roughness, these two parameters gradually decrease. For the damaged area of the ITO thin film with the undamaged substrate, the refractive index and absorption coefficient are lower than those of the undamaged area. Therefore, the variation in the terahertz time-domain and frequency-domain spectra could be utilized to distinguish the damage of the optical thin film irradiated by laser, which provides a new approach for the laser-induced damage identification and the technical support in effect of the laser-induced damage on the properties of the optical thin film element in the terahertz band.

Integrated system of traditional THz time-domain spectroscopy and asynchronous optical sampling

Terahertz time-domain spectroscopy (THz-TDS) system, as a new means of spectral analysis and detection, plays an increasingly pivotal role in basic scientific research. However, owing to the long scanning time of the traditional THz-TDS system and the complex control of the asynchronous optical scanning (ASOPS) system, which requires frequent calibration, we combine traditional THz-TDS and ASOPS systems to form a composite system and propose an all-fiber trigger signal generation method based on the time overlapping interference signal generated by the collinear motion of two laser pulses. Finally, the time-domain and frequency-domain spectra are obtained by using two independent systems in the integrated systems. It is found that the full width at half maximum (FWHM) of the time-domain spectra and the spectral width of the frequency-domain spectra are almost the same, but the sampling speed of the ASOPS system is significantly faster than that of the traditional THz-TDS system, which conduces to the study of the transient characteristics of substances.

Effect of acetylcholine deficiency on neural oscillation in a brainstem-thalamus-cortex neurocomputational model related with Alzheimer’s disease

Previous works imply that involving brainstem in neuropathological studies of Alzheimer’s disease (AD) is of clinically significant. This work constructs a comprehensive neural mass model for cholinergic neuropathogenesis that involves brainstem, thalamus and cortex, wherein how acetylcholine deficiency in AD affects neural oscillation of the model output is systematically explored from the perspective of neurocomputation. By decreasing synapse connectivity parameters in direct cholinergic pathway from brainstem to thalamus or in indirect glutamatergic synapse pathway from cortex to brainstem to mimic the pathological condition of reduced acetylcholine release in patients with AD, the property of neural oscillation in this model is numerically investigated by means of power spectrum in frequency domain and amplitude distribution in time domain. Simulated results demonstrate that decreasing synapse connectivity whether in the direct cholinergic pathway or in the indirect glutamatergic synapse pathway can alter the neural oscillation significantly in three aspects: it induces an obvious decrease of dominant frequency; it leads to a degraded rhythmic activity in the alpha frequency band as well as an enhanced rhythmic activity in the theta frequency band; it results in reduced oscillation amplitude of the model output. These results are agreement with the characteristic of electrophysiological EEG measurement recorded in AD, especially support the hypothesis that cholinergic deficiency is a promising pathophysiological origin of EEG slowing in AD. Our analysis indicates that targeting the cholinergic system may have potential prospects in early diagnosis and treatment of AD.