Spectrum Decomposition Method Research Articles

Theoretical framework for calibrating the depth-dependent optical scattering in layered human skin using spatially offset measurements.

Spatially offset spectroscopy offers an alternative non-invasive method for enabling deep probing of structures and chemical molecules, which is clinically significant for the characterization of chemical and physical alterations in human skin. However, a more precise depth-resolved quantification using the spatially offset measurements still remains a challenge due to the mixed inhomogeneous scattering. Herein, we report a Monte-Carlo-based quantification modeling platform combined with a novel, to the best of our knowledge, scattering spectrum decomposition method to explore the depth-dependent optical scattering contributions in human skin. In the simplified modeling, human skin was empirically set to be composed of multiple layers, and each layer possessed different photon weights for the spatially offset scattering intensity measurements. The modeling results of photon transportation in-and-out of the layered skin substantially discovered that the layer-dependent scattering contribution was compositely encoded into the spatially offset measurements and varied with the illumination incidence angle. For calibrating the layer-dependent scattering contribution, a modified nonlinear independent component processing algorithm was applied to the spatially offset measurements by decomposing the photon weights of each layer. The calibration results figured out the major scattering contribution of each layer along the offset axis under different incidence angles, which were consistent with previous experimental observations. The proposed theoretical framework establishes a feasible approach for spatially offset optical spectroscopies enabling non-invasive quantitative A-line characterization of the concentrations of skin components.

Real-imaginary spectrum decomposition of the transparency spectra in microwave dressed Rydberg systems

To distinguish the contributions of electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) in their applications in precision laser spectroscopy, we propose a real-imaginary spectrum decomposition method to investigate the transparency spectra in a four-level microwave (MW) dressed Rydberg system. We show that the opening transparency windows in the absorption spectra of probe field is a prominent character by EIT, EIT-ATS crossover, and ATS when the MW field is turned off and the intensity of the control field is adjusted. When the MW field is turned on and gradually increased, the EIT is destroyed and disappears. In addition, the most prominent characters that open a transparency window are the EIT-ATS crossover and the ATS. Then, if we further increase the intensity of the MW field, we find that the transparency windows open mainly due to the ATS. Compared to the previous considerations of this issue, which were limited to three-level systems, our four-level scheme reported here is useful for understanding the features of quantum interference in multilevel atomic systems, and has potential applications to study enhanced sensitivity, measurement spectroscopic, quantum processing, quantum communication, and transmission.

Description and reconstruction of typical structured light beams with vector spherical wave functions.

It is well known that the generalized Lorenz-Mie theory (GLMT) is a rigorous analytical method for dealing with the interaction between light beams and spherical particles, which involves the description and reconstruction of the light beams with vector spherical wave functions (VSWFs). In this paper, a detailed study on the description and reconstruction of the typical structured light beams with VSWFs is reported. We first systematically derive the so-called beam shape coefficients (BSCs) of typical structured light beams, including the fundamental Gaussian beam, Hermite-Gaussian beam, Laguerre-Gaussian beam, Bessel beam, and Airy beam, with the aid of the angular spectrum decomposition method. Then based on the derived BSCs, we reconstruct these structured light beams using VSWFs and compare the results of the reconstructed beams with those of the original beams. Our results will be useful in the study of the interaction of typical structured light beams with spherical particles in the framework of GLMT.

Dual-isotope imaging method for Actinium-225 and Bismuth-213 using alpha imaging detector

Recently, 225Ac has received considerable attention for its use in targeted alpha therapy because it has a relatively long half-life and yields four more alpha-particles from the daughter nuclides. The performance evaluation should separately assess the distribution of 225Ac and 213Bi because daughter nuclides, including 213Bi, can cause renal toxicity, which may hinder the widespread use of 225Ac for targeted alpha therapy. In this study, we describe and validate a spectrum decomposition method for dual-isotope imaging of 225Ac and 213Bi using an alpha imaging detector. We implemented an experiment to demonstrate the feasibility of using the alpha imaging detector to obtain distribution images using therapeutic amounts of 225Ac. In addition, we designed and conducted a Monte Carlo simulation under realistic conditions based on the experimental results to evaluate the spectrum decomposition method for dual-isotope imaging. The alpha imaging detector exhibited a detection efficiency of 18.5% and an energy resolution of 13.4% at 5.5 MeV. In the simulation, the distributions of 225Ac and 213Bi were obtained in each region with a relative error of 5%. The results of this study confirmed the feasibility of the dual-isotope imaging method for discriminating alpha-emitters using small amounts of 225Ac.

Generalized adaptive singular spectrum decomposition and its application in fault diagnosis of rotating machinery under varying speed

Rotating machinery fault signals often consist of multiple components with time varying frequencies under variable speed conditions. Spectral overlap exists among these components, making it difficult to independently separate the features of the components. Singular spectrum decomposition (SSD), a singular spectrum analysis-based signal decomposition method, has shown its great potential in suppressing background noise and extracting fault-related components in complex background noise environments. However, SSD is a frequency domain decomposition method with equivalent filtering characteristics, and it is susceptible to the mode mixing when processing signals with spectral overlap. Moreover, the choice of a key parameter in the iteration decomposition process of SSD, the embedding dimension, is determined using an empirical formula, which might cause suboptimal decomposition outcomes. To address these issues, this paper proposes a generalized adaptive singular spectrum decomposition (GASSD) method, which combines generalized demodulation with improved embedding dimension selection for SSD. GASSD incorporates SSD into the framework of adaptive generalized demodulation to separate specific frequency domain features. Firstly, for an effective generalized demodulation analysis, a region block synchronous ridge extraction method is proposed to accurately estimate the instantaneous frequency ridges from the time-frequency plane, which helps construct proper demodulation phase functions. Secondly, to achieve optimal analysis of SSD, a Gini moderation decomposition index is designed to improve the construction of the trajectory matrix by determining an appropriate embedding dimension. Finally, the reliability of the proposed method is demonstrated by analyzing wind turbine generator bearing fault signals and rotor rubbing fault signals.

Adaptive spectrum segmentation Ramanujan decomposition and its application to gear fault diagnosis

Ramanujan Fourier mode decomposition (RFMD) is a novel non-stationary signal decomposition method, which can decompose a complex signal into several components and extract the periodic characteristics of the signal. However, the mode generation method adopted by RFMD does not consider the physical meaning of the component signal, which makes over-decomposition when dealing with real-life gear signals with complex modulation characteristics, thus destroying the integrity of the signal sideband, increasing the difficulty of subsequent analysis, and even losing key fault information. The iterative envelope-segmentation algorithm combines the modulation characteristics of the local fault gear signal and divides the original signal into a limited number of dominant frequency bands containing the modulation region in the Fourier spectrum, thereby ensuring that the obtained frequency bands contain rich fault information. Based on the above algorithm, a new adaptive decomposition method is proposed in this paper, which is adaptive spectrum segmentation Ramanujan decomposition (ASSRD). ASSRD uses fault envelope harmonic noise ratio as the index to evaluate the fault information content of component signals and uses it to assist the iterative envelope-segmentation algorithm to complete the adaptive segmentation of the Fourier spectrum. Finally, based on the segmentation result, the inverse RFT reconstruction of each frequency band is performed. Thus, the signal is decomposed into a finite number of component signals containing rich fault information. In addition, through the experiment on the gear simulation signal and the measured crack fault gear signal, the ASSRD method is compared with the original RFMD method and the existing ensemble empirical mode decomposition (EMD), variational mode decomposition, empirical wavelet transform, and singular spectrum decomposition method, verifying the feasibility and superiority of ASSRD in gear fault diagnosis. Besides, a comparative experiment based on compound faults diagnosis is carried out, in which ensemble EMD, Fourier decomposition method, empirical wavelet transform, and sparse decomposition are involved. The results show that the proposed method can extract the local fault information in the gear signal more effectively, and the performance is better than the comparison method.

Expanding non-axisymmetric beams in spherical coordinates with cylindrical wave spectrum decomposition

Description of structured beams in spherical coordinates is critical in studying the interaction between beams and spherical particles. The work extends the cylindrical wave spectrum decomposition (CWSD) method to non-axisymmetric beams, applied herein to the elliptical Gaussian beam, cosine Gauss beam and Hermite-Gauss beam as examples. It is shown that for these beams the beam shape coefficients (BSCs) can be expressed in one dimensional integrations and hence numerical calculations can be performed very efficiently. The beam fields reproduced by using these BSCs show satisfactory faithfulness to the rigorous expression of the given fields. Typically, the difference between them is less than 10−8.

Particle Scattering Induced Orbital Angular Momentum Spectrum Change of Vector Bessel–Gaussian Vortex Beam

In this paper, we obtain the intensity and phase distributions of the scattering and external fields of a vector Bessel–Gaussian vortex beam in the far-field region after being scattered by a particle. In our analysis, we use the Generalized Lorenz–Mie theory (GLMT) and the angular spectrum decomposition method (ASDM). The orbital angular momentum (OAM) spectra of the fields are analyzed by using the spiral spectrum expansion method, which is a frequently used tool for studying the propagation of vortex beams in turbulent atmospheres. Both scattered and external fields show a significant difference in spiral spectra for particles with different characteristic parameters, such as the size and complex refractive index. We also examine sampling the phase along with a circle and show that it is unable to fully express the information of the fields. This study can provide a theoretical basis for the inversion of characteristic parameters of the Bessel–Gaussian vortex beam and spherical particle by OAM spectra with applications in remote sensing engineering.

Universal time-domain Prony fitting decomposition for optimized hierarchical quantum master equations.

In this Communication, we propose the time-domain Prony fitting decomposition (t-PFD) as an accurate and efficient exponential series method, applicable to arbitrary bath correlation functions. The resulting numerical efficiency of hierarchical equations of motion (HEOM) formalism is greatly optimized, especially in low temperature regimes that would be inaccessible with other methods. For demonstration, we calibrate the present t-PFD against the celebrated Padé spectrum decomposition method, followed by converged HEOM evaluations on the single-impurity Anderson model system.

Scattering of Laguerre-Gauss light beam by a sphere: the angular spectrum decomposition method and a comparison with the localized approximation method

Evaluation of the beam shape coefficients (BSC) in the spherical wave expansion of the incident beam is vital in analyzing light scattering by spherical particles. Different methods have been developed for this purpose. In this work, the formulas of the BSCs for the Laguerre-Gauss beam (LGB) are derived in the angular spectrum decomposition (ASD) method. Under the paraxial condition, these ASD-BSCs are approximated to the expressions in either series or single integrals. Besides, the BSCs for the LGB are also obtained in the localized approximation (LA) method. It is found that the approximate ASD-BSCs are same as those LA-BSCs. Numerical calculation is implemented for verifying the BSC calculations. The validity of the approximate BSC calculation is discussed, together with the distribution of the angular spectrum of the beam. The work offers another example of the shaped beams for mathematically justifying the LA method and suggests another way to discuss the validity of the LA method.

Angular spectrum decomposition method and quadrature method in the generalized Lorenz–Mie theory for evaluating the beam shape coefficients of TEM[formula omitted] doughnut beam

The evaluation of beam shape coefficients (BSCs) which encodes the description of the illuminating beam is an essential issue in light scattering theories of spherical particles, such as the generalized Lorenz–Mie theory (GLMT). Different methods have been developed in this context, including the traditional (quadratures, finites series, localized approximations), to be complemented by use of the angular spectrum decomposition (ASD). The present paper is devoted to a comprehensive study of the relationship between the traditional quadrature method and the ASD method to the evaluation of BSCs. We shall establish that evaluation of BSCs using the quadrature method can be modified into expressions in the spectral space, leading to the same results as those obtained using the ASD. These BSCs are afterwards approximated under the paraxial conditions, leading to the same results as these obtained by using the localized approximations. The TEM0l∗ doughnut beam is taken as an example of the shaped beam and the theoretical analysis is confirmed by numerical calculations.

Angular spectrum representation of the Bessel-Gauss beam and its approximation: A comparison with the localized approximation

The angular spectrum representation of the vector Bessel-Gauss beam is used for discussing the connection between the angular spectrum decomposition (ASD) method and the quadrature method of the generalized Lorenz-Mie theory (GLMT). Under the paraxial condition, the beam shape coefficients (BSCs) obtained in the ASD method can be approximated to the same expressions as those obtained in the localized approximation method. The validity of the approximate method for evaluating the BSCs is numerically studied, based on both the beam's angular spectrum and the off-axis distance.

Attenuation characteristics of Bessel Gaussian vortex beam by a wet dust particle

The potential applications of complex optical fields for environmental detection have attracted a lot of attention. In this study, dusty medium is equivalent to a uniformly charged sphere and a non-uniform concentric layered sphere that satisfying the single scattering condition, respectively. The interaction between a high-order polarized Bessel Gaussian beam and a spherical particle is investigated using the generalized Lorenz–Mie theory and the angular spectrum decomposition method. The location of incident beam is considered for the first time. The extinction efficiency results of a wet charged particle are compared with those of a wet neutral particle. Simulations show that the difference in extinction between these two kinds of particles mentioned above is more evident in the smaller size parameter range, which is similar to the case of plane wave incidence. In addition, the influence of complex refractive index and size proportion of heterogeneous medium on the extinction effect is analyzed. The characteristic parameters of the incident beam are considered and find out that how they affect the differences in extinction is independent of the illuminated particle. This study lays the foundation for analyzing the transmission capacity of a Bessel Gaussian vortex beam with various parameters in a dust particle cluster.

Cylindrical wave spectrum decomposition method for evaluating the expansion coefficients of the shaped beams in spherical coordinates

In the analysis of light scattering by spherical particles, the incident beam is expanded into an infinite series of spherical wave functions weighted by the beam shape coefficients (BSCs). Different techniques have been developed for evaluating the BSCs in the context of generalized Lorenz-Mie theory (GLMT). In this work, the spectrum decomposition method which we call cylindrical wave spectrum decomposition (CWSD) is recast and is extended to beams having simple dependence on the azimuth angle. The method first expands the beam field in the cylindrical coordinate system and then expands the cylindrical waves into the spherical waves based on the relations between the cylindrical and spherical waves. The CWSD method offers a deep insight into the effects of the beam distribution and the beam's location to the BSCs. Numerical calculations are performed to verify the method. The CWSD method may serve as a powerful tool for studying the light scattering, in the similar way to the angular spectrum decomposition (ASD) method.

Scattering of arbitrary-shaped optical polarized beams by a PEMC sphere

The generalized Lorenz-Mie theory (GLMT) for a laser beam of arbitrary shape illuminating a perfect electromagnetic conductor (PEMC) sphere is presented. Making use of the vector angular spectrum decomposition method (VASDM), and the multipole expansion method (MEM), in which any beam is expressed in terms of vector spherical wave functions (VSWFs) and beam shape coefficients (BSCs), the BSCs are obtained and expressed by a vector angular spectrum. The incident and scattering waves are expanded using VSWFs. A relation between the coefficients of the scattering fields and the BSCs of the incident beam is established considering the appropriate boundary conditions at the surface of the PEMC sphere. Expressions for the extinction, scattering, and absorption cross-sections are derived and computed. By isolating the co-polarization and cross-polarization components of the scattering coefficients, individual expressions of these physical quantities are also provided. Considering the vector Bessel and Airy polarized beams as examples, the total electric field intensity, scattering cross-section and its co-polarized and cross-polarized components are numerically computed and discussed. The effects of beam polarization, size parameter of the sphere, the admittance M, and beam parameters are analyzed. It has been found that the intensity and distribution of the total (incident + scattered) electric field intensity in the transverse (yz) plane depends on the incident beam characteristics and its polarization states. As the dimensionless size ka increases, the amplitude of the scattering cross-section increases and then decreases as ka increases. As the admittance parameter M changes, there are different characteristics if the incident beam is different. Nonetheless, there is a common behavior that the trend of the co-polarized component of the scattering cross-section decreases first and then increases regardless of the beam and its polarization state. When it comes to the trend of the cross-polarized component versus M, it is opposite to that of the co-polarized component. A few resonance peaks are manifested in the plots when the incident beam is radially or azimuthally polarized. The results may have promising applications in scattering, particle manipulation, optical trapping, and other related researches dealing with a sphere exhibiting rotary polarization.

A robust approach for outlier imputation: Singular spectrum decomposition

Singular spectrum analysis (SSA) is a nonparametric method for separating time series data into a sum of small numbers of interpretable components (signal + noise). One of the steps of the SSA method, which is referenced to Embedding, is extremely sensitive to contamination of outliers which are often founded in time series analysis. To reduce the effect of outliers, SSA based on Singular Spectrum Decomposition (SSD) method is proposed. In this article, the ability of SSA based on SSD and basic SSA are compared in time series reconstruction in the presence of outliers. It is noteworthy that the matrix norm used in Basic SSA is the Frobenius norm or L 2-norm. There is a newer version of SSA that is based on L 1-norm and called L 1-SSA. It was confirmed that L 1-SSA is robust against outliers. In this regard, this research is also introduced a new version of SSD based on L 1-norm which is called L 1-SSD. A wide empirical study on both simulated and real data verifies the efficiency of basic SSA based on SSD and L 1-norm in reconstructing the time series where polluted by outliers.

Research on anti-Narrowband AM jamming of Ultra-wideband impulse radio detection radar based on improved singular spectrum analysis

Considering the problem that the ultra-wideband detection system is susceptible to be jammed, the mechanism of narrowband suppressive jamming on ultra-wideband radio impulse detection radar is mathematically analyzed at first in this paper. As typical suppressive jamming, the noise amplitude modulation signal is selected as research object, and the average signal-to-jamming is defined as an evaluation index. Simulation results show that the center frequency of jamming signal has the most significant influence on the impulse signal among a series of optimal jamming parameters. Afterwards, combined with genetic algorithm, an optimized singular spectrum decomposition method is proposed to realize adaptive extraction of the impulse signal. Error of the reconstructed signal based on proposed method is much smaller than that of threshold methods. The results provide a reference for subsequent anti-jamming and waveform optimization.

Comparison of a standard elliptical Bessel beam and a refracted circular Bessel beam at oblique incidence

An analytical expression of an elliptical Bessel beam (EBB) is deduced on the basis of the angular spectrum decomposition (ASD) method, starting from an elliptical Bessel-like profile in the initial transverse plane. The angular spectrum representation is also obtained for another approximate EBB that is produced by the refraction of a circular Bessel beam at an interface in oblique incidence. The expressions are further expanded into a series of vector spherical harmonic functions for describing the scattering of the beams by a spherical particle. Numerical calculations are implemented with different parameters and the results are discussed. A length parameter is obtained for evaluating the variation of the EBB along the propagation. It is confirmed that the refracted CBB at small incident angle behaves in a similar way to the EBB. When the incident angle increases, the asymmetry of the transverse beam profile becomes serious and the propagation of the beam deviates gradually from the predicted direction.

Fault Diagnosis of Wind Turbine Bearing Based on Optimized Adaptive Chirp Mode Decomposition

Periodic impacts are considered as the important defect signatures of wind turbine bearing. However, it is difficult to separate the weak periodic impacts from collected signal under serious interference environment. Facing with this issue, the recently developed signal processing technique named adaptive chirp mode decomposition (ACMD) is firstly introduced into the fault diagnosis field of wind turbine bearing. And the influences of instantaneous frequency and weighting coefficient parameters of ACMD are researched through simulated fault signal. In additional, the L-kurtosis fluctuation spectrum (LFS) guided instantaneous frequency selection strategy and the cuckoo search algorithm (CSA) guided weighting coefficient determination strategy are respectively put forward to automatically confirm the optimal influencing parameters without requiring priori knowledge. Combined with these two specific strategies, an innovation optimized adaptive chirp mode decomposition (OACMD) method is further proposed for defect identification of wind turbine bearing. The experimental signals and the engineering signal are in turn adopted to demonstrate the reliability of this proposed diagnostic method. The obtained analysis results show that the informative target mode with obvious periodic impact signatures can be effectively extracted, and the key defect characteristic frequencies are able to be successfully identified. Furthermore, the conventional spectral kurtosis method, the minimum entropy deconvolution method and the singular spectrum decomposition method are respectively employed for performance comparison. And it is validated that the proposed OACMD method has outstanding advantage on weak defect detection of wind turbine bearing.

Scattering of a non-paraxial Bessel pincer light-sheet by a dielectric sphere of arbitrary size

The scattering of a non-paraxial Bessel pincer light-sheet by a dielectric sphere of arbitrary size is studied in the framework of generalized Lorenz-Mie theory (GLMT). The electrical field of the Bessel pincer light-sheet is expanded using the vector angular spectrum decomposition method (VASDM), and its beam shape coefficients (BSCs) are derived using the method of multipole expansion and vector spherical wave functions (VSWF). By this way, the incident field, scattering field and near-surface field, and absorption and extinction efficiency factors are numerically calculated. Also, the effects of the beam order, scaling parameter, and polarization are mainly discussed. Numerical results represent that the intensity distribution of incident field, scattering field and near-surface field is intensely sensitive to the scaling parameters and the beam order. For the incident field, the bigger the order, the smaller the bending angle, and the closer the focus is to the source. By contrast, for the scattering and total field, the bigger the order, the larger the bending angle, and the farther the focus is to the source. Such results have potential applications in the imaging around steep corners and particle manipulation applications with minimal obstruction by particles.