Zero-frequency Component Research Articles

Investigation of the Zero-Frequency Component of Nonlinear Lamb Waves in a Symmetrical Undulated Plate.

When an ultrasonic pulse propagates in a thin plate, nonlinear Lamb waves with higher harmonics and a zero-frequency component (ZFC) will be generated because of the nonlinearity of materials. The ZFC, also known as the static displacement or static component, has its unique application on the evaluation of early-stage damages in the elastic symmetrical undulated plate. In this study, analysis of the excitation mechanism of the ZFC and the second harmonic component (SHC) was theoretically and numerically investigated, and the material early-stage damage of a symmetrical undulated was characterized by studying the propagation of nonlinear Lamb waves. Both the ZFC and SHC can be effectively employed in monitoring the material damages of the undulated plate in its early stage. However, several factors must be considered for the propagation of the SHC in an undulated plate because of the geometric curvature and interference between the second harmonics during propagation, preventing efficient application of this technique. If the fundamental wave can propagate in the plate regardless of the plate boundary conditions, an accumulative effect always exists for the ZFC in a thin plate, indicating that the ZFC is independent of the structural geometry. This study reveals that the ZFC-based inspection technique is more efficient and powerful in characterizing the damages of a symmetrical undulated plate in the early stage of service compared to the second harmonic method.

Micro-crack in solids evaluation based on zero-frequency component of the critically refracted longitudinal wave

Abstract Micro-crack in engineering materials may cause subtle changes in mechanical properties, which can lead to serious engineering accidents. It is of great significance to study the identification of micro-cracks. In this paper, it is discovered that when the critically refracted longitudinal (LCR) wave propagates in elastic solids containing micro-crack, the waveform of ultrasonic waves becomes distorted, resulting in the generation of a zero-frequency component. The generated zero-frequency component provides a new research idea for micro-crack detection. Firstly, the paper derives the wave equation for nonlinear LCR wave and provides a preliminary analytical solution with a zero-frequency component. Subsequently, through a combined approach involving numerical simulation and experimental observation, along with micro-crack modeling, the study delves deeper into the acoustic nonlinear characteristics of the zero-frequency component under the breathing behavior of micro-crack. Finally, both numerical simulation and experimental methods show that the zero-frequency component based on LCR wave is feasible to detect micro-crack, and it is also proved that the zero-frequency component has higher sensitivity to micro-crack damage than the second and third harmonics.

Background-extracted extended Kalman filter-based phase shift estimation algorithm for phase shifting profilometry system

The accuracy of phase shift in the phase-measuring profilometry (PMP) directly affect the result of the three-dimensional reconstruction. A robust phase shifting estimation method based on the extended Kalman filter (EKF) is proposed to address the imprecise phase shift induced by the mechanical projector and dynamic object. Unlike the traditional fringe projection profilometry (FPP) in which the zero frequency is suppressed and the fundamental frequency is extracted, the zero-frequency component is extracted by using two-dimensional variational mode decomposition and bidimensional empirical mode decomposition (2D-VMD-BEMD) algorithm, and is used to establish the predicted observations of the measurement process in the EKF. The coefficient of the quadratic phase in a selected window is employed to estimate the actual phase step by using EKF and subsequently the accurate reconstructed phase map is obtained. This paper develops a novel 2D-VMD-BEMD EKF estimator to evaluate the actual phase shift and enhance the accuracy of the phase reconstruction, and simultaneously provides a reliable and effective method for the extraction of background under unfavorable conditions. Simulation and experimental results demonstrate that the proposed region-wise estimation method effectively removes the effect of the unexpected phase shift, and can be widely available for N-step phase shifting algorithm in phase shifting profilometry.

Resolution enhancement via guided filtering for spatial-frequency multiplexing single-shot high-speed imaging.

The frequency recognition algorithm for multiple exposures (FRAME) is a progressive single-shot high-speed videography technique that employs the spatial-frequency multiplexing concept to provide high temporal and spatial resolution. However, the inherent crosstalk from the zero-frequency component to the carrier-frequency component leads to resolution degradation and artifacts. To improve recovered frames' quality, we propose a FRAME reconstruction method using guided filters for a removal of the zero-frequency component, which can minimize the artifacts while enhance spatial resolution. A total variation (TV) denoising operation is involved to remove artifacts further to achieve optimized performances. Simulations and experiments were conducted to demonstrate the robust and efficient post-processing capability of the proposed method. With a two-frame experimental system, the results of a USAF 1951 resolution target reveal a 1.8-fold improvement in spatial resolution from 16 lp/mm to 28.5 lp/mm. For complex dynamic scenarios, the wide field of high-speed fuel spray was shot and the proposed method can resolve two droplets with a 30 μm distance which outperforms the traditional method.

Suppressing the Zero-Frequency Components in Single Quantitative Phase Imaging by Filtering the Low-Frequency Intrinsic Mode Function Components

In off-axis quantitative phase imaging, existing methods of suppressing the zero-frequency component (ZFC) always cause the loss of high-frequency phase information, thus degrading the accuracy of phase reconstruction. To overcome these problems, this paper proposes to preserve the high-frequency information by filtering the intrinsic mode function. In this method, empirical mode decomposition is employed to decompose the interferometric image into a series of intrinsic mode function (IMF) components from high to low frequencies. The decomposed low-frequency IMF components are processed by Gaussian high-pass filters for ZFC suppression, and the high-frequency IMF components and the filtered low-frequency IMF components are combined to obtain the reconstructed hologram. Hilbert transform is then performed on the reconstructed hologram to filter out the conjugate image, leaving only the original image. In order to verify the performance of our proposed method, the phase maps processed by our proposed method are compared with those processed by the Fourier filtering method, wavelet transform-based method and Laplace operator method. The experimental results show that the proposed method not only suppresses ZFC but also achieves higher accuracy in phase reconstruction.

Locating mutation damage based on the zero-frequency component of nonlinear Lamb waves

Degradation, such as micro-voids, dislocation, persistent bands, and micro-cracks, can give rise to local material nonlinearity and cause early-stage material local damage. The material nonlinearity of a plate can be represented as a distribution function. Depending on whether the nonlinearity distribution function of a plate is smooth or not, early-stage material local damage can be divided into gradual and mutation damage. Gradual damage is usually caused by lattice distortion, and the nonlinearity distribution function is smooth. In contrast, mutation damage is usually induced by a discontinuous interface, and the nonlinearity distribution function is not smooth but stepped. Mutation damage is more harmful than gradual damage. To ensure safety, it is important to locate and evaluate mutation damage. The conventional nonlinear Lamb wave technique has limitations in resolving the location and spatial distribution of mutation damage owing to several reasons. To address these issues, a novel method for locating mutation damage based on the zero-frequency component is proposed in this paper. The theoretical solution of the zero-frequency component generated by the Lamb wave pulse is derived based on certain ideal assumptions. Other complex behaviors of the zero-frequency component can be understood by the contribution of this theory. The region of mutation damage is modeled by enhancing local three-order elastic coefficients, and mutation damage can be located simply and efficiently by using the proposed zero-frequency component-based method. The proposed damage detection based on the zero-frequency component of nonlinear Lamb waves has significant advantages compared to the second harmonic and mixing-wave detection techniques.

Decreased breathing variability is associated with poorer outcome in mechanically ventilated patients.

Breathing is a cyclic activity that is variable by nature. Breathing variability is modified in mechanically ventilated patients. We aimed to evaluate whether decreased variability on the day of transition from assist-control ventilation to a partial mode of assistance was associated with a poorer outcome. This was an ancillary study of a multicentre, randomised, controlled trial comparing neurally adjusted ventilatory assist to pressure support ventilation. Flow and the electrical activity of the diaphragm (EAdi) were recorded within 48 h of switching from controlled ventilation to a partial mode of ventilatory assistance. Variability of flow and EAdi-related variables were quantified by the coefficient of variation, the amplitude ratio of the spectrum's first harmonic to its zero-frequency component (H1/DC) and two surrogates of complexity. 98 patients ventilated for a median duration of 5 days were included. H1/DC of inspiratory flow and EAdi were lower in survivors than in nonsurvivors, suggesting a higher breathing variability in this population (for flow, 37% versus 45%, p=0.041; for EAdi, 42% versus 52%, p=0.002). By multivariate analysis, H1/DC of inspiratory EAdi was independently associated with day-28 mortality (OR 1.10, p=0.002). H1/DC of inspiratory EAdi was lower in patients with a duration of mechanical ventilation <8 days (41% versus 45%, p=0.022). Noise limit and the largest Lyapunov exponent suggested a lower complexity in patients with a duration of mechanical ventilation <8 days. Higher breathing variability and lower complexity are associated with higher survival and lower duration of mechanical ventilation.

Measuring fine molecular structures with luminescence signal from an alternating current scanning tunneling microscope

In scanning tunneling microscopy-induced luminescence (STML), the photon count is measured to reflect single-molecule properties, e.g., the first molecular excited state. The energy of the first excited state is typically shown by a rise of the photon count as a function of the bias voltage between the tip and the substrate. It remains a challenge to determine the precise rise position of the current due to possible experimental noise. In this work, we propose an alternating current version of STML to resolve the fine structures in the photon count measurement. The measured photon count and the current at the long-time limit show a sinusoidal oscillation. The zero-frequency component of the current shows knee points at the precise voltage as the fraction of the detuning between the molecular gap and the DC component of the bias voltage. We propose to measure the energy level with discontinuity of the first derivative of such a zero-frequency component. The current method will extend the application of STML in terms of measuring molecular properties.

Поправка к статье Усиление электрической площади импульса при отражениях от движущегося зеркала" Оптика и спектроскопия 130 (9), 1402--1404 (2022)

It is indicated that sets of plane-parallel layers of linear materials do not reflect the zero-frequency component of the incident pulse and therefore cannot serve as mirrors for unipolar pulses. The amplification of the electric area is possible with Fresnel reflection from an unlimited medium with a refractive index lower than that of the medium in which the incident pulse propagates. The same is realized in the case of a thick layer of such a medium with the exclusion of the influence of reflection by its rear face due to the slope or roughness of the face. The movement of the boundary does not lead to an additional amplification of the electric area, since the increase in the peak amplitude of the wave upon reflection is compensated by a decrease in the pulse duration.

Complex-amplitude single-pixel imaging using coherent structured illumination

This research presents a coherent structured illumination single-pixel imaging scheme to image objects with complex amplitudes. By utilizing a phase-only spatial light modulator for phase modulation, we can efficiently generate the Hadamard basis structured light and the reference light that interfere with each other to form the coherent structured illumination. Using the 4-step phase-shifting, the spectrum of the object is acquired by detecting the zero-frequency component of the object light with a single-pixel photodetector. The desired complex-amplitude image can be further retrieved by applying an inverse Hadamard transform. The proposed scheme is experimentally demonstrated by imaging two etched glass objects, a dragonfly wing, and a resolution test chart. Benefiting from the phase modulation, this scheme has a high efficiency, a high imaging quality, a high spatial resolution, and a simple and stable configuration to obtain both the phase and amplitude information of the target object. The proposed scheme provides a promising complex-amplitude imaging modality with single-pixel detection. Thus it might find broad applications in optical metrology and biomedical science.

Coherence control of directional nonlinear photocurrent in spatially symmetric systems

The interplay between crystal symmetry and its optical responses is at the heart of tremendous recent advances in light-matter interactions and applications. Nonlinear optical processes that produce electric currents, for example the bulk photovoltaic (BPV) effect, require inversion-symmetry-broken materials, such as ferroelectrics. In this work, we demonstrate that such BPV current could be generated in centrosymmetric materials with excitation of out-of-equilibrium coherent phonons. This is very different from the generally studied static or thermally excited states. We show that depending on the coherent phonon phase factor, the photoconductivity contains a static zero-frequency component, as well as THz frequency components. This indicates that a unidirectional current may emerge under synergistic effects of atomic vibration and light irradiation. We also generalize the conventional injection charge current into angular momentum (spin and orbital) degrees of freedom, and demonstrate spin and orbital BPV photoconductivities under coherent phonons. Our findings open the pathway to exploring the exotic phonon-photon-electron coherent interactions in quantum materials.

Stochastic Parker Spirals in the Solar Wind

Abstract An analytic model for the angular dispersion of magnetic field lines resulting from the turbulence in the solar wind and at the solar source surface is presented. The heliospheric magnetic field lines in our model are derived from a Hamiltonian with the pair of canonically conjugated variables the cosine of the heliographic colatitude μ and the longitude ϕ. In the diffusion approximation, the Parker spirals are modeled by a set of stochastic differential equations for θ and ϕ as functions of r. These stochastic Parker spirals are realizations of a standard random walk on a sphere of increasing radius, superimposed on an angular drift due to solar rotation. The Green function solution of the Fokker–Planck equation describing the angular diffusion of the field line density is obtained in terms of spherical harmonics. Magnetic field lines traced from an observer back to the Sun are realizations of a Brownian bridge. Our model incorporates the effect of the random footpoint motions at the source surface, which is associated with the zero-frequency component of the solar wind turbulence. Assuming that the footpoint motion is diffusive, its contribution to the angular diffusivity of the stochastic Parker spirals is then given by the angular diffusivity of the footpoints divided by the solar wind speed and is controlled by a unique parameter, which is the Kubo number.

A Protection Method of VSC-HVDC Cables Based on Generalized S-Transform

Generalized S-transform is a time-frequency analysis method which has higher resolution than S-transform. It can precisely extract the time-amplitude characteristics of different frequency components in the signal. In this paper, a novel protection method for VSC-HVDC (Voltage source converter based high voltage DC) based on Generalized S-transform is proposed. Firstly, extracting frequency component of fault current by Generalized S-transform and using mutation point of high frequency to determine the fault time. Secondly, using the zero-frequency component of fault current to eliminate disturbances. Finally, the polarity of sudden change currents in the two terminals is employed to discriminate the internal and external faults. Simulations in PSCAD/EMTDC and MATLAB show that the proposed method can distinguish faults accurately and effectively.

Improved Field Theoretical Approach to Noninteracting Brownian Particles in a Quenched Random Potential

We construct a dynamical field theory for noninteracting Brownian particles in the presence of a quenched Gaussian random potential. The main variable for the field theory is the density fluctuation which measures the difference between the local density and its average value. The average density is spatially inhomogeneous for given realization of the random potential. It becomes uniform only after averaged over the disorder configurations. We develop the diagrammatic perturbation theory for the density correlation function and calculate the zero-frequency component of the response function exactly by summing all the diagrams contributing to it. From this exact result and the fluctuation dissipation relation, which holds in an equilibrium dynamics, we find that the connected density correlation function always decays to zero in the long-time limit for all values of disorder strength implying that the system always remains ergodic. This nonperturbative calculation relies on the simple diagrammatic structure of the present field theoretical scheme. We compare in detail our diagrammatic perturbation theory with the one used in a recent paper [B.\ Kim, M.\ Fuchs and V.\ Krakoviack, J.\ Stat.\ Mech.\ (2020) 023301], which uses the density fluctuation around the uniform average, and discuss the difference in the diagrammatic structures of the two formulations.

The zero-frequency component of bulk waves in solids with randomly distributed micro-cracks

When a longitudinal wave (bulk wave) propagates in elastic solids with randomly distributed micro-cracks, the acoustic nonlinear behavior including the zero-frequency component and higher harmonics can be generated due to the clapping and slipping behavior of micro-cracks. In this paper, the analytical solution based on the bi-linear stiffness model of micro-cracks and the numerical simulation with random micro-crack modeling are implemented to investigate the behavior of the zero-frequency component. The theoretical and numerical results both show that the zero-frequency component of bulk waves can be generated by the micro-cracks, which is more sensitive than the conventional second harmonics. Meanwhile, we find that the acoustic nonlinearity parameter based on the zero-frequency component increases linearly with the crack density, the length of the micro-crack region and the fundamental frequency in the low-frequency region. Moreover, the zero-frequency component of the reflected waves is also investigated, indicating it can be used to locate the micro-crack region.

Lacunarity of the zero crossings of Gaussian processes.

A lacunarity analysis of the zero crossings derived from Gaussian stochastic processes with oscillatory autocorrelation functions is evaluated and reveals distinct multiscaling signatures depending on the smoothness and degree of anticorrelation of the process. These bear qualitative similarities and quantitative distinctions from an oscillatory deterministic signal and a Poisson random process both possessing the same mean interval size between crossings. At very small and large scales compared with the correlation length of the random processes, the lacunarity is similar to the Poisson but exhibits significant departures from Poisson behavior if there is a zero-frequency component to the process's power spectrum. A comparison of exact results with the gliding box technique that is frequently used to determine lacunarity demonstrates its inherent bias.

Short-time series optical coherence tomography angiography and its application to cutaneous microvasculature.

We present a new optical coherence tomography (OCT) angiography method for imaging tissue microvasculature in vivo based on the characteristic frequency-domain flow signature in a short time series of a single voxel. The angiography signal is generated by Fourier transforming the OCT signal time series from a given voxel in multiple acquisitions and computing the average magnitude of non-zero (high-pass) frequency components. Larger temporal variations of the OCT signal caused by blood flow result in higher values of the average magnitude in the frequency domain compared to those from static tissue. Weighting of the signal by the inverse of the zero-frequency component (i.e., the sum of the OCT signal time series) improves vessel contrast in flow regions of low OCT signal. The method is demonstrated on a fabricated flow phantom and on human skin in vivo and, at only 5 time points per voxel, shows enhanced vessel contrast in comparison to conventional correlation mapping/speckle decorrelation and speckle variance methods.

Holographic pump probe spectroscopy

We study the non-linear response of a 2+1 dimensional holographic model with weak momentum relaxation and finite charge density to an oscillatory electric field pump pulse. Following the time evolution of one point functions after the pumping has ended, we find that deviations from thermality are well captured within the linear response theory. For electric pulses with a negligible zero frequency component the response approaches the instantaneously thermalizing form typical of holographic Vaidya models. We link this to the suppression of the amplitude of the quasinormal mode that governs the approach to equilibrium. In the large frequency limit, we are also able to show analytically that the holographic geometry takes the Vaidya form. A simple toy model captures these features of our holographic setup. Computing the out-of-equilibrium probe optical conductivity after the pump pulse, we similarly find that for high-frequency pulses the optical conductivity reaches its final equilibrium value effectively instantaneously. Pulses with significant DC components show exponential relaxation governed by twice the frequency of the vector quasinormal mode that governs the approach to equilibrium for the background solution. We explain this numerical factor in terms of a simple symmetry argument.

Image quality analysis method under background radiation in turbid atmosphere

Image quality is seriously degraded when propagating through the turbid atmosphere. It is practical to characterize the degradation process in terms of modulation transfer function (MTF). The MTF can describe the effect of the turbid medium on imaging quantitatively in spatial frequency domain, including attenuation and multiple scattering. It is inherent property of the turbid medium. The whole spatial frequency characteristic of the turbid atmosphere MTF can be acquired through the equivalence principle, i, e., the equivalence between the MTF of a turbid medium and the transmitted radiance from the medium under isotropic diffuse illumination. In practice, the image quality is not only affected by the turbid medium MTF but also related tightly to the background radiation. The influence of scattered background radiation on imaging was almost not considered in the past when dealing with the imaging problem in the turbid atmosphere. In this paper, this issue is considered in detail. The analysis results demonstrate that the scattered background radiation increases the zero frequency component of image in spatial frequency domain. As a result, it degrades the image contrast seriously in spatial domain. Based on the optical model of image degradation in the atmosphere, the theoretical analysis is carried out to study the image quality degradation process in spatial frequency domain. The formalized MTF is proposed, which considers the effects of attenuation, multiple scattering and scattered background radiation by the turbid medium on image quality. The quantitative relation among the formalized MTF, turbid medium MTF and background radiation is confirmed. Image blur simulations show that the results from the formalized MTF are more consistent with actual scenes than results only from turbid medium MTF. Thus, the formalized MTF can describe the image degradation process through atmosphere comprehensively. The image restoration results indicate that the formalized MTF method performs better than dark channel prior method. In order to evaluate different image restoration methods effectively in spatial frequency domain, spectrum area (AS) is proposed. The AS is the area of middle-high frequency information of the region of interest in restored image. So AS can represent the scene details in the restored image. The higher the AS, the better the image quality is, which is demonstrated in this paper. In conclusion, the formalized MTF provides a more effective method for image quality analysis and assessment. Additionally, it also supplies a new standpoint for researching atmospheric degradation mechanism and correction method for imaging in turbid atmosphere. Then, AS can be an effective reference for correction to the method evaluation.

Time reversal invariance for a nonlinear scatterer exhibiting contact acoustic nonlinearity

The time reversal invariance of an ultrasonic plane wave interacting with a contact interface characterized by a unilateral contact law is investigated analytically and numerically. It is shown analytically that despite the contact nonlinearity, the re-emission of a time reversed version of the reflected and transmitted waves can perfectly recover the original pulse shape, thereby demonstrating time reversal invariance for this type of contact acoustic nonlinearity. With the aid of finite element modelling, the time-reversal analysis is extended to finite-size nonlinear scatterers such as closed cracks. The results show that time reversal invariance holds provided that all the additional frequencies generated during the forward propagation, such as higher harmonics, sub-harmonics and zero-frequency component, are fully included in the retro-propagation. If the scattered waves are frequency filtered during receiving or transmitting, such as through the use of narrowband transducers, the recombination of the time-reversed waves will not exactly recover the original incident wave. This discrepancy due to incomplete time invariance can be exploited as a new method for characterizing damage by defining damage indices that quantify the departure from time reversal invariance. The sensitivity of these damage indices for various crack lengths and contact stress levels is investigated computationally, indicating some advantages of this narrowband approach relative to the more conventional measurement of higher harmonic amplitude, which requires broadband transducers.