Born Series Research Articles

Cause of inaccuracies in the Padé approximant of the Born series for strong electromagnetic scattering problems

Cause of inaccuracies in the Padé approximant of the Born series for strong electromagnetic scattering problems

Mask structure optimization for beyond EUV lithography.

Beyond extreme ultraviolet (BEUV) lithography with a 6 × nm wavelength is regarded as a future technique to continue the pattern shirking in integrated circuit (IC) manufacturing. This work proposes an optimization method for the mask structure to improve the imaging quality of BEUV lithography. Firstly, the structure of mask multilayers is optimized to maximize its reflection coefficient. Then, a mask diffraction near-field (DNF) model is established based on the Born series algorithm, and the aerial image of BEUV lithography system can be further calculated. Additionally, the mask absorber structure is inversely designed using the particle swarm optimization (PSO) algorithm. Simulation results show a significant improvement of the BEUV lithography imaging obtained by the proposed optimization methods. The proposed workflow can also be expanded to areas of EUV and soft x ray imaging.

Analysis of capacitive discharges in motor bearings under different operation conditions

AbstractDespite being a well‐known problem, bearing faults are still one of the major challenges that the industry face. The growing use of voltage source inverters imposed the alertness of possible bearing damage due to their high‐frequency signals. The aim of this paper is to investigate the effect of capacitive discharges on a rolling element bearing to obtain a series of faulty bearings with different deterioration levels. An ageing test bench is built to generate bearing roughness using Electric Discharge Machining. The purpose is to study the effect of operation conditions, such as frequency of drive, amplitude of shaft voltage, radial load level as well as rotational speed, on the capacitive discharge occurrence within the bearing. Having the desire to further understand this phenomenon, the influence of each parameter on the discharge activity and the discharge waveform is analysed. A worst‐case scenario is conducted and applied to a series of bearings. Finally, the bearing damage is examined, and a quantitative fault detection method is presented based on a microscopic inspection of the bearing's surface.

Calculation of operational parameter variation of infinitely long slider bearings with stochastic roughness

In the framework of stochastic representation of surface roughness, a novel Reynolds-type Equation has been derived recently by the authors and utilized to calculate the average values of a bearing’s operational parameters. To acquire an improved insight to the hydrodynamic lubrication phenomena in rough bearings, the stochasticity of the operational parameters should be described, by calculating their higher-order moments, such as the variation. The present work aims at deriving equations for calculation and quantification of these higher-order moments. More specifically, in the present paper equations for the variation of a slider bearing operational parameters (pressure, load carrying capacity, friction force and friction coefficient) are derived. The obtained results are validated against the deterministic Reynolds Equation solution, for a series of bearings with different random Gaussian surface roughness profiles, over a wide range of bearing design and operational parameters.

A learned born series for highly scattering media

The Helmholtz equation with heterogeneous material properties is essential in various fields requiring single-frequency wave simulations, including optics, seismology, acoustics, and electromagnetics. Traditional methods for solving this equation, such as the Born Series, face limitations in converging for high-contrast scattering potentials. To address this challenge, we introduce a novel method called the Learned Born Series (LBS). The LBS is derived from the convergent Born Series but employs components that are learned through training. It demonstrates significantly improved accuracy compared to the conventional convergent Born Series, especially in scenarios with high-contrast scatterers, while maintaining similar computational complexity. The LBS can rapidly generate reasonably accurate predictions of the global pressure field with only a few iterations, and the errors decrease as more iterations are learned. We show its effectiveness through experiments on simulated datasets. The LBS offers promising prospects for accelerating simulations in scenarios with strong sound speed contrasts, potentially revolutionizing applications in transcranial treatment planning and full waveform inversion.

Rapid computation of steady state acoustic fields in heterogeneous and nonlinear media using the Acoustic Field Propagator

The Acoustic Field Propagator is a method for rapidly computing steady state complex acoustic fields in homogeneous media from spatially arbitrary single frequency sources. Here, an extension of the Acoustic Field Propagator to the computation of steady state fields in arbitrary heterogeneous, absorbing and nonlinear media, using nested iterations of the Convergent Born Series and a multi-frequency Helmholtz equation expansion, will be described.

Estimation of the Born data in inverse scattering of layered media

The first term in the Born series, as we call the Born data, is linear with the scatterers. Here we present a scheme to map the total field data to the Born data in layered media using only the single-input single-output (SISO) setup. This nonlinear mapping is based on the reduced order model (ROM) approach, which constructs ROMs of the original wave operator. Normally, the construction of ROMs requires multi-input multi-output data. By introducing fictitious sensors, we estimate the Born data with SISO data in layered media. We give a simple way of using the time-domain Green’s function to estimate the received data for other fictitious sensors without calculating the complicated Sommerfeld integral. The resulting Born data contains only the single-scattering component, which can be helpful for many imaging applications. A numerical example is given incorporating the direct imaging back-propagation method. It validates the linearity of the Born data by providing an artifact-free image without the optimization process.

Born and inverse Born series for scattering problems with Kerr nonlinearities

We consider the Born and inverse Born series for scalar waves with a cubic nonlinearity of Kerr type. We find a recursive formula for the operators in the Born series and prove their boundedness. This result gives conditions which guarantee convergence of the Born series, and subsequently yields conditions which guarantee convergence of the inverse Born series. We also use fixed point theory to give alternate explicit conditions for convergence of the Born series. We illustrate our results with numerical experiments.

The inverse Rytov series for diffuse optical tomography

The Rytov approximation is known in near-infrared spectroscopy including diffuse optical tomography. In diffuse optical tomography, the Rytov approximation often gives better reconstructed images than the Born approximation. Although related inverse problems are nonlinear, the Rytov approximation is almost always accompanied by the linearization of nonlinear inverse problems. In this paper, we will develop nonlinear reconstruction with the inverse Rytov series. By this, linearization is not necessary and higher order terms in the Rytov series can be used for reconstruction. The convergence and stability are discussed. We find that the inverse Rytov series has a recursive structure similar to the inverse Born series.

EUV mask model based on modified Born series.

Mask model is a critical part of computational lithography (CL). Owing to the significant 3D mask effects, it is challenging to accurately and efficiently calculate the near field of extreme ultraviolet (EUV) masks with complex patterns. Therefore, a method based on the modified Born series (MBS) was introduced for EUV mask modeling. With comparable accuracy, the MBS method was two orders of magnitude faster than the finite-difference time-domain method for the investigated examples. Furthermore, the time required for MBS was further reduced when the mask pattern was slightly changed. The proposed method shows great potential for constructing an accurate 3D mask model in EUV CL with high efficiency.

A novel method to repair missing vibration data in rolling bearing vibration signals based on improved optimized measurement matrix

Missing data, caused by many factors such as equipment short circuits or data cleaning, affect the accuracy of condition monitoring for rotating machinery. To improve the precision of missing data recovery, a compressed sensing-based vibration data repair method is developed. First, based on the Gaussian random matrix, an improved optimized measurement matrix (OMM) is proposed to accurately sample data. Then, a sparse representation of the vibration signal, through a discrete cosine transform, is utilized to make the noisy vibration signal sparse. Finally, the orthogonal matching pursuit algorithm is employed to reconstruct the missing signal. The effectiveness of the proposed method is verified by analyzing constant and variable speed time series of rolling bearings. Compared with other data repair methods, it is shown that the OMM has a higher repair precision at different loss rates.

Condition Evaluation of Steam Turbine Generator Using Minute-Interval Integrated Vibration Signals

Vibration levels are a primary indicator for condition monitoring of Electrical Machine (EM) systems. This work employs Singular Spectrum Analysis (SSA) to analyze vibration time series of shaft and bearings of a real 250MW industrial power plant steam turbine Synchronous Generator (SG) in Greece. The SG operates under reduced power due to increased vibration conditions according to threshold guidelines. This work attempts to retrieve fault indications from the minute-interval integrated signal sample via its trend and periodicity components to predict vibrations under full load operation and establish correlations to discern whether the reduced output is justified. The successful application of this novel procedure is important due to ease of storing and handling low frequency signals, especially in remote environments. Rules are established using fuzzy logic due to the nature of the dataset and industrial application. The predictor employed is based on Sugeno-based Adaptive Neuro Fuzzy Inference System (ANFIS).

Application of 1D inverse scattering and projection onto convex sets to inversion of seismic data

The Born series provides a framework for constructing a connection between earth model parameters and a wavefield characterised by perturbation about a known reference wavefield. The inverse scattering series provides a linear and a nonlinear expression for approximating earth's model parameters. Based on our results, the linear expression provides an accurate approximation of the 1D depth varying velocity profile. However, with increasing contrast, one has to utilise the nonlinear expression for increased accuracy. In seismic inversion, a major problem relates to the bandlimited nature of recorded seismic data, limiting the inversion for absolute amplitudes. To reconstruct missing low frequencies, we employ a frequency extrapolation method, in this case, projection onto convex sets (POCS) to reconstruct missing low frequencies critical for accurate inversion and reconstruction of depth varying velocity profile. Numerical results on 1D synthetic data and succeeding results on 1D physical modelling data demonstrate the efficiency of POCS in reconstructing critical missing low frequencies and subsequent advantage of nonlinear inverse scattering in approximating the change in velocity profile. In comparison, the linear scattering expression fails to provide a reasonable estimate of reflectors beyond the first interface.

Born approximation study of the strong disorder in magnetized surface states of a topological insulator

In this study we investigate the effect of random point disorder on the surface states of a topological insulator with out-of-plane magnetization. We consider the disorder within a high order Born approximation. The Born series converges to the one branch of the self-consistent Born approximation (SCBA) solution at low disorder. As the disorder strength increases, the Born series converges to another SCBA solution with the finite density of states within the magnetization induced gap. Further increase of the disorder strength leads to a divergence of the Born series, showing the limits of the applicability of the Born approximation. We find that the convergence properties of this Born series are closely related to the properties of the logistic map, which is known as a prototypical model of chaos. We also calculate the longitudinal and Hall conductivities within the Kubo formulas at zero temperature with the vertex corrections for the velocity operator. Vertex corrections are important for describing transport properties in the strong disorder regime. In the case of strong disorder, the longitudinal conductivity is weakly dependent on the disorder strength, while the Hall conductivity decreases with increasing disorder.

A learned Born series for highly-scattering media

A new method for solving the wave equation is presented, called the learned Born series (LBS), which is derived from a convergent Born series but its components are found through training. The LBS is shown to be significantly more accurate than the convergent Born series for the same number of iterations, in the presence of high contrast scatterers, while maintaining a comparable computational complexity. The LBS is able to generate a reasonable prediction of the global pressure field with a small number of iterations, and the errors decrease with the number of learned iterations.

A novel method to measure static and dynamic complexity of time series based on visualization curves.

In this paper, reverse transition entropy (RTE) is proposed and combined with refined composite multi-scale analysis and generalized fractional-order entropy to construct the refined composite multi-scale reverse transition generalized fractional-order complexity-entropy curve (RCMS-RT-GFOCEC). This measure aims to characterize and identify different complex time series. First, RTE is used to extract the static and dynamic transition probabilities of the temporal structure. Then, the distribution area and variation law of the visualization curves are adopted to characterize different time series. Finally, the time series are identified by the multi-scale curves of RTE, Hα min, and Cα max. The characteristic curves ( Hq min and Cq max) of the refined composite multi-scale q complexity-entropy curves (RCMS-q-CECs) for the comparative analysis are irregular. The experimental results indicate that the RCMS-RT-GFOCEC method could effectively characterize both artificial and empirical temporal series. Moreover, this method can effectively track the dynamical changes of rolling bearing and turbine gearbox time series. The accuracies of the proposed method reach 99.3% and 98.8%, while the recognition rates based on the RCMS-q-CEC method are only 95.7% and 97.8%, suggesting that the proposed method can effectively characterize and identify different complex temporal systems.

Wavelength scaling of strong-field Rydberg-state excitation: Toward an effective S -matrix theory

$S$-matrix theory and the Born expansion, the lowest-order term of which is known as the ``strong-field approximation'' (SFA), play an indispensable role in our understanding of atomic and molecular processes in intense laser fields. Most phenomena in this field are reproduced by the first two terms of the Born series. However, for a long-range potential such as the Coulomb potential, the second-order term may be larger than the SFA term, raising the problem of the convergence of the Born series. By simultaneously measuring and simulating ionization and Rydberg-state excitation of an argon atom subject to a strong laser field for various wavelengths, we demonstrate that the wavelength scaling law of the measured ratio of ${\mathrm{Ar}}^{*}$ over ${\mathrm{Ar}}^{+}$ and the period of its oscillation with respect to the laser intensity can be well reproduced by the second-order term of the $S$-matrix expansion in terms of the Coulomb potential, but not by the lowest-order (SFA) term. We conjecture that the second-order term of the $S$-matrix expansion may provide an effective theory for the intense-laser--atom interaction.

Reduced inverse Born series: a computational study.

We investigate the inverse scattering problem for scalar waves. We report conditions under which the terms in the inverse Born series cancel in pairs, leaving only one term at each order. We refer to the resulting expansion as the reduced inverse Born series. The reduced series can also be derived from a nonperturbative inversion formula. Our results are illustrated by numerical simulations that compare the performance of the reduced series to the full inverse Born series and the Newton-Kantorovich method.

Unified treatment of exact and approximate scalar electromagnetic wave scattering.

Under conditions of strong scattering, a dilemma often arises regarding the best numerical method to use. Main competitors are the Born series, the beam propagation method, and direct solution of the Lippmann-Schwinger equation. However, analytical relationships between the three methods have not yet, to our knowledge, been explicitly stated. Here, we bridge this gap in the literature. In addition to overall insight about aspects of optical scattering that are best numerically captured by each method, our approach allows us to derive approximate error bounds to be expected under various scattering conditions.

Born-Padé approach to electromagnetic scattering in complex one-dimensional inhomogeneous slabs

Perturbation theory is applied to one-dimensional scattering systems consisting of a general class of inhomogeneous and isotropic slabs having size $L$ described by the relative permittivity $\varepsilon(z) = 1 + \alpha \chi(z)$, where $\chi(z)$ is the electric susceptibility and $\alpha$ the perturbation parameter. The transmitted and reflected amplitudes are shown to be written as Born series in powers of $\alpha$ and Pad\'e approximants are used to obtain analytical results with a high and arbitrary degree of accuracy. The approach is very general and can handle oblique incidence. Examples are given for the transmission and reflection amplitudes of plane waves interacting with Hermitian and non-Hermitian structures with known and unknown exact solutions.