High Frequency Scattering Research Articles

Modeling and reduction of high frequency scatter noise at LIGO Livingston

The sensitivity of aLIGO detectors is adversely affected by the presence of noise caused by light scattering. Low frequency seismic disturbances can create higher frequency scattering noise adversely impacting the frequency band in which we detect gravitational waves. In this paper, we analyze instances of a type of scattered light noise we call ‘Fast Scatter’ that is produced by motion at frequencies greater than 1 Hz, to locate surfaces in the detector that may be responsible for the noise. We model the phase noise to better understand the relationship between increases in seismic noise near the site and the resulting Fast Scatter observed. We find that mechanical damping of the arm cavity baffles led to a significant reduction of this noise in recent data. For a similar degree of seismic motion in the 1– 3 Hz range, the rate of noise transients is reduced by a factor of ~50.

A Quantized Tensor Train Method for High-Frequency Scattering Problems Involving Heterogeneous Dielectric Layers

We present a new numerical scheme to solve efficiently scattering problems involving an elongated and flat heterogeneous dielectric material assumed to be invariant along a direction of space. The technique consists of compressing the integral operators of an integro-differential formulation with a so-called quantized tensor train (QTT) algorithm whose use is rather original in this context. We show that it allows to compute and store operators with a notably small memory footprint while having at the same time a fast matrix-vector product (MVP) leading to a competitive method compared with the more classical <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}$ </tex-math></inline-formula> -matrix approach.

Review of High-frequency Scattering Model of Canonical Geometric Primitives

Review of High-frequency Scattering Model of Canonical Geometric Primitives

Detection of Wavy Sea Surface Oil-Derivative Contamination with Forward Specular High-Frequency Scattering

Abstract A spectrum of low-frequency (20–30 Hz) amplitude fluctuations of the ultrasonic (10 MHz) signal specularly scattered from water surfaces covered with monomolecular and thicker crude oil origin films of well-defined, oceanographically relevant viscoelastic properties was examined in laboratory and at-sea conditions. The relationship between the surface water wave (30 Hz) damping coefficient and the oil layer thickness was established, and compared to the one predicted by the classical Stokes theory. The depression of the spectral energy density of wind-driven waves by surface films was inferred from the ratio of acoustic signal fluctuations spectra with/without films, and compared to that resulting from the Marangoni damping theory applicable to monolayers of particular surface viscoelasticity. The agreement between the theory and experimental data was satisfactory. As shown in at-sea experiments performed with a free-floating, buoy-like acoustic system, and an artificial oil slick spread over the Baltic Sea surface, the film’s rheological surface properties can be recovered from acoustic surface probing, as well as oil spill edge detection. Simultaneous statistical analyses of the scattered signal amplitude distribution parameters turned out to be unequivocally related to the oil substance fraction weight, oil layer thickness, and the form of oil contamination.

A CIP-FEM for High-Frequency Scattering Problem with the Truncated DtN Boundary Condition

A CIP-FEM for High-Frequency Scattering Problem with the Truncated DtN Boundary Condition

Shadow Radiation Iterative Physical Optics Method for High-Frequency Scattering

A shadow-radiation-based fast iterative physical optics (IPO) scheme, for the analysis of the scattering from large complex geometries involving multiple reflection and occlusion effects, is proposed. By employing a “shadow-radiation” mechanism, the scheme alleviates the need for expensive computation and storage of a geometric visibility function. In a nested fashion, shadow radiation iterations are performed for each “bounce” in the conventional multiple reflection IPO scheme. The resulting method makes use of simple field integrals which are all accelerable using a multilevel nonuniform grid-based field evaluation algorithm, with a modification tailored to the scheme’s integral kernels. The proposed scheme is also shown analytically to be a more stable (faster converging) equivalent of existing IPO schemes. The method is studied in terms of accuracy and performance for representative examples and compared with alternative physical optics and numerically exact solution techniques.

Implementation of a Boundary Element Method for High Frequency Scattering by Convex Polygons with Impedance Boundary Conditions

Implementation of a Boundary Element Method for High Frequency Scattering by Convex Polygons with Impedance Boundary Conditions

High-Frequency Scattering From Radially Uniaxial Dielectric Sphere

High-frequency backscattering caused by a large uniaxial dielectric sphere is presented in this letter. The term high frequency implies ${Ka} \gg 1$ where $K$ and $a$ are the propagation constant and radius of the sphere, respectively. Using a modified Watson transformation, the slowly convergent generalized Mie series summation for a uniaxial dielectric sphere is transformed into a rapidly convergent contour integral. The generalized Debye series of the uniaxial dielectric spheres is introduced, and the Mie series coefficients are replaced by their equivalent Debye series formulations. An expression for the high-frequency backscattered field is proposed, and the monostatic radar cross section (RCS) of a large uniaxial dielectric sphere is calculated.

The High-frequency Scattering of the S0 Lamb Mode by a Circular Blind Hole in a Plate

The scattering problem of an incident high-frequency S0 Lamb wave in a plate with a circular blind hole is investigated. The study is not limited to the low-frequency range of this wave, in which the popular approximate plate theories are inapplicable. A 3D analytical approach is used where the wave fields are expanded in all possible Lamb modes, including propagating and evanescent modes. Due to the non-symmetric blind hole defect, the scattered fields will contain higher order converted modes in addition to the fundamental S0 and A0 modes. The far field scattering amplitudes of various propagating Lamb modes for different hole sizes are inspected. The results are compared with those of low frequencies and some different phenomena are found.

Extraction of Uniformly Accurate Phase Functions Across Smooth Shadow Boundaries in High Frequency Scattering Problems

Several recent numerical schemes for high frequency scattering simulations are based on the extraction of known phase functions from an oscillatory solution. The remaining function is typically no longer oscillatory, and as such it can be approximated numerically with a number of degrees of freedom that does not depend on the frequency of the original problem. Knowledge of the phase of a solution typically comes from asymptotic analysis, for example, from geometrical optics. We consider integral equation formulations of time-harmonic scattering by a smooth and convex obstacle and focus on the so-called shadow boundaries. They are the points where the incoming waves are tangential to the boundary of the scatterer. We devise a numerical method that incorporates advanced results from asymptotic analysis which describe the frequency-dependent transitional behavior of the solution uniformly across these points. We describe and resolve an apparent conflict between two theories that describe the asymptotic behavior of this problem. They are the well-known geometric theory of diffraction and the rigorous asymptotic analysis by Melrose and Taylor, based on microlocal analysis.

A Fast Direct Solver for High Frequency Scattering from a Large Cavity in Two Dimensions

We present a fast direct solver for the simulation of electromagnetic scattering from an arbitrarily shaped, large, empty cavity embedded in an infinite perfectly conducting half-space. The governing Maxwell equations are reformulated as a well-conditioned second kind integral equation, and the resulting linear system is solved in nearly linear time using a hierarchical matrix factorization technique. We illustrate the performance of the scheme with several numerical examples for complex cavity shapes over a wide range of frequencies.

The Wedge-Type Problem: The Building Brick in High-Frequency Scattering from Complex Objects

This paper presents the problem of high-frequency scattering in a ray-tracing context. It focuses on the wedge problem as the most relevant contribution to the diffracted field from complex objects. The wedge problem's solution is then treated either analytically or numerically. It is treated analytically by resorting to the Malyuzhinets spectral technique and a subsequent approximate solution. It is treated numerically by deriving a parabolic equation from the original elliptic problem, which can then be easily and efficiently solved numerically via finite differences.

Оптический эффект малого смещения наблюдаемого положения источника излучения, полученный математическим моделированием задачи высокочастотного рассеяния

Оптический эффект малого смещения наблюдаемого положения источника излучения, полученный математическим моделированием задачи высокочастотного рассеяния

A Priori Estimates for High Frequency Scattering by Obstacles of Arbitrary Shape

High frequency estimates for the Dirichlet-to-Neumann and Neumann-to-Dirichlet operators are obtained for the Helmholtz equation in the exterior of bounded obstacles. These a priori estimates are used to study the scattering of plane waves by an arbitrary bounded obstacle and to prove that the total cross section of the scattered wave does not exceed four geometrical cross sections of the obstacle in the limit as the wave number k → ∞. This bound of the total cross section is sharp.

High Frequency Scattering by a Classically Invisible Body

We consider a polyhedron with zero classical resistance, i.e., a polyhedron invisible to an observer viewing only the paths of geometrical optics rays. The corresponding problem of scattering of plane waves by the polyhedron is studied. The quasi-classical approximation is obtained and justified in the case of impedance boundary conditions with nonzero absorbtion. It is shown that the total momentum transmitted to the obstacle vanishes as the frequency k tends to infinity and that the total cross section oscillates at high frequencies. When the impedance $\lambda_0$ is real (i.e., there is no absorption), it is shown that there exists a sequence of frequencies $k_n$ such that the average of the total cross section over shrinking intervals around $\lambda_0 $ tends to zero as $k_n \to \infty$.

Polynomial Representation of NURBS and Its Application to High Frequency Scattering Prediction

This article presents a method that uses physical optics (PO) techniques to compute the monostatic radar cross section (RCS) of electrically large conducting objects modeled by non-uniform rational B-spline (NURBS) surfaces. At the beginning, a new algorithm to convert recursive B-spline basis function into piecewise polynomials in power form is presented. Then, algorithm computes the polynomial representation of B-spline basis functions and NURBS surface geometric parameters are obtained. The PO integral over NURBS surfaces of an electrically large conducting object is used to predict the object's RCS. The NURBS surface is divided into small piecewise polynomial parametric patches by isoparametric curves, and the PO integral expression over the parametric domain of each polynomial parametric patch is reduced to an analytical expression which permits an accurate and effective computation of the PO integral by using a modified Ludwig's algorithm. The RCS of the object can be obtained by adding up the PO integral contribution of each polynomial parametric patch. The effectiveness of this method is verified by numerical examples.

A beam stop based correction procedure for high spatial frequency scatter in industrial cone-beam X-ray CT

In the energy range of industrial cone-beam CT (a 450kV X-ray tube is used), the detector scatter (veiling glare) turned out to be the most important source of secondary radiation for a digital imaging system working in the indirect conversion mode. It has been shown that the detector scatter drives the shape of the total image scatter. As a consequence, the latter may be characterized by an important high spatial frequency content questioning the hypothesis, frequently invoked in the scatter correction techniques, of a slowly varying scatter. We propose a beam stop array (BSA) based method for the evaluation/subtraction of the image scatter. The technique has the potential of simultaneously manage all sources of scattering radiation. It can be used in the high spatial frequency scatter case at the condition of opportunely selecting the BSA effective sampling step. It has been shown that the BSA approach can be also successfully combined with a beam hardening correction scheme based on the linearisation method. The work we present is supported by experimental measurements performed with two test objects at two different beam qualities: (i) 200kV+2.5mm of Cu and (ii) 400kV+4mm of Pb and 1mm of Cd. The detector scatter represents about 36% and 65% of the total white field image for the two investigated beam qualities, respectively.

A Galerkin Boundary Element Method for High Frequency Scattering by Convex Polygons

In this paper we consider the problem of time‐harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well‐known second kind combined‐layer‐potential integral equation. We provide a proof that this equation and its adjoint are well‐posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains.

A Sparse Discretization for Integral Equation Formulations of High Frequency Scattering Problems

We consider two-dimensional scattering problems, formulated as an integral equation defined on the boundary of the scattering obstacle. The oscillatory nature of high-frequency scattering problems necessitates a large number of unknowns in classical boundary element methods. In addition, the corresponding discretization matrix of the integral equation is dense. We formulate a boundary element method with basis functions that incorporate the asymptotic behavior of the solution at high frequencies. The method exhibits the effectiveness of asymptotic methods at high frequencies with only few unknowns, but retains accuracy for lower frequencies. New in our approach is that we combine this hybrid method with very effective quadrature rules for oscillatory integrals. As a result, we obtain a sparse discretization matrix for the oscillatory problem. Moreover, numerical experiments indicate that the accuracy of the solution actually increases with increasing frequency. The sparse discretization applies to problems where the phase of the solution can be predicted a priori, for example in the case of smooth and convex scatterers.

The Parabolic Equation Method for the High-frequency Scattering from a Convex Perfectly Conducting Wedge with Curved Faces

The parabolic equation method permits one to develop valuable and flexible techniques to solve high frequency scattering problems in wedge shaped regions. This method is here applied to solve the two-dimensional problem of plane wave scattering from a convex perfectly conducting wedge with curved faces. The results provided by the parabolic model are compared on a test-case problem with the numerical results obtained by a hybrid Finite Element-based approach. These results prove that in the far-field scattering region the parabolic equation approach is able to provide results of the same quality of the hybrid Finite Element approach, but with a 96% reduction of the computational time.