Computation of Electromagnetic Fields Scattered From Objects With Uncertain Shapes Using Multilevel Monte Carlo Method

Computational tools for characterizing electromagnetic scattering from objects with uncertain shapes are needed in various applications ranging from remote sensing at microwave frequencies to Raman spectroscopy at optical frequencies. Often, such computational tools use the Monte Carlo (MC) method to sample a parametric space describing geometric uncertainties. For each sample, which corresponds to a realization of the geometry, a deterministic electromagnetic solver computes the scattered fields. However, for an accurate statistical characterization the number of MC samples has to be large. In this work, to address this challenge, the continuation multilevel Monte Carlo (CMLMC) method is used together with a surface integral equation solver. The CMLMC method optimally balances statistical errors due to sampling of the parametric space, and numerical errors due to the discretization of the geometry using a hierarchy of discretizations, from coarse to fine. The number of realizations of finer discretizations can be kept low, with most samples computed on coarser discretizations to minimize computational cost. Consequently, the total execution time is significantly reduced, in comparison to the standard MC scheme.Comment: 25 pages, 10 Figure

Scattering and Doppler Spectral Analysis for a Fast-Moving Target above Time-Varying Lossy Dielectric Sea Surface

A numerical electromagnetic method based on the physical optics with physical optics method (PO-PO) is employed to calculate backscattered returns from a missile-like target above sea surface. Surfaces are time-varying Monte Carlo simulations initialized as realizations of a Pierson–Moskowitz spectrum. The monostatic normalized radar cross section of composite model by the hybrid PO-PO method is calculated and compared with those by the conventional method of moments, as well as the runtime and memory requirements. The results are found to be in good agreement. The runtime shows that the hybrid PO-PO method enables large-scale time-varying Monte Carlo simulations. The numerical simulations of the Doppler spectrum from the fast-moving target above time-varying lossy dielectric sea surface are obtained, and the Doppler spectra of backscattered signals from this model are discussed for different incident angles, speed of flying target, wind speeds, incident frequencies, and target altitudes in detail. Finally, the coupling effects on Doppler spectra are analyzed. All the results are obtained at the incidence of horizontal polarization wave in this study

Autonomous Vehicles: MMW Radar Backscattering Modeling of Traffic Environment, Vehicular Communication Modeling, and Antenna Designs

77 GHz Millimeter-wave (mmWave) radar serves as an essential component among many sensors required for autonomous navigation. High-fidelity simulation is indispensable for nowadays’ development of advanced automotive radar systems because radar simulation can accelerate the design and testing process and help people to better understand and process the radar data. The main challenge in automotive radar simulation is to simulate the complex scattering behavior of various targets in real time, which is required for sensor fusion with other sensory simulation, e.g. optical image simulation. In this thesis, an asymptotic method based on a fast-wideband physical optics (PO) calculation is developed and applied to get high fidelity radar response of traffic scenes and generate the corresponding radar images from traffic targets. The targets include pedestrians, vehicles, and other stationary targets. To further accelerate the simulation into real time, a physics-based statistical approach is developed. The RCS of targets are fit into statistical distributions, and then the statistical parameters are summarized as functions of range and aspect angles, and other attributes of the targets. For advanced radar with multiple transmitters and receivers, pixelated-scatterer statistical RCS models are developed to represent objects as extend targets and relax the requirement for far-field condition. A real-time radar scene simulation software, which will be referred to as Michigan Automotive Radar Scene Simulator (MARSS), based on the statistical models are developed and integrated with a physical 3D scene generation software (Unreal Engine 4). One of the major challenges in radar signal processing is to detect the angle of arrival (AOA) of multiple targets. A new analytic multiple-sources AOA estimation algorithm that outperforms many well-known AOA estimation algorithms is developed and verified by experiments. Moreover, the statistical parameters of RCS from targets and radar images are used in target classification approaches based on machine learning methods. In realistic road traffic environment, foliage is commonly encountered that can potentially block the line-of-sight link. In the second part of the thesis, a non-line-of-sight (NLoS) vehicular propagation channel model for tree trunks at two vehicular communication bands (5.9 GHz and 60 GHz) is proposed. Both near-field and far-field scattering models from tree trunk are developed based on modal expansion and surface current integral method. To make the results fast accessible and retractable, a macro model based on artificial neural network (ANN) is proposed to fit the path loss calculated from the complex electromagnetic (EM) based methods. In the third part of the thesis, two broadband (bandwidth > 50%) omnidirectional antenna designs are discussed to enable polarization diversity for next-generation communication systems. The first design is a compact horizontally polarized (HP) antenna, which contains four folded dipole radiators and utilizing their mutual coupling to enhance the bandwidth. The second one is a circularly polarized (CP) antenna. It is composed of one ultra-wide-band (UWB) monopole, the compact HP antenna, and a dedicatedly designed asymmetric power divider based feeding network. It has about 53% overlapping bandwidth for both impedance and axial ratio with peak RHCP gain of 0.9 dBi.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163001/1/caixz_1.pd

On the Convergence of the Born Series in Optical Tomography with Diffuse Light

We provide a simple sufficient condition for convergence of Born series in the forward problem of optical diffusion tomography. The condition does not depend on the shape or spatial extent of the inhomogeneity but only on its amplitude.Comment: 23 pages, 7 figures, submitted to Inverse Problem

Reflection Matrix Method for Controlling Light After Reflection From a Diffuse Scattering Surface

This research focuses on reflective inverse diffusion, which was a proof-of-concept experiment that used phase modulation to shape the wavefront of a laser causing it to refocus after reflection from a rough surface. By refocusing the light, reflective inverse diffusion has the potential to eliminate the complex radiometric model of indirect photography by creating a virtual light source at the first diffuse reflector that satisfies the line-of-sight requirement of dual photography. However, the initial reflective inverse diffusion experiments provided no mathematical background and were conducted under the premise that the process operated similarly to transmissive inverse diffusion. In this research, diffraction modeling of the reflective inverse diffusion experiments led to the development of Fourier transform-based simulations. Simulations and experimentation were used to develop reflection matrix methods that determine the proper phase modulation to refocus light after reflection to any location in the observation plane. These techniques provide a new method for controlled illumination of an occluded scene that can be used in conjunction with dual photography. This document provides the mathematical background for reflective inverse diffusion, the reflection matrix methods for phase modulation, and describes the simulations and experiments conducted

Fast Numerical Algorithms for 3-D Scattering from PEC and Dielectric Random Rough Surfaces in Microwave Remote Sensing

abstract: We present fast and robust numerical algorithms for 3-D scattering from perfectly electrical conducting (PEC) and dielectric random rough surfaces in microwave remote sensing. The Coifman wavelets or Coiflets are employed to implement Galerkin’s procedure in the method of moments (MoM). Due to the high-precision one-point quadrature, the Coiflets yield fast evaluations of the most off-diagonal entries, reducing the matrix fill effort from O(N^2) to O(N). The orthogonality and Riesz basis of the Coiflets generate well conditioned impedance matrix, with rapid convergence for the conjugate gradient solver. The resulting impedance matrix is further sparsified by the matrix-formed standard fast wavelet transform (SFWT). By properly selecting multiresolution levels of the total transformation matrix, the solution precision can be enhanced while matrix sparsity and memory consumption have not been noticeably sacrificed. The unified fast scattering algorithm for dielectric random rough surfaces can asymptotically reduce to the PEC case when the loss tangent grows extremely large. Numerical results demonstrate that the reduced PEC model does not suffer from ill-posed problems. Compared with previous publications and laboratory measurements, good agreement is observed.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201