Three-Dimensional Electromagnetic Scattering from Layered Media with Rough Interfaces for Subsurface Radar Remote Sensing

The objective of this dissertation is to develop forward scattering models for active microwave remote sensing of natural features represented by layered media with rough interfaces. In particular, soil profiles are considered, for which a model of electromagnetic scattering from multilayer rough surfaces with/without buried random media is constructed. Starting from a single rough surface, radar scattering is modeled using the stabilized extended boundary condition method (SEBCM). This method solves the long-standing instability issue of the classical EBCM, and gives three-dimensional full wave solutions over large ranges of surface roughnesses with higher computational e±ciency than pure numerical solutions, e.g., method of moments (MoM). Based on this single surface solution, multilayer rough surface scattering is modeled using the scattering matrix approach and the model is used for a comprehensive sensitivity analysis of the total ground scattering as a function of layer separation, subsurface statistics, and sublayer dielectric properties. The buried inhomogeneities such as rocks and vegetation roots are considered for the first time in the forward scattering model. Radar scattering from buried random media is modeled by the aggregate transition matrix using either the recursive transition matrix approach for spherical or short-length cylindrical scatterers, or the generalized iterative extended boundary condition method we developed for long cylinders or root-like cylindrical clusters. These approaches take the field interactions among scatterers into account with high computational efficiency. The aggregate transition matrix is transformed to a scattering matrix for the full solution to the layered-medium problem. This step is based on the near-to-far field transformation of the numerical plane wave expansion of the spherical harmonics and the multipole expansion of plane waves. This transformation consolidates volume scattering from the buried random medium with the scattering from layered structure in general. Combined with scattering from multilayer rough surfaces, scattering contributions from subsurfaces and vegetation roots can be then simulated. Solutions of both the rough surface scattering and random media scattering are validated numerically, experimentally, or both. The experimental validations have been carried out using a laboratory-based transmit-receive system for scattering from random media and a new bistatic tower-mounted radar system for field-based surface scattering measurements.Ph.D.Electrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91459/1/xduan_1.pd

Elastic wave scattering from randomly rough surfaces

Elastic wave scattering from randomly rough surfaces and a smooth surface are essentially different. For ultrasonic nondestructive evaluation (NDE) the scattering from defects with smooth surfaces has been extensively studied, providing fundamental building blocks for the current inspection techniques. However, all realistic surfaces are rough and the roughness exists in two dimensions. It is thus very important to understand the rough surface scattering mechanism, which would give insight for practical inspections. Knowledge of the stochastics of scattering for different rough surfaces would also allow the detectability of candidate rough defects to be anticipated. Hence the main motivation of this thesis is to model and study the effect of surface roughness on the scattering field, with focus on elastic waves. The main content of this thesis can be divided into three contributions. First of all, an accurate numerical method with high efficiency is developed in the time domain, for computing the scattered waves from obstacles with arbitrary shapes. It offers an exact solution which covers scenarios where approximation-based algorithms fail. The method is based on the hybrid idea to combine the finite element (FE) and boundary integral (BI) methods. The new method efficiently couples the FE equations and the boundary integral formulae for solving the transient scattering problems in both near and far fields, which is implemented completely in the time domain. Several numerical examples are demonstrated and sufficiently high accuracy is achieved with different defects. It enables the possibility for Monte Carlo simulations of the elastic wave scattering from randomly rough surfaces in both 2D and 3D. The second contribution relates to applying the developed numerical method to evaluate the widely used Kirchhoff approximation (KA) for rough surface scattering. KA is a high-frequency approximation which limits the use of the theory for certain ranges of roughness and incidence/scattering angles. The region of validity for elastic KA is carefully examined for both 1D and 2D random surfaces with Gaussian spectra. Monte Carlo simulations are run and the expected scattering intensity is compared with that calculated by the accurate numerical method. An empirical rule regarding surface parameters and angles is summarized to establish the valid region of both 2D and 3D KA. In addition, it is found that for 3D scattering problems, the rule of validity becomes stricter than that in 2D. After knowing the region of validity, KA is applied to investigate how the surface roughness affects the statistical properties of scattered waves. An elastodynamic Kirchhoff theory particularly for the statistics of the diffused field is developed with slope approximations for the first time. It provides an analytical expression to rapidly predict the expected angular distribution of the scattering intensity, or the scattering pattern, for different combinations of the incidence/scattering wave modes. The developed theory is verified by comparison with numerical Monte Carlo simulations, and further validated by the experiment with phased arrays. In particular the derived formulae are utilized to study the effects of the surface roughness on the mode conversion and the 2D roughness caused depolarization, which lead to unique scattering patterns for different wave modes.Open Acces

Rough Mirror as a Quantum State Selector: Analysis and Design

We report analysis of rough mirrors used as the gravitational state selectors in neutron beam and similar experiments. The key to mirror properties is its roughness correlation function (CF) which is extracted from the precision optical scanning measurements of the surface profile. To identify CF in the presence of fluctuation-driven fat tails, we perform numerical experiments with computer-generated random surfaces with the known CF. These numerical experiments provide a reliable identification procedure which we apply to the actual rough mirror. The extracted CF allows us to make predictions for ongoing GRANIT experiments. We also propose a radically new design for rough mirrors based on Monte Carlo simulations for the 1D Ising model. The implementation of this design provides a controlled environment with predictable scattering properties

A New Model for Cross-polarization Scattering from Perfect Conducting Random Rough Surfaces in Backscattering Direction

abstract: Scattering from random rough surface has been of interest for decades. Several methods were proposed to solve this problem, and Kirchho approximation (KA) and small perturbation method (SMP) are among the most popular. Both methods provide accurate results on rst order scattering, and the range of validity is limited and cross-polarization scattering coecient is zero for these two methods unless these two methods are carried out for higher orders. Furthermore, it is complicated for higher order formulation and multiple scattering and shadowing are neglected in these classic methods. Extension of these two methods has been made in order to x these problems. However, it is usually complicated and problem specic. While small slope approximation is one of the most widely used methods to bridge KA and SMP, it is not easy to implement in a general form. Two scale model can be employed to solve scattering problems for a tilted perturbation plane, the range of validity is limited. A new model is proposed in this thesis to deal with cross-polarization scattering phenomenon on perfect electric conducting random surfaces. Integral equation is adopted in this model. While integral equation method is often combined with numerical method to solve the scattering coecient, the proposed model solves the integral equation iteratively by analytic approximation. We utilize some approximations on the randomness of the surface, and obtain an explicit expression. It is shown that this expression achieves agreement with SMP method in second order.Dissertation/ThesisMasters Thesis Electrical Engineering 201

The topology and electrical properties of nanoparticle networks

Includes bibliographical references.The bulk and surface network topologies of milled silicon nanoparticle aggregates in layers deposited on porous and non-porous substrates have been quantitatively characterised using laboratory and synchrotron based small angle X-ray scattering and ultra-small angle X-ray scattering, as well as with a new surface scattering technique developed for this research, which can be described as wide angle low q scattering. A new scaling model applied to the small angle and ultra-small angle X-ray scattering data which was originally developed to describe branched polymers was shown to be applicable to the description of the networks of silicon particles. The milled particles which have a highly polydisperse size distribution, form agglomerates, which in turn cluster to form larger structures with a very high degree of aggregation. Results from the new scattering technique showed the rough surface of the printed layers to have a fractal structure with step heights of 10% to 20% between adjacent particles. This value is consistent with the topology of the particle aggregates in the layer inferred from ultra-small angle X-ray scattering. Flow properties of the inks on different substrates lead to quantitative differences in the mean aggregate separation, with slowly curing systems on materials which allow good capillary flow resulting in denser networks with smaller aggregates and better contact between particles. The electrical conductance of the layers was shown to be linearly related to parallel connections of the minimum paths of particles through the aggregates as determined from the analysis of ultra-small angle X-ray scattering data. The capacitance of the layers was shown to have a linear dependence on both the separation between primary particles and series connection of the minimum paths

Comparison of PARASOL Observations with Polarized Reflectances Simulated Using Different Ice Habit Mixtures

Insufficient knowledge of the habit distribution and the degree of surface roughness of ice crystals within ice clouds is a source of uncertainty in the forward light scattering and radiative transfer simulations required in downstream applications involving these clouds. The widely used MODerate Resolution Imaging Spectroradiometer (MODIS) Collection 5 ice microphysical model assumes a mixture of various ice crystal shapes with smooth-facets except aggregates of columns for which a moderately rough condition is assumed. When compared with PARASOL (Polarization and Anisotropy of Reflectances for Atmospheric Sciences coupled with Observations from a Lidar) polarized reflection data, simulations of polarized reflectance using smooth particles show a poor fit to the measurements, whereas very rough-faceted particles provide an improved fit to the polarized reflectance. In this study a new microphysical model based on a mixture of 9 different ice crystal habits with severely roughened facets is developed. Simulated polarized reflectance using the new ice habit distribution is calculated using a vector adding-doubling radiative transfer model, and the simulations closely agree with the polarized reflectance observed by PARASOL. The new general habit mixture is also tested using a spherical albedo differences analysis, and surface roughening is found to improve the consistency of multi-angular observations. It is suggested that an ice model incorporating an ensemble of different habits with severely roughened surfaces would potentially be an adequate choice for global ice cloud retrievals

Directional characteristics of thermal-infrared beaming from atmosphereless planetary surfaces - a new thermophysical model

We present a new rough-surface thermophysical model (Advanced Thermophysical Model or ATPM) that describes the observed directional thermal emission from any atmosphereless planetary surface. It explicitly incorporates partial shadowing, scattering of sunlight, self-heating and thermal–infrared beaming (re-radiation of absorbed sunlight back towards the Sun as a result of surface roughness). The model is verified by accurately reproducing ground-based directional thermal emission measurements of the lunar surface using surface properties that are consistent with the findings of the Apollo missions and roughness characterized by an rms slope of ∼32°. By considering the wide range of potential asteroid surface properties, the model implies a beaming effect that cannot be described by a simple parameter or function. It is highly dependent on the illumination and viewing angles as well as surface thermal properties and is predominantly caused by macroscopic rather than microscopic roughness. Roughness alters the effective Bond albedo and thermal inertia of the surface as well as moving the mean emission away from the surface normal. For accurate determination of surface properties from thermal–infrared observations of unresolved bodies or resolved surface elements, roughness must be explicitly modelled, preferably aided with thermal measurements at different emission angles and wavelengths