Adrian Doicu

Light scattering from a particle on or near a surface

Abstract The problem of light scattering by a particle on or near a surface is treated using the extended boundary condition methods solution for scattering by a particle in a homogeneous medium and the integral representation of spherical vector wave functions over plane waves for the calculation of the reflection of the scattered field by the surface. An approximate solution is also given by assuming that the scattered field, reflecting off the surface and interacting with the particle, is incident upon the surface at near-normal incidence. The range of validity of the approximate method is checked from a numerical point of view

Numerical Regularization for Atmospheric Inverse Problems

The subject of this book is a hot topic with currently no monographic support. It is more advanced, specialized and mathematical than its competitors, and a comprehensive book on regularization techniques for atmospheric science is much needed for further development in this field. Written by brilliant mathematicians, this research monograph presents and analyzes numerical algorithms for atmospheric retrieval, pulling together all the relevant material in a consistent, very powerful manner. The first chapter presents the typical retrieval problems encountered in atmospheric remote sensing. Chapter 2 introduces the concept of ill-posedness for linear discrete equations, illustrating the difficulties associated with the solution of the problems by considering a temperature retrieval test problem and analyzing the solvability of the discrete equation by using the singular value decomposition of the corresponding matrix. A detailed description of the Tikhonov regularization for linear problems is the subject of Chapter 3, in which the authors introduce a set of mathematical and graphical tools to characterize the regularized solution. The goal of Chapter 4 is to reveal the similitude between Tikhonov regularization and statistical inversion regarding the regularized solution representation, the error analysis, and the design of parameter choice methods. The following chapter briefly surveys some classical iterative regularization methods such as the Landweber iteration and semi-iterative methods, and then treats the regularization effect of the conjugate gradient method applied to the normal equations. Having set the stage in the first part of the book, the remaining chapters dealing with nonlinear ill-posed problems. The authors introduce four test problems that are used throughout the rest of the book to illustrate the behaviour of the numerical algorithms and tools. These deal with the retrieval of ozone and BrO in the visible spectral region, and of CO and temperature in the infared spectral domain. Chapter 6 looks at the practical aspects of Tikhonov regularization for nonlinear problems, while Chapter 7 presents the relevant iterative regularization methods for nonlinear problems. The following chapter reviews the truncated and the regularized total least squares method for solving linear ill--posed problems, and include the similarity with the Tikhonov regularization. Chapter 9 brings the list of nonlinear methods to a close. It describes the Backus-Gilbert approach as a representative member of mollifier methods and finally, addresses the maximum entropy regularization. For the sake of completeness and in order to emphasize the mathematical techniques which are used in the classical regularization theory, five appendices at the end of the book present direct and iterative methods for solving linear and nonlinear ill-posed problems.

Iteratively Regularized Gauss--Newton Method for Atmospheric Remote Sensing

Abstract In this paper we present an inversion algorithm for nonlinear ill-posed problems arising in atmospheric remote sensing. The proposed method is the iteratively regularized Gauss–Newton method. The dependence of the performance and behaviour of the algorithm on the choice of the regularization matrices and sequences of regularization parameters is studied by means of simulations. A method for improving the accuracy of the solution when the identity matrix is used as regularization matrix is also discussed. Results are presented for atmospheric temperature retrievals from a far infrared spectrum observed by an airborne uplooking heterodyne instrument.

Calculation of the T matrix in the null-field method with discrete sources

The problem of computing the transition matrix (T matrix) in the framework of the null-field method with discrete sources is treated. Numerical experiments are performed to investigate the symmetry property of the T matrix when localized and distributed vector spherical functions are used for solution construction.

Iterative regularization methods for atmospheric remote sensing

In this paper we present different inversion algorithms for nonlinear ill-posed problems arising in atmosphere remote sensing. The proposed methods are Landwebers method (LwM), the iteratively regularized Gauss-Newton method, and the conventional and regularizing Levenberg-Marquardt method. In addition, some accelerated LwMs and a technique for smoothing the Levenberg-Marquardt solution are proposed. The numerical performance of the methods is studied by means of simulations. Results are presented for an inverse problem in atmospheric remote sensing, i.e., temperature sounding with an airborne uplooking high-resolution far-infrared spectrometer.

Null-field method to electromagnetic scattering from uniaxial anisotropic particles

The electromagnetic scattering by a three-dimensional uniaxial anisotropic particle is studied. Electromagnetic fields in a uniaxial medium are expressed in terms of a system of vector functions which are similar to the system of regular spherical vector wave functions. The scattering problem is solved by using the null-field method. Numerical simulations for uniaxial anisotropic ellipsoids are presented.

Equivalent refractive index of a sphere with multiple spherical inclusions

In this paper we analyse the scattering by a spherical particle with multiple spherical inclusions. Our analysis is focused on the equivalence between the inhomogeneous sphere and a homogeneous sphere with an equivalent refractive index. The equivalent sphere reproduces the differential scattering cross section of the inhomogeneous sphere reasonably accurately. This equivalence is investigated for small and large size parameters of the inclusions.

Iteratively Regularized Gauss-Newton Method for Bound-Constraint Problems in Atmospheric Remote Sensing

In this paper two algorithms for the solution of nonlinear ill-posed problems with simple bounds on the variables are presented. The proposed algorithms are bound-constraint versions of the iteratively regularized Gauss-Newton method. The numerical performances of the algorithms are studied by means of simulations concerning the retrieval of molecular concentrations from limb sounding observations. For these examples, the unconstrained algorithm leads to unreasonable solutions.

Null-field method with discrete sources to electromagnetic scattering from layered scatterers

A novel formulation for improving the numerical stability of the null-field method for highly elongated and flattened layered scatterers is presented. The key step in this approach is to approximate the surface current densities by the lowest-order multipoles located in the complex plane. The accuracy of the proposed method is investigated from a numerical point of view.

T-matrix method for electromagnetic scattering from scatterers with complex structure

Abstract We describe a T-matrix program for light scattering calculations from particles with complex structure. The code treats the cases of homogeneous, layered and composite scatterers. These results are combined with basic results concerning the scattering by inhomogeneous scatterers and aggregates to apply to more general types of scatterers. Some numerical simulations are presented.