Low observable technology is used in order to prevent detection, or to delay detection. Radar cross section is an important parameter in aircraft survivability since it measures how detectable an object is with radar. To find the radar cross section Maxwell's equations are solved numerically in the time-domain using a finite difference scheme. This numerical method called Finite Difference Time Domain is very suitable for structures including complex materials. However, this numerical method needs to be verified for large scale simulations, due to numerical dispersion errors. Therefore it is desirable to verify the accuracy of the numerical simulations. In this project, the analytical solution to the multiple scattering by two spheres is implemented using the T-matrix formulation. The analytical solution to the scattering problem is first validated with the analytical Mie-series solution then compared to the Finite Difference Time Domain implementation. The results imply that the difference between the numerical and analytical solution is larger for higher frequencies and larger computational volumes. / Smygteknik används för att förhindra detektering, eller för att fördröja detektion av ett flygplan. Radarmålarea är en viktig parameter för skyddsprestanda hos flygplan eftersom den mäter hur detekterbar ett föremål är med radar. För att hitta radarmålarean löses Maxwells ekvationer numeriskt i tidsdomänen med hjälp av ett finit differensschema. Den numeriska metoden som kallas Finita differensmetoden i tidsdomän, är mycket lämplig för strukturer med komplexa material. Den numeriska metoden behöver valideras för storskaliga simuleringar eftersom det förekommer felaktigheter på grund av den numeriska dispersionen. Därför är det önskvärt att kontrollera riktigheten av de numeriska simuleringarna. I detta projekt, är den analytiska lösningen till multipelspridning av två sfärer implementerad med hjälp av T-matrismetoden. Den analytiska lösningen på spridningsproblemet valideras först mot den analytiska Mie-serielösningen och sedan jämförs den med resultatet av simuleringarna med Finita differensmetoden i tidsdomän. Resultaten antyder att skillnaden mellan den numeriska och analytiska lösningen är större för högre frekvenser och större beräkningsvolymer.

Identification of the resonances and the local determination of the radius of curvature of an acoustically rigid sphere from simulated transient input-output data is presented. The scattering from the sphere is formulated using three techniques: the classic Mie-Lorenz series, the singularity expansion method (SEM), and the asymptotic series approximation. The Mie-Lorenz series is used to provide synthetic data. The SEM and the asymptotic series are used to develop two parametric inverse models. The scattered velocity potential is separated into three components: the reflection, the first creeping wave, and the second creeping wave. The effect of removing various components of the scattered potential on the resonance identification is shown, along with the effect of adding small amounts of noise. We find that the identification of a few resonances requires a relatively high order autoregressive, moving-average model. In addition, we show that removing the reflection from the synthetic output has only a small effect on the single or multiple output identified resonances. However, we find that changing the time origin, removing the second creeping wave, or adding small amounts of noise results in large errors in the identified resonances. We find that the radius of curvature can be accurately determined from synthetic data using the asymptotic series based identification. In addition, the identification is robust in the presence of noise, and requires only a low order asymptotic series model.

by Yip Sung-tat. / Bibliography: leaves 120-123 / Thesis (M.Ph.)--Chinese University of Hong Kong, 1984

Inverse problems arise in numerous fields of science and engineering where one tries to find out the desired information of an unknown object or the cause of an observed effect. They are of fundamental importance in many areas including radar and sonar applications, nondestructive testing, image processing, medical imaging, remote sensing, geophysics and astronomy among others. This study is concerned with three issues in scattering theory, fractional operators, as well as some of their inverse problems. The first topic is scattering problems for electromagnetic waves governed by Maxwell equations. It will be proved in the current study that an inhomogeneous EM medium with a corner on its support always scatters by assuming certain regularity and admissible conditions. This result implies that one cannot achieve invisibility for such materials. In order to verify the result, an integral of solutions to certain interior transmission problem is to be analyzed, and complex geometry optics solutions to corresponding Maxwell equations with higher order estimate for the residual will be constructed. The second problem involves the linearized elastic or seismic wave scattering described by the Lamei system. We will consider the elastic or seismic body wave which is composed of two different type of sub-waves, that is, the compressional or primary (P-) and the shear or secondary (S-) waves. We shall prove that the P- and the S-components of the total wave can be completely decoupled under certain geometric and boundary conditions. This is a surprising finding since it is known that the P- and the S-components of the elastic or seismic body wave are coupled in general. Results for decoupling around local boundary pieces, for boundary value problems, and for scattering problems are to be established. This decoupling property will be further applied to derive uniqueness and stability for the associated inverse problem of identifying polyhedral elastic obstacles by an optimal number of scattering measurements. Lastly, we consider a type of fractional (and nonlocal) elliptic operators and the associated Calderoin problem. The well-posedness for a kind of forward problems concerning the fractional operator will be established. As a consequence, the corresponding Dirichlet to Neumann map with certain mapping property is to be defined. As for the inverse problem, it will be shown that a potential can be uniquely identified by local Cauchy data of the associated nonlocal operator, in dimensions larger than or equal to two.

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Scalar and vector electromagnetic boundary-value theories of surface scattering have been applied to a microrough sample of fused silica coated with aluminum. Surface profiles were made with a mechanical and interferometric profilometer. The resulting values of rms surface height and autocorrelation length were used to calculate the scattering for various angles, wavelengths, and polarization conditions. Bidirectional reflectance distribution function (BRDF) measurements associated with scatter value were made and their corresponding power spectra were generated. Both were used to compare with the theoretical values. Special attention was also paid to the various methods of determining optical parameters with the BRDF data and the corresponding power spectra.

A system consisting of a sphere sitting on a clean mirror was modeled as a two particle system: the real sphere and its image sphere, treating the mirror as a conducting plane. When the system was irradiated with a plane-polarized collimated laser beam with varying angles of incidence, the scattering from each particle was assumed to follow Mie's solution for light scattering by a sphere. Phase difference between the scattering by the real sphere and the one by its image sphere was assessed by the geometry of the model. The far field solutions from each of the spheres were added to yield a phase dependent intensity function. Another model assumed no phase correlation between the two and the intensities from each spheres were added. Also discussed is the Double Interaction Mode, which takes the mirror-sphere separation into consideration. These theoretical results were converted to Bidirectional Reflectance Distribution Functions (BRDF). The theoretical as well as the empirical surface scattering from a good quality optical surface was introduced. The BRDF values thus calculated were added to the background scattering by the mirror since no interaction was assumed between the spheres and the rough metallic surface of the mirror. The test sample was prepared with polystyrene spheres with the nominal diameter of 0.984 μm on a high quality aluminum mirror. The BRDF data from this sample with 6328Å and 4416Å were compared with the one obtained with the model described above. The comparison strongly indicated that there existed no phase correlation between the scatterings by the two spheres. Determination of the sphere size and practical applicability for estimating the sphere number density on the surface are also discussed.

Elastic scattering and inelastic excitation of the second, unbound, state 9Be (5/2ˉ, 2.43 MeV) for the identical-particle fermionic system 9Be + 9Be have been measured at the highest incident beam energy presently available ELab(9Be) = 25 MeV. A 9Be beam, produced by the General Ionex Corporation model 860C sputter ion-source, was accelerated by the EN Tandem Van de Graaff accelerator of the iThemba LABS (Gauteng) and was used to bombard a thin 9Be target. The experimental equipment associated with the C-line includes a high resolution ΔE-E gas-ionisation detector coupled to a small scattering chamber. Energy loss and residual energy signals were processed using a CAMAC-based plus OS/2 WIMPS2 data acquisition system running on an online computer. The ΔE-E plots were used to identify the reaction products and their kinematic energies, thereby determining the elastic and inelastic scattering cross-sections. The elastic and inelastic scattering data were analysed in terms of the optical model and Distorted Wave Born Approximation, respectively. Angular distribution data for the elastic scattering for 9Be + 9Be conformed well to the optical model predictions using an energy-independent optical model potential. Inelastic scattering cross-sections were determined up to θc.m.  135° and symmetry effects were investigated. As such, excitation of the second, unbound, state 9Be (5/2ˉ, 2.43 MeV) via a strong E2 one-step two-body interaction from the 9Be (3/2ˉ, g.s.) did not show effects due to symmetry in the entrance channel. These results were consistent with a previous study at ELab(9Be) = 16 MeV.