An exact formulation for the internal field equation of an assembly of small spherical particles irradiated by an electromagnetic wave is presented. It is demonstrated that the formulation is reduced to the existing solutions by suitable approximations of the self-contribution field term and satisfies the energy conservation (optical theorem) requirement. Further analysis shows that the Jones solution, the Purcell-Pennypacker PP and the Iskander-Chen-Penner ICP solutions violate the energy requirement whereas the Goedecke-O'Brien GO solution was found to be the lowest order compatible approximation of the exact solution, and as such satisfies the conservation of energy. Furthermore, the obtained field equation is invariant to coordinate transformation and yields an invariant T matrix which accounts correctly for multiple scattering effects. Comparisons of the results were carried out with the Jones solution, the PP, ICP and GO solutions. In addition, the applicability of the solution to the inversion of light scattering data, especially from sooting flames, is assessed.
A new, improved, and more efficient algorithm for calculation of the scattering, extinction, and absorption characteristics of agglomerates consisting of Rayleigh-size primary particles is presented. The computer code is based on a new formulation of the light scattering for such agglomerates and is more than 10 times faster than the codes based on previous formulations. The computational times required by the old and the new algorithms, run on VAX 7000, IBM 3090, and UNIX RS6000 mainframe computers, are compared for different agglomerate configurations, such as straight chains, clusters, and randomly branched chains. A distributed-parallel-computing scheme was used to run the new algorithm on four UNIX RS6000 processors concurrently, resulting in computational times 47 times faster than required for the calculations. Furthermore, the robustness and convenience of the algorithm are assessed.
This study focuses on the development of an in situ method which makes use of inverse scattering, namely the utilization of scattering measurements to infer morphological features and optical properties of the scatterer itself. Specifically, use is made of an exact formulation, developed recently by the authors, for the internal field of agglomerated structures composed of Rayleigh-size primary particles. All possible combinations of the scattering/extinction quantities with respect to the incident/scattered polarization state of the radiation field as well as the scattering angle are considered. Closed form (exact) expressions for the partial derivatives are presented for the selected quantities and the most suitable sets for data inversion are selected using the criteria for maximum sensitivity and maximum accuracy. The depolarization ratio in the vertical polarization state and the extinction normalized differential scattering intensities were identified as the most suitable set for inverting the corresponding measured quantities for the real and imaginary parts of the refractive index. Specific inversion examples are presented for the real and imaginary parts of the refractive index of primary particles agglomerated in the forms of straight chains, clusters and randomly branched chains. It is demonstrated that, for refractive indices typical of carbonaceous materials, such as flame soot, the present methodology yields reliable values. In addition it provides the prototype for extending the inversion scheme to higher than two-dimensional problems.
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