The New Solution of the Ill-Posed Inverse Problems of Electromagnetic Waves Diffraction. 1. General Theory
A.Y. Perelman, I.V. Bulavinscky
St. Petersburg State Forest Technical Academy, 5, Institutskyi Lane, St. Petersburg 194021, Russia
Address all correspondence to I.V. Bulavinscky E-mail: Bulavinscky@rambler.ru
K.S. Shifrin
The Oregon State University, Oreg. USA (retired)
Abstract
The new method to solve the ill-posed inverse problems of the electromagnetic wave diffraction by spherical particles is developed. The method is based on the generalization of the known direct and inverse integral transforms. Both of them are exactly expressed in terms of the elementary and conventional special functions providing the correct regularization of the initial ill-posed inverse problems. The generalized cosine transform (GCT) is introduced and investigated in detail. The modified inversion formula for a typical collection (the Q-model) of the integral coefficients (IC) is derived. This formula simplifies the general inverse GCT. The important optical characteristics of a spherical particle can be fairly well uniformly approximated within the framework of the GCT. It allows obtaining the exact solutions of some ill-posed inverse optical problems. Examples illustrating the effectiveness of the proposed theory are given. In particular, GCT essentially simplifies the known algorithms of transparency, scattering pattern and other methods of the optical inversion. The paper is with the exposition of the ideas and approaches recently obtained by Prof K.S. Shifrin with the integral transform applied to optics.
KEY WORDS: particle size distribution, complex refractive index, inverse problem, generalized cosine transform
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