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A two dimensional inverse scattering problem in which an acoustic plane wave is incident on a cylindrical object with the index of refraction varying only in two spatial directions is discussed. First, a modified method of lines procedure is developed to and the scattering amplitudes of the wave scattered from the object and compared with exact scattering amplitudes for some exactly solvable examples to verify its performance. Then, an inversion procedure is developed that uses the scattering amplitude for finding the object's profile. For that, Reese T. Prosser's procedure for the inversion in three dimensions is modified to our two dimensional case. Then, the back-scattered data is used to find both the Born approximation and Reese T. Prosser's first order approximation to find inversion results. Since the procedure requires the data to be available both for on-shell and off-shell values of the wave number, an interpolation method is developed to recover the needed data and inversion results are compared with exact values for a solid cylinder, a hollow cylinder and a shifted cylinder with constant index of refraction.
Inverse Problems in Scattering and Imaging is a collection of lectures from a NATO Advanced Research Workshop that integrates the expertise of physicists and mathematicians in different areas with a common interest in inverse problems. Covering a range of subjects from new developments on the applied mathematics/mathematical physics side to many areas of application, the book achieves a blend of research, review, and tutorial contributions. It is of interest to researchers in the areas of applied mathematics and mathematical physics as well as those working in areas where inverse problems can be applied.
The purpose of this text is to present the theory and mathematics of inverse scattering, in a simple way, to the many researchers and professionals who use it in their everyday research. While applications range across a broad spectrum of disciplines, examples in this text will focus primarly, but not exclusively, on acoustics. The text will be especially valuable for those applied workers who would like to delve more deeply into the fundamentally mathematical character of the subject matter.Practitioners in this field comprise applied physicists, engineers, and technologists, whereas the theory is almost entirely in the domain of abstract mathematics. This gulf between the two, if bridged, can only lead to improvement in the level of scholarship in this highly important discipline. This is the book's primary focus.
A careful exposition of a research field of current interest. This includes a brief survey of the subject and an introduction to recent developments and unsolved problems.