A note on an extended born method in inverse scattering problems

✍ Scribed by S.C. Jun; U.J. Choi

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 238 KB
• Volume: 12
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/s0893-9659(98)00175-x

✦ Synopsis

The open question suggested by Murch in [1] is how the vectors al,a2,..., can be obtained from the scattering data for some wavenumbers k and for all incident waves. In this paper, it is suggested how the constants a0 and al can be used for reconstruction from the scattering data with the other an, n > 2 being ignored. Numerical implementation is presented for comparison with Murch's work. (~) 1999 Elsevier Science Ltd. All rights reserved.

Keywords--Born approximation, Inverse scattering problems, Extended born method, Far field pattern.

Let space ]~2 be partitioned as R 2 -S+ U S_,

where S_ represents the region of space in which the body of interest exists and S+ is the background media. We consider scalar two-dimensional wave motion which is time harmonic with free-space wave number k and suppress the time dependence of e ~t. The wave field satisfies