Far Field Amplitudes And Inverse Diffraction Theory

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Far Field Amplitudes And Inverse Diffraction Theory
Samuel Karp
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It is of interest to consider the case when is fixed or o also, the case of variable 0, 0 . The program to be followed would be to use f to determine v and hence u, and then to find the locus on which u obeys the boundary conditions. This is obviously difficult in general. In the present paper we prove some simple results which relate f and S under special circumstances. The present section is concerned with properties which arise from a consideration of determinants formed from f(0, 0 ), i. E.... Det(f. . ). We treat the boundary conditions u = 0, Su/Sn == in this paper. The main results will now be listed.
Case a ). Soft obstacles, boundary condition u. = 0. We prove the following theorems.
Theorem la . If det(f . . ) = 0, where {0. } = 0-, ,0^, . . . , 0 are n ij 1 1 2' ' n different angles modulo 2n, and if no subdeterrainant vanishes, then there exist n nonvanishing constants (A ) such that the necessary and sufficient condition for (x, y) to be on S is that n > A exp ik(x cos + y sin ) = .


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