Multipoint formulas for scattered far field in multidimensions

We give asymptotic formulas for finding the scattering amplitude at fixed frequency and angles (scattered far field) from the scattering wave function given at n points in dimension d ⩾ 2. These formulas are explicit and their precision is proportional to n. To our knowledge these formulas are new f...

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Bibliographic Details
Published in:Inverse problems 2020-09, Vol.36 (9), p.95001
Main Author: Novikov, R G
Format: Article
Language:English
Subjects:
Analysis of PDEs
Helmholtz equation
inverse scattering problems
Mathematical Physics
Mathematics
scattered far field
scattered near field
Schrödinger equation
Vandermonde matrix
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Summary:We give asymptotic formulas for finding the scattering amplitude at fixed frequency and angles (scattered far field) from the scattering wave function given at n points in dimension d ⩾ 2. These formulas are explicit and their precision is proportional to n. To our knowledge these formulas are new for n ⩾ 2; whereas they reduce to a classical result for n = 1.
ISSN:0266-5611
1361-6420
DOI:10.1088/1361-6420/aba891