Phaseless inverse scattering with background information

We consider phaseless inverse scattering for the multidimensional Schrödinger equation with unknown potential v using the method of known background scatterers. In particular, in dimension d ⩾ 2, we show that | f 1 | 2 at high energies uniquely determines v via explicit formulas, where f 1 is the sc...

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Bibliographic Details
Published in:Inverse problems 2021-05, Vol.37 (5), p.55011
Main Authors: Novikov, R G, Sivkin, V N
Format: Article
Language:English
Subjects:
Analysis of PDEs
Mathematical Physics
Mathematics
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Summary:We consider phaseless inverse scattering for the multidimensional Schrödinger equation with unknown potential v using the method of known background scatterers. In particular, in dimension d ⩾ 2, we show that | f 1 | 2 at high energies uniquely determines v via explicit formulas, where f 1 is the scattering amplitude for v + w 1 , w 1 is an a priori known nonzero background scatterer, under the condition that supp  v and supp  w 1 are sufficiently disjoint. If this condition is relaxed, then we give similar formulas for finding v from | f | 2 , | f 1 | 2 , where f is the scattering amplitude for v . In particular, we continue studies of Novikov (2016 J. Geom. Anal. 26 346–59) and Leshem et al (2016 Nat. Commun. 7 1–6).
ISSN:0266-5611
1361-6420
DOI:10.1088/1361-6420/abf36c