Phaseless inverse scattering with background information. (21st April 2021)

• Record Type: Journal Article
• Authors: Novikov, R G; Sivkin, V N
• Is Part Of: Inverse problems. Volume 37:Number 5(2021)
• Publication Date: 2021-04-21
• Subjects: Schrödinger equation -- Helmholtz equation -- phaseless inverse scattering -- phase retrieval problem; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abf36c
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: 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).