Two reconstruction procedures for a 3D phaseless inverse scattering problem for the generalized Helmholtz equation. (10th December 2015)

• Record Type: Journal Article
• Authors: Klibanov, Michael V; Romanov, Vladimir G
• Is Part Of: Inverse problems. Volume 32:Number 1(2016:Jan.)
• Publication Date: 2015-12-10
• Subjects: phaseless inverse scattering problem -- generalized Helmholtz equation -- reconstruction; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/1/015005
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: The 3D inverse scattering problem of the reconstruction of the unknown dielectric permittivity in the generalized Helmholtz equation is considered. Applications are in imaging of nanostructures and biological cells. The main difference with the conventional inverse scattering problems is that only the modulus of the scattering wave field is measured. The phase is not measured. The initializing wave field is the incident plane wave. On the other hand, in the previous recent works of the authors about the 'phaseless topic' the case of the point source was considered (Klibanov and Romanov 2015 J. Inverse Ill-Posed Problem 23 415–28 ; J. Inverse Ill-Posed Problem 23 187–93 ). Two reconstruction procedures are developed.