Two reconstruction procedures for a 3-d phaseless inverse scattering problem for the generalized Helmholtz equation

TL;DR

This paper introduces two novel reconstruction procedures for a 3D phaseless inverse scattering problem involving the generalized Helmholtz equation, enabling dielectric permittivity imaging without phase measurements, applicable to nanostructures and biological cells.

Contribution

The paper develops two new linearized reconstruction methods for a 3D phaseless inverse scattering problem that do not rely on the Born approximation, maintaining stability at high frequencies.

Findings

Two reconstruction procedures successfully recover dielectric permittivity.

Methods are stable at high frequencies unlike the Born approximation.

Applications demonstrated in nanostructure and biological cell imaging.

Abstract

The 3-d inverse scattering problem of the reconstruction of the unknown dielectric permittivity in the generalized Helmholtz equation is considered. 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 [20,21,22]. Two reconstruction procedures are developed for a linearized case. However, the linearization is not the Born approximation. This means that, unlike the Born approximation, our linearization does not break down when the frequency tends to the infinity. Applications are in imaging of nanostructures and biological cells.