# Uniqueness of a 3-D coefficient inverse scattering problem without the phase information

## TL;DR

This paper proves a uniqueness theorem for a 3-D inverse scattering problem where only the magnitude of the scattered wave is measured, which is relevant for imaging nanostructures and biological cells.

## Contribution

It introduces a new method to establish uniqueness in a phase-less inverse scattering problem for the 3-D Helmholtz equation, advancing imaging techniques without phase information.

## Key findings

- Proves uniqueness for the phase-less inverse scattering problem
- Applicable to imaging nanostructures and biological cells
- Develops a new mathematical approach for inverse problems

## Abstract

We use a new method to prove uniqueness theorem for a coefficient inverse scattering problem without the phase information for the 3-D Helmholtz equation. We consider the case when only the modulus of the scattered wave field is measured and the phase is not measured. The spatially distributed refractive index is the subject of the interest in this problem. Applications of this problem are in imaging of nanostructures and biological cells.