Phase recovery from phaseless scattering data for discrete Schr\"{o}dinger operators

TL;DR

This paper develops formulas to recover phase information from phaseless near-field scattering data for discrete Schrödinger operators on square lattices, aiding inverse scattering problems.

Contribution

It introduces a method to determine phased scattering amplitudes solely from phaseless data for discrete Schrödinger operators.

Findings

Formulas for phased scattering amplitude recovery

Applicable to compactly supported potentials on lattice

Advances inverse scattering techniques

Abstract

We consider scattering for the discrete Schr\"{o}dinger operator on the square lattice $\mathbb{Z}^d$, $d \ge 1$, with compactly supported potential. We give formulas for finding the phased scattering amplitude from phaseless near-field scattering data.