Transport of Intensity Phase Retrieval of Arbitrary Wave Fields Including Vortices

TL;DR

This paper presents an advanced Transport of Intensity Equation (TIE) method that accurately reconstructs the phase of arbitrary wave fields, including those with zeros and partial coherence, broadening its applicability across multiple scientific disciplines.

Contribution

It introduces a rigorous TIE solution for wave fields with zeros using boundary conditions and extends phase reconstruction to partially coherent waves.

Findings

Reconstruction of wave phase with zeros using boundary conditions.

Modified TIE reconstructs curl-free current density under partial coherence.

Applicable to diverse fields like astrophysics, geophysics, and microscopy.

Abstract

The phase problem can be considered as one of the cornerstones of quantum mechanics intimately connected to the detection process and the uncertainty relation. The latter impose fundamental limits on the manifold phase reconstruction schemes invented to date in particular at small magnitudes of the quantum wave. Here, we show that a rigorous solution of the Transport of Intensity Reconstruction (TIE) scheme in terms of a linear elliptic partial differential equation for the phase provides reconstructions even in the presence of wave zeros if particular boundary conditions (BCs) are given. We furthermore discuss how partial coherence hampers phase reconstruction and show that a modified version of the TIE reconstructs the curl-free current density at arbitrary (in-)coherence. This opens the way for a large variety of new applications in fields as diverse as astrophysics, geophysics, photonics, acoustics, and electron microscopy, where zeros in the respective wave field are a ubiquitous feature.