On Phase Unwrapping via Digital Wavefront Sensors

TL;DR

This paper introduces a novel phase unwrapping method by leveraging digital wavefront sensor reconstruction techniques, treating wrapped phase as wavefront aberration, and demonstrates its effectiveness through numerical tests in optical communication scenarios.

Contribution

It presents a new phase unwrapping approach based on wavefront sensor principles, bridging optical wavefront reconstruction and phase unwrapping tasks.

Findings

The method effectively unwraps phase in simulated optical communication data.

It compares favorably with existing state-of-the-art algorithms.

Numerical results validate the approach's potential in practical applications.

Abstract

In this paper, we derive a new class of methods for the classic 2D phase unwrapping problem of recovering a phase function from its wrapped form. For this, we consider the wrapped phase as a wavefront aberration in an optical system, and use reconstruction methods for (digital) wavefront sensors for its recovery. The key idea is that mathematically, common wavefront sensors are insensitive to whether an incoming wavefront is wrapped or not. However, typical reconstructors for these sensors are optimized to compute smooth wavefronts. Thus, digitally "propagating" a wrapped phase through such a sensor and then applying one of these reconstructors results in a smooth unwrapped phase. First, we show how this principle can be applied to derive phase unwrapping algorithms based on digital Shack-Hartmann and Fourier-type wavefront sensors. Then, we numerically test our approach on an unwrapping problem appearing in a free-space optical communications project currently under development, and compare the results to those obtained with other state-of-the-art algorithms.