On Phase Unwrapping via Digital Wavefront Sensors

In this paper wederive 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.