  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.
