  Wavefront sensing is a non-interferometric, single-shot, and quantitative
technique providing the spatial-phase of a beam. The phase is obtained by
integrating the gradient of the wavefront. This integration step is especially
delicate in the presence of optical vortices, which are topologically stable
singular structures that spontaneously appear in wavefields, and that are
associated with non-conservative gradient-maps. Unlike incomplete
reconstructions typically achieved in such cases, we demonstrate a systematic
approach for high-resolution wavefront sensing of complex wavefronts. The
method consists in applying an image processing algorithm to the Helmholtz
decomposition of the wavevector field. This improvement is expected to benefit
to several fields ranging from diffraction tomography to adaptive optics in
scattering media.
