Wavefront sensing is a widely used non-interferometric, single-shot, and quantitative technique providing the spatial-phase of a beam. The phase is obtained by integrating the measured wavefront gradient. Complex and random wavefields intrinsically contain a high density of singular phase structures (optical vortices) associated with non-conservative gradients making this integration step especially delicate. Here, using a high-resolution wavefront sensor, we demonstrate experimentally a systematic approach for achieving the complete and quantitative reconstruction of complex wavefronts. Based on Stokes' theorem, we propose an image segmentation algorithm to provide an accurate determination of the charge and location of optical vortices. This technique is expected to benefit to several fields requiring complex media characterization.
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