  We propose and implement a broadband, compact, and low-cost wavefront sensing
scheme by simply placing a thin diffuser in the close vicinity of a camera. The
local wavefront gradient is determined from the local translation of the
speckle pattern. The translation vector map is computed thanks to a fast
diffeomorphic image registration algorithm and integrated to reconstruct the
wavefront profile. The simple translation of speckle grains under local
wavefront tip/tilt is ensured by the so-called "memory effect" of the diffuser.
Quantitative wavefront measurements are experimentally demonstrated both for
the few first Zernike polynomials and for phase-imaging applications requiring
high resolution. We finally provided a theoretical description of the
resolution limit that is supported experimentally.
