Zonal reconstruction of photonic wavefunction via momentum weak measurement

Direct measurement of wave functions has attracted great interests and many different methods have been developed. However, the precision of current techniques is limited by the use of Fourier transform lenses. These measurements require to shear cut the part of particles with momentum P=0, which greatly restricts the efficiency and application of the approaches. Here, we propose and experimentally demonstrate a method to directly measure two-dimensional photonic wave functions by combining the momentum weak measurement technology and the zonal wavefront restoration algorithm. Both the Gaussian and Laguerre-Gaussian wave functions are experimentally well reconstructed. Our method avoids using the Fourier lens and post selection on the momentum P=0. We further apply it to measure wavefronts with ultra-high spatial frequency, which is difficult for traditional Shack-Hartmann wavefront sensing technologies. Our work extends the ability of quantum weak measurement and would be useful for wavefront sensing.