Experimental demonstration of Monge-Ampère equation for coherent beam field reconstruction

High-precision phase reconstruction is crucial for beam analysis and control. In a previous work, we proposed a phase retrieval method based on the Monge-Ampère equation (MAE). Similar to the commonly-used transport of intensity equation (TIE), the MAE is also a partial differential equation (PDE) that describes the relationship between irradiance and phase. However, in the framework of geometric optics, the MAE could be a more accurate and general method for solving the phase retrieval problem compared to the TIE. In this paper, we apply the MAE to reconstruct the field of a laser beam. By capturing two irradiance distributions at two different planes that are perpedicular to the propagation direction, the complex amplitude distribution at the first plane can be retrieved based on the MAE method. The angular spectrum method is employed to determine the complex amplitude distributions at different positions along the beam propagation direction. The factor of the laser beam is calculated based on the reconstructed beam field. Results show that the factor values computed based on the MAE method have small deviations from that tested with a commercial beam profiler.