Wavefront retrieval through random pupil plane phase probes: Gerchberg-Saxton approach

A pupil plane wavefront reconstruction procedure is proposed based on analysis of a sequence of focal plane images corresponding to a sequence of random pupil plane phase probes. The developed method provides the unique nontrivial solution of wavefront retrieval problem and shows global convergence to this solution demonstrated using a Gerchberg-Saxton implementation. The method is general and can be used in any optical system that includes deformable mirrors for active/adaptive wavefront correction. The presented numerical simulation and lab experimental results show low noise sensitivity, high reliability and robustness of the proposed approach for high quality optical wavefront restoration. Laboratory experiments have shown $\lambda$/14 rms accuracy in retrieval of a poked DM actuator fiducial pattern with spatial resolution of 20-30$~\mu$m that is comparable with accuracy of direct high-resolution interferometric measurements.