Hybrid phase retrieval using moment-based wavefront sensing and Gerchberg-Saxton iterative transform method

The iterative phase retrieval method has the intrinsic weakness in computational speed. However, its ability to capture fine spatial phase structure is clearly the benefit much needed in characterizing image quality of an instrument in an end-to-end fashion. The empirical wisdom of any iterative process is that the convergence becomes a lot faster when the initial guess is close to the phase solution. As an adaptation of this wisdom, we present the hybrid phase retrieval method where phase retrieval is conducted in combination of the moment-base wavefront sensing (MWFS) method and the Gerchberg-Saxton (GS) type iterative transform method. The moment-based method captures the large low-order phase based on the linear relation between the modal phase coefficients and the focal plane image moments. The MWFS estimate is then fed to the GS iterative method as the initial phase guess and diversity. At each GS iteration, the estimated phase is updated to the phase diversity. The iteration continues until the phase update is smaller than a pre-defined limit. For coarse spatial resolution systems, the MWFS estimate can be sufficient to determine the phase, while the hybridization with the GS process permits capturing much finer scale phase structures for systems requiring diffraction-scale spatial resolution. A case study is presented.