Optimizing the Regularization in Broadband Wavefront Control Algorithm for WFIRST Coronagraph

The WFIRST/AFTA 2.4 m space telescope currently under study includes a stellar coronagraph for the imaging and the spectral characterization of extrasolar planets. The coronagraph employs sequential deformable mirrors to compensate for phase and amplitude errors. Using the optical model of an Occulting Mask Coronagraph (OMC) testbed at the Jet Propulsion Laboratory (JPL), we have investigated and compared through modeling and simulations the performance of several actuator regularization-schemes in broadband wavefront control algorithm used to generate dark holes in an OMC, such as a Hybrid Lyot Coronagraph (HLC). Using the concept of a Tikhonov filter constituting the G-matrix, we have explained what the different regularization schemes do to singular-modes during a wavefront control process called Electric Field Conjugation (EFC). In some cases we confirmed the numerical predictions with the testbed measured results. We present our findings in this paper.