Focal-plane electric field sensing with pupil-plane holograms

The direct detection and spectral characterization of exoplanets requires a coronagraph to suppress the diffracted star light. Amplitude and phase aberrations in the optical train fill the dark zone of the coronagraph with quasi-static speckles that limit the achievable contrast. Focal-plane electric field sensing, such as phase diversity introduced by a deformable mirror (DM), is a powerful tool to minimize this residual star light. The residual electric field can be estimated by sequentially applying phase probes on the DM to inject star light with a well-known amplitude and phase into the dark zone and analyzing the resulting intensity images. The DM can then be used to add light with the same amplitude but opposite phase to destructively interfere with this residual star light. Using a static phase-only pupil-plane element we create holographic copies of the point spread function (PSF), each superimposed with a certain pupil-plane phase probe. We therefore obtain all intensity images simultaneously while still retaining a central, unaltered science PSF. The electric field sensing method only makes use of the holographic copies, allowing for correction of the residual electric field while retaining the central PSF for uninterrupted science data collection. In this paper we demonstrate the feasibility of this method with numerical simulations.