Advancing Wavefront Control Algorithms for Dark Hole Creation and Maintenance

Abstract

To directly image exoplanets, advanced wavefront control methods will be required to generate and maintain high contrast regions in an image plane. This is due to the fact that host stars and exoplanets will have relatively small angular separations and very high flux ratios. As an example, an Earth-Sun analog system at a distance of 10 parsec would have an angular separation of 100 mas and a flux ratio approaching 1E10. This combination of challenges means an exoplanet will be overwhelmed by diffracted starlight in the image plane. Instruments known as coronagraphs have been developed to reject the on-axis signal of a star, but manufacturing errors on the optical surfaces of the telescope and instrument result in diffracted residuals known as ``speckles'' that often limit coronagraphs near the 1E-5 contrast regime. To further suppress these speckles, a family of high order wavefront sensing and control (HOWFSC) techniques have been developed to iteratively sense and suppress the speckles using deformable mirrors (DMs). These DMs have high actuator counts that allow HOWFSC techniques to control many high order modes and create regions of high contrast in the image known as ``dark holes''. But due to the sensitivity of coronagraph instruments to pointing errors and other low order aberrations, the wavefront must also be stabilized for long observation periods using a low order wavefront sensing and control (LOWFSC) scheme. Here, various HOWFSC algorithms have been implemented and tested both with simulations and testbed experiments to understand and advance their capabilities. The first work studied the implicit electric field conjugation (iEFC) method in the context of the coronagraph instrument for the Roman Space Telescope. This study utilized an end-to-end physical optics model to simulate performance of iEFC where we showed that a contrast of 1E-8 can likely be achieved for a specific mode of the Roman Coronagraph. The second study compared the standard EFC method with the newer adjoint EFC (aEFC) technique for a vortex coronagraph. While EFC requires a Jacobian, which can take extended compute times to generate along with large memory allocation space, aEFC uses algorithmic differentiation to solve for the DM commands with nonlinear optimization. For this work, an adjoint model for a vortex coronagraph is hand-derived and implemented using open-source programming and demonstrated aEFC achieving sub-1E-8 contrasts on the Space Coronagraph Optical Bench (SCoOB). Lastly, SCoOB was used to perform experiments that demonstrate how to combine a HOWFSC method with a Lyot-based LOWFSC scheme for a vortex coronagraph. Here, LOWFSC is used to correct for low order aberrations while iEFC is simultaneously used to create a dark hole. This work demonstrates that the iEFC algorithm can be calibrated and achieve 1E-8 contrasts while Lyot-LOWFSC maintains a stable wavefront. Together, these works demonstrate a variety of HOWFSC methods needed to achieve contrast ratios that will enable exoplanet imaging and how Lyot-LOWFSC can be combined with HOWFSC to maintain high contrasts.