Control algorithms for dual-wavefront sensor single-conjugate adaptive optics

High-contrast imaging systems using active control with adaptive optics (AO) are often limited by non-common path (NCP) aberrations that are seen only at the final science image. AO systems employing focal-plane wavefront sensors (FP-WFSs) are able to simultaneously correct NCP aberrations and measure science images, but they typically require a second stage of control that adds system cost and complexity. We present control algorithms to augment AO systems with FP-WFSs within their existing control setup. We demonstrate inter-arm NCP aberration transfer can be mitigated through temporal filtering, present frequency- and time-domain validation of controller stability and performance, and discuss the optimality of the chosen controllers. This work will enable the development, testing, and installation of FP-WFS technologies for direct imaging of exoplanets.