The challenges of high contrast imaging (HCI) for detecting exoplanets for both ground and space applications can be met with extreme adaptive optics (ExAO), a high-order adaptive optics system that performs wavefront sensing (WFS) and correction at high speed. We describe two ExAO optical system designs, one each for ground-based telescopes and space-based missions, and examine them using the angular spectrum Fresnel propagation module within the Physical Optics Propagation in Python (POPPY) package. We present an end-to-end (E2E) simulation of the MagAO-X instrument, an ExAO system capable of delivering 6$times10^{-5}$ visible-light raw contrast for static, noncommon path aberrations without atmosphere. We present a laser guidestar (LGS) companion spacecraft testbed demonstration, which uses a remote beacon to increase the signal available for WFS and control of the primary aperture segments of a future large space telescope, providing on order of a factor of ten factor improvement for relaxing observatory stability requirements. The LGS E2E simulation provides an easily adjustable model to explore parameters, limits, and trade-offs on testbed design and characterization.
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