Millisecond exoplanet imaging: I. method and simulation results.

One of the top priorities in observational astronomy is the direct imaging and characterization of extrasolar planets (exoplanets) and planetary systems. Direct images of rocky exoplanets are of particular interest in the search for life beyond the Earth, but they tend to be rather challenging targets since they are orders-of-magnitude dimmer than their host stars and are separated by small angular distances that are comparable to the classical λ/D diffraction limit, even for the coming generation of 30 m class telescopes. Current and planned efforts for ground-based direct imaging of exoplanets combine high-order adaptive optics (AO) with a stellar coronagraph observing at wavelengths ranging from the visible to the mid-IR. The primary barrier to achieving high contrast with current direct imaging methods is quasi-static speckles, caused largely by non-common path aberrations (NCPAs) in the coronagraph optical train. Recent work has demonstrated that millisecond imaging, which effectively "freezes" the atmosphere's turbulent phase screens, should allow the wavefront sensor (WFS) telemetry to be used as a probe of the optical system to measure NCPAs. Starting with a realistic model of a telescope with an AO system and a stellar coronagraph, this paper provides simulations of several closely related regression models that take advantage of millisecond telemetry from the WFS and coronagraph's science camera. The simplest regression model, called the naïve estimator, does not treat the noise and other sources of information loss in the WFS. Despite its flaws, in one of the simulations presented herein, the naïve estimator provides a useful estimate of an NCPA of ∼0.5 radian RMS (≈λ/13), with an accuracy of ∼0.06 radian RMS in 1 min of simulated sky time on a magnitude 8 star. The bias-corrected estimator generalizes the regression model to account for the noise and information loss in the WFS. A simulation of the bias-corrected estimator with 4 min of sky time included an NCPA of ∼0.05 radian RMS (≈λ/130) and an extended exoplanet scene. The joint regression of the bias-corrected estimator simultaneously achieved an NCPA estimate with an accuracy of ∼5×10-3 radian RMS and an estimate of the exoplanet scene that was free of the self-subtraction artifacts typically associated with differential imaging. The 5σ contrast achieved by imaging of the exoplanet scene was ∼1.7×10-4 at a distance of 3λ/D from the star and ∼2.1×10-5 at 10λ/D. These contrast values are comparable to the very best on-sky results obtained from multi-wavelength observations that employ both angular differential imaging (ADI) and spectral differential imaging (SDI). This comparable performance is despite the fact that our simulations are quasi-monochromatic, which makes SDI impossible, nor do they have diurnal field rotation, which makes ADI impossible. The error covariance matrix of the joint regression shows substantial correlations in the exoplanet and NCPA estimation errors, indicating that exoplanet intensity and NCPA need to be estimated self-consistently to achieve high contrast.

Millisecond exoplanet imaging: II. regression equations and technical discussion.

The leading difficulty in achieving the contrast necessary to directly image exoplanets and associated structures (e.g., protoplanetary disks) at wavelengths ranging from the visible to the infrared is quasi-static speckles (QSSs). QSSs are hard to distinguish from planets at the necessary level of precision to achieve high contrast. QSSs are the result of hardware aberrations that are not compensated for by the adaptive optics (AO) system; these aberrations are called non-common path aberrations (NCPAs). In 2013, Frazin showed how simultaneous millisecond telemetry from the wavefront sensor (WFS) and a science camera behind a stellar coronagraph can be used as input into a regression scheme that simultaneously and self-consistently estimates NCPAs and the sought-after image of the planetary system (exoplanet image). When run in a closed-loop configuration, the WFS measures the corrected wavefront, called the AO residual (AOR) wavefront. The physical principle underlying the regression method is rather simple: when an image is formed at the science camera, the AOR modules both the speckles arising from NCPAs as well as the planetary image. Therefore, the AOR can be used as a probe to estimate NCPA and the exoplanet image via regression techniques. The regression approach is made more difficult by the fact that the AOR is not exactly known since it can be estimated only from the WFS telemetry. The simulations in the Part I paper provide results on the joint regression on NCPAs and the exoplanet image from three different methods, called ideal, naïve, and bias-corrected estimators. The ideal estimator is not physically realizable (it is useful as a benchmark for simulation studies), but the other two are. The ideal estimator uses true AOR values (available in simulation studies), but it treats the noise in focal plane images via standard linearized regression. Naïve regression uses the same regression equations as the ideal estimator, except that it substitutes the estimated values of the AOR for true AOR values in the regression formulas, which can result in problematic biases (however, Part I provides an example in which the naïve estimate makes a useful estimate of NCPAs). The bias-corrected estimator treats the errors in AOR estimates, but it requires the probability distribution that governs the errors in AOR estimates. This paper provides the regression equations for ideal, naïve, and bias-corrected estimators, as well as a supporting technical discussion.