Millisecond exoplanet imaging: I. method and simulation results
Authors: Rodack Alexander T. , Frazin Richard A. , Males Jared R. , Guyon Olivier 
Published: August 2021

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

5
σ

contrast achieved by imaging of the
exoplanet scene was

∼

1.7
×

10

−
4

at a distance of

3
λ

/

D

from the star and

∼

2.1
×

10

−
5

at

10
λ

/

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.