  The performance of high-contrast imaging instruments is limited by wavefront
errors, in particular by non-common path aberrations (NCPAs). Focal-plane
wavefront sensing (FPWFS) is appropriate to handle NCPAs because it measures
the aberration where it matters the most, that is to say at the science focal
plane. Phase retrieval from focal-plane images results, nonetheless, in a sign
ambiguity for even modes of the pupil-plane phase. The phase diversity methods
currently used to solve the sign ambiguity tend to reduce the science duty
cycle, that is, the fraction of observing time dedicated to science. In this
work, we explore how we can combine the phase diversity provided by a vortex
coronagraph with modern deep learning techniques to perform efficient FPWFS
without losing observing time. We applied the state-of-the-art convolutional
neural network EfficientNet-B4 to infer phase aberrations from simulated
focal-plane images. The two cases of scalar and vector vortex coronagraphs (SVC
and VVC) were considered using a single post-coronagraphic point spread
function (PSF) or two PSFs obtained by splitting the circular polarization
states, respectively. The sign ambiguity has been properly lifted in both cases
even at low signal-to-noise ratios (S/Ns). Using either the SVC or the VVC, we
have reached a very similar performance compared to using phase diversity with
a defocused PSF, except for high levels of aberrations where the SVC slightly
underperforms compared to the other approaches. The models finally show great
robustness when trained on data with a wide range of wavefront errors and noise
levels. The proposed FPWFS technique provides a 100% science duty cycle for
instruments using a vortex coronagraph and does not require any additional
hardware in the case of the SVC.

Instrumentation and Methods for Astrophysics