  Direct imaging of Earth-like planets is one of the main science cases for the
next generation of extremely large telescopes. This is very challenging due to
the star-planet contrast that must be overcome. Most current high-contrast
imaging instruments are limited in sensitivity at small angular separations due
to non-common path aberrations (NCPA). The NCPA leak through the coronagraph
and create bright speckles that limit the on-sky contrast and therefore also
the post-processed contrast. We aim to remove the NCPA by active focal plane
wavefront control using a data-driven approach. We developed a new approach to
dark hole creation and maintenance that does not require an instrument model.
This new approach is called implicit Electric Field Conjugation (iEFC) and it
can be empirically calibrated. This makes it robust for complex instruments
where optical models might be difficult to realize. Numerical simulations have
been used to explore the performance of iEFC for different coronagraphs. The
method was validated on the internal source of the Magellan Adaptive Optics
eXtreme (MagAO-X) instrument to demonstrate iEFC's performance on a real
instrument. Numerical experiments demonstrate that iEFC can achieve deep
contrast below $10^{-9}$ with several coronagraphs. The method is easily
extended to broadband measurements and the simulations show that a bandwidth up
to 40% can be handled without problems. Experiments with MagAO-X showed a
contrast gain of a factor 10 in a broadband light and a factor 20 to 200 in
narrowband light. A contrast of $5\cdot10^{-8}$ was achieved with the Phase
Apodized Pupil Lyot Coronagraph at 7.5 $\lambda/D$. The new iEFC method has
been demonstrated to work in numerical and lab experiments. It is a method that
can be empirically calibrated and it can achieve deep contrast. This makes it a
valuable approach for complex ground-based high-contrast imaging systems.

Instrumentation and Methods for Astrophysics;Earth and Planetary Astrophysics