  Context. Spectroscopy of exoplanets is very challenging because of the high
star-planet contrast. A technical difficulty in the design of imaging
instruments is the noncommon path aberrations (NCPAs) between the adaptive
optics (AO) sensing and the science camera, which induce planet-resembling
stellar speckles in the coronagraphic science images. In an observing sequence
of several long exposures, quickly evolving NCPAs average out and leave behind
an AO halo that adds photon noise to the planet detection. Static NCPA can be
calibrated a posteriori using differential imaging techniques. However, NCPAs
that evolve during the observing sequence do not average out and cannot be
calibrated a posteriori. These quasi-static NCPAs are one of the main
limitations of the current direct imaging instruments such as SPHERE, GPI, and
SCExAO.
  Aims. Our aim is to actively minimize the quasi-static speckles induced in
long-exposure images. To do so, we need to measure the quasi-static speckle
field above the AO halo.
  Methods. The self-coherent camera (SCC) is a proven technique which measures
the speckle complex field in the coronagraphic science images. It is routinely
used on the THD2 bench to reach contrast levels of <10^{-8} in the range 5-12
{\lambda}/D in space-related conditions. To test the SCC in ground conditions
on THD2, we optically simulated the residual aberrations measured behind the
SPHERE/VLT AO system under good observing conditions.
  Results. We demonstrate in the laboratory that the SCC can minimize the
quasi-static speckle intensity in the science images down to a limitation set
by the AO halo residuals. The SCC reaches 1{\sigma} raw contrast levels below
10^{-6} in the region 5-12 {\lambda}/D at 783.25 nm in our experiments.
