  With its high sensitivity, the Pyramid wavefront sensor (PyWFS) is becoming
an advantageous sensor for astronomical adaptive optics (AO) systems. However,
this sensor exhibits significant non-linear behaviours leading to challenging
AO control issues. In order to mitigate these effects, we propose to use, in
addition to the classical pyramid sensor, a focal plane image combined with a
convolutive description of the sensor to perform a fast tracking of the PyWFS
non-linearities, the so-called optical gains (OG). We show that this additional
focal plane imaging path only requires a small fraction of the total flux,
while representing a robust solution to estimate the PyWFS OG. Finally, we
demonstrate the gain brought by our method with the specific examples of
bootstrap and Non-Common Path Aberrations (NCPA) handling.
