  Almost all current and future high-contrast imaging instruments will use a
Pyramid wavefront sensor (PWFS) as a primary or secondary wavefront sensor. The
main issue with the PWFS is its nonlinear response to large phase aberrations,
especially under strong atmospheric turbulence. Most instruments try to
increase its linearity range by using dynamic modulation, but this leads to
decreased sensitivity, most prominently for low-order modes, and makes it blind
to petal-piston modes. In the push toward high-contrast imaging of fainter
stars and deeper contrasts, there is a strong interest in using the PWFS in its
unmodulated form. Here, we present closed-loop lab results of a nonlinear
reconstructor for the unmodulated PWFS of the Magellan Adaptive Optics eXtreme
(MagAO-X) system based on convolutional neural networks (CNNs). We show that
our nonlinear reconstructor has a dynamic range of >600 nm root-mean-square
(RMS), significantly outperforming the linear reconstructor that only has a 50
nm RMS dynamic range. The reconstructor behaves well in closed loop and can
obtain >80% Strehl at 875 nm under a large variety of conditions and reaches
higher Strehl ratios than the linear reconstructor under all simulated
conditions. The CNN reconstructor also achieves the theoretical sensitivity
limit of a PWFS, showing that it does not lose its sensitivity in exchange for
dynamic range. The current CNN's computational time is 690 microseconds, which
enables loop speeds of >1 kHz. On-sky tests are foreseen soon and will be
important for pushing future high-contrast imaging instruments toward their
limits.
