  In this manuscript we demonstrate a method to reconstruct the wavefront of
focused beams from a measured diffraction pattern behind a diffracting mask in
real-time. The phase problem is solved by means of a neural network, which is
trained with simulated data and verified with experimental data. The neural
network allows live reconstructions within a few milliseconds, which previously
with iterative phase retrieval took several seconds, thus allowing the
adjustment of complex systems and correction by adaptive optics in real time.
The neural network additionally outperforms iterative phase retrieval with high
noise diffraction patterns.
