  We investigate methods to calibrate the non-common path aberrations at an
adaptive optics system having a wavefront-correcting device working at an
extremely high resolution (larger than 150x150). We use focal-plane images
collected successively, the corresponding phase-diversity information and
numerically efficient algorithms to calculate the required wavefront updates.
The wavefront correction is applied iteratively until the algorithms converge.
Different approaches are studied. In addition of the standard Gerchberg-Saxton
algorithm, we test the extension of the Fast & Furious algorithm that uses
three images and creates an estimate of the pupil amplitudes. We also test
recently proposed phase-retrieval methods based on convex optimisation. The
results indicate that in the framework we consider, the calibration task is
easiest with algorithms similar to the Fast & Furious.
