Maximum likelihood co-phasing of segmented mirrors with a pyramid in the visible: simulation vs. experiment

We demonstrate numerically the phasing of a telescope with a primary segmented mirror consisting of 800 hexagonal segments using a pyramid wavefront sensor, supported by experiments. The segments are initially misaligned in piston/tip/tilt with median inter-segment steps of several micrometers. We simulate a mirror with some missing segments and a telescope spider with large optical phase discontinuities across its six vanes. The physical optics simulation is validated by experiments on the LOOPS optical bench at LAM. The correct combination of step solutions is selected by maximum likelihood methods. We emulate different star magnitudes and seeing conditions.