Phasing of segmented mirrors: a new algorithm for piston detection

The point spread function of a segmented-mirror telescope is severely affected by segment misalignment, which can nullify the performance of adaptive optics systems. The piston and tilt of each segment must be precisely adjusted in relation to the other segments. Furthermore, the direct detection of the alignment error with natural stars would be desirable in order to monitor the errors during astronomical observation.

We have studied the lost information of the piston error caused by the presence of atmospheric turbulence in the measurements of curvature, and present a new algorithm for obtaining the local piston using the curvature sensor. A phase-wrapping effect is shown as responsible for the loss of curvature information and so the piston errors can no longer adequately be mapped; this happens not only in the presence of atmospheric turbulence, but also in its absence.

Good results are obtained using a new iterative method for obtaining the local piston error map. In the presence of atmospheric perturbation, the turbulent phase information obtained from a Shack–Hartmann sensor is introduced in our new iterative method. We propose a hybrid sensor composed of a curvature sensor and a Shack–Hartmann sensor, in order to complete all the information for the phasing. This design takes a short computation time and could be used in real time inside an adaptive optics system, where tilt and piston errors must be corrected.