Authors

M.Zhariy, R.Ramlau, A.Obereder

Affiliations

Institute for Industrial Mathematics, Johannes Kepler University Linz, A.Obereder - Mathconsult GmbH

Abstract

In this presentation, we report about the progress made on eXtreme Adaptive Optics (XAO) within the Austrian Adaptive Optics (AAO) group project Mathematical algorithms and software for E-ELT Adaptive Optics.

We consider the problem of wavefront reconstruction from the Pyramid wavefront sensor (P-WFS) measurements. First, we concentrate on the non-modulated Pyramid WFS case. A good reconstructor relies on a sufficiently good forward model, so analysis of the model is needed. We have studied two analytical models which can be found in the literature, with and without interference, and developed appropriate simulations. Under the closed loop assumption an approximation to the model involving Hilbert transforms has been derived. Our reconstruction algorithm is based on the inversion of the Hilbert transform. We present analytical proofs as well as numerical results for the algorithm.

In addition, a Pyramid WFS with circular modulation is considered. We have derived an analytical model without interference for the modulated Pyramid WFS case. The simulation can be easily extended from the non-modulated case by adding modulation tilts to the incoming phase.

Finally, the relations between the modulated Pyramid WFS and the more conventional Shack-Hartmann WFS as well as with the Roof WFS are discussed.