Fourier transform-wavefront reconstruction for the pyramid wavefront sensor

The application of Fourier-transform reconstruction techniques to the py ramid wavefront sensor has been investigated. A preliminary study based on end-to-end simulations of an adaptive optics system with 40x40 subapertures and actuators shows that the performance of the Fourier-transform reconstructor (FTR) is of the same order of magnitude than the one obtained with a conventional matrix-vector multiply (MVM) method. In this paper we will present a preliminary study on the application of the Fourier Transform Recon- structor (FTR) to the pyramid wavefront sensor. This work is relevant, for instance, for the extreme AO system of EPICS (the planet finder for the E-ELT), in which t he pyramid has been indentified as an optimal wavefront sensor for its halo rejection capabilities at small angular separations (1). It is envisaged that this XAO system will comprise 30000 actuators and subapertures. Clearly, the FTR would be advantageous to cope with such system dimensions. Fourier-domain reconstruction techniques have been widely studied for the Shack-Hartmann wave- front sensor (SHWFS). Di erent inverse filters based on simple sensor models (i.e. the Hudgin or the Fried geometries) have been proposed so far (2). In this work we have studied the applicability of these inverse filters to the pyramid wavefront sensor. We wil l show that even using these simple mod- els (not tuned for the pyramid sensor) we can achieve a good wavefront reconstruction and correction. The derivation of ad-hoc inverse filters for the pyramid sens or is beyond the scope of this preliminary work. We have studied the performance of the Fourier reconstruction techniques with numerical simu- lations. We have considered the case of an 8-m class AO system. The number of subapertures and actuators that will be considered in this study is 40x40. This system configuration is similar to the XAO systems currently under investigation for the VLT.