Distributed Wavefront Reconstruction using measurements of the spatial derivatives of the wavefront for real-time large scale adaptive optics control

We present a novel method for distributed wavefront reconstruction from spatial derivatives of the wavefront with application to large-scale adaptive optics systems, like the extreme adaptive optics (XAO) system of the EPICS instrument of the European Extremely Large Telescope (E-ELT). The new method, indicated as D-SABRE (Distributed Spline based ABerration REconstruction), is an extension of the recently presented SABRE method for wavefront reconstruction which uses B-spline basis functions defined on triangular partitions. D-SABRE aims to not only greatly increase the computational efficiency of the wavefront reconstruction operation, but also to remove the need for centralized reconstruction. The D-SABRE is demonstrated on simulated E-ELT turbulence wavefronts. We show that the D-SABRE obtains a reconstruction accuracy that is within 1% of the reconstruction accuracy of a global (non-distributed) method.