Nijboer-Zernike phase retrieval for high contrast imaging

We introduce a novel phase retrieval method for astronomical applications based on the Nijboer-Zernike (NZ) theory of diffraction. We present a generalized NZ phase retrieval process that is not limited to small and symmetric aberrations and can therefore be directly applied to astronomical imaging instruments. We describe a practical demonstration of this novel method that was recently performed using data taken on-sky with NAOS-CONICA, the adaptive optics system of the Very Large Telescope. This demonstration presents the first online on-sky phase retrieval results ever obtained, and allows us to plan subsequent refinements on a well-tested basis. Among the potential refinements, and within the framework of high-contrast imaging of extra-solar planetary systems (which requires exquisite wavefront quality), we introduce an extension of the generalized NZ to the high-dynamic range case, and particularly to its use with the vector vortex coronagraph. This induces conjugated phase ramps applied to the orthogonal circular polarizations, which can be used to instantaneously retrieve the complex amplitude of the field, yielding a real-time calibration of the wavefront that does not need any other modulation such as focus or other deformable mirror probe patterns. Paper II (Riaud et al. 2012, A&A, 545, A151) presents the mathematical and practical details of the new method.