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Atmospheric tomography is a key element for many adaptive optics architectures on which the com- ing Extremely Large Telescopes rely. When modeling atmospheric tomography, the samples of the wavefronts in the turbulent layers are not aligned with the subapertures after propagation down to the wavefront sensors (WFS). So the classical models of Shack-Hartmann WFS (e.g. Fried's model) include resampling before performing the standard slopes calculation. This operation introduces errors and only approximates the response of the WFS (error of 10 to 20% of the standard deviation of the slopes). We introduce a continuous model that represents the wavefronts on a basis of continuous functions in the turbulent layers. Propagation and gradient measurements are then computed analytically, without any resampling. Assuming the separability of the basis functions on the two dimensions, we obtain a sparse operator that can be factorized in two components. This factorization enhances the speed close to that of the standard approach using interpolation. We obtain a fast accurate continuous WFS model suitable to wide field adaptive optics systems on ELTs.

Fast continuous model of Shack-Hartmann wavefront sensors for atmospheric tomography on ELTs