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Fourier-based wavefront sensors, such as the Pyramid Wavefront Sensor (PWFS),are the current preference for high contrast imaging due to their highsensitivity. However, these wavefront sensors have intrinsic nonlinearitiesthat constrain the range where conventional linear reconstruction methods canbe used to accurately estimate the incoming wavefront aberrations. We proposeto use Convolutional Neural Networks (CNNs) for the nonlinear reconstruction ofthe wavefront sensor measurements. It is demonstrated that a CNN can be used toaccurately reconstruct the nonlinearities in both simulations and a labimplementation. We show that solely using a CNN for the reconstruction leads tosuboptimal closed loop performance under simulated atmospheric turbulence.However, it is demonstrated that using a CNN to estimate the nonlinear errorterm on top of a linear model results in an improved effective dynamic range ofa simulated adaptive optics system. The larger effective dynamic range resultsin a higher Strehl ratio under conditions where the nonlinear error isrelevant. This will allow the current and future generation of largeastronomical telescopes to work in a wider range of atmospheric conditions andtherefore reduce costly downtime of such facilities.

Nonlinear wavefront reconstruction with convolutional neural networks for Fourier-based wavefront sensors