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