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Focal plane wavefront sensing (FPWFS) is appealing for several reasons.Notably, it offers high sensitivity and does not suffer from non-common pathaberrations (NCPA). The price to pay is a high computational burden and theneed for diversity to lift any phase ambiguity. If those limitations can beovercome, FPWFS is a great solution for NCPA measurement, a key limitation forhigh-contrast imaging, and could be used as adaptive optics wavefront sensor.Here, we propose to use deep convolutional neural networks (CNNs) to measureNCPA based on focal plane images. Two CNN architectures are considered:ResNet-50 and U-Net which are used respectively to estimate Zernikecoefficients or directly the phase. The models are trained on labelled datasetsand evaluated at various flux levels and for two spatial frequency contents (20and 100 Zernike modes). In these idealized simulations we demonstrate that theCNN-based models reach the photon noise limit in a large range of conditions.We show, for example, that the root mean squared (rms) wavefront error (WFE)can be reduced to < $\lambda$/1500 for $2 \times 10^6$ photons in one iterationwhen estimating 20 Zernike modes. We also show that CNN-based models aresufficiently robust to varying signal-to-noise ratio, under the presence ofhigher-order aberrations, and under different amplitudes of aberrations.Additionally, they display similar to superior performance compared toiterative phase retrieval algorithms. CNNs therefore represent a compelling wayto implement FPWFS, which can leverage the high sensitivity of FPWFS over abroad range of conditions.

Focal Plane Wavefront Sensing using Machine Learning: Performance of Convolutional Neural Networks compared to Fundamental Limits