Focal plane wavefront sensing using machine learning: performance of convolutional neural networks compared to fundamental limits

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