Physics-driven self-supervised learning for non-modulated pyramid wavefront sensing.

Non-modulated pyramid wave-front sensors (PWFS) deliver high sensitivity for extreme adaptive optics (ExAO) yet suffer from severe nonlinearity. While deep learning can alleviate these issues, conventional models rely heavily on large-scale labeled datasets and lack physical interpretability. To overcome these limitations, we propose PINN-Pyr, a physics-informed neural network for self-supervised wavefront reconstruction. By embedding a differentiable forward optical model into a U-Net, the network maps intensity patterns to Zernike coefficients without paired training data. PINN-Pyr significantly extends the linear dynamic range of the PWFS owing to its nonlinear mapping capability. Furthermore, among the conventional matrix-vector-multiplication (MVM), pure data-driven, and PINN-Pyr methods, PINN-Pyr achieves the lowest residual root-mean-square (RMS) error and superior Strehl ratio (SR) stability under strong turbulence and low signal-to-noise ratio (SNR) conditions. This physics-constrained scheme provides a robust, efficient solution for next-generation large-aperture telescopes.