Single-shot, reference-less computational wavefront sensing for complex optical fields.

Optical waves carry rich information in their spatial profiles and topological structures. Characterization of optical wavefronts is a key prerequisite in broad applications across fundamental research and industrial technologies. However, existing wavefront sensing techniques typically compromise between spatiotemporal resolution, compactness, and versatility. Here, we present Spatial And Fourier-domAin Regularized Inversion (SAFARI), a computational wavefront sensing approach that exploits the intrinsic physical properties such as smoothness to enable reliable reconstruction of complex wavefronts from a single exposure. Using a compact, diffuser-based wavefront sensor, we experimentally demonstrate single-shot, reference-less characterization of diverse complex wavefronts, including aberrations with up to 200 Zernike modes, structured beams carrying a topological charge of 150, and speckle fields containing more than 190,000 spatial modes. The proposed wavefront sensor offers high versatility while achieving performance comparable to or surpassing state-of-the-art task-specific solutions, making it a promising tool for coherent imaging and sensing at unprecedented resolution and complexity.