Provable and Robust Wavefront Sensing via Self-Reference Interferometry

Wavefront sensing involves estimating the phase and intensity of light, enabling a wide range of imaging applications, from adaptive optics and astronomy to biomedical imaging. Since conventional image sensors can only measure the spatial intensity distribution, phase retrieval arises as the central problem in wavefront sensing. Conventional interferometric approaches like phase-shifting interferometry (PSI) can recover phase information, but they rely on a stable reference beam that is difficult to realize in practical settings. To overcome this limitation, we propose a novel self-reference framework that relies on interference between shifted copies of the incoming wave; this results in pairwise phase differences between shifted pixels. We formulate an analytical solution for the complete phase retrieval based on the propagation of these differences across a connected graph. Furthermore, we provide a theoretical analysis of optimal measurement patterns, proving that co-prime shifts guarantee a connected graph and bound worst-case error accumulation, yielding a provably robust method. Extensive simulations demonstrate that complete phase profiles can be recovered from as few as eight shifted measurements, outperforming several existing approaches. Finally, we validate our framework using a hardware prototype, demonstrating real experiments for optical phase profile recovery, auto-refocusing, and imaging through scattering media.