Poisson wavefront imaging in photon-starved scenarios

Low-photon phase imaging is essential in applications where the signal is limited by short exposure times, faint targets, or the need to protect delicate samples. We address this challenge with Poisson Wavefront Imaging (PWI), an optimization-based method that incorporates Poisson photon statistics and a smoothness prior to improve wavefront reconstruction. By using multiple spatial light modulator's phase patterns, PWI enhances Fisher information, boosting theoretical accuracy and regularizing the retrieval process effectively. In simulations, PWI approaches the theoretical phase error limit, and in experiments it reduces phase error by up to 1.6x compared to the Gerchberg-Saxton algorithm, achieving 1.8x higher resolution wavefront imaging in low photon regime. This method advances photon-limited imaging with applications in astronomy, semiconductor metrology, and biological systems.