Poisson wavefront imaging in photon-starved scenarios

TL;DR

Poisson Wavefront Imaging (PWI) is a novel optimization-based technique that improves wavefront reconstruction accuracy in photon-starved conditions by leveraging Poisson statistics and multiple phase patterns, outperforming traditional algorithms.

Contribution

This paper introduces PWI, a new method that enhances wavefront imaging accuracy in low-photon scenarios using Poisson statistics and multiple phase patterns, approaching theoretical limits.

Findings

PWI approaches the theoretical phase error limit in simulations.

PWI reduces phase error by up to 1.6x compared to Gerchberg-Saxton.

PWI achieves 1.8x higher resolution in low photon regimes.

Abstract

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.