Wavefront Estimation From a Single Measurement: Uniqueness and Algorithms

Wavefront estimation is an essential component of adaptive optics where the goal is to recover the underlying phase from its Fourier magnitude. While this may sound identical to classical phase retrieval, wavefront estimation faces more strict requirements regarding uniqueness as adaptive optics systems need a unique phase to compensate for the distorted wavefront. Existing real-time wavefront estimation methodologies are dominated by sensing via specialized optical hardware due to their high speed, but they often have a low spatial resolution. A computational method that can perform both fast and accurate wavefront estimation with a single measurement can improve resolution and bring new applications such as real-time passive wavefront estimation, opening the door to a new generation of medical and defense applications. In this paper, we tackle the wavefront estimation problem by observing that the non-uniqueness is related to the geometry of the pupil shape. By analyzing the source of ambiguities and breaking the symmetry, we present a joint optics-algorithm approach by co-designing the shape of the pupil and the reconstruction neural network. Using our proposed lightweight neural network, we demonstrate wavefront estimation of a phase of size $128\times 128$ at $5,200$ frames per second on a CPU computer, achieving an average Strehl ratio up to $0.98$ in the noiseless case. We additionally test our method on real measurements using a spatial light modulator. Code is available at https://pages.github.itap.purdue.edu/StanleyChanGroup/wavefront-estimation/.