Wavefront Estimation From a Single Measurement: Uniqueness and Algorithms

Nicholas Chimitt†, Ali Almuallem†, Qi Quo†, Stanley H. Chan†
†Purdue University
IEEE Transactions on Computational Imaging, 2025.
Paper arXiv Supplementary (soon) Code (soon)
Main Figure

Overview of adaptive optics (AO) and the position of our method among hardware and alternative computational methods for wavefront estimation.

Abstract

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 problems, wavefront estimation faces more strict requirements regarding uniqueness because the adaptive optics system needs 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. It has been suggested that if a computational method could perform fast and accurate wavefront estimation with a single measurement, one can possibly do real-time passive estimation and compensation, hence 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 by breaking the symmetry, we present a joint optics-algorithm approach by co-designing the shape of the pupil and the recon- struction neural network. Using our proposed lightweight neural network, we demonstrate wavefront estimation of a phase of size 128 × 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

Wrong estimate, what's the big deal?

Weight distance correlation Toy example illustrating the impact of pupil geometry on recovery. Symmetrical pupils like a circle have more than one local minimum.
Directional Weight Score Estimating the wrong phase will result in corrupting the wavefront (and therefore the captured image) further instead of correcting it.

Evaluation on Real Data

Directional Weight Score
Ground Truth
Recovered
Coefficient Image
Directional Weight Score
Ground Truth
Recovered
Coefficient Image
Directional Weight Score
Ground Truth
Recovered
Coefficient Image
Evaluation on real data [Top] Measured PSFs. [Middle] SLM phase pattern (left) and estimated phase (right) for each case. [Bottom] Basis coefficient comparison (blue as ground truth, red as recovered). All cases shown (a-c) are validation data. Here we use a version of our MLPs (MLP1 method), hence runtime is ∼ 3700 Hz which is applicable for real-time applications.

Optical Setup

BibTeX

@ARTICLE{11229883,
            author={Chimitt, Nicholas and Almuallem, Ali and Guo, Qi and Chan, Stanley H.},
            journal={IEEE Transactions on Computational Imaging}, 
            title={Wavefront Estimation From a Single Measurement: Uniqueness and Algorithms}, 
            year={2025},
            volume={11},
            number={},
            pages={1600-1613},
            keywords={Estimation;Real-time systems;Adaptive optics;Optical distortion;Pupils;Imaging;Vectors;Discrete Fourier transforms;Phase measurement;Optical variables measurement;Wavefront estimation;wavefront sensing;adaptive optics;phase retrieval;neural representation},
            doi={10.1109/TCI.2025.3629320}}
      }