Fried Parameter Estimation from Single Wavefront Sensor Image with Artificial Neural Networks

TL;DR

This work tackles real-time estimation of the Fried parameter $r_{0}$ from a single WFS image in adaptive optics, using a CNN trained on COMPASS-simulated data for both Shack-Hartmann and pyramid sensors in open- and closed-loop configurations. The authors demonstrate millimeter-scale accuracy with sub-millisecond inference on consumer GPUs, and show robustness to guide-star brightness and noise through data augmentation and combined training. They also reveal that high-spatial-frequency features—beyond the AO loop’s correction range—drive the estimation, supporting real-time AO control and potential sky profiling for FSO. While validated in simulation, the approach offers a practical, sensor-agnostic pathway to dynamic turbulence parameter estimation with significant implications for AO optimization and observational efficiency.

Abstract

Atmospheric turbulence degrades the quality of astronomical observations in ground-based telescopes, leading to distorted and blurry images. Adaptive Optics (AO) systems are designed to counteract these effects, using atmospheric measurements captured by a wavefront sensor to make real-time corrections to the incoming wavefront. The Fried parameter, r0, characterises the strength of atmospheric turbulence and is an essential control parameter for optimising the performance of AO systems and more recently sky profiling for Free Space Optical (FSO) communication channels. In this paper, we develop a novel data-driven approach, adapting machine learning methods from computer vision for Fried parameter estimation from a single Shack-Hartmann or pyramid wavefront sensor image. Using these data-driven methods, we present a detailed simulation-based evaluation of our approach using the open-source COMPASS AO simulation tool to evaluate both the Shack-Hartmann and pyramid wavefront sensors. Our evaluation is over a range of guide star magnitudes, and realistic noise, atmospheric and instrument conditions. Remarkably, we are able to develop a single network-based estimator that is accurate in both open and closed-loop AO configurations. Our method accurately estimates the Fried parameter from a single WFS image directly from AO telemetry to a few millimetres. Our approach is suitable for real time control, exhibiting 0.83ms r0 inference times on retail NVIDIA RTX 3090 GPU hardware, and thereby demonstrating a compelling economic solution for use in real-time instrument control.

Figures (10)

• Figure 1: Diagram of a typical Adaptive Optics system.
• Figure 2: A simplified 1-dimensional example of the Shack-Hartmann wavefront sensor lenslets, illustrating the displacement of the focal point on the sensor due to the aberrated wavefront. This displacement $\Delta x$ is then used to calculate the local wavefront gradient.
• Figure 3: A comparison of images captured by the Shack-Hartmann wavefront sensor (left) and pyramid wavefront sensor (right), using the COMPASS AO simulation software.
• Figure 4: A typical pyramid wavefront sensor setup, illustrating the splitting of the incoming wavefront by the pyramid-shaped prism into four separate pupil images.
• Figure 5: A comparison of Shack-Hartman wavefront sensor images taken from a telescope with a diameter of $8m$, with $r_{0} = 5cm$ (left) and $r_{0} = 20cm$ (right).