Super-resolution wavefront reconstruction in adaptive-optics with pyramid sensors

TL;DR

This work extends the concept of super-resolution to pyramid wavefront sensing in adaptive optics, showing that a single PyWFS can reconstruct spatial frequencies beyond the detector Nyquist limit by offsetting quadrant sampling and exploiting diversity. It demonstrates that PyWFS measurements contain both Hermitian (phase) and non-Hermitian (amplitude) information, enabling joint estimation of phase and amplitude under suitable conditions. The paper develops both analytic and numerical demonstrations, including 1-D toy models and 2-D simulations, showing that SR can double the effective frequency bandwidth and substantially increase the number of controllable modes with manageable computational cost. The approach promises improved AO performance and robustness to misregistration, with practical implications for next-generation large-telescope instruments (e.g., Keck, ELT) and high-contrast imaging, while outlining experimental validation steps and trade-offs between SR and amplitude estimation.

Abstract

Super-resolution (SR) refers to a combination of optical design and signal processing techniques jointly employed to obtain reconstructed wave-fronts at a higher-resolution from multiple low-resolution samples, overcoming the intrinsic limitations of the latter. After compelling examples have been provided on multi-Shack-Hartman (SH) wave-front sensor (WFS) adaptive optics systems performing atmospheric tomography with laser guide star probes, we broaden the SR concept to pyramid sensors (PyWFS) with a single sensor and a natural guide star. We revisit the analytic PyWFS diffraction model to claim two aspects: i) that we can reconstruct spatial frequencies beyond the natural Shannon-Nyquist frequency imposed by the detector pixel size and/or ii) that the PyWFS can be used to measure amplitude aberrations (at the origin of scintillation). SR offers the possibility to control a higher actuator density deformable mirror from seemingly fewer samples, the quantification of which is one of the goals of this paper. A super-resolved PyWFS is more resilient to mis-registration, lifts alignment requirements and improves performance (against aliasing and other spurious modes AO systems are poorly sensitive to) with only a factor up to 2 increased real-time computational burden.

Figures (14)

• Figure 1: Original, high-resolution input signal and its averaged, down-sampled version.
• Figure 2: Left: Input, down-sampled and reconstructed signal from one sampling sequence. Right: power-spectral analysis. LPF stands for low-pass filter used to isolate the band pass of interest.
• Figure 3: Left: Input, down-sampled and reconstructed signal from two offset sample sequences. Right: power-spectral analysis.
• Figure 4: 1-dimensional PyWFS system.
• Figure 5: Top: Input phase and amplitude aberrations at 5 cycles/pupil. Middle: its measurements in the left and right PyWFS planes. Bottom: the reconstructed phase and amplitude as Fourier coefficients in cycles/pupil.