Temporal regularization of petal modes in single conjugate adaptive optics systems. The soft-limiter approach
Year: 2026
Type: article
Abstract: The next generation of extremely large telescopes (ELTs) relies on segmented mirrors and thick support structures that fragment the optical pupil of the instrument. In single conjugate adaptive optics (SCAO) systems, this fragmentation leads to the emergence of differential piston errors, or petal modes. The pyramid wavefront sensor (PWFS), baseline for instruments such as ANDES, MICADO, HARMONI, and GMT-NGSAO, suffers from poor sensitivity to these petal modes when operating at visible wavelengths under realistic residual turbulence. Our aim is to prevent the resulting ``island effect,'' where poorly observed differential pistons accumulate and degrade the point spread function, without compromising the correction of continuous atmospheric modes. We propose a deterministic and computationally efficient control strategy: the minimum mean square error (MMSE) soft-limiter. Rather than relying on an instantaneous spatial reconstruction of the phase steps, we utilized a subspace MMSE estimator derived from von Kármán statistical priors coupled with a continuous temporal regularization. This acts as a localized leaky integrator applied strictly to the relative petal degrees of freedom. End-to-end SPECULA simulations for the ELT ANDES instrument show that while a classical integrator loses lock and wanders across multiple fringes under degrading seeing (ge 1.0''), the MMSE soft-limiter confines the differential piston within a single fringe across the full 0.6-1.2'' range. This prevents control-induced divergence, bounds the petal excursion, and reduces its science-band impact under severe turbulence while retaining optimal continuous-mode correction at good seeing without the steady-state Strehl penalty incurred by spatial mitigation strategies such as edge actuator coupling. We theoretically derived and numerically verified the operating window for the leakage gain, g łesssim g_ eff /π. Below this threshold, the fast loop retains the full fractional range of genuine physical steps, up to λ_ WFS /2 with a small droop; above it, retention degrades gradually. This temporal regularization maintains a stable modulo-λ_WFS wavefront on the fast PWFS, allowing for a slower phasing sensor to resolve integer ambiguities. Because the operating window narrows with turbulence, the boundaries cross at roughly 1.0'' seeing. Beyond this point, retaining physical discontinuities becomes the exclusive responsibility of the phasing channel---a key design driver for segmented ELT-class facilities.
Source: Astronomy and Astrophysics
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,865
OpenAlex ID: W7224957698