Distortion sensing of off-axis vortex beams enabled by a differentiable neural model.

Adaptive optics (AO) can mitigate optical aberrations in vortex beams. However, the vortex phase structure interferes with retrieving true aberrations, complicating AO correction. Existing methods often rely on known vortex characteristics or additional techniques to bypass phase interference, increasing system complexity and limiting applicability. Additionally, off-axis singularities caused by misalignments inherently pose challenges but are often overlooked. This work focuses on analyzing distorted vortex slope data measured by the Shack-Hartmann Wavefront Sensor, a widely used technique in AO systems. The error mechanism induced by vortex phases is examined, revealing how divergence-free vortex slopes couple into astigmatism-type artifacts, with coefficients dependent on singularity position and topological charge. To address these challenges, the vortex-aberration slope decoupling method, driven by a differentiable neural model, is proposed. This method eliminates vortex phase interference without requiring pre-alignment, additional beams, or extensive data training, and it is suitable for real-time AO integration. Simulations demonstrate the method's robustness across various vortex parameters and input aberrations. The experimental results demonstrate an approximately 9-fold reduction in errors compared to the direct least mean square method commonly employed for zonal wavefront reconstruction. Furthermore, the analysis of far-field focal spot shapes under specific scenarios is carried out, which highlights the method's effectiveness in achieving accurate AO correction.