Frequency-domain filtering-based neural network for Shack–Hartmann super-resolution wavefront reconstruction

The increasing aperture of next-generation telescopes demands higher-resolution wavefront sensing. The sensing resolution of the Shack-Hartmann wavefront sensor (SHWFS), a key component in adaptive optics, is fundamentally limited by its sub-aperture density. To overcome this limitation, we introduce a frequency-domain filter-based neural network (FF-Net) for super-resolution wavefront reconstruction (SRWR). Inspired by the physical imaging principles of the SHWFS and the convolution theorem, FF-Net utilizes learnable Gabor filters to extract aberration features across various frequency bands. This approach enables more effective feature decoupling from aliased sub-aperture spots compared to standard convolutional kernels, leading to high-precision reconstruction. Numerical simulations demonstrate that FF-Net achieves state-of-the-art SRWR performance. Notably, with an under-sampled SHWFS, our method outperforms the low-order reconstruction accuracy of the conventional method employing four times the sub-aperture density, while simultaneously retrieving higher-order modes. Furthermore, its GPU-accelerated inference time of under 1 ms meets the real-time requirements of most astronomical adaptive optics systems. FF-Net demonstrates that physics-informed network design is a powerful strategy for developing more accurate, robust, and interpretable deep learning solutions in adaptive optics.