Single‐Pass Wavefront Reconstruction via Depth Heterogeneity Self‐Supervised Neural Operator for Turbulence Correction

Abstract Turbulence‐induced distortion remains a major bottleneck for high‐fidelity applications such as optical wireless communication and laser‐based remote sensing, as conventional adaptive optics systems struggle to meet the combined demands of bandwidth efficiency, low‐delay and environmental adaptability. Here, a Depth Heterogeneity Self‐supervised Neural Operator (DHSNO) is proposed, a multi‐physics heterogeneous model integrated neural architecture tailored to correct turbulence wavefronts in a single pass without the need for labeled training data. By leveraging dual‐mode intensity detection in a depth‐heterogeneous receiver, DHSNO inherently regularizes the ill‐posed wavefront retrieval problem to deliver robust, high‐accuracy, and low‐latency reconstruction. This capability is validated in both an emulated 50‐meter underwater turbulence channel and a real‐world 5‐meter underwater salinity‐gradient channel, where DHSNO achieves a normalized residual wavefront error below 0.06 with an inference time of 3.6 ms under varying turbulent strengths. Furthermore, this prototype system enabled 12‐Gb/s 4K‐120fps video transmission with near‐perfect fidelity (SSIM > 0.9999) under severe turbulence conditions. These findings not only advance the state‐of‐the‐art in adaptive optics but also provide a scalable framework for next‐generation free‐space and underwater optical systems, underscoring the transformative potential for turbulence correction of integrating physical constraints with data‐driven neural networks.