Large dynamic range Shack-Hartmann wavefront sensing based on a graph-theoretic computational model

The Shack-Hartmann wavefront sensor (SHWS) is a widely used non-interferometric wavefront measurement technique. However, for high-slope wavefronts, spot crosstalk and asymmetric distortion cause severe matching ambiguity and centroiding errors. This creates an inherent conflict between dynamic range and reconstruction accuracy. To address this, a graph-theoretic computational model named G-SHWS is proposed. By minimizing the global pairing cost of a bipartite graph constructed between fitted and actual spots, G-SHWS drives the fitted distribution to approximate the true distribution and maps the subaperture attribution of the fitted spots to the actual spots, achieving precise spot-subaperture matching under severe aliasing. Furthermore, incorporating a Graph Attention Network (GAT) embedded with SHWS matching topology, the model utilizes a graph structure to explicitly encode the matching relationships obtained from the matching process, and combines the spatial features and intensity morphology of spots to achieve high-precision reconstruction of strongly distorted wavefronts, effectively circumventing the inherent centroiding errors under large aberrations. Experimental results demonstrate that G-SHWS extends the measurable range of SHWS to 21 times the conventional limit while maintaining a reconstruction error of less than $0.05\lambda$ , and remains robust under severe spot loss. These advancements significantly enhance the SHWS's ability to measure complex aberrations, providing a reliable computational framework for large dynamic range wavefront sensing.