Neural network algorithm for under-sampled wavefront reconstruction: mathematical analysis and implementation.

The Shack-Hartmann wavefront sensor (SHWFS) is critical in adaptive optics (AO) for measuring wavefronts via centroid shifts in sub-apertures. Under extreme conditions like strong turbulence or long-distance transmission, wavefront information degrades significantly, leading to undersampled slope data and severely reduced reconstruction accuracy. Conventional algorithms struggle in these scenarios, and existing neural network approaches are not sufficiently advanced.