Analytical framework for guide-star arrangement optimization in solar ground-layer adaptive optics

Solar Ground-Layer Adaptive Optics (GLAO) is the preferred solution for achieving wide-field, high-resolution imaging in ground-based solar telescopes. However, current GLAO guide-star (GS) arrangement optimization relies on extensive iterative simulations, which are time-consuming and resource-intensive, and do not provide a prior reference for system design. To address this issue, an analysis of GLAO wavefront sensing in the spatial frequency is conducted. A filter is constructed to optimize the detection of conformal aberrations, leading to the development of an analytical framework for GS arrangement optimization. This framework provides accurate prior optimization results for any GS configuration. The correctness of the theory is validated through comparison with Monte Carlo simulations, and the practical utility of this method in optimizing solar GLAO system performance is demonstrated.