Anisoplanatic Optical Turbulence Simulation for Near-Continuous $C_n^2$ Profiles without Wave Propagation

For the simulation of anisoplanatic optical turbulence, split-step propagation is the gold standard. Within the context of the degradations being limited to phase distortions, one instead may focus on generating the phase realizations directly, a method which has been utilized in previous so-called multi-aperture simulations. Presently, this modality assumes a constant $C_n^2$ profile. This work presents an alternative derivation for Zernike correlations under anisoplanatic conditions. Multi-aperture simulation may easily incorporate these correlations into its framework and achieve a significantly higher degree of accuracy with a minimal increase in time. We additionally use our developed methodology to explain previously reported discrepancies in an empirical implementation of split-step with the analytic tilt correlation. Finally, we outline a major limitation for Zernike-based simulation which still remains.