Asymptotic analytical modeling of astigmatic rainbow refractometry

We report an asymptotic analytical model for astigmatic rainbow refractometry, synthesized from complex angular momentum theory and the generalized 4D Collins formula. This closed-form solution describes astigmatic wavefront evolution while moving beyond the phenomenological limits of conventional geometric models. The proposed framework elucidates the phase-coupling mechanism behind fringe rotation and characterizes the fine-scale interference ripple structure. These results establish a theoretical foundation for quantitative volumetric diagnostics of complex spray systems.