Systematic analysis of the tilt-parameter in short-exposure turbulence imaging under G-tilt and Z-tilt removal definitions

The wavefront tilt parameter a plays a critical role in the formulation of the short-exposure optical transfer function for imaging through atmospheric turbulence. In this work, we present a systematic and comprehensive numerical investigation of a using split-step wave optics simulations under two commonly used tilt-removal definitions, namely Z -tilt and G-tilt. The dependence of a on turbulence strength and aperture size is quantified over a wide range of conditions spanning weak to strong turbulence regimes. The results show that, under Z -tilt removal, a exhibits weak dependence on turbulence strength and is primarily determined by aperture size, consistent with classical short-exposure theory. In contrast, under G-tilt removal, a depends strongly on both aperture size and turbulence strength, exhibiting distinct piecewise behavior, particularly in the small-aperture regime. Empirical expressions are developed for both cases to enable efficient estimation of a in practical applications. These findings provide a unified interpretation of discrepancies reported in previous studies and highlight the importance of tilt definition in modeling turbulence-degraded imaging systems.