Scaling laws for the noise-equivalent angle and C-tilt, G-tilt anisoplanatism due to scintillation

In this paper, we derive single-integral solutions, applicable in the weak-to-moderate scintillation regime, for both the noise equivalent angle (NEA) due to scintillation and the scintillation-induced root mean squared error (RMSE) between gradient tilt (G-tilt) and centroid tilt (C-tilt). In practice, the NEA due to scintillation gives a measure of the scintillation-induced track error, whereas the scintillation-induced RMSE between C-tilt and G-tilt gives a measure of the C-tilt, G-tilt anisoplanatism due to scintillation. Assuming spherical-wave propagation, we fit closed-form expressions to the numerically integrated solutions. These closed-form expressions serve as "scaling laws," and we validate their use with wave-optics simulations. At large, we determine that the one-axis NEA due to scintillation scales as a function of aperture size, propagation distance, wavelength, and Rytov number, whereas the one-axis scintillation-induced RMSE between C-tilt and G-tilt scales proportionally to the Rytov number when normalized by the diffraction angle. These findings will aid in the design of active electro-optical systems, which inevitably experience the effects of scintillation when imaging through distributed-volume turbulence.