Parametric analytical model of the MTF for turbid atmospheres at high optical thickness

To address the severe degradation of imaging quality caused by multiple scattering under low-visibility weather conditions, a parametric analytical model of the MTF for turbid atmospheres at high optical thickness is proposed. Based on the equivalence principle of the MTF in turbid media, the discrete ordinates (DISORT) algorithm of radiative transfer is employed to construct an MTF model database for optical thicknesses of 2.0–3.0. Critical spatial frequencies in the low- and high-frequency ranges are determined by difference method, and the entire spatial frequency domain is divided into low-, medium-, and high-frequencies. Nonlinear fitting and linear interpolation are then applied to establish models relating optical thickness, single scattering albedo, and asymmetry factor to critical spatial frequencies and the MTF. Experimental results indicate that, within optical thicknesses of 2.0–3.0, single-scattering albedos of 0.1–1.0, and asymmetry factors of 0.05–0.95, the maximum mean relative error (MRE) and root mean square error (RMSE) of the model are 16.75% and 0.0329, respectively. Compared with the computationally intensive but highly accurate DISORT algorithm, the proposed model exhibits high computational efficiency, making it well-suited for integration into image restoration systems operating under adverse weather conditions and offering promising engineering applicability.