Numerical Analysis of Long-Exposure Imaging Quality in a Joint-Turbulence Environment

Refractive index fluctuations in turbulent media severely degrade optical imaging quality. Airborne electro-optic systems often involve optical propagation through both atmospheric turbulence (AT) and compressible turbulence (CT), which forms a joint-turbulence (JT) environment. Current models evaluate this by multiplying the optical transfer functions (OTFs) of individual turbulence types and implicitly assume statistical independence. By analyzing phase fluctuation superposition on the receiving aperture, we derive a new wave-structure function for JT that includes a cross correlation term parameterized by a mutual correlation coefficient. We then establish a long-exposure OTF model for JT imaging which reduces to the conventional method when the fields are uncorrelated. Simulations using resolution test targets and natural scene images evaluated via structural similarity and peak signal-to-noise ratio metrics show that JT degrades image quality significantly more than AT or CT alone. This degradation intensifies monotonically with increases in the correlation coefficient, CT propagation distance, and CT strength. Enlarging the receiving aperture effectively compensates for this degradation. These findings prove that correlation-aware JT models are essential for accurately evaluating image quality and provide a theoretical foundation for advanced-imaging system design.