Laser radar, airborne optical communication, and high-speed optical imaging systems often operate in the near field of supersonic targets, where optical waves pass through compressible boundary layers, shear layers, wakes, and local shock structures. Rapid density, temperature, and pressure fluctuations in these flow structures produce refractive-index disturbances, cause aero-optical distortion, and lead to random intensity fluctuations of the returned laser signal. Conventional Kolmogorov, von Kármán, and Tatarskii-type spectra mainly describe temperature-induced refractive-index fluctuations in incompressible or weakly compressible atmospheric turbulence, and are therefore insufficient for supersonic near-wall flows where pressure fluctuations are non-negligible.
To describe this effect, an analytical scintillation model is developed for a Gaussian laser echo beam propagating through compressible turbulence. A modified refractive-index spectrum containing both temperature-related and pressure-related contributions is introduced into the generalized Huygens-Fresnel framework. Based on the modified Rytov theory, the small-scale and large-scale log-amplitude variances are derived with the inner-scale and outer-scale effects included, and the radial and on-axis intensity-fluctuation components are combined to obtain the scintillation index. Numerical calculations are performed for a near-field propagation distance of 1 m and a beam waist of 10 mm. The inner scales are 1 mm and 10 mm, the outer scales are 0.08 m and 0.8 m, and the wavelengths are 1.06 μm, 1.55 μm, 3.8 μm, and 10.6 μm.
The results show that, in the weak-to-moderate fluctuation regime, the scintillation index first increases rapidly with turbulence strength and then exhibits a peak followed by a slow decrease or saturation-like behavior. This trend is related to the saturation correction in the modified Rytov theory. The outer scale has a stronger influence on echo scintillation than the inner scale because a larger outer scale enhances the low-spatial-frequency refractive-index spectrum and strengthens the contribution of large coherent eddies to received intensity fluctuations. The inner scale mainly modifies the high-spatial-frequency cutoff, and its effect becomes more evident at longer wavelengths or under moderate fluctuation conditions. The wavelength dependence is also significant: the 1.06 μm beam gives the strongest scintillation, whereas the 3.8 μm and 10.6 μm beams show much weaker intensity fluctuations.
Compared with the conventional temperature-only atmospheric-turbulence baseline, the modified compressible turbulence spectrum predicts a higher scintillation index under the same optical and turbulence parameters. This enhancement originates from the pressure-induced refractive-index fluctuation term, which increases the effective optical-turbulence spectral density in compressible flow. The model is applicable to near-field Gaussian-beam propagation through locally isotropic, weak-to-moderate compressible turbulence, especially in supersonic near-wall environments. The results provide theoretical guidance for wavelength selection, optical-window arrangement, and optical-path design in supersonic-target detection, airborne optical communication, and high-speed optical imaging systems.