物理学报2026，Vol.75Issue(17)：87-95,9.DOI:10.7498/aps.75.20260415
可压缩湍流中激光回波的闪烁指数
Scintillation index of laser echo waves in compressible turbulence
摘要
Abstract
Laser radar,airborne optical communication,and high-speed optical imaging systems often operate in the near field of supersonic targets,where optical waves traverse compressible boundary layers,shear layers,wakes,and local shock structures.Rapid density,temperature,and pressure fluctuations in these flow structures cause refractive-index disturbances,induce aero-optical distortion,and lead to random intensity fluctuations in 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 address this,an analytical scintillation model is developed for a Gaussian laser echo beam propagating through compressible turbulence.A modified refractive-index spectrum containing both temperature-and pressure-related contributions is introduced into the generalized Huygens-Fresnel framework.Based on the modified Rytov theory,the small-and large-scale log-amplitude variances are derived with the inner-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 and 10 mm,the outer scales are 0.08 m and 0.8 m,and the wavelengths are 1.06,1.55,3.8,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.Wavelength dependence is also significant:the 1.06 μm beam exhibits the strongest scintillation,while the 3.8 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.关键词
可压缩湍流/高斯光束/闪烁指数/气动光学Key words
compressible turbulence/Gaussian beam/scintillation index/aero-optics引用本文复制引用
薛积禹,宁泽华,吴雨欣,吴振森,武红鹏,董磊..可压缩湍流中激光回波的闪烁指数[J].物理学报,2026,75(17):87-95,9.基金项目
国家自然科学基金(批准号:62501370)和山西省基础研究计划(批准号:202303021222034)资助的课题. Project supported by the National Natural Science Foundation of China(Grant No.62501370)and the Fundamental Research Program of Shanxi Province,China(Grant No.202303021222034). （批准号:62501370）
