Computational Study of Aero-Optical Distortion by Turbulent Wake

Optical aberrations induced by turbulent flows are a serious concern in airborne communication and imaging systems. In these applications an optical beam is required to be transmitted through a relatively long distance, over which the quality of the beam can degrade due to variations of the index of refraction along its path. For air and many fluids, the refractive index is linearly related to the density of the fluid through the Gladstone-Dale relation (see Wolf & Zizzis 1978), and therefore density fluctuations due to flow turbulence are the root cause of optical aberrations. An airborne optical beam generally encounters two distinct turbulent flow regimes: the turbulence in the vicinity of the aperture produced by the presence of solid boundaries, and atmospheric turbulence. Aero-optics is the study of optical distortions by the near-field turbulent flows, typically involving turbulent boundary layers, mixing layers, and wakes (see Gilbert 1982). The depth of the aberrating flowfield is usually smaller than or comparable to the projecting (or imaging) aperture. When an initially planar optical wavefront passes a compressible flow, different parts of the wavefront experience different density in the medium and hence have different propagation speeds. Consequently the wavefront becomes deformed. A small initial deformation of the wavefront can lead to large errors on a distant target. The consequences of such deformations include optical beam deflection (bore-sight error) and jitter, beam spread, and loss of intensity. Wavefront distortions can also cause reductions of resolution, contrast, effective range, and sensitivity for airborne electro-optical sensors and imaging systems (Jones & Bender 2001). Research in the area of turbulent distortions of optical waves can be traced back to the 1950s and 1960s (see, for example, Chernov 1960; Tatarski 1961) when the scattering of acoustic and electromagnetic waves due to random fluctuations of refractive index were studied, mostly in the context of atmosphere propagation. Most of the early studies are based on statistical analysis with simplifying assumptions such as homogeneous and isotropic turbulence, and therefore are not directly applicable in realistic aero-optical flowfields. Sutton (1969) characterized different regimes based on optical and flow parameters for the case of homogeneous and isotropic turbulence and developed statistical models to predict far-field optical aberrations. It was in the late 1980s when aero-optics in the modern sense, i.e., the study of optical distortions due to near-aperture turbulence, came into consideration. Many experimental studies have been performed to develop high-speed wavefront measurement tools (e.g., Jumper & Fitzgerald 2001; Cheung & Jumper 2004), study the refractive index structures (e.g., Catrakis & Aguirre 2004; Dimotakis et al. 2001; Fitzgerald & Jumper 2004), develop distortion scaling laws (e.g., Gordeyev et al. 2003), and devise control techniques to suppress or modify optically important turbulence structures (e.g., Gordeyev et al. 2004; Sinha et al. 2004). Despite advances in wavefront sensor technology, significant limitations