# Non-Classic Atmospheric Optical Turbulence: Review
## 2 Measurements and Synthesis
### Anisotropic Turbulence
In addition, the anisotropy of stratospheric turbulence was revealed in (36), with the help of a two-component (isotropic/anisotropic) power spectrum. The validity of such a spectrum was verified by balloon-borne experiments showing that the major contribution to scintillation comes from the anisotropic component. Recently, several experimental campaigns aimed for extending the results in [32] to the assessment of turbulent air anisotropy in all directions, not solely horizontal and vertical, while doing so in the actual atmosphere. The field measurements of the boundary-layer turbulent anisotropy were carried in [PERSON] et al. [37] on the grounds of the University of Miami, by means of the two-point intensity-intensity correlation function of a nearly spherical wave, i.e., a divergent Gaussian beam (over 200 m path, up to 2 m from the grassy field). The measurements were taken along three horizontal links (differing slightly with respect to effects of the wind penetration) at three heights from the ground. The intensity-intensity correlation function (each recorded pixel correlated with the center of the beam) revealed an elliptic form inclined at an angle of about 30 degrees with respect to horizontal. Both the ellipse's eccentricity and orientation angle were shown to be link- and height-dependent. Figure 3 (top row) shows the results of (sequential) measurements carried out for the same path at three heights. The ellipse is the most stretched and rotated for the path closest to the ground. Figure 3 (bottom row) shows the results for three different links taken over the same (middle) height. The ellipse in the two-point intensity-intensity correlations can be directly related to the mean-path averaged anisotropy ellipse of the turbulent eddies. A similar measurement campaign obtained the intensity covariance function of a plane wave propagating in the vicinity of a runway (2 km path, 2 m above the ground) [38]. As Figure 4 illustrates, a more precise anisotropy structure was revealed in which both positive and negative correlations are seen. The orientation angle was shown to vary up to 90\({}^{\circ}\) to the vertical, depending on the path length and meteorological parameters. The data were  
Figure 2: Measurement of anisotropic turbulence. Structure functions of the mean positions of two beams: (**A**) horizontal \(D_{y}\); (**B**) vertical \(D_{z}\), normalized by saturation values \(D_{j,sat}=4\sqrt{\pi}\langle n\rangle^{2}L^{3}R_{ox}/3R_{oj}\), \(j=y,z\), respectively. Here, \(\langle n\rangle^{2}\) is the root-mean square value of the refractive index fluctuations, \(L\) is the range, and \(R_{oj}\); \(j=x,y,z\) are constants on the order of outer scale. Reprinted with permission from Reference [32]. well matched with the suggested theoretical model. It was also confirmed in Reference [39] that the ellipse's parameters may have the signature of seasons and time of the day and night. A field measurement of the two-point optical field correlation (mutual coherence) function and the wave structure function (sub 100 m paths, 1.5 m from ground) were also recently carried out at the University of Maryland facilities by means of a plenoptic sensor in Reference [40]. The elliptic shapes, having a substantial orientation angle with respect to the horizontal direction, were also captured in these statistics. While the elliptic shape appearing in various light statistics can be readily explained with the ellipsoid-like eddy correlation function of the turbulent eddies, the qualitative and quantitative justification for the varying orientation angle remains obscure. Figure 4: Experimental field measurements compared with theoretical results showing anisotropy ellipse of intensity covariance function: (**a**) measurement; (**b**) theory; (**c**,**d**) are major and minor cross-sections (solid curves: measurement; triangles: theory). Horizontal and vertical axes in (**a**,**b**) have extent (\(-6\) cm, \(6\) cm).