refractiveindexstructuurparameter

The refractiveindexstructuurparameter, commonly referred to as the refractive index structure parameter and denoted Cn^2, is a statistical quantity that describes the strength of refractive-index fluctuations caused by optical turbulence in a transparent medium. It is most often applied to the Earth's atmosphere, where turbulent air leads to small-scale variations in the refractive index that affect the propagation of light.

Mathematically, the refractive-index structure parameter is linked to the two-point structure function of the refractive index. If n(x) is the refractive index at position x, the structure function Dn^2(r) = ⟨ [n(x + r) − n(x)]^2 ⟩ follows Dn^2(r) = Cn^2 r^(2/3) for r in the inertial range of Kolmogorov turbulence. The units of Cn^2 are m^(-2/3). Cn^2 varies with altitude, time, and atmospheric conditions, and the line-of-sight integral of Cn^2 gives the overall turbulence strength that governs optical propagation effects such as seeing, scintillation, and beam wander.

Measurement and profiling of Cn^2(z) (the vertical distribution) employ several techniques, including SCIDAR, SLODAR, and DIMM, as well as microthermal sensors and balloon-borne probes. Remote sensing methods like LIDAR can also contribute to profiling. Standard altitude-dependent models, such as Hufnagel-Valley type profiles, provide practical approximations for simulations and instrument design.

Applications of Cn^2 include astronomy (seeing estimation and adaptive optics tuning), laser and free-space optical communication (beam propagation and scintillation prediction), and atmospheric research. Typical atmospheric values span roughly 10^−17 to 10^−13 m^−2/3, with larger values corresponding to stronger turbulence in the boundary layer or during adverse weather.