Optical Turbulence
This webdemo simulates the effect of atmospheric turbulence on free space optical (FSO-) signals. Turbulences occur because of the random fluctuation of the refractive index $\mathrm{n}$ due to variations in temperature and pressure.
Indeed, the refractive index $n$ of the air for visible wavelengths is a function of the temperature $T$, the pressure $P$ and the wavelength $\lambda$ according to the following equation [1]
\begin{align}
n(r) = 1 + 7.66 \cdot 10^{-6} (1+7.52\cdot 10^{-3} \cdot \lambda^{-2}) \left(\frac{P(r)}{T(r)}\right) ≈ 1+79 \cdot 10^{-6} \left(\frac{P(r)}{T(r)}\right)
\end{align}
For the refractive index fluctuation, the temperature variation is more important than the variation of pressure and $\lambda$ .
According to the above equation we can thus write for the refractive index fluctuation: \begin{align} \partial n = -79 \cdot 10^{-6} \left(\frac{P}{T^{2}}\right) \partial T \end{align} \begin{align} \text{Let} C_{n} = \frac{\partial n}{\partial T} C_{T} = -79 \cdot 10^{-6}\left(\frac{P}{T^{2}}\right) C_{T} \implies C^{2}_{n}= \left(79 \cdot 10^{-6} \left(\frac{P}{T^{2}}\right)\right)^{2} C^{2}_{T} \end{align} $C^{2}_{T}\Bigl[\frac{\mathrm{deg}^2}{\mathrm{m}^{2/3}}\Bigr]$ is the temperature structure constant. It is a measure of the temperature fluctuation between 2 points separated by a certain distance along the propagation path [1].
$C^{2}_{n}\bigl[\mathrm{m}^{-\frac{2}{3}}\bigr]$ is called refractive index structure constant and is a measure of the strength of fluctuations in the refractive index [1]. $C^{2}_{n}$ ranges generally between $10^{-17}$ (or less) in case of weak turbulence, $10^{-16}$ in case of moderate turbulence and $10^{-15}$ (or more) for strong turbulence.
According to the above equation we can thus write for the refractive index fluctuation: \begin{align} \partial n = -79 \cdot 10^{-6} \left(\frac{P}{T^{2}}\right) \partial T \end{align} \begin{align} \text{Let} C_{n} = \frac{\partial n}{\partial T} C_{T} = -79 \cdot 10^{-6}\left(\frac{P}{T^{2}}\right) C_{T} \implies C^{2}_{n}= \left(79 \cdot 10^{-6} \left(\frac{P}{T^{2}}\right)\right)^{2} C^{2}_{T} \end{align} $C^{2}_{T}\Bigl[\frac{\mathrm{deg}^2}{\mathrm{m}^{2/3}}\Bigr]$ is the temperature structure constant. It is a measure of the temperature fluctuation between 2 points separated by a certain distance along the propagation path [1].
$C^{2}_{n}\bigl[\mathrm{m}^{-\frac{2}{3}}\bigr]$ is called refractive index structure constant and is a measure of the strength of fluctuations in the refractive index [1]. $C^{2}_{n}$ ranges generally between $10^{-17}$ (or less) in case of weak turbulence, $10^{-16}$ in case of moderate turbulence and $10^{-15}$ (or more) for strong turbulence.