SEEING

The seeing effect is due to turbulent fluctuations of the index of refraction. The index of refraction N varies with the density and composition of the medium. In air it may be expressed by Cauchy's formula (extended by Lorenz for humidity) as a function of wavelength $\lambda$, pressure P (mb), absolute temperature T (K) and water vapor pressure v(mb):

$$N-1 = \frac{77.6 \cdot 10^{-6}}{T} \left( 1+7.52 \cdot 10^{-3}\lambda^{-2} \right) \left(P + 4810\, \frac{v}{T} \right)$$ (1)

Fluctuations of humidity are only significant in extreme cases like fog or near the sea surface which are not relevant to astronomical observations. In fact the best astronomical sites, such as Mauna Kea on Hawaii and La Silla in Chile, experience very low humidity values (generally < 20%). Therefore the effects of humidity can be safely neglected in the discussion of astronomical seeing.

Since also pressure fluctuations have negligible effects on the index of refraction, this quantity is affected practically only by the air temperature fluctuations. Therefore the turbulent fluctuations of the index of refraction are intimately linked to the structure of thermal turbulence in the atmosphere.