Similar statistical properties may be applied to the index of refraction and one may define a structure coefficient of the index of refraction , related to by:

where is the wavelength. Normally one considers as a reference the wavelength = 500 nm and the previous equation becomes:

The seeing effect through an atmospheric layer of height H can then be expressed an integral function of the index of refraction structure coefficient , whereby the Fried parameter is given by

where is the zenithal angle of the direction of observation.

Recalling equation (), the FWHM of the seeing disk in arcsec is then given by:

where is the zenithal angle of the direction of observation.

For a vertical direction and = 500 nm, the
FWHM is expressed as:

Combining with equation (), for typical conditions of astronomical mountain sites (pressure 770 mb, temperature 10) one obtains:

The diagram at fig. illustrates the order of magnitude of the seeing effect with respect to a mean value of and the integration distance.

Depending on the geometric scale of the phenomenon causing seeing, the critical values of will be very different: for instance, if we set at 0.1 arcsec an arbitrary threshold for "bad" seeing from a single cause, the corresponding critical (mean) value of will be

- for the dome interior
(distance scale 10 m): 10 Km
- for the atmospheric
surface layer (distance scale 30 m):
Km
- for seeing caused by convection flow at the surface
of the telescope mirrors (distance scale 1-40 mm) the
critical values are much higher, of
the order of
**10**Km .

Lorenzo Zago, zago@elgc.epfl.ch, Sun Feb 26 22:57:31 GMT+0100 1995