Analog statistical properties may be applied to
the index of refraction and one may define a
structure coefficient of the index of refraction 
.
From equation (
) and ignoring the very minor
effect of humidity, 
is 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 spread 
of the seeing disk
in arcsec is then given by:
For a vertical direction and 
= 500 nm, the
FWHM angle is expressed as:
[IMAGE ]
Figure: Parameterisation of seeing FWHM with respect to a
mean value of
(K
m
) integrated over a distance z.
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
10 m): 
10
K
m
30 m):
K
m
1-40 mm) the
critical 
values are much higher, of
the order of 10 K
m
.
) and following show that the overall seeing
effects may be considered a 5/3-exponent sum of different terms
corresponding to the different atmospheric layers. Thus if 
is natural seeing FWHM, caused by the boundary layer and upward, and
is the local seeing, the overall seeing is:
The best astronomical sites are reported to have a natural seeing varying between 0.3 to 0.6 arcsec (FWHM), which is roughly equally divided between the high atmosphere and the atmospheric boundary layer. Acceptable sites for astronomical research will have natural seeing up to 2 arcsec.
Local seeing, that is the
seeing caused by the telescope and the surrounding structures
can represent anything from
zero to about 2 arcsec and can be the cause of very significant
differences of image quality among telescopes located on the same site.
Fig. (page )
shows the monthly average of seeing
values logged at different telescopes located close to one another
at the La Silla observatory. The common trends of
the plot let observe the seasonal variation of the natural
seeing at La Silla, which becomes generally worse during the (austral)
winter months. One will also note the
large differences among the telescopes and with respect to the
DIMM seeing monitor,
which are often of the order or 0.5 arcsec and
sometimes reach 1 arcsec. Understanding and decreasing these
differences, unequivocally caused by the enclosure and the atmospheric
environment in the immediate surrounding of the telescope,
is the challenge faced by all future telescope projects.
![[IMAGE ]](img116.gif){kind=link}