We have performed a number of simulations using the 4-layers fit of
Roggermann et al. (1995) to various models published in the
literature, rescaling them for different values of 
.
Namely the Greenwood good seeing model (Greenwood 1977) is denoted
by G-77; the fit with Maui (Hawaii) U.S. Air Force Optical Station (Miller
et al. 1976) is denoted by SLC-N and the Hufnagel-Valley
model (Hufnagel 1974) with an upper atmospheric wind of 54 miles per hour
(
) is denoted by HV-54.
We have generated series of 65536 tilts for each of the four layers in a
grid of 6 different 
values for each of the 3 different atmosphere
models adopted. For each layer a normal distributed tilt with a
dispersion given by (Sarazin & Roddier 1990):
has been calculated and propagated up to the mesospheric Sodium layer.
The effective tilt height has been computed together with the residual
jitter for each of the 65536 time-points taken into consideration.
Figure 3: The histograms for 
and 
for D=8 m,
m in the HV-54 model. The run is composed by 65536 realizations.
As it can be seen 
follows roughly a Gaussian distribution, while
the 
distribution is much more platicurtic
As it can be easily seen in Fig. 3 (click here) the distribution of the effective
height is far from a Gaussian shape; however the final residual tilt
distribution is very well fitted by a Gaussian distribution, so that it
can be identified by the single figure of the dispersion
.
Following Sandler et al. (1994) one can determine the Strehl ratio
degradation contribution due only to the problem pointed out in this
paper using the relationship:
The results of the simulation are collected in Tables 1 (click here) and 2 (click here) and in
Fig. 4 (click here) for the cases of D = 3.58 m and D = 8.00 m
telescopes; the fluctuations of the mean effective height 
are due to the different realizations of the same multi-layer models.
In order to get a deeper insight on the meanings of the published
numbers it is here recalled that the diffraction limit capabilities for
a 
nm wavelengths, 
are respectively 33.9 mas
and 15.2 mas for the two telescope aperture taken into consideration.
Table 1: The results for the perfomed simulation in the
D=3.58 m case
Table 2: The same as for Table 1 (click here), in the D = 8.00 m telescope case
Figure 4: Behaviour of SR vs. 
for D = 3.58 m (upper panel) and
D = 8.00 m (lower panel) telescope