In this case (see Fig. 2 (click here)) every layer introduces a tilt term 
.
For each of these layers one can define a 
using Eq. (1).
Figure 2: Also in the multi-layer case a tiny difference between 
and 
will be experienced
The position of the LGS can be obtained, in the previous approximation, by:
for the red beam path,
while following the blue beam:
As usual, equating the expressions given by Eqs. (5) and (6)
the apparent displacement 
is
obtained as:
Using Eq. (1) the latter can be written as:
Using Eq. (8)
we define an effective tilting height
such that:
where 
is the overall tilt at the primary
wavelength.
Equating the expressions given in Eqs. (8) and (9) one obtains:
It is easy to realize that such effective tilting height 
is a
time-dependent parameter.
Moreover, it is to be pointed out that 
is allowed to have any
value between
and 
: when, occasionally, 
the result of Eq. (10) will diverge.
In the established conditions there is no way to retrieve the current value
for 
. However one can think to introduce a mean effective height
and use such a number to deduce the overall tilt 
. Using
this approach some error 
will be introduced and one can write:
and using Eq. (9) the error 
can be worked out:
One can see that in the limiting case 
(a
single layer) or
(the case of an NGS), the error 
will become zero.