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.

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