Table 1: List of parameters necessary to compute the SNR.
$N^l_{\rm ph}(r)$ Number of photons per second per square meter per bandwidth in a given layer l of the

atmosphere, depending on the guide stars geometry, and magnitude

$N^l_{\rm gs}(r)$ number of stars whose footprints contribute at r in the layer l.

$\tau$ Coherence time of the whole atmosphere

$\tau_l$ Coherence time of layer l

$\Delta t$ Integration time employed for the whole atmosphere

$\Delta t_l$ Integration time employed for layer l

d Sampling pitch for the wavefront measurements in NUMLO approach.

d_l Sampling pitch for the wavefront measurements in OPTLO approach, layer l.

r₀ Fried parameter describing the whole atmosphere.

r_0,l Fried parameter associated to layer l.

$r_0(\lambda_{\rm wfs})$ Fried parameter describing the whole atmosphere at the wavefront-sensing wavelength.

RON read-out noise of the CCD detector.

$\alpha_l$ fraction of light arriving to the detector l in the optical layer

oriented measurements due to the beam splitter.

$N_{\rm bg}$ number of background photons $\rm s^{-1}~m^{-2}~arcsec^{-2}$

$Q_{\rm e}$ quantum efficiency (it includes also optical transmission)

**Table 1:** List of parameters necessary to compute the *SNR*.
$N^l_{\rm ph}(r)$	Number of photons per second per square meter per bandwidth in a given layer l of the
	atmosphere, depending on the guide stars geometry, and magnitude
$N^l_{\rm gs}(r)$	number of stars whose footprints contribute at r in the layer l.
$\tau$	Coherence time of the whole atmosphere
$\tau_l$	Coherence time of layer l
$\Delta t$	Integration time employed for the whole atmosphere
$\Delta t_l$	Integration time employed for layer l
d	Sampling pitch for the wavefront measurements in NUMLO approach.
d_l	Sampling pitch for the wavefront measurements in OPTLO approach, layer l.
r₀	Fried parameter describing the whole atmosphere.
r_0,l	Fried parameter associated to layer l.
$r_0(\lambda_{\rm wfs})$	Fried parameter describing the whole atmosphere at the wavefront-sensing wavelength.
RON	read-out noise of the CCD detector.
$\alpha_l$	fraction of light arriving to the detector l in the optical layer
	oriented measurements due to the beam splitter.
$N_{\rm bg}$	number of background photons $\rm s^{-1}~m^{-2}~arcsec^{-2}$
$Q_{\rm e}$	quantum efficiency (it includes also optical transmission)

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