In diffraction limited mode with adaptive optics the PSF is approximately composed of two functions:
 The core: This is an airy function of the telescope
 The halo: It is given by a Moffat function
I_{Moffat}(r) = I_{,}(r) = 1 + 
(7) 
I_{,}(r) 
: 
Intensity at the distance r with parameters and 

: 
Parameter is used to fix the FWHM for a given 

: 
Parameter to fix the amount of light in the lobes 
r 
: 
Distance to the center
(r = ) 
FWHM 
: 
2 
An example of such combined PSF is shown in Figure 1.
Figure 1:
Simplified description of an observed AOPSF: It is built by a core (Airy function) and a halo (Moffat function).

For comparing the peak intensity of an ideal diffractionlimited optical system with a real system the Strehl parameter was introduced.
Strehl = 
(8) 
This parameter is the ratio of the observed peak intensity at the detection plane of a telescope or other imaging system from a point source compared to the theoretical maximum peak intensity of a perfect imaging system working at the diffraction limit. For calculating the fraction of the halo and core component to achieve a certain strehl ratio the parameter F0 is introduced in this ETC. It has to fulfill the following equation:
In this mode the SNR is calculated for a disk with a radius of twice the radius of the airy disk.
Andre Germeroth
20161104