Diffraction Limited Mode

For comparing the peak intensity of a diffraction-limited optical system with a real system the Strehl parameter was introduced.

$${\frac{{I\mathrm{_{obs}}}}{{I\mathrm{_{theo}}}}}$$ (6)

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. In diffraction limited mode the PSF is approximately composed of two functions:

1. The core: This is an airy function of the telescope multiplied by the Strehl ratio

   $$\sim \left(\vphantom{\frac{2\cdot \mathrm{Bessel}(x)}{x} }\right. {\frac{{2\cdot \mathrm{Bessel}(x)}}{{x}}} \left.\vphantom{\frac{2\cdot \mathrm{Bessel}(x)}{x} }\right)^{2}_{}$$ (7)

   
   
   Bessel(x) is the order 1 Bessel function of the first kind.
2. The halo: It is given by a Moffat function (9) multiplied by (1-Strehl)

   $$\sim \alpha \beta$$ (8)

   
   

This combined AO-PSF is shown in Figure 1.

Figure 1: Simplified description of an AO-PSF: It is built by a core (Airy function) and a halo (Moffat function)