Seeing Limited Mode

The simulation uses two different point spread functions. The PSF is approximated by a Moffat function (9) in the seeing-limited case. In contrast to a Gaussian-shaped function it contains more light in the wings. The parameter $\beta$ is responsible for the amount of light in the wings. $\beta$ = 2.5 is used for point sources.

$$\alpha \beta {\frac{{\beta -1}}{{\pi \alpha^2}}} \left(\vphantom{1+\frac{r^2}{\alpha^2} }\right. {\frac{{r^2}}{{\alpha^2}}} \left.\vphantom{1+\frac{r^2}{\alpha^2} }\right)^{{-\beta}}_{}$$ (9)

I$\alpha$,$\beta$(r)	:	Intensity at the distance r with parameters $\alpha$ and $\beta$
	:	Another parameter (is used to fix the FWHM for a given $\beta$)
$\beta$	:	Parameter to fix the amount of light in the lobes
r	:	Distance to the center (r = $\sqrt{{x^2+y^2}}$)
FWHM	:	2$\sqrt{{2^{1/\beta}-1}}$