formula

$f_{psf}=\frac{f_{core}}{2\pi\sigma_{core}^{2}}exp \left [ -\left (\frac{x^2}{2\sigma_{core}^{2}} + \frac{y^2}{2\sigma_{core}^{2}} \right) \right ] + \frac{f_{halo}}{2\pi\sigma_{halo}^{2}}exp \left [ -\left (\frac{x^2}{2\sigma_{halo}^{2}} + \frac{y^2}{2\sigma_{halo}^{2}} \right) \right ]$