# Double Gaussian model¶

The impact of the PSF on performance depends on the size of the PSF but also its energy distribution.
The simplest way to model different energy distribution in the PSF is to use a double gaussian profile.
The modified aXeSIM code, used in TIPS, able such model in simulate separately the to gaussian component of the double gaussian profile.
The normalized PSF is then expressed :

{{latex($PSF = \frac{c e^{-\frac{\rho^2}{2 \sigma_1^2}}}{2 \pi \sigma_1^2}+\frac{(1-c) e^{-\frac{\rho^2}{2 \sigma_2^2}}}{2 \pi \sigma_2^2}$)}}

{{latex($\rho=\sqrt{X^2+Y^2}$)}}

This PSF model is very interesting because it can describe a wide variety of energy distribution with only three parameters.

The PSF model is describe in the aXeSIM configuration file with the keywords:

PSFSIG1 _float_
PSFSIG2 _float_
PSFC _float_