What are IRFs?

The instrument response functions (IRFs) provide a mathematical description that links the reconstructed photon arrival direction $p'$, energy $E'$ and trigger time $t'$ of an event to the true incident direction $p$, energy $E$ and time $t$ of a photon. The following figure illustrates this relationship:

$I(p,E,t)$ is the gamma-ray intensity arriving at Earth as a function of direction $p$, energy $E$ and time $t$. $e(p',E',t')$ is the expected event rate as function of the reconstructed direction $p'$, energy $E'$ and trigger time $t'$. The expected event rate is obtained by integrating the product of the instrumental response function $R(p',E',t'|p,E,t)$ and the emitted intensity $I(p,E,t)$ over the direction, energy and time.