IRF Theory

TODO: do a detailed writeup of how IRFs are implemented and used in Gammapy.

For high-level gamma-ray data analysis (measuring morphology and spectra of sources) a canonical detector model is used, where the gamma-ray detection process is simplified as being fully characterized by the following three “instrument response functions”:

• Effective area $A(p, E)$ (unit: $m^2$)

• Point spread function $PSF(p'|p, E)$ (unit: $sr^{-1}$)

• Energy dispersion $D(E'|p, E)$ (unit: $TeV^{-1}$)

The effective area represents the gamma-ray detection efficiency, the PSF the angular resolution and the energy dispersion the energy resolution of the instrument.

The full instrument response is given by

$$R(p', E'|p, E) = A(p, E) \times PSF(p'|p, E) \times D(E'|p, E),$$

where $p$ and $E$ are the true gamma-ray position and energy and $p'$ and $E'$ are the reconstructed gamma-ray position and energy.

The instrument function relates sky flux models to expected observed counts distributions via

$$N(p', E') = t_{obs} \int_E \int_\Omega R(p', E'|p, E) \times F(p, E) dp dE,$$

where $F$, $R$, $t_{obs}$ and $N$ are the following quantities:

• Sky flux model $F(p, E)$ (unit: $m^{-2} s^{-1} TeV^{-1} sr^{-1}$)

• Instrument response $R(p', E'|p, E)$ (unit: $m^2 TeV^{-1} sr^{-1}$)

• Observation time: $t_{obs}$ (unit: $s$)

• Expected observed counts model $N(p', E')$ (unit: $sr^{-1} TeV^{-1}$)

If you’d like to learn more about instrument response functions, have a look at the descriptions for Fermi, for TeV data analysis and for GammaLib.

TODO: add an overview of what is / isn’t available in Gammapy.