.. _irf-theory: 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 :math:`A(p, E)` (unit: :math:`m^2`) * Point spread function :math:`PSF(p'|p, E)` (unit: :math:`sr^{-1}`) * Energy dispersion :math:`D(E'|p, E)` (unit: :math:`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 .. math:: R(p', E'|p, E) = A(p, E) \times PSF(p'|p, E) \times D(E'|p, E), where :math:`p` and :math:`E` are the true gamma-ray position and energy and :math:`p'` and :math:`E'` are the reconstructed gamma-ray position and energy. The instrument function relates sky flux models to expected observed counts distributions via .. math:: N(p', E') = t_{obs} \int_E \int_\Omega R(p', E'|p, E) \times F(p, E) dp dE, where :math:`F`, :math:`R`, :math:`t_{obs}` and :math:`N` are the following quantities: * Sky flux model :math:`F(p, E)` (unit: :math:`m^{-2} s^{-1} TeV^{-1} sr^{-1}`) * Instrument response :math:`R(p', E'|p, E)` (unit: :math:`m^2 TeV^{-1} sr^{-1}`) * Observation time: :math:`t_{obs}` (unit: :math:`s`) * Expected observed counts model :math:`N(p', E')` (unit: :math:`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.