.. _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.