From 46a274688648367ea2d32fe7c84f1ca8bb3bd074 Mon Sep 17 00:00:00 2001 From: Jürgen Knödlseder Date: Mon, 1 Apr 2019 11:06:51 +0200 Subject: [PATCH] Update IRF section of User Manual --- doc/source/users/user_manual/irfs.jpg | Bin 28217 -> 0 bytes doc/source/users/user_manual/likelihood.rst | 6 +++--- doc/source/users/user_manual/response.rst | 54 ++++++++++++++++++++++++++++-------------------------- 3 files changed, 31 insertions(+), 29 deletions(-) mode change 100755 => 100644 doc/source/users/user_manual/irfs.jpg diff --git a/doc/source/users/user_manual/irfs.jpg b/doc/source/users/user_manual/irfs.jpg old mode 100755 new mode 100644 index c60bb63..51260cf Binary files a/doc/source/users/user_manual/irfs.jpg and b/doc/source/users/user_manual/irfs.jpg differ diff --git a/doc/source/users/user_manual/likelihood.rst b/doc/source/users/user_manual/likelihood.rst index 021b9fa..31b6e2b 100755 --- a/doc/source/users/user_manual/likelihood.rst +++ b/doc/source/users/user_manual/likelihood.rst @@ -210,7 +210,7 @@ Model fitting using the Levenberg-Marquardt algorithm is implemented by :ref:`ctlike`. -Statistical Parameter errors +Statistical parameter errors ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Statistical errors on the model parameters :math:`\delta a_k` are determined @@ -256,8 +256,8 @@ fluctuations only. For :math:`n=1` the significance in Gaussian sigma is given by :math:`\sqrt{TS}`. -Upper limits -~~~~~~~~~~~~ +Upper flux limits +~~~~~~~~~~~~~~~~~ If gamma-ray emission from a source is not detected, an upper flux limit can be derived by determining the flux :math:`F_\mathrm{up}` that leads to a diff --git a/doc/source/users/user_manual/response.rst b/doc/source/users/user_manual/response.rst index c04fe1e..65e83a5 100755 --- a/doc/source/users/user_manual/response.rst +++ b/doc/source/users/user_manual/response.rst @@ -7,40 +7,32 @@ What are instrument response functions? ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The instrument response functions provide a mathematical description that -links the measured quantities :math:`\vec{d}` of an event to the physical -quantities :math:`\vec{p}` of the incident photon. The following figure -illustrates this relationship: +links the reconstructed photon arrival direction :math:`p'`, energy :math:`E'` +and trigger time :math:`t'` of an event to the true incident direction +:math:`p`, energy :math:`E` and time :math:`t` of a photon. The following +figure illustrates this relationship: .. figure:: irfs.jpg :width: 70% -:math:`I(\vec{p})` is the gamma-ray intensity arriving at Earth as a -function of photon properties :math:`\vec{p}` -(which usually are true photon energy, true photon incident direction, -and true photon arrival time), -while :math:`e(\vec{d})` is the expected event rate as function of event -properties :math:`\vec{d}` (which usually are the measured photon energy, -measured or reconstructued photon incident direction, and measured photon -arrival time). The expected event rate is obtained by integrating the -product of -the instrumental response function :math:`R(\vec{d}|\vec{p},\vec{a}`) -and the emitted intensity :math:`I(\vec{p})` over the photon properties -:math:`\vec{p}`. -The argument :math:`\vec{a}` in the response function comprises any -auxiliary parameter on which the response function may depend on (e.g. -pointing direction, triggered telescopes, optical efficiencies, -atmospheric conditions, etc.). All these quantities and hence the -instrument response function may depend on time. +:math:`I(p,E,t)` is the gamma-ray intensity arriving at Earth as a function of +direction :math:`p`, energy :math:`E` and time :math:`t`. :math:`e(p',E',t')` +is the expected event rate as function of the reconstructed direction +:math:`p'`, energy :math:`E'` and trigger time :math:`t'`. The expected event +rate is obtained by integrating the product of the instrumental response +function :math:`R(p',E',t'|p,E,t)` and the emitted intensity :math:`I(p,E,t)` +over the direction, energy and time. CTA response functions ~~~~~~~~~~~~~~~~~~~~~~ -The instrument response functions for CTA are factorised into +The instrument response functions for CTA (as well as the other IACTs such as +H.E.S.S., VERITAS and MAGIC) are factorised into the effective area :math:`A_{\rm eff}(p, E, t)` (units :math:`cm^2`), the point spread function :math:`PSF(p' | p, E, t)`, and the energy dispersion :math:`E_{\rm disp}(E' | p, E, t)` -following: +following .. math:: R(p', E', t' | p, E, t) = @@ -48,7 +40,17 @@ following: PSF(p' | p, E, t) \times E_{\rm disp}(E' | p, E, t) -ctools are shipped with so called ``prod2`` response functions for the northern +where + +.. math:: + \int PSF(p' | p, E, t) dp' = 1 + +and + +.. math:: + \int E_{\rm disp}(E' | p, E, t) dE' = 1 + +ctools are shipped with the CTA ``prod2`` response functions for the northern and southern arrays, and variants are available that have been optimised for exposure times of 0.5 hours, 5 hours and 50 hours. In total, the following six instrument response functions are available: @@ -56,9 +58,9 @@ In total, the following six instrument response functions are available: ``South_5h``, and ``South_50h``. .. note:: - In cases for which the CTA instrument response functions are used in a - research project, we ask to add the following acknowledgement in any - resulting publication: + If you use the CTA instrument response functions for a research project + and specifically for a presentation or publication, we ask to add the + following acknowledgement to the presentation or publication: *This research has made use of the CTA instrument response functions provided by the CTA Consortium and Observatory.* -- libgit2 0.21.4