diff --git a/README.rst b/README.rst index c8d38a7..3b39ee5 100644 --- a/README.rst +++ b/README.rst @@ -87,7 +87,7 @@ Thus its matrix ``G`` is the unit-matrix. As a result, the blue scenario's area for the signal is the area for the signal estimated in the instrument's response-function. As matrix ``G`` does not mix true and reconstructed energy, the blue scenario shows the true gamma-ray-energy, what is good. The matrix ``B`` is also the unit-matrix so that this scenario's rate of background is the estimated rate in the instrument's response-function. -But ofcourse the blue scenario falls short when the instrumen's confusion in energy is significant. +But of course the blue scenario falls short when the instrumen's confusion in energy is significant. +-------------------------------------+--------------------------------------------+ | Matrix ``G`` | Matrix ``B`` | @@ -113,10 +113,12 @@ But ofcourse the blue scenario falls short when the instrumen's confusion in ene Yellow ------ -The ``yellow`` scenario not only takes the signal in the energy-bin under investigation into account, but also other bins in reconstructed gamma-ray-energy where the true gamma-ray-energy was confused to. +The ``yellow`` scenario not only takes the signal in the energy-bin under investigation into account, +but also other bins in reconstructed gamma-ray-energy where the true gamma-ray-energy was confused to. This is done by setting the matrix ``G`` to be the confusion of the instrument. Thus in the yellow scenario the area of the signal can exceed the area estimated in the instrument's response function. -Unfortunately, the yellow scenario's matrix ``G`` has non zero elements off its diagonal what makes the interpretation of this scenario's energy-axis difficult. +Unfortunately, the yellow scenario's matrix ``G`` has non zero elements off its diagonal what makes the +interpretation of this scenario's energy-axis difficult. It is no longer only true gamma-ray-energy. @@ -142,9 +144,14 @@ It is no longer only true gamma-ray-energy. Green ----- -The ``green`` scenario sets its matrix ``G`` to only the diagonal of the instrument's confusion. -With only zero off its diagonal, the matrix ``G`` allows the green scenario to show true gamma-ray-energy. -However, the green scenario is rather conservative in most astronomical applications as it represents the sensitivity to detect a source which only emits gamma-rays in a narrow range of energies. +The ``green`` scenario sets its matrix ``G`` to only the diagonal of the instrument's +confusion. +With only having zeros off its diagonal, the matrix ``G`` allows the green scenario to +show true gamma-ray-energy. +However, the green scenario is rather conservative in most astronomical applications +as it represents the sensitivity to detect a source which only emits gamma-rays in a +narrow range of energies and further ignores all the signal which was confused to +different energies. +-------------------------------------+--------------------------------------------+ | Matrix ``G`` | Matrix ``B`` | @@ -176,9 +183,9 @@ The ``black`` scenario was proposed by Werner Hofmann and takes a different appr Instead of altering the area of the signal, this scenario alters the rate of the background. The black scenario widens the energy-range in the background to the range required to collect one sigma (68%) of the signal. This means that matrix ``B`` now collects contributions from multiple bins in reconstructed gamma-ray-energy. -The wider range in energy is estimated using the instruments confusion in energy by estimating the range in reconstructed gamma-ray-energy which contains 68% of the gamma-rays. -To represent the containment of 68% in the signal, this scenarios area in signal uses a matrix ``G`` with the elements on its diagonal being ``0.68``. -The advantage here is, that matrix ``G`` has only zeros off its diagonal and thus the black scenario can show the true gamma-rays-energy on its energy-axis. +The wider range in energy is estimated using the instruments confusion in energy by estimating the range in reconstructed gamma-ray-energy which contains 68% of the signal. +To represent the containment of 68% in the signal, this scenario's matrix ``G`` has the elements on its diagonal set to ``0.68``. +Matrix ``G`` has only zeros off its diagonal and thus the black scenario can show the true gamma-rays-energy on its energy-axis. +-------------------------------------+--------------------------------------------------------------------------+ | Matrix ``G`` | Matrix ``B`` |