psf_3gauss
format¶
Multi-Gauss mixture models are a common way to model distributions (for source intensity profiles, PSFs, anything really), see e.g. 2013PASP..125..719H. For H.E.S.S., radial PSFs have been modeled as 1, 2 or 3 two-dimensional Gaussians \(dP/d\Omega\).
Note
A two-dimensional Gaussian distribution \(dP/d\Omega = dP/(dx dy)\) is equivalent to an exponential distribution in \(dP/x\), where \(x=r^2\) and a Rayleigh distribution in \(dP/dr\).
In this format, the triple-Gauss distribution is parameterised as follows:
where \(S\) is SCALE
, \(\sigma_i\) is SIGMA_i
and
\(A_i\) is AMPL_i
(see columns listed below).
TODO: give analytical formula for the integral, so that it’s easy to check if the PSF is normalised for a given set of parameters.
TODO: give test case value and Python function for easy checking?
Note
By setting the amplitudes of the 3rd (and 2nd) Gaussians to 0 one can implement double (or single) Gaussian models as well.
Columns:
THETA_LO
,THETA_HI
– ndim: 1, unit: deg- Field of view offset axis
ENERG_LO
,ENERG_HI
– ndim: 1, unit: TeV- Energy axis
SCALE
– ndim: 2, unit: none- Absolute scale of the 1st Gaussian
SIGMA_1
,SIGMA_2
,SIGMA_3
– ndim: 2, unit: deg- Model parameter (see formula above)
AMPL_2
,AMPL_3
– ndim: 2, unit: none- Model parameter (see formula above)
Recommended axis order: ENERGY
, THETA
Header keywords: none
Example data file: TODO: add HESS HAP example file as soon as available.