XMM-Newton Science Analysis System


asmooth (asmooth-2.32.1) [xmmsas_20230412_1735-21.0.0]

Single gaussian convolver

smoothstyle=`simple', convolverstyle=`gaussian'.

The convolving kernel is a rotationally-symmetric gaussian, truncated onto a square array of side length $2N+1$:

$$c_{x,y} = A \, \exp(-[x^2+y^2]/2\sigma^2) \textrm{ for $\vert x\vert,\vert y\vert \le N$, 0 else.}$$

The width $\sigma$ is read from the parameter width and $N$ is set equal to 1 plus the integer part of $5\sigma$. If normalize=`yes', $A$ is set from

$$A^{-1} = \sum_{x=-N}^{N} \sum_{y=-N}^{N} \exp(-[x^2+y^2]/2\sigma^2);$$

otherwise $A$ = 1.