Calibration Access and Data Handbook

Procedure

This routine computes the value of the PSF enclosed energy fraction (EE) according to the input arguments described below. The encircled energy (EE) depends on the energy, on the position of the object within the EPIC FOV and on the radius and position of the circular window in which it has to be calculated.

The encircled energy function is calculated by integrating the PSF, described as a single King function, out to the input radius by:

$$\begin{eqnarray*} EE(R) = \frac{1 - \frac{1}{\left[1+(\frac{R}{r_{c}})^{2}\righ... ... 1 - \frac{1}{\left[1+(\frac{5'}{r_{c}})^{2}\right]^{\alpha-1}}} \end{eqnarray*}$$

Where $r_{c}$ is the core radius in arcseconds and $\alpha$ is the slope.

The parameters of the King function have been measured for the three mirror modules and described in terms of photon energy and off-axis angle by the formulae:

$$\begin{eqnarray*} r_{\mbox{\scriptsize c}} &=& a + b1 \cdot E + b2 \cdot E^{2} + c\cdot\theta + d\cdot E\cdot\theta \end{eqnarray*}$$

$$\begin{eqnarray*} \alpha = x + y1 \cdot E + y2 \cdot E^{2} + z\cdot\theta + w\cdot E\cdot\theta \end{eqnarray*}$$

From these formulae the parameters $r_{c}$ and $\alpha$ have been tabulated as a function of energy and $\theta$ and stored in the CCF components XRT?_XPSF. This routine uses spline fitting to interpolate between these tabulated values.