Point Response and Encircled Energy Functions

An image of an on-axis point source at 6.627 keV is shown in Figure 19. The structure in the image is due to the quadrant supports and poorly shaped foils near quadrant boundaries. The azimuthally averaged point response functions measured at 6.627, 8.837, and 11.046 keV, and their integrals, the encircled energy functions, are shown in Figure 20 and Figure 21, respectively. As in section 3.2, the encircled energy is assumed to be 1.0 in a circle of diameter 105$^{\prime}$.

Despite the image asymmetry, the azimuthally averaged point response function may be adequately represented by the simple function

psf(r) = (a₁/r) e^{-0.5(r/b₁)2} + a₂ e^-r/b₂ + a₃ e^-r/b₃

where r is expressed in arc-minutes, and the constants have the values shown in Table 4.

 

Table 4: Point Response Function Model Parameters

Parameter	6.6627 keV	8.837 keV	11.046 keV
a1	0.01732	TBD	TBD
b1	1.835	TBD	TBD
a2	0.0024	TBD	TBD
b2	2.659	TBD	TBD
a3	3.047 $\times 10^{-5}$	TBD	TBD
b3	14.559	TBD	TBD

 

  

Figure 17: SODART on-axis effective area for a single module. The curve represents the effective area for an ideal x-ray telescope with the SODART parameters, normalized to measured effective areas at energies of 6.627, 8.837, and 11.046 keV.

  

Figure 18: SODART vignetting function measured at three different energies and various off-axis angles. The solid lines are included to guide the eye only, and do not represent a functional fit.

  

Figure 19: On-axis image of a point source at 6.627 keV in FM1. The data were recorded by an imaging detector similar to LEPC. Adjacent contours are spaced by a factor of e.

  

Figure 20: Point Response Function of the SODART MM at three different energies. The function is estimated from the same data used to derive the encircled energy function.

  

Figure 21: Encircled Energy Function of the SODART MM at three different energies.