XMM-Newton Science Analysis System


omscattered (omscattered-1.5) [xmmsas_20230412_1735-21.0.0]

Computing the scaling factor with mode=2 and mode=3

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The second and third methods of calculating the scaling factor (mode=2 and mode=3) are auxiliary and might be used in some difficult cases when the input image is contaminated by a multitude of other scattered light features (like, “huge deformed donuts”, smoke rings, modulo-8 pattern around bright sources, etc.).

These algorithms use two annular regions (instead of a single region, as in the case of the mode 1): the larger one is the same as in the case of the mode-1 algorithm and is used for finding the background levels of the input ($B_1$) and the calibrated ($B_2$) images.

Figure 4: Two ring-shaped regions for finding the background of the input image (the larger ring covering the peripheral parts of the image) and for computing the counts of the central scattered light feature (the smaller ring in the centre enclosing the scattered light feature). These are used for two auxiliary algorithms (mode=2 and mode=3) of calculating the calibration scaling factor.

The smaller region (see Fig.4) corresponds to the known sizes of the “donut” of the central scattered light feature. The count numbers within this region ($C_1$ for the input image and $C_2$ for the calibrated image) are found by building histograms of the pixel values, as described in Sec.8.1.

Then, in the case of the mode-2 algorithm, the calibration scaling factor is computed as

$$S=\frac{C_1-B_1}{C_2-B_2},$$

and the output image is obtained by subtraction of the scaled and background-free calibration image:

$$I_{\rm output}=I_{\rm input}-S\cdot (I_{\rm calibrated}-B_2).$$

In the case of mode=3 the latter subtraction is made for the scaling factor varied (in a loop) with small steps (of 0.02) from the values 0.2 to 2.8. The optimal scaling factor ($S_{\rm opt}$) is then assumed to correspond to the minimum of the absolute value of the difference between the background $B_1$ and the number of counts within the smaller annulus. The final output image will then be:

$$I_{\rm output}=I_{\rm input}-S_{\rm opt }\cdot (I_{\rm calibrated}-B_2).$$