XMM-Newton Science Analysis System


omscattered (omscattered-1.5) [xmmsas_20230412_1735-21.0.0]

Using the peripheral background for computing the scaling factor (mode=1)

.

The first method of scaling the calibrated scattered light feature is based upon the assumption that the number of counts corresponding to this feature scales linearly with the background level of the OM image.

Figure 3: The ring-shaped region used for finding the background levels of the input image (left) and the calibration image (right) in the case of the default algorithm (mode=1) for calculation of the scaling factor of the calibrated image.

The background is calculated for the same ring-shaped region of both the input ($B_1$) and calibration ($B_2$) images (Fig.3). The scaling factor applied to the calibrated image in this case will be

$$S=\frac{B_1}{B_2}$$

and the output image is obtained by subtracting the scaled calibrated image from the input image and restoring the constant background level of the input image:

$$I_{\rm output}=I_{\rm input}-I_{\rm calibrated}*S+B_1.$$

Systematic error is reduced in the background calculation by masking sources in the data image. These are identified by an "Emboss-filtering" technique which compares modified versions of the image, shifted by a few pixels in the horizontal and vertical directions.

A histogram of the remaining pixels is computed. The background value is measured from only the most-populated 10% of pixel values. This reduces bias in the measurement from residual structure such as irregular scattered light.

Thus, $B_1$ is then obtained as the weighted average of the values of these most populated pixels:

$$B_1=\frac{\sum_{p_c>0.9p_{c^{\rm max}}} p_c \cdot c}{\sum_{p_c>0.9p_{c^{\rm max}}} p_c},$$

where $c$ is the number of counts (histogram slot); $p_c$ is the number of pixels having this number of counts; and $p_{c^{\rm max}}$ is the maximal histogram value corresponding to the most populated count number $c^{\rm max}$. The value of $B_1$ is usually close to $c^{\rm max}$.