XMM-Newton Science Analysis System


epreject (epreject-5.18.1) [xmmsas_20230412_1735-21.0.0]

Correction of the energy scale in specific pixels

The usual mode of operating the EPIC-pn camera consists of computing an offset map immediately before the beginning of an exposure. Ideally, this map contains the energy offset for each pixel (expressed in analog–to–digital units, adu). During the exposure, these offsets are subtracted onboard from the measured signals, and only events where the difference exceeds a lower threshold (usually 20 adu, which formally corresponds to 100 eV) are transmitted to Earth.

High–energy particles hitting the EPIC-pn CCD during the offset map calculation may cause the affected pixels to get offset values which are incorrect by a few adu. As a consequence, the energies of all events in these pixels appear to be shifted by the same amount. Due to the specific method of deriving the offset map onboard, the affected areas occur often in blocks of four consecutive pixels along readout direction. Depending on the orientation of the trail caused by the high–energy particle with respect to the CCD, these areas may also extend over several consecutive pixels perpendicularly to the readout direction. The affected pixels usually get an offset which is too small. If the affected area extends over several pixels along a CCD row (perpendicularly to the readout direction), then the remaining pixels within this CCD row may get an offset which is too high.

If the offset to be subtracted is too small, then the adu values which are assigned onboard to events in such pixels become too high. Thus, events which have adu values below the lower threshold and which would normally be rejected, may show up in the data set. As most of such events are due to detector noise, which is steeply increasing towards lower energies (Fig. 1), any reduction of the lower energy threshold leads to a considerable increase in the number of events. An immediately apparent consequence of this effect is the occurrence of bright patches in EPIC-pn images which are accumulated at low energies (e.g. Fig. 3). A less obvious consequence is a shift in the energy scale over the whole spectral bandwidth. This shift degrades the energy resolution for extended objects. For point sources, the X–ray spectrum may be shifted by some 10 eV, in most cases towards higher energies, if the position of the source happens to coincide with one of these patches.

Task epreject provides two methods to correct the energy scale:

1. If offset maps are available these can be used directly to estimate the offset errors: Since the effected chip areas are limited to regions where the chip was hit by high–energy particles during the offset map calculation, the offset error can be determined by subtracting the value of the offset map in the effected areas from the value in the unaffected areas. This is achieved by in turn subtracting its median value from each column and each row of the offset maps. The values in the remaining residual offset map can then be regarded as the offset errors which need to be subtracted from each event falling into the respective pixels.

2. If no offset maps are available the offset errors can be corrected using a method based on the count images accumulated in the lowest energy channel. As the detector noise is monotonically increasing towards lower energies, a correlation is expected between the brightness of such pixels at low energies and the amount of offset shift which they have received. Evidence for such a correlation was indeed found, in particular when only the lowest transmitted adu value (usually 20) is used for determining the pixel brightness. However, this correlation is disturbed by the fact that the brightness of a pixel at 20 adu is also influenced by other factors, in particular by its individual noise properties. In order to separate offset–induced changes of the 20 adu pixel brightness from other brightness variations at 20 adu across the detector, a reference image is subtracted from the 20 adu image. This reference image contains for each pixel the nominal, i.e. temporally constant, value of its 20 adu brightness (Fig. 2). The reference image was derived by accumulating images at 20 adu from long FF exposures with no bright X–ray sources in the field, and computing the median value for each pixel.
   The intensity in the subtracted, normalized 20 adu images is then used to reconstruct the value of the offset shift, which was incorrectly applied onboard, and the raw amplitudes of all events in the corresponding pixels are shifted back by this amount to their nominal value (Fig. 4). The reconstruction of the offset shift is done by using calibration data which were derived from exposures where offset maps were available.

X-ray loading: For the fast modes (TIMING and BURST) X-ray loading may affect the offset map calculation and thus shift the energy scale across the PSF. This effect is absent if the offset map is calculated in CLOSED filter position.
If withxrlcorrection=Y the tasks checks for the fast modes the FILTER position during offset map calculation (keyword OTFILTER) and if not CLOSED it re-shifts the energies by comparison of the actual offset map with a master offset map. Note, that this requires that offset maps are available in the ODF (is generally the case except for early observations) and that the use of offset maps is enabled (is the default, i.e., withoffsetmap=Y).
The underlying caorrection algorithm in the case of non-CLOSED filter during offset map calculation is as follows:

1. get the CLOSED filter master offset map for mode (TI or BU) and time period from the calibration area and compute the median of each column.
2. determine the general level (for “master”) via averaging the median values over columns 2–10, and subtract this value from the medians
3. get the offset map for this exposure from the ODF and compute the median of each column
4. determine the general level (for “exposure”) via averaging the median values over columns 2–10, and subtract this value from the medians
5. determine the difference of medians per column “exposure” – “master” and add this value (modified by a linear function) to the corresponding PHA values of the events.

Remarks: Although this task re-adjusts the energy scale, there are some effects left which cannot be corrected for:

• If the energy scale has to be corrected towards lower energies, then events may get raw amplitudes which are below the low energy threshold applied onboard. In order to re–establish a common lower energy threshold, such events should be removed in a subsequent step.
• If the energy scale has to be corrected towards higher energies, then events with very low raw amplitudes are missing (because they were not included in the telemetry). In order to re–establish a common lower energy threshold, this threshold could be increased by the maximum shift which was applied towards higher energies. However, while a shift towards higher energies is usually required only for very few pixels, information about the lowest energies would then be lost for all pixels. Furthermore, the area around the object of interest might not be affected at all. Therefore, it should be checked in each specific case whether a general increase of the lower threshold is appropriate.

Caveats:

In option (2), above, the task attempts to reconstruct the offset shifts from the brightness of pixels at 20 adu. While it is guaranteed that the offset shifts can only occur at discrete adu steps, the correspondence between the 20 adu brightness and the value of the offset shift is not always unique. The presence of Poissonian noise in the 20 adu images, in particular for short exposures, limits the sensitivity for spotting the bright patches and deriving the appropriate energy correction. The parameter sigma which specifies the minimum significance which a block of four consecutive pixels along readout direction must have in order to trigger the offset shift correction task for this block, can be set by the user. Tests indicate that setting this parameter to $\sim4\,\sigma$ is a good choice for short ( $\sim5\mbox{ ks}$) exposures; for longer exposures this parameter can be increased (to $\sim5$ – $6\,\sigma$ for more than 20 ks). It is recommended to control the results by accumulating an image below 20 adu after this task: this image shows the pixels where an offset shift was applied (Fig. 5).

Figure 1: Number of events as a function of PHA [adu] for quadrant 0, obtained during 50.7 ks in a closed FF exposure (0059_0122320701_PNS003). The peak at 20 adu corresponds to an event rate of 0.75 events/frame/quadrant, or $2\cdot 10^{-5}\mbox {\,events/frame/pixel}$ .

Figure 2: Reference image for the 20 adu intensities per pixel, normalized to an exposure of 1 ks. It was obtained by accumulating images at 20 adu from long FF exposures with no bright X–ray sources in the field, and computing the median value for each pixel. This image contains for each pixel the temporally constant value of its 20 adu brightness.

Figure 3: Events with raw amplitudes of 20 adu in the closed 23.2 ks FF exposure 0462_0134521601_PNS005. The number of events per pixel is color coded according to the color bar at top, ranging from zero (black) to 50 (white).

Figure 4: Same as Fig. 3, but after applying the task epreject for correcting the energy scale in specific pixels.

Figure 5: Pixels in the exposure 0462_0134521601_PNS005 where offset shifts were applied. This image was accumulated from events with $\mbox {PHA}<20\mbox { adu}$, after running the task epreject. A $4\,\sigma$ threshold was applied for the identification of bright patches.

Figure 6: Events with raw amplitudes of 20 adu in the closed 23.2 ks FF exposure 0462_0134521601_PNS005, after correcting the offset shifts and after suppressing the noise. Note that the intensity scale extends now from 0 to 3, while it covered the range from 0 to 50 in Figs. 3 and 4.