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F.6 Correction of Spatial Gain Variations (SGC)

Figure F.8: Spatial gain correction terms according to Eq.(F.12). Top panel: tex2html_wrap_inline18578 for PSPC-C (solid) and PSPC-B (dashed). Middle panels: tex2html_wrap_inline18580 for PSPC-C (upper) and PSPC-B (lower). Bottom panel: tex2html_wrap_inline18582 (equal for both PSPCs).

Figure F.9: Effect of the spatial gain correction (SGC) in low-gain mode tex2html_wrap_inline18584 for PSPC-B. Top: SGC as a function of the measured y-coordinate ( tex2html_wrap_inline18588 , perpendicular to the anode wire direction) for 3 values of the measured pulse-height: tex2html_wrap_inline18590 (solid), 100 (dotted), and 50 (dashed). Bottom: SGC as a function of the measured pulse-height tex2html_wrap_inline18596 for three different measured positions: tex2html_wrap_inline18598 (solid), 4275 (dotted), and 4276 (dashed). SGC does not depend on tex2html_wrap_inline18600 (parallel to anode wire direction). tex2html_wrap_inline18602 , tex2html_wrap_inline18604 , and tex2html_wrap_inline18606 correspond in the figure to RAW_AMPL RAWX and RAWY, respectively.

Figure F.10: Spatial gain correction effect tex2html_wrap_inline18610 as a function of PSPC-B position ( tex2html_wrap_inline18612 , top to bottom) and raw amplitude ( tex2html_wrap_inline18614 , left to right) for tex2html_wrap_inline18616 ; the color bar ranges from -22 to +22 channels.

Figure F.11: Spatial gain correction: effect of interchange of x and y axis as a function of PSPC-B position (detector coordinates tex2html_wrap_inline18630 and tex2html_wrap_inline18632 , i.e., the central quarter of the PSPC): again tex2html_wrap_inline18634 and tex2html_wrap_inline18636 have been used, the color bar ranges from -10 to +10 channels. The small-scale inhomogeneities reflect the anode wire spacing.

Besides the temporal gain variations (cf. Sect. F.4) spatial variations in the gain of the PSPC effect the measured pulse-height. Mechanical inaccuracies of the grid system lead to different electric field strengths and hence different gains. Additionally, the anode wire grid causes a ``binning'' with the period of the anode wire distance (1mm, about tex2html_wrap_inline18642 detector pixels). During pre-flight ground calibrations using slit masks instead of the PSPC entrance window spatial gain variations have been determined. Significant effects have been found perpendicular to the anode wire direction (i.e., in y-direction) while parallel to the anodes the effect was negligible ( tex2html_wrap_inline18646 ). The effect also depends on the depth within the counter where the photon is absorbed (and therefore on the photon energy).

In SASS the pulse height tex2html_wrap_inline18648 is obtained depending on the electronic position corrected coordinate tex2html_wrap_inline18650 according to Eq. (F.12). The energy-dependent term tex2html_wrap_inline18652 has been determined at the Al K tex2html_wrap_inline18654 line energy and should thus be normalized to unity at channel 151; it is shown in Fig. F.8 (bottom). The spatial corrections are expressed in a low-frequency term tex2html_wrap_inline18656 (see Fig. F.8, top) and a high-frequency term tex2html_wrap_inline18658 (see Fig. F.8, middle) which reflects the anode wire spacing. In practice SASS uses tex2html_wrap_inline18660 (nearest integer of tex2html_wrap_inline18662 ); if tex2html_wrap_inline18664 then the value for tex2html_wrap_inline18666 is taken. The spatial correction tables tex2html_wrap_inline18668 used by SASS have 800 elements with tex2html_wrap_inline18670 ; for tex2html_wrap_inline18672 the corresponding value for tex2html_wrap_inline18674 is used. This has no effect as the table values for tex2html_wrap_inline18676 (PSPC-B) and tex2html_wrap_inline18678 (PSPC-C) are constant anyway.

Figure F.9 illustrates the effect of the spatial gain correction close to the detector center ( tex2html_wrap_inline18680 , PSPC-B) in low-gain mode ( tex2html_wrap_inline18682 ). The top panel contains the relation of the effect with coordinate tex2html_wrap_inline18684 (for 3 values of the measured pulse-height). The bottom panel shows how strong the effect depends on the position which results from the use of the roughly binned correction tables and introduces spectral artifacts. Figure F.10 gives the spatial gain correction tex2html_wrap_inline18686 as a function of amplitude tex2html_wrap_inline18688 (from left to right, 1 to 256) and position tex2html_wrap_inline18690 (from top to bottom, 1 to 8192). Obviously, the effect becomes more important for higher channels. The color bar ranges from -22 to +22.

Another inconsistency is of a more severe nature. [Hasinger and Snowden1990] as well as Chap. 3 (PSPC) and Chap. 8 (SASS) use the x-coordinate as input in the correction formula Eq. (F.12) instead of the y-coordinate [Turner et al.1995]. This means, that no correction had been applied by SASS perpendicular to the anode wires as required but parallel to the anode wire direction. For positions tex2html_wrap_inline18700 this error vanishes. However, as the on-axis position is not in the detector center, (4119|3929) instead of (4096|4096), the target positions are significantly offset from this line and the improper applied correction has a net effect. On the other hand, this effect is reduced due to the wobble motion ( tex2html_wrap_inline18706 , equivalent to tex2html_wrap_inline18708 detector pixels in x as well as in y direction) as the source position (relative to the detector) moves by more than the anode wire spacing. The wobble is performed parallel to x = y there is still a major effect on the amplitudes. This error has recently been corrected in SASS. The REV2 survey data as well as pointed data processed with SASS release 7.2 (or later) have the correct SGC applied. Figure F.11 gives the spatial gain correction tex2html_wrap_inline18716 if the x and y axis are interchanged in the correction procedure (SASS versions 7.1 and lower) as a function of detector position ( tex2html_wrap_inline18722 from left to right and tex2html_wrap_inline18724 from top to bottom). The color bar ranges here from -10 to +10.

After the spatial gain correction the amplitude tex2html_wrap_inline18730 should not depend on where the photon has been detected in the PSPC. Finally, the value tex2html_wrap_inline18732 is written into the photon event table (pulse-height invariant channel PI).




SASS source code: package PSPC, bubble CT, subroutine DCORG

SASS files:

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