If pulse amplitude were the only thing affecting whether a pulse is double-counted, then it might be easy to develop a correction to the scalar rates by examining the event pulse-heights of the telemetered events. In order to assess this possibility I have looked at the data from ObsIDs 147, 151, and 157, calibration observations of G21.5-0.9 with single HRC-S MCP segments selected via edge-blanking.
Pulse amplitudes were determined in two ways: 1) reported event PHA, which is the result of an analog summation of all of the CGCD amplifier signals, and 2) a scaled summation of the six reported CGCD tap signals used for fine-position determination. The second of these has the advantage of not saturating until a higher amplitude. Before scaling the six tap values I corrected the AMP_SF values using the method described in the memo "An Improved AMP_SF Correction Scheme". In order to make a rough comparison between the two amplitude determinations I divided the scaled sum of the six taps by 52.9. The fraction of events with amplitude greater than a given channel are plotted in figure 1; the curves for the different MCP segments are presented in different colors.
In the "Telemetered vs Processed Events" memo the ratio of the number of telemetered events to the reported number of valid events was determined for each of the ObsIDs. Average values were 0.753, 0.788, and 0.912 for ObsIDs 151 (+Y MCP), 157(-Y MCP), and 147 (Center MCP) respectively. Since telemetry was not saturated, the ratio was expected to be 1.0. If f is the fraction of events that are double-counted then the observed ratio will be given by 1/(1+f). The horizontal dotted lines in figure 1 are drawn at the derived value for f for each of the observations.
Figure 1: ObsIDs 147, 151, and 157 - fraction of events with pulse-height greater than the channel number. The solid line is a scaled version of the sum of the six position tap signals and the dashed line is the PHA value. Different colors label data from different ObsIDs or equivalently different HRC-S MCP segments. The horizontal dotted lines indicate the fraction of events that are required to generate doubled-counted pulses in order to produce the observed discrepancy between the reported number of valid events and the number of telemetered events. |
The fact that the intersection of the horizontal lines and the corresponding pulse amplitude curves do not occur at the same channel for the three ObsIDs (scaled sum of taps values of 402, 231, and 285 for ObsIDs 147, 151, 157 respectively) means that pulse amplitude is not the sole determinant of whether an event is double-counted. I expect that the pulse shapes are different among the three MCP segments, making the development of a correction scheme more complicated.
We have performed several observation over the coarse of the mission where we have used the HRC edge-blanking function to select the individual MCP segments. I have extracted these observations from the Chandra archive and performed the same processing described above on them to determine the "scaled sum-of-taps" value above which double-counting occurred. Some ObsIDs were filtered to select non-flaring background time intervals. The results are given in the following table.
ObsID | Telem. Rate | Valid Rate | Double-count Fraction | Scaled SUMAMPS |
---|---|---|---|---|
Center Segment | ||||
147 | 59.357578 | 65.138626 | 0.097393593 | 402 |
146 | 42.675339 | 46.711128 | 0.094569610 | 404 |
148 | 34.744350 | 37.638418 | 0.083296069 | 409 |
2868 | 53.164745 | 56.143219 | 0.056023473 | 408 |
997 | 48.135204 | 51.295918 | 0.065663234 | 402 |
2589 | 40.532703 | 43.460392 | 0.072230282 | 410 |
+Y Segment | ||||
151 | 65.424187 | 86.897301 | 0.32821369 | 231 |
150 | 78.139664 | 98.553848 | 0.26125253 | 229 |
152 | 51.909367 | 65.936447 | 0.27022253 | 227 |
2598 | 41.903954 | 53.074860 | 0.26658358 | 227 |
-Y Segment | ||||
157 | 61.762547 | 78.568329 | 0.27210313 | 284 |
1407 | 52.645958 | 66.138618 | 0.25629053 | 287 |
1467 | 47.461239 | 60.680717 | 0.27853210 | 281 |
154 | 75.877686 | 91.722534 | 0.20882093 | 289 |
155 | 41.144112 | 50.239307 | 0.22105705 | 288 |
1807 | 41.929676 | 50.609032 | 0.20699792 | 288 |
As can be seen by the table the amplitude, above which events are double-counted, is consistent between ObsIDs for a given segment. This suggests that the following algorithm can be used to determine the fraction of the reported valid events can be attributed to double-counting.
from DTF1 file -------------- telem event rate = 116.81277 valid event rate = 141.50784 total event rate = 164.14001 ==> fraction double counted = 0.21140726 from EVT1 file -------------- # events = 976333 +Y segment (crsv=:64) ---------- # events = 314282 # events with spha=230: = 95573 Center segment (crsv=65:127) ---------- # events = 326177 # events with spha=402: = 268 -Y segment (crsv=128:) ---------- # events = 335874 # events with spha=285: = 76840 ==> estimated fraction double counted = 0.17686691
from DTF1 file -------------- telem event rate = 63.451042 valid event rate = 74.499260 total event rate = 162.26006 ==> fraction double counted = 0.17412193 from EVT1 file -------------- # events = 617819 +Y segment (crsv=:64) ---------- # events = 195513 # events with spha=230: = 57675 Center segment (crsv=65:127) ---------- # events = 206630 # events with spha=402: = 18247 -Y segment (crsv=128:) ---------- # events = 215676 # events with spha=285: = 47175 ==> estimated fraction double counted = 0.19924444
from DTF1 file -------------- telem event rate = 117.83839 valid event rate = 138.28098 total event rate = 280.26785 ==> fraction double counted = 0.17347980 from EVT1 file -------------- # events = 883310 +Y segment (crsv=:64) ---------- # events = 250126 # events with spha=230: = 84306 Center segment (crsv=65:127) ---------- # events = 355818 # events with spha=402: = 24501 -Y segment (crsv=128:) ---------- # events = 277366 # events with spha=285: = 68904 ==> estimated fraction double counted = 0.20118758
from DTF1 file -------------- telem event rate = 183.83963 valid event rate = 394.26620 total event rate = 677.37531 ==> fraction double counted = ? - telemetry saturated so this cannot be determined from DTF data from EVT1 file -------------- # events = 460248 +Y segment (crsv=:64) ---------- # events = 164880 # events with spha=230: = 42305 Center segment (crsv=65:127) ---------- # events = 146049 # events with spha=402: = 4858 -Y segment (crsv=128:) ---------- # events = 149319 # events with spha=285: = 31426 ==> estimated fraction double counted = 0.17075359
For the three non-flaring examples the estimated double-count fraction is within a few percent of the one calculated from the rate scalars. To demonstrate the quality of the improvement in the dead-time calculation that can be achieved, we can take the ObsID 62426 source events (Capella) from the flaring interval, correct them for the dead-time caused by telemetry saturation and compare the rate to the non-flaring interval rate, with and without correcting for double-counted events.
Capella events Number during non-flaring time = 110977 --> Raw rate = 14.7969 Number during flaring time = 20286 --> Raw rate = 8.1144 DT fraction with telemetered valid rate = (394.3-183.8)/394.3 = 0.534 corrected rate = 8.1144/(1-DTF) = 17.4129 double-count fraction = 0.171 on valid rate of 394.3 --> corrected valid rate = 336.7 DT fraction with corrected valid rate = (336.7-183.8)/336.7 = 0.454 corrected rate = 8.1144/(1-DTF) = 14.8615The deadtime corrected rate with the correction for double-counting is a much better match to the non-flaring source rate.
Last modified: Thu Jun 27 09:48:53 EDT 2002
Dr. Michael Juda
Harvard-Smithsonian Center for Astrophysics
60 Garden Street, Mail Stop 70
Cambridge, MA 02138, USA
Ph.: (617) 495-7062
Fax: (617) 495-7356