HRC-I Degap Lookup Table


An additional contribution to the size of the point-source PSF (beyond those due to the HRMA, aspect solution, and the intrinsic resolution of the HRC MCP and crossed-grid charge detector) and errors in the dispersion relation in the HRC-S/LETG can both be attributed to residual errors in the HRC event position reconstruction. There are two major causes for these residual errors: incomplete correction for ringing on the tap signals and what appears to be mis-matching between the amplification and digitization paths of the crossed-grid charge detector (CGCD) signals. In principle, we might correct for both of these causes with the application of an appropriate set of degapping corrections; so, the residual errors in the event position reconstruction can be thought of as errors in the degapping corrections.

Work by the LETG members of the calibration group has resulted in a method of correcting the dispersion relation via a lookup table. The CIAO tool hrc_process_events has been modified to use a lookup table for degapping rather than the fifth-order polynomial that has been in use since shortly after launch. While the correction values for the HRC-I lookup table can be populated by calculation using the current fifth-order polynomial, it would be beneficial if corrections for the "observed" deviations could be applied. Below I present a method for deriving improved degap corrections using the Chandra aspect solution to predict where a point-source should appear on the detector.

De-constructing the Aspect Solution

The aspect solution consists of a time history of the Chandra pointing direction (RA, Dec, and Roll) along with offsets of the instrument focal plane relative to a nominal position derived via observations of the instrument fiducial lights. In standard pipeline processing, the event positions within the detector are translated to celestial positions using the aspect solution, removing the spacecraft dither motion and any drifts in the instrument alignment. The nominal position of the focal plane is accounted for the different instrument selections and varying Science Instrument Module translation positions using tables in the geometry files in the calibration database.

Just as a position on the detector can be mapped to the sky via the aspect solution, a position on the sky can be mapped back to a location on the detector by inverting the steps. The spacecraft dither will move an on-axis point source over a range of detector positions and the small PSF of that source will allow us to map the un-degapped, RAW event positions to a location on the detector. Figure 1 shows the path in RAW coordinates of events within a 8-pixel radius centered on AR Lac in ObsID 1385 as the spacecraft dithers. The horizontal and vertical breaks are the gaps produced by the loss of information intrinsic to the three-tap readout of the CGCD. The over-plotted red curve is the location of AR Lac as determined by inversion of the aspect solution as described below.

RAW event path for AR Lac
Figure 1: RAW positions of events from an 8-pixel radius centered on AR Lac in ObsID 1385. The red over-plotted curve shows the path of AR Lac based on an inversion of the aspect solution.

For a given celestial source I invert the aspect solution through the following steps:

  1. Determine the mean SKY (x,y) position of the source
  2. Using the mean SKY position determine the mean offset from the nominal on-axis position (16384.5, 16384.5)
  3. Using the mean offset position determined above and the nominal roll angle of the observation (ROLL_NOM from the aspect file header) determine the radial offset and position-angle of the mean offset position
  4. Use the radial offset and position angle of the mean offset position and the geometry that describes the alignment of the HRC axes with the spacecraft to determine the location relative to the nominal HRC U,V position for the nominal SIM-Z position for the detector
  5. Adjust the U,V position determined above for any offset of the SIM from its nominal translation position to determine the location of the source relative to the nominal U,V position
  6. Use the time history of the RA and Dec in the aspect solution and the nominal RA and Dec to determine a time history of the RA and Dec offsets from the nominal direction.
  7. Use the time history of the Roll from the aspect solution and the geometry that describes the alignment of the HRC axes with the spacecraft to determine the time history of the rotation of the RA and Dec offsets relative to the HRC axes
  8. Use the time histories of RA and Dec offsets and their rotation angle relative to the HRC axes to determine the path of the nominal pointing direction in HRC U,V
  9. Add the location of the source relative to the nominal U,V position to the time history of the path of the nominal pointing direction in HRC U,V to get the predicted source location on the HRC

A bias can be introduced in the predicted detector locations by the first step. The event positions that we start with are affected by the residual errors in their positions. If the dither pattern is such that a significant number of events have large errors in a particular direction a bias in the derived mean position can be introduced that will propagate through to the predictions.

Deriving Degap Corrections

If we accept the above method for determining the location of a source on the detector, then the degap correction can be derived statistically by finding the mean RAW values for events taken from within a small region around a point source when the point source is at a given location on the detector. The difference between the mean RAW coordinate and the predicted source location is the degap correction for that RAW coordinate. We expect that the two HRC axes can be treated independently; in other words, the mean RAWX value for a given HRC U-axis location does not depend on the V-axis locations used and the converse for the mean RAWY.

Starting with the events from the source and the aspect solution, the predicted source location on the detector can be calculated for every event. Then given a large number of events the mean RAWX (RAWY) coordinate can then be calculated for all events at a given U-axis (V-axis) position. With a large enough number of events at any location and a small enough region of source events selected the difference of the source location and the mean RAW coordinate is the degap amount that would be applied to the RAW coordinate. However, in working back from a predicted location on the detector we have to be careful around the gaps between tap centers. At the half-way point between taps events can produce RAW coordinates on either side of the gap and given a finite source event extraction size there will be events on the opposite side of the gap from the predicted source location. In addition, because of the incomplete ringing correction and possible mis-matching in the amplifiers, we should anticipate the possibility that there would be different degap corrections for different amplifier scale (AMP_SF) values. Accounting for these two issues results in differences between the mean RAW coordinate and predicted source location on the detector for events centered on a specific tap (CRSU or CRSV) and using a specific amplifier scale factor; figures 2 and 3 below show examples from the U- and V-axis, respectively.

Modeled-Raw differences
for CRSU = 29
Figure 2: Mean of the differences between the modeled source location on the detector along the U-axis, derived from the aspect solution, and the reported RAWX value. Only events that were reported as centered on U-axis tap number 29 are included. Error bar sizes are calculated from the standard deviation of the differences divided by the square-root of the number of events with the predicted source position. Different colors are used to distinguish the values calculated from data with different amplifier scale factors (AMP_SF). Also plotted in the difference that results using the fifth-order polynomial degapping correction in the calibration database.

Modeled-Raw differences
for CRSV = 30
Figure 3: Similar to figure 2 but for the V-axis with a V-axis tap number of 30.

Events from sources from multiple observations or from multiple sources in a single observation can be combined to improve the statistics at a given location and to extend the coverage of position on the detector for which the degap value can be determined. Using multiple targets could help to minimize the potential bias discussed earlier by moving where on the detector the dither pattern samples. Including observations with non-standard SIM translation positions will also increase the areal coverage. As an initial trial in deriving degap correction for a lookup table I have used data from the ObsIDs given in the table below. The observations were selected to be nominally within 3 arcmin of on-axis and that were of sufficient duration and/or brightness to provide at least a few thousand counts in a 8-pixel radius extraction region around the source. ObsID 87 is an HRC-I/LETG observation where the zeroth-order events provide a large signal and which is one of the few observations with a non-standard SIM translation position. ObsID 6093 is another suitable observation with a non-standard SIM translation offset.

ObsIDObjectSIM ZExposureNumber of EventsY OffsetZ Offset
87CYG X-2122.98029698.38785270.00.0
4613C 273126.98320097.02061370.00.0
996AR Lac126.9851318.339030.00.0
1286AR Lac126.983873.123220.00.0
1321AR Lac126.985984.528350.00.0
1382AR Lac126.985789.129500.00.0
1385AR Lac126.98519554.21138200.00.0
1484AR Lac126.9851287.867790.00.0
1485AR Lac126.9851290.966512.00.0
1486AR Lac126.9851287.958512.0-2.0
1487AR Lac126.9851291.067430.0-2.0
1488AR Lac126.9851287.85306-2.0-2.0
1489AR Lac126.9851288.96031-2.00.0
1490AR Lac126.9851287.84974-2.02.0
1491AR Lac126.9851288.958460.02.0
1492AR Lac126.9851289.848982.02.0
1918GRS 1758-258126.9839949.8384590.00.0
2345AR Lac126.9851168.352462.00.0
2346AR Lac126.9851191.645692.0-2.0
2347AR Lac126.9851182.754490.0-2.0
2348AR Lac126.9851194.14810-2.0-2.0
2349AR Lac126.9851183.55682-2.00.0
2350AR Lac126.9851196.65023-2.02.0
2351AR Lac126.9851216.060110.02.0
2352AR Lac126.9851198.549622.02.0
2604AR Lac126.9851363.230142.02.0
2608AR Lac126.9851189.556770.00.0
2609AR Lac126.9851188.545642.0-2.0
2610AR Lac126.9851193.85645-2.00.0
2611AR Lac126.9851186.453140.02.0
2617AR Lac126.9851186.450452.00.0
2618AR Lac126.9851191.551970.0-2.0
2619AR Lac126.9851188.53825-2.02.0
2624AR Lac126.9851658.64395-2.0-2.0
3812CYG X-3126.98014694.01330410.00.0
4290AR Lac126.9851361.430062.02.0
4294AR Lac126.9851176.953540.00.0
4295AR Lac126.9851178.439282.0-2.0
4296AR Lac126.9851175.74811-2.00.0
4297AR Lac126.9851180.351710.02.0
4303AR Lac126.9851179.753562.00.0
4304AR Lac126.9851177.451910.0-2.0
4305AR Lac126.9851167.34003-2.02.0
4310AR Lac126.9851953.54200-2.0-2.0
5060AR Lac126.9831137.454730.00.0
5061AR Lac126.9831150.646882.00.0
5062AR Lac126.983461.616540.02.0
5063AR Lac126.9851060.63905-2.00.0
5064AR Lac126.9851071.540000.0-2.0
5065AR Lac126.9851082.832242.0-2.0
5066AR Lac126.9851078.031942.02.0
5067AR Lac126.9851083.02980-2.02.0
5068AR Lac126.9851073.83395-2.0-2.0
6133AR Lac126.9851076.750600.00.0
6134AR Lac126.9851071.847962.00.0
6135AR Lac126.9851569.348560.02.0
62507AR Lac126.9851628.820310.00.0

For each ObsID the tool hrc_process_events was re-run on the level 1 event list as necessary to apply all the latest corrections and obtain the current-best event positions. The center of the extraction region was determined by finding the centroid of the events within a 20-pixel-radius circle centered "by-eye" on the (near) on-axis source. The final events for analysis were selected using an 8-pixel-radius circle at the above determined centers and applying the standard status bits filter. Figure 4 shows the RAW positions of all the source events used while figure 5 shows histograms of the number of events at each modeled source position on the U- and V-axis and for the various AMP_SF values that were available for determining the mean RAW value. The events extracted here were also used to produce the difference data shown in figures 2 and 3. The extremely different SIM translation position of ObsID 6093 is clearly seen in the histograms as the peak to the left and illustrates how the entire raw coordinate range could be mapped using different SIM translation offsets with the dither pattern over-lapping between observations.

RAW positions of source events used
Figure 4: RAW positions of selected source events used in determining values for the trial degap lookup table. The dashed line indicates the active area of the HRC-I.

histograms of events vs
modeled position
Figure 5: Histograms of the number of events as a function of modeled position that were used in deriving the trial degap lookup table.

The links below are to plots similar to those in Figures 2 and 3 for all of the coarse positions that have events from the combined sources.

CRSU: 7 8 9 23 24 25 26 27 28 29 30 31 32 33 34 35
CRSV: 8 9 10 24 25 26 27 28 29 30 31 32 33 34 35 36

The degapping correction will be applied to the instrument RAW coordinate; however, the calculated differences (shown in figures 2 and 3) are of the mean RAW coordinate relative to the "corrected" location on the detector. The degapping correction at a given RAW coordinate can be obtained by interpolation or extrapolation of the calculated differences into a fixed grid of RAW coordinates using the mean RAW values for the modeled positions. The degapping corrections are placed into a lookup table with a RAW coordinate index; the tap number that supplies the differences used for a given range of RAW coordinates is the integer result of RAW/256 (i.e. CRSU = 29 is used for RAWX from 7424 to 7679). The places where this method of deriving a degap doesn't work, due to too few or no events, can be filled in using values calculated from the fifth-order polynomial degap coefficients in the calibration database.

For each coarse position and amplifier scale factor (AMP_SF) that had events from the combined, selected sources, I smoothed the calculated modeled-RAW differences by performing a running five-point weighted average of the differences. Only if the five consecutive modeled positions had data were they averaged and considered for further processing. A visual inspection of plots comparing the smoothed data to the input were used to decide if sufficient data existed in the range to continue. The modeled position - averaged difference pairs that were in the nominal coarse position range were then used to calculate a corresponding RAW position - difference pair and these pairs were interpolated to a fixed grid of RAW coordinates within the coarse position range using a least-squares quadratic fit to the four points surrounding the interpolate. I visually examined plots comparing the calculated deviations and interpolated degapping correction as a final quality check and rejected the segments that performed poorly (always due to too few events). The final candidate HRC-I degap lookup table is hrciD1999-07-22gaplookupN0002.fits I have used this file in CIAO 3.2 hrc_process_events to re-process the events for a few select observations; the resulting level 2 event lists can be obtained below:

In each of these observations the central source is smaller than when using the current degap solution. As an example of the improvement, figure 6 shows a comparison of the encircled counts fraction profile of AR Lac from ObsID 1385 between event positions calculated using the current and candidate degaps.

encircled counts fraction
Figure 6: Fractional encircled counts as a function of radius for the on-axis source AR Lac (ObsID 1385). The black curve is the resulting curve using the degap from the fifth-order polynomial, The red curve is the result using the candidate degap derived by the method described in this memo.


The approach to deriving degap values for the lookup table that is outlined here appears to result in a reduction of the residual blur in HRC event positions. However, obtaining degapping corrections using this approach is constrained by the available data. It would be possible to fill the entire lookup table or the portion that covers the central "sweet-spot" by obtaining a set of calibration observations using AR Lac on-axis but at a range of SIM translation offsets that allow for over-lapping dither patterns on the detector. Some work still remains in determining what the observation durations and SIM translation offsets should be for such a calibration data set.

Last modified: Tue Aug 2 10:43:08 EDT 2005

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