HRC-I Degap Lookup from Capella Data - 2007

Summary

In this memo I describe the derivation of a new set of HRC-I degapping corrections. These corrections were determined from the complete set of Capella observations, performed at varying SIM translation offsets during 2005 December to 2006 January and 2007 January. The new corrections provide a major improvement in the CRSU = 12-13 region and smaller improvements elsewhere.

Introduction

In and earlier memo, HRC-I Degap Lookup from Capella Data, I described an initial version of the HRC-I degap lookup corrections derived from the 2005 December to 2006 January Capella observations. These corrections provided updates in the central portion of the HRC-I and in a corner where observations of bright sources had been performed in order to limit the dose to the central region. These observations were also used to determine the relative rotation of the HRC-I to the SIM translation axis (HRC-I Rotation Angle).

A goal in the earlier analysis was to avoid using the observed location of the events in the detector in making the predictions of where the events should appear. The known celestial position of Capella was used with the aspect solution to make a prediction of where the aim-point fell on the detector. Unfortunately, this goal could not be maintained with the inclusion of the 2007 January data. As shown in figure 1, when the SIM-Z offset goes negative there are large deviations in the observed position from where we expect based on the aspect solution. A likely origin for the deviation is in the reconstruction of the detector location with respect to the aim-point using the fiducial lights; the light path may be on different facets of the retroreflector/collimator.

Observed
CHIPX deviation from expected trend with SIM-Z

Observed
CHIPY deviation from expected trend with SIM-Z

Figure 1: Deviations of the mean observed CHIP positions from expectations given the known position of Capella, the aspect solution, and the previously determined orientation of the HRC-I on the SIM. ObsIDs of the observations are indicated. The red points are the 2007 January data.

Given this set-back an alternative approach of using the observed mean location of source events in predicting the expected detector locations, deriving updated degap corrections and applying them, and iterating was developed.

Reduction Steps

Much of the reduction follows that of the earlier proto-typing work that is documented in HRC-I Degap Lookup Table. The following is brief listing of the steps used in each iteration.

For each observation:
1. Determine the mean SKY (x,y) position of the source
2. Select events within an 8-pixel radius of the mean position
3. Using the mean SKY position determine the mean offset from the nominal on-axis position
4. 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
5. 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
6. 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
7. 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.
8. 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
9. 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
10. 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
11. Use the derived time history of the predicted source location on the HRC to determine the U,V for the time of each of the selected events
Combining the events from all the observations
1. Sort events based on their AMP_SF, CRSU (or CRSV), and predicted U (or V) position and for each AMP_SF, CRSU[V], U[V] collection determine the mean RAW position, RAWX[Y], and deviation of the mean RAW position from the integerized, predicted position
2. For a given CRS position and AMP_SF range select the predicted position bins that lie in the nominal CRS position range and which have more that a specified minimum number of events (minimum number = 5)
3. From the selected predicted position bins use the mean RAW position at each bin and the mean deviation of the RAW position from the predicted position, smooth over a specified number of samples in the RAW position (smoothing number = 5), and interpolate the correction into integer RAW position bins within the nominal CRS position range
4. If there are inadequate statistics or coverage for the CRS-position/AMP_SF combination use the existing correction
At low and high CRS position the statistics on AMP_SF = 3 are low. If the AMP_SF = 1 and 2 corrections are different from the prior version but the AMP_SF = 3 are not then update the AMP_SF = 3 correction with the average of the AMP_SF 1 and 2 corrections.

The updated degapping corrections from these steps were used to re-process the Capella observations and then the steps repeated. A total of ten iterations were performed. Figure 2 shows the evolution of a measure of the size of the source at the various SIM_Z offsets as the iterations proceeded. The size was determined by first finding the best center via iteratively-clipped centroiding, using dmstat to calculate the standard deviation in x and y of the events within a 20-pixel radius of that center, and taking the square-root of the sum of their squares. The large peak in the initial iteration at a SIM-Z offset of ~40 mm was due to a particularly bad set of corrections around CRSU&nbps;=&nbps;12 that we have unknowingly been using since the start of the mission. The poor degap correction is evident in the initial processing ObsID 8358, which shows a jet-like extension; the GO ObsID 8225 is similarly affected. Most of the size improvement occurs within the first two or three iterations; however, there is an overall continuing small improvement with additional iterations. The reason for the larger size in the SIM-Z Offset ranges of -15 — -5 mm and 50 — 60 mm is not clear at this time.

source size at SIM-Z
offset for iterations

Figure 2: Size of Capella image for various SIM-Z offsets with iterations of derived degapping corrections.

The degap corrections from the tenth iteration are available at

capella_2007_candidate_gaplookup.fits

Performance Examples

In order to evaluate the performance of the degap correction updates I have re-processed our long AR Lac observation, ObsID 1385, with each of the iterations, starting with the current version of the degap lookup. Table 1 lists measures of the source size with as a function of the iteration of the degap correction.

Table 1: ObsID 1385 Source Size
Iteration	X stddev	Y stddev	Radial Size
0	3.3108	3.1590	4.5761
1	3.2927	3.1572	4.5617
2	3.2872	3.1579	4.5583
3	3.2778	3.1622	4.5545
4	3.2737	3.1634	4.5524
5	3.2744	3.1672	4.5555
6	3.2718	3.1670	4.5535
7	3.2735	3.1718	4.5581
8	3.2711	3.1737	4.5577
9	3.2741	3.1751	4.5608
10	3.2728	3.1738	4.5590

There is a slight overall improvement from the current degap correction (iteration 0) using any of the iterations; although the differences are at a small fraction of an HRC pixel. The best radial size result comes with iteration 4 and iterations 8 and 3 produce the smallest standard deviations for the X and Y, respectively.

ObsID 8225 provides a more significant example of the improvement the updated degapping corrections provide. ObsID 8225, one of a series of observations of Cyg X-2, was strongly affected by the poor degapping corrections around CRSU = 12. Figure 3 shows a comparison of an image of the source using the current degap lookup (hrciD1999-07-22gaplookupN0002.fits) and using iteration 10. The improvement is obvious.

Before and after comparison of
ObsID 8225

Figure 3: ObsID 8225, Cyg X-2, image comparison of processing with the (left) original degap correction, hrciD1999-07-22gaplookupN0002.fits and (right) updated corrections.

Table 2 below lists the radial size as a function of the degapping correction iteration. After the first couple of iterations the improvement is at the level of a small fraction of an HRC pixel.

Table 2: ObsID 8225 Source Size
Iteration	Radial Size
0	8.5650
1	7.5312
2	7.3496
3	7.2893
4	7.2510
5	7.2264
6	7.2108
7	7.2007
8	7.1915
9	7.1844
10	7.1850

Last modified: Fri Jul 6 15:45:18 EDT 2007

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
E-mail: mjuda@cfa.harvard.edu