[Last Change: 30 Mar 2011 (rev 3)]

Plate scale and relative chip (plate) positions

Maxim Markevitch, 3 Dec 01

Method

Once the absolute sky coordinates of the aimpoint in a given observation are determined (see this collection of memos), the plate scale, relative ACIS chip (or HRC plate) positions and the detector orientation are used to calculate the coordinates of the off-axis sources. These parameters were calibrated using observations of the star cluster NGC 2516 and LMC X-1.

The optical astrometry of NGC 2516 is described in this memo. The LMC X-1 sky coordinates have been measured from two optical CCD exposures (taken at CTIO, courtesy Dr. Ed Totten) using the Tycho-2 reference stars, and are (84.911842, -69.743193) deg 0.2".

The table below lists calibration observations (all performed in 1999 - early 2000):

Detector Chip NGC2516 OBSIDs LMC X-1 OBSIDs
ACIS-S S0 - 1068 1069 1070 1071
  S1 - 1072 1073 1074 1075
  S2 1458 1076 1077
  S3 66 1229 1458 -
  S4 - 1078 1079 1080 1081
  S5 - 1082 1083 1084 1085
ACIS-I 0123 65 1232 -
ACIS-S(I) * - 1094 1095 1097
ACIS-I(S) ** - 1088 1089 1090 1457
HRC-I   27 1405 1116 1117 1118 1119
HRC-S 3 - 1162 1163 1164 1165
  2 68 1158 1159 1160 1161
  1 - 1154 1155 1156 1157

* ACIS-S chips with ACIS-I in aimpoint
** ACIS-I chips with ACIS-S in aimpoint

The calibration procedure consists of finding centroids of the X-ray sources in each detector of interest (each ACIS chip and HRC plate) and identifying them with stars from the optical catalog (for the NGC 2516 observations). The centroids were derived in 2 iterations, first calculating the centroid of photons within r=2*r90 of the approximate position determined by eye (r90 is the PSF 90% encircled energy radius), then recalculating it within r=r90 of the new position. The band was restricted to 0.5-2 keV for ACIS, and the background was approximately subtracted from the images (although it has a negligible effect). Far off-axis, where the faint stars of NGC 2516 are not useful, LMC X-1 was used (which in turn is not useful near axis due to the ACIS pileup and HRC safety). For LMC X-1, we tried either centroiding or cross-correlation with the simulated PSF images taken from the CALDB. With good statistics, the "struts" in the PSF image allow a rather accurate cross-correlation (to 1" or better) even when the PSF is very wide. The difference between these methods within 20' off axis was negligible; cross-correlation was used beyond 20'.

The observed X,Y (or sky) source coordinates were then compared to the predicted ones, calculated from the known celestial positions and the event file WCS keywords that correspond to the current knowledge of the detector geometry. A linear coordinate transformation (including offsets along the detector X,Y axes, rotation and scale factors along the two directions) was fitted to the coordinate differences by the least-squares method. Each star's offset was weighted by N/R^2, where N is the number of photons from the star and R is the PSF width at that position.

On output, we obtained corrections to the assumed detector geometry and plate scale, detecting a rotation of ACIS-S as a whole by 0.03 deg and HRC-S by 0.07 deg, a 0.1% error in the plate scale (consistent between the DETX,DETY directions), and up to 1" offsets for some ACIS chips. The plate scale error was in part explained by the incorrect ACIS physical pixel size used in data processing, and the rest was absorbed into the correction of the mirror focal length (see this memo). For ACIS-S, the combined corrections turned out to be consistent with the interchip gaps determined independently and more accurately from the gratings data (see a note elsewhere in the cal. pages), therefore we have kept the gaps intact. The corrections were applied by Jonathan McDowell to the PIXLIB GEOM file used in data processing. Its updated version was released in October 2001 as part of CALDB v2.9.

Final accuracy

For each detector, we have reprocessed one or more calibration observations with the new GEOM file and rerun the procedure described above to verify that the best-fit rotations and shifts are consistent with 0 and the best-fit sky pixel sizes are consistent with the assumed values of 0.492" for ACIS and 0.1318" for HRC. (Note that as of CALDB 2.9, the sky pixel size is no longer tied to the physical detector pixel size -- instead, sky pixels have the above values by definition. The difference is about 0.1%.) As shown below, the new GEOM file produces acceptable sky coordinates for all detectors; the residual errors are well within 1" in the areas normally used for imaging observations.

ACIS-S

S3

The table below gives the best-fit average offset along DETX,DETY directions, sky pixel size and rotation angle derived from obsid 1229 (one of the three NGC2516 observations used for the original measurement). The old values are given for comparison, together with the 68% stat. intervals:

S3 old new
DETX,DETY offset 0.7" 0.2" 0.5" 0.1"
pixel size 0.4913" (0.4912 0.4914) 0.4919" (0.4918 0.4920)
rotation 0.04 (0.04 0.05) 0.00 (-0.01 0.01)

The new values are in good agreement with what they should be. The average offset is consistent with the expected absolute aspect uncertainty. The residual coordinate deviations for individual stars are given in this table.

S2

Using the NGC2516 obsid 1458 (without the two LMC X-1 pointings used in the original measurement), the best-fit offset, scale and rotation are given below (with 68% intervals):

S2 old new
DETX,DETY offset 0.0" -0.3" 0.4" -0.1"
pixel size 0.4915" (0.4914 0.4916) 0.4920" (0.4916 0.4921)
rotation 0.06 (0.05 0.07) 0.04 (0.01 0.05)

Again, the new results are good (the rotation is consistent with 0 within the 90% interval).

S0, S1, S4, S5

Using four LMC X-1 pointings for each chip, which were cross-correlated with the respective simulated PSF images (for large off-axis angles) or centroided (closer to the axis), the average chip coordinate errors are as follows:

Chip old DETX,DETY new DETX,DETY
S0 -0.7" -0.5" 1.1" 0.4"
S1 -0.5" -0.4" 0.9" 0.2"
S4 1.4" 0.4" 0.4" 0.1"
S5 1.6" 0.9" -0.1" 0.4"

The S4 and S5 coordinates are now good. The residual S0 and S1 offsets are close to 1" due to the detector rescaling while keeping the interchip gaps fixed. These offsets could have been corrected, but given the PSF 50% encircled-energy radius of >10" at those off-axis angles, we have chosen to keep the gaps correct and ignore the 1" image offset.

ACIS-I

Simultaneous fitting of obsids 65+1232 (the same dataset as used for the original measurement) for each chip gives the following quantities, with 68% intervals, when processed with the old and new GEOM files. The new DETX,DETY offsets in the first table are derived for the rotation angle and the pixel size fixed at their nominal 0 and 0.492" values (as seen from the tables that follow, their best-fit values are consistent with the nominal values):

Chip old DETX,DETY new DETX,DETY
I0 0.3" -0.3" 0.0" 0.1"
I1 0.7" -0.5" -0.2" 0.0"
I2 0.6" 0.3" 0.0" 0.1"
I3 0.8" 0.2" -0.2" 0.1"
 
Chip old pix new pix (68%)
I0 0.4914" 0.4921" (0.4920 0.4924)
I1 0.4911" 0.4919" (0.4914 0.4923)
I2 0.4913" 0.4921" (0.4919 0.4923)
I3 0.4917" 0.4923" (0.4921 0.4924)
 
Chip old rot new rot (68%)
I0 -0.08 -0.05 (-0.07 -0.03)
I1 -0.03 0.02 (-0.04 0.07)
I2 -0.01 -0.01 (-0.01 0.02)
I3 -0.01 0.00 (-0.02 0.02)

There is a clear improvement of offsets and scales for all chips; all new quantities are consistent within their 90% intervals with what they are supposed to be (except a 95% deviation for the I0 rotation angle, which we decided doesn't warrant a correction). For illustration, the residual deviations for individual stars in I3 are given in this table.

ACIS-S / ACIS-I

The new GEOM file was not designed to fix the problem with the coordinate errors in S chips when ACIS-I is in the aimpoint and vice versa, so they are still there. Work is underway to correct this. Below are the errors of the LMC X-1 coords in different chips with the old and new GEOM files:

ACIS-S in aimpoint
Chip obsid old DETX,DETY new DETX,DETY
I0 1090 -2.0" 0.2" -2.2" -0.8"
I1 1088 -1.9" -0.3" -1.7" -1.1"
I2 1089 -1.8" 0.2" -1.8" -0.1"
I3 1457 -2.0" -0.1" -1.7" -0.4"

ACIS-I in aimpoint
Chip obsid old DETX,DETY new DETX,DETY
S2 1097 -0.2" -1.7" 0.3" -0.1"
S3 1094 0.1" -1.6" 0.8" 0.9"
S3 1095 -0.2" -1.6" 0.6" 0.2"

HRC-I

The results for obsid 27, the longer NGC2516 observation of the two used for the original measurement, are shown below (with 68% intervals). The data cover the central r=5' region:

  old new
DETX,DETY offset 0.0" -0.4" 0.4" -0.1"
pixel size 0.13173" 0.13187" (0.13184 0.13192)
rotation -0.04 -0.04 (-0.06 -0.02)

The new sky pixel size marginally includes the nominal 0.1318" value at the end of the 90% stat. interval. This is consistent with the difference between our final HRMA focal length and its value derived from the HRC-I data alone ( this link). The adopted confidence interval on the focal length that includes systematic uncertainties (basically, this difference) stretches from the HRC-I value to the ACIS value. The marginally significant detector rotation shown in the table was not seen in the four LMC X-1 pointings (15' offsets), so it is ignored in the new GEOM file, possibly causing a negligible absolute displacement at the useful off-axis angles. The residual deviations for individual stars are given in this table.

HRC-S

For each plate, the four LMC X-1 offset pointings used for the original calibration were analyzed. The average residual errors for each plate are given below:

Chip old DETX,DETY new DETX,DETY
3 -1.4" -3.2" 0.9" 0.1"
2 -0.1" -0.7" 0.6" 0.4"
1 0.7" 1.5" 0.5" 0.4"

In each plate, residual coordinate errors of the four individual pointings are consistent with a systematic offset of the plate (and are thus likely to be due to the absolute aspect error), and none is much bigger than an arcsecond (the biggest is 1.2", it is a 20' offset in plate 3).

Appendices

Residuals for the NGC2516 observations:

ACIS S3

Coordinate deviations for stars in obsid 1229 (chip S3) using the CALDB 2.9 geometry file, after removing the best-fit absolute offset of (0.5",0.1") along the DETX,DETY axes. r" is the coordinate deviation in arcsec, r50" is the PSF 50% encircled energy radius at the star's position in arcsec, Nphot is the number of events from the star. The only large deviation (#11) is for a star with 12 photons.

No. r" r/r50 r50" Nphot
1 0.05 0.04 1.38 61
2 0.22 0.26 0.82 27
3 0.29 0.25 1.17 73
4 0.01 0.02 0.58 50
5 0.19 0.18 1.06 59
6 0.19 0.15 1.28 84
7 0.43 0.52 0.82 15
8 0.05 0.03 1.57 44
9 0.53 0.22 2.42 65
10 0.07 0.11 0.64 97
11 1.04 1.23 0.85 12
12 0.23 0.33 0.69 15
13 0.16 0.29 0.56 17
14 0.03 0.05 0.56 16
15 0.10 0.16 0.61 20
16 0.09 0.09 0.96 32
17 0.07 0.10 0.72 73
18 0.25 0.36 0.69 14
19 0.05 0.09 0.61 22
20 0.05 0.08 0.64 103
21 0.13 0.12 1.14 67
22 0.22 0.20 1.09 121
23 0.24 0.22 1.09 40
24 0.54 0.21 2.55 163

ACIS I3

Coordinate deviations for stars in obsids 65 and 1232 (chip I3) using the CALDB 2.9 geometry file, after removing the best-fit absolute offset of (-0.2",0.1") along the DETX,DETY axes. r" is the coordinate deviation in arcsec, r50" is the PSF 50% encircled energy radius at the star's position in arcsec, Nphot is the number of events from the star.

No. r" r/r50 r50" Nphot
1 0.61 0.26 2.34 20
2 0.36 0.19 1.91 16
3 0.65 0.41 1.59 14
4 0.20 0.17 1.22 19
5 0.21 0.23 0.93 31
6 0.24 0.40 0.58 16
7 0.18 0.22 0.82 16
8 0.20 0.17 1.20 79
9 0.32 0.19 1.65 17
10 0.36 0.14 2.60 42
11 0.67 0.20 3.27 46
12 0.39 0.14 2.68 77
13 0.43 0.17 2.52 16
14 0.68 0.23 3.00 35
15 0.24 0.12 2.05 28
16 0.89 0.53 1.67 27
17 0.11 0.08 1.38 26
18 0.10 0.14 0.72 29
19 0.39 0.34 1.14 24
20 0.07 0.05 1.43 89
21 0.91 0.39 2.34 17
22 0.62 0.18 3.51 83
23 0.54 0.13 4.30 44
24 0.80 0.22 3.56 55
25 0.86 0.26 3.32 22

HRC-I

Coordinate deviations for stars in obsid 27 (HRC-I, central r=5') using the CALDB 2.9 geometry file, after removing the best-fit absolute offset of (0.4",-0.1") along the DETX,DETY axes. r" is the coordinate deviation in arcsec, r50" is the PSF 50% encircled energy radius at the star's position in arcsec, Nphot is the number of events from the star. The only relatively big deviation (#15) is a star with 19 photons.

No. r" r/r50 r50" Nphot
1 0.19 0.16 1.14 42
2 0.14 0.06 2.33 64
3 0.20 0.20 1.00 60
4 0.08 0.13 0.63 39
5 0.36 0.30 1.20 105
6 0.22 0.08 2.68 222
7 0.15 0.10 1.45 36
8 0.13 0.20 0.61 23
9 0.24 0.38 0.63 44
10 0.13 0.17 0.73 15
11 0.15 0.15 1.05 74
12 0.63 0.26 2.41 55
13 0.90 0.35 2.56 70
14 0.63 0.33 1.88 22
15 1.12 0.71 1.59 19
16 0.25 0.12 2.06 52
17 0.21 0.18 1.17 23
18 1.18 0.40 2.97 39
19 0.41 0.33 1.24 15
20 0.12 0.16 0.77 26
21 0.47 0.36 1.31 26
22 0.55 0.09 5.88 351
23 1.27 0.24 5.21 204
| 24 | 0.52 | 0.18 | 2.90 | 64 |
 
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