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 ID 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
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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.
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.
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, deg 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.
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, deg 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).
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:
----------------------------------
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.
-----------------------------------------
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"
-----------------------------------------
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)
-----------------------------------------
old rot, deg 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 in aimpoint:
---------------------------------------------------
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:
---------------------------------------------------
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"
---------------------------------------------------
------------------------------------------------------------------ old new ------------------------------------------------------------------ DETX,DETY offset 0.0" -0.4" 0.4" -0.1" pixel size 0.13173" 0.13187" (0.13184 0.13192) rotation, deg -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.
------------------------------------------- chip_id 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).