CASU analysis of WFCAM commissioning data - III Microstep Offsets

Document number: VDF-TRE-IOA-00008-0007 Version 0.1

14th February 2005

Background

Data from WFCAM will suffer a lack of spatial resolution due to the fact that the pixel size (roughly 0.4 arcsec) is very similar to the median FWHM seeing in some wave bands. In order to recover some of that lost resolution it has been proposed that the data be taken in microstepped sequences. That is, a series of observations is done and each image in the series is shifted in pixel space by a very precise amount from the previous one. The most common proposed pattern would be a 2x2 series. The shifts of the last three relative to the first exposure would be something like (N+0.5,0), (N+0.5,M+0.5), (0,M+0.5), where M and N are exact integers. This would allow us to interleave the pixels in the four images into a single map with roughly twice the number of pixels on each axis. Obviously a scheme like this depends critically on the ability of the telescope to offset by such exact amounts. The purpose of this report is to look at the expected offsets from many microstepped sequences commpared with the true offsets as calculated from object positions and to see whether UKIRT is offsetting with anything like the accuracy needed to achieve the objective.

We looked at a series microstepped sequences from 20041127 from run numbers 1041 to 1060. These are observations in Z of an uncrowded bright standard star region. For this test we generated catalogues of objects on all four detectors from each observation. Using the first image in each microstep sequence as a reference we calculated the x,y offsets implied by matching the positions of the objects. Next we took the centre of the reference image and calculated an ra and dec based on the WCS in the header (with the correct value of PV2_3 edited in). These equatorial coordinates were converted to x,y in the other three images in the series and thus a pixel offset as implied from the headers. The table below summarises the results. The first column gives the values of the run number, the reference run number and the detector number connected with colons. The next two numbers are the pixel shifts implied by the stellar objects on the fields. The next two numbers is the x,y shifts found by looking at the WCS in the headers (what the telescope thinks the shifts should have been). The next two are the differences between the wcs and the object shifts (in pixels). The final two columns are the errors in equtorial coordinates implied by the pixel differences between the wcs and object shifts (got that?).


                  object           wcs       wcs-object   
obs:ref:det      dx     dy      dx     dy     dx    dy    dRA   dDec
1042:1041:1    11.62   0.06   11.52   0.02  -0.11 -0.04  -0.02  0.04
1043:1041:1    11.43 -11.39   11.50 -11.50   0.07 -0.11  -0.05 -0.03
1044:1041:1     0.31 -11.55   -0.02 -11.52  -0.33  0.03   0.01  0.13
1042:1041:2     0.00 -11.62   -0.02 -11.52  -0.02  0.10  -0.01  0.04
1043:1041:2   -11.52 -11.45  -11.53 -11.53  -0.01 -0.08  -0.00 -0.03
1044:1041:2   -11.61  -0.32  -11.52  -0.02   0.09  0.30   0.04  0.12
1042:1041:3   -11.60  -0.10  -11.52  -0.02   0.08  0.08  -0.03  0.03
1043:1041:3   -11.45  11.43  -11.50  11.50  -0.05  0.07  -0.03 -0.02
1044:1041:3    -0.32  11.57    0.02  11.52   0.34 -0.05   0.02  0.14
1042:1041:4    -0.13  11.63    0.02  11.52   0.15 -0.11  -0.06  0.05
1043:1041:4    11.46  11.46   11.54  11.54   0.08  0.08  -0.03 -0.03
1044:1041:4    11.52   0.40   11.52   0.02  -0.00 -0.38   0.00  0.15
1046:1045:1    11.08   0.05   11.52   0.02   0.44 -0.03  -0.01 -0.18
1047:1045:1    11.46 -11.46   11.50 -11.50   0.05 -0.04  -0.01 -0.02
1048:1045:1    -0.10 -11.39   -0.02 -11.52   0.08 -0.13  -0.05 -0.03
1046:1045:2    -0.01 -11.07   -0.02 -11.52  -0.01 -0.45  -0.00 -0.18
1047:1045:2   -11.45 -11.36  -11.53 -11.53  -0.08 -0.18  -0.03 -0.07
1048:1045:2   -11.35   0.19  -11.52  -0.02  -0.17 -0.21  -0.07 -0.08
1046:1045:3   -11.14  -0.02  -11.52  -0.02  -0.38  0.01  -0.00 -0.15
1047:1045:3   -11.36  11.46  -11.50  11.50  -0.14  0.04  -0.02 -0.06
1048:1045:3     0.19  11.41    0.02  11.52  -0.17  0.11  -0.04 -0.07
1046:1045:4    -0.01  11.08    0.02  11.52   0.03  0.44  -0.01 -0.18
1047:1045:4    11.44  11.41   11.53  11.53   0.10  0.13  -0.04 -0.05
1048:1045:4    11.41  -0.17   11.52   0.02   0.10  0.19  -0.04 -0.08
1050:1049:1    11.40  -0.20   11.52   0.02   0.12  0.22   0.09 -0.05
1051:1049:1    11.36 -11.32   11.50 -11.50   0.14 -0.18  -0.07 -0.06
1052:1049:1    -0.17 -11.32   -0.02 -11.52   0.15 -0.19  -0.08 -0.06
1050:1049:2    -0.12 -11.40   -0.02 -11.52   0.10 -0.12   0.04 -0.05
1051:1049:2   -11.39 -11.41  -11.53 -11.53  -0.14 -0.12  -0.06 -0.05
1052:1049:2   -11.27   0.27  -11.52  -0.02  -0.25 -0.29  -0.10 -0.11
1050:1049:3   -11.40   0.14  -11.52  -0.02  -0.12 -0.16   0.06 -0.05
1051:1049:3   -11.38  11.35  -11.50  11.50  -0.12  0.15  -0.06 -0.05
1052:1049:3     0.25  11.32    0.02  11.52  -0.23  0.19  -0.08 -0.09
1050:1049:4     0.24  11.32    0.02  11.52  -0.22  0.20   0.09 -0.08
1051:1049:4    11.42  11.45   11.53  11.53   0.11  0.08  -0.05 -0.03
1052:1049:4    11.29  -0.21   11.52   0.02   0.22  0.23  -0.09 -0.09
1054:1053:1    11.26   0.00   11.52   0.02   0.25  0.02   0.01 -0.10
1055:1053:1    11.19 -11.28   11.50 -11.50   0.31 -0.21  -0.09 -0.12
1056:1053:1    -0.27 -11.56   -0.02 -11.52   0.25  0.04   0.02 -0.10
1054:1053:2     0.03 -11.34   -0.02 -11.52  -0.04 -0.18  -0.02 -0.07
1055:1053:2   -11.29 -11.24  -11.53 -11.53  -0.24 -0.29  -0.10 -0.12
1056:1053:2   -11.40   0.24  -11.52  -0.02  -0.12 -0.26  -0.05 -0.10
1054:1053:3   -11.35  -0.01  -11.52  -0.02  -0.17 -0.01   0.00 -0.07
1055:1053:3   -11.21  11.32  -11.50  11.50  -0.28  0.18  -0.07 -0.11
1056:1053:3     0.31  11.36    0.02  11.52  -0.29  0.16  -0.06 -0.12
1054:1053:4     0.10  11.30    0.02  11.52  -0.09  0.22   0.04 -0.09
1055:1053:4    11.32  11.13   11.53  11.54   0.22  0.40  -0.09 -0.16
1056:1053:4    11.58  -0.26   11.52   0.02  -0.06  0.28   0.03 -0.11
1058:1057:1    11.55   0.14   11.52   0.02  -0.03 -0.12  -0.05  0.01
1059:1057:1    11.40 -11.42   11.50 -11.50   0.10 -0.08  -0.03 -0.04
1060:1057:1    -0.05 -11.41   -0.02 -11.52   0.03 -0.11  -0.04 -0.01
1058:1057:2    -0.05 -11.54   -0.02 -11.52   0.03  0.02   0.01  0.01
1059:1057:2   -11.62 -11.24  -11.53 -11.53   0.09 -0.29   0.04 -0.12
1060:1057:2   -11.44   0.11  -11.52  -0.02  -0.08 -0.13  -0.03 -0.05
1058:1057:3   -11.64  -0.08  -11.52  -0.02   0.12  0.07  -0.03  0.05
1059:1057:3   -11.52  11.42  -11.50  11.50   0.02  0.08  -0.03  0.01
1060:1057:3     0.12  11.52    0.02  11.52  -0.10 -0.00   0.00 -0.04
1058:1057:4    -0.07  11.73    0.02  11.52   0.09 -0.22  -0.04  0.09
1059:1057:4    11.47  11.60   11.53  11.53   0.07 -0.07  -0.03  0.03
1060:1057:4    11.39   0.00   11.52   0.02   0.13  0.02  -0.05 -0.01
1062:1061:1    11.40  -0.00   11.52   0.02   0.12  0.02   0.01 -0.05
1063:1061:1    11.19 -11.24   11.50 -11.50   0.31 -0.26  -0.10 -0.12
1064:1061:1    -0.04 -11.38   -0.02 -11.52   0.02 -0.13  -0.05 -0.01
1062:1061:2    -0.04 -11.41   -0.02 -11.52   0.02 -0.11   0.01 -0.04
1063:1061:2   -11.45 -11.28  -11.53 -11.53  -0.09 -0.25  -0.03 -0.10
1064:1061:2   -11.22  -0.05  -11.52  -0.02  -0.30  0.03  -0.12  0.01
1062:1061:3   -11.52   0.02  -11.52  -0.02   0.00 -0.03   0.01  0.00
1063:1061:3   -11.36  11.46  -11.50  11.50  -0.14  0.05  -0.02 -0.06
1064:1061:3    -0.11  11.27    0.02  11.52   0.13  0.25  -0.10  0.05
1062:1061:4     0.09  11.50    0.02  11.52  -0.07  0.02   0.03 -0.01
1063:1061:4    11.34  11.43   11.54  11.54   0.20  0.11  -0.08 -0.04
1064:1061:4    11.37   0.08   11.52   0.02   0.15 -0.07  -0.06  0.03
1066:1065:1    11.36  -0.07   11.52   0.02   0.16  0.08   0.03 -0.06
1067:1065:1    11.48 -11.56   11.50 -11.50   0.02  0.06   0.02 -0.01
1068:1065:1    -0.19 -11.48   -0.02 -11.52   0.17 -0.03  -0.01 -0.07
1066:1065:2    -0.14 -11.42   -0.02 -11.52   0.12 -0.10   0.05 -0.04
1067:1065:2   -11.68 -11.40  -11.53 -11.53   0.14 -0.13   0.06 -0.05
1068:1065:2   -11.56   0.22  -11.52  -0.02   0.04 -0.24   0.02 -0.10
1066:1065:3   -11.50   0.11  -11.52  -0.02  -0.02 -0.13   0.05 -0.01
1067:1065:3   -11.62  11.59  -11.50  11.50   0.12 -0.09   0.04  0.05
1068:1065:3     0.05  11.48    0.02  11.52  -0.03  0.04  -0.02 -0.01
1066:1065:4     0.11  11.48    0.02  11.52  -0.09  0.04   0.04 -0.02
1067:1065:4    11.73  11.48   11.53  11.53  -0.20  0.05   0.08 -0.02
1068:1065:4    11.59  -0.14   11.52   0.02  -0.08  0.16   0.03 -0.06
1070:1069:1    11.41   0.03   11.52   0.02   0.11 -0.02  -0.01 -0.04
1071:1069:1    11.22 -11.28   11.50 -11.50   0.28 -0.22  -0.09 -0.11
1072:1069:1     0.04 -11.36   -0.02 -11.52  -0.06 -0.15  -0.06  0.02
1070:1069:2    -0.05 -11.46   -0.02 -11.52   0.03 -0.06   0.01 -0.02
1071:1069:2   -11.55 -11.20  -11.53 -11.53   0.02 -0.33   0.01 -0.13
1072:1069:2   -11.42   0.08  -11.52  -0.02  -0.10 -0.09  -0.04 -0.04
1070:1069:3   -11.56   0.05  -11.52  -0.02   0.04 -0.07   0.03  0.02
1071:1069:3   -11.33  11.46  -11.50  11.50  -0.17  0.04  -0.01 -0.07
1072:1069:3    -0.04  11.47    0.02  11.52   0.05  0.05  -0.02  0.02
1070:1069:4    -0.06  11.50    0.02  11.52   0.08  0.02  -0.03 -0.01
1071:1069:4    11.32  11.37   11.53  11.53   0.22  0.17  -0.09 -0.07
1072:1069:4    11.36   0.04   11.52   0.02   0.15 -0.02  -0.06  0.01
1074:1073:1    11.18   0.00   11.52   0.02   0.34  0.02   0.01 -0.13
1075:1073:1    11.19 -11.23   11.50 -11.50   0.31 -0.26  -0.11 -0.13
1076:1073:1     0.10 -11.48   -0.02 -11.52  -0.11 -0.04  -0.02  0.04
1074:1073:2    -0.16 -11.23   -0.02 -11.52   0.15 -0.28   0.06 -0.11
1075:1073:2   -11.34 -11.22  -11.53 -11.53  -0.19 -0.32  -0.08 -0.13
1076:1073:2   -11.50  -0.03  -11.52  -0.02  -0.02  0.02  -0.01  0.01
1074:1073:3   -11.20   0.08  -11.52  -0.02  -0.32 -0.09   0.04 -0.13
1075:1073:3   -11.23  11.31  -11.50  11.50  -0.27  0.19  -0.08 -0.11
1076:1073:3    -0.11  11.52    0.02  11.52   0.13 -0.00   0.00  0.05
1074:1073:4     0.02  11.24    0.02  11.52  -0.00  0.28   0.00 -0.11
1075:1073:4    11.26  11.30   11.53  11.54   0.28  0.23  -0.11 -0.09
1076:1073:4    11.47   0.22   11.52   0.02   0.05 -0.20  -0.02  0.08
1078:1077:1    11.29   0.10   11.52   0.02   0.22 -0.09  -0.03 -0.09
1079:1077:1    11.22 -11.38   11.50 -11.50   0.28 -0.12  -0.05 -0.11
1080:1077:1     0.10 -11.43   -0.02 -11.52  -0.12 -0.09  -0.03  0.05
1078:1077:2     0.06 -11.38   -0.02 -11.52  -0.08 -0.13  -0.03 -0.05
1079:1077:2   -11.58 -11.17  -11.53 -11.53   0.05 -0.37   0.02 -0.15
1080:1077:2   -11.54  -0.03  -11.52  -0.02   0.02  0.02   0.01  0.01
1078:1077:3   -11.29  -0.07  -11.52  -0.02  -0.23  0.05  -0.02 -0.09
1079:1077:3   -11.15  11.50  -11.50  11.50  -0.34  0.00  -0.00 -0.14
1080:1077:3    -0.01  11.57    0.02  11.52   0.03 -0.05   0.02  0.01
1078:1077:4    -0.13  11.36    0.02  11.52   0.14  0.16  -0.06 -0.06
1079:1077:4    11.33  11.25   11.53  11.53   0.20  0.28  -0.08 -0.11
1080:1077:4    11.32   0.13   11.52   0.02   0.19 -0.11  -0.08  0.05


dRA: -0.0213579 0.0456037
dDec: -0.0441016 0.0811598

The first thing to notice is that the shifts as given by the objects are internally consistent between the detectors. (Notwithstanding the fact that the detectors are all at different orientations. So for example the object dx in detector 1 should be the same as the object dy in detector 2 with a different sign). This gives us confidence that whatever disagreement there might be between the object and the WCS shifts, it's not due to faulty object centring or a bad matching algorithm as the shifts for all four detectors were done independently.

The next thing to notice is that there is good agreement between the shifts as given by the WCS and that given by the objects. The WCS and the object shifts both seem to imply the sort of fractional shift you need to do proper 2x2 interleaving (i.e. a fractional shift of 0.5). The final statistic at the end of the table is a mean and standard deviation for the equatorial coordinate shift 'errors' in the last two columns. A histogram of these two columns does show that a strong tendency for negative residuals in both axes, but with a fairly large spread as indicated by the sigmas.


Jim Lewis (jrl@ast.cam.ac.uk)
Last modified: Wed Feb 16 14:10:24 2005