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THE MISALIGNMENT OF LE1 WITH THE STAR TRACKER

1. Introduction

A previous report (ref. 1) discussed the derivation of absolute source positions from EXOSAT images. Here we follow up the suggestion in that report that there was a ~16" misalignment calibration error between the LE1 CMA and the operational star tracker.

The misalignment between LE1 and the star tracker is given in the CCF (data type BD) in the form of a matrix which specifies the values of the misalignment angles (star tracker to LET). They are denoted as alpha, beta and gamma for the misalignments about the spacecraft roll, pitch and yaw axes respectively, (the transformations are discussed in detail in refs. 1 and 2). The misalignment values in the CCF have been 12.44", 0.87" and -1.91" for the three angles respectively throughout the mission. Any error in these values would cause the derived sky locations of sources to change as a function of the spacecraft roll angle. This effect was noted for 2 sources in the previous report and is confirmed here for many more.

The misalignment angles are measured anti-clockwise when looking at the spacecraft. An increase in misalignment about the pitch axis would translate into a decrease in the image x coordinate of the source. An increase in yaw misalignment translates into an increase in the image y coordinate. An increase in the roll misalignment would produce an anti-clockwise rotation of source positions about the centre of the image. These shifts can be translated into right ascension and declination when the spacecraft roll angle is known. This is the clockwise angle measured from the north direction to the spacecraft Z axis (yaw axis) looking at the sky. The CMA roll angle theta, quoted in the tables, is measured anti-clockwise from the Ex axis to the north direction looking at the sky. This is thus approximately equal to the spacecraft roll minus 180°.

In this report calibration errors refer to differences from the misalignment values given in the CCF and are denoted by delta alpha, delta beta, delta gamma, whereas the absolute misalignment angles that are to replace those given in the CCF are denoted by alpha prime,beta prime, gamma prime. So alpha prime = delta prime + alpha, ... We initially assumed the roll misalignment error to be zero and made a preliminary determination of the other misalignment errors. With these preliminary pitch and yaw misalignment errors (equivalent to image x and y shifts) included, we then searched for a roll misalignment error using off axis sources. We determined this error to be unmeasurably small. We then derived final pitch and yaw errors and checked them with an independent data set.

2. Procedure

A few comments on the best way to accumulate an image for maximum positional accuracy are in order.

1) The image must be deblurred. The inertial spacecraft attitude given as a function of time in the housekeeping data (parameters A511 to A513) must be taken into account when accumulating an image. The x coordinate of an event should be increased by the pitch offset and the y coordinate shoula be decreased by the yaw offset. Randomisation may be desirable to avoid effects due to the pixel size of 4". (Roll deblurring is not currently done at ESOC). Deblurring is important because there is a real 5" rotation about the pitch axis which appears in the housekeeping and not in the auxiliary data (see ref. 3). It also safeguards against spacecraft pointing changes and reduces the radius of the source count distribution.

2) The correct star tracker boresight position must be used. The star tracker was recalibrated last year, and FOT's for observations after 0900 12.8.85 have the updated auxiliary data. However, this is not the case for earlier observations. This recalibration led to derived position changes of 1"-2".

3) Only those observations for which two guide stars give the attitude reconstruction should be used at present. There was a calibration error in the fine sun sensor which led to a slow drift in the true pointing position of the spacecraft when the star tracker was used in its single star mode. In this mode attitude reconstruction is achieved using the measured position of the sun together with that of the star. The star tracker mode in use during an observation is given in the auxiliary data (see ref. 4).

In this work, we have used a simple routine which calculates the barycentre of the event distribution in order to derive the source location in detector units.

3. Results

The existence of an error in the misalignment values in the CCF was confirmed by a study of the derived positions of AM Her. This is shown in Figure 1. Using the catalogue position of ref. 5, a mean radial offset of 12.8" was determined (ie. pitch error delta beta = -10.6", yaw error delta gamma = 7.2").

Observations of E2003+225 (day 257 1983), which has a UV emitting early type star association around it, and the Pleiades (day 39 1984), both of which fill a substantial fraction of the whole FOV, were used to determine if there was a roll misalignment error. Table 1 gives the details of the positions, derived positions and implied roll misalignment error of the sources seen.

The average roll misalignment is delta alpha = 0.05° ± 0.25° when all sources are given equal weight. (The increase in width of the point spread function with distance from the image centre counteracts the advantage of using distant sources). Thus there is no measurable roll misalignment error. It is cl ear from this work that the roll misalignment of 12.4", which has been in the CCF since the early days of the mission is not a significant measurement. It was based on the derived positions of 3 on-axis sources during the performance verification phase.

The next step was to determine the pitch and yaw misalignment error accurately using a large number of observations. We determined the positions of sources in 42 observations of 6 objects using the technique described above and the CCF misalignment values.

The individual results are given in table 2. The mean pitch and yaw misalignment errors determined were delta beta = -7.62" ± 0.55, delta gamma= 9.59 ± 0.57. The true misalignments are thus beta prime = -6.75", gamma prime = 7.68".

Subtraction of the mean misalignment error values from the individual values listed in table 2 gives a distribution of residual radial offset errors. This distribution is plotted as a dotted histogram in figure 2. 90% of all derived positions lie within 7" of their catalogue positions.

In order to ensure that no unexpected effects had been missed we have re- determined the residual misalignment errors once the new misalignment values derived from table 2 were in use. We looked at 29 observations, the details are given in table 3. The average residual misalignment errors were reduced to delta beta = -1.42", delta gamma = -0.27", the difference from zero is only of marginal significance.

Of the 71 observations analysed, 65 had radial position errors of less than 8" and 68 had errors of less than 10", the mean error is 5.6". The total distribution is shown in figure 2 as a solid histogram.

On this basis, for other on-axis sources analysed in this way, we suggest that authors give a 90% confidence region with a radius of 8" or a 95% confidence region with a radius of 10".

We have been able to find no special characteristics of those observations which produce large position errors. In particular, weak sources ( less equal30 counts) do not have significantly larger position errors than stronger sources, nor do sources lying at large distances from the image centre (30 less squared root of x square plus y square).

4. For the Future

It is possible that an indication of the absolute accuracy could be given by the value of the housekeeping parameter A510, the guide star separation error. This parameter is the difference between the separation of the guide stars observed by the star tracker and that expected from the ESOC catalogue compilation. It is only valid when there are two guide stars. The star tracker specifications suggest that this parameter should have values not significantly greater than 3", however larger values have been reported. The effects of this on position determination will be investigated in the future.

The Orbit and Attitide Department of ESOC have recently recalibrated the stable pointing positions for the entire mission. In the near future they will also provide a routine to give the time resolved attitude for observations made using the fine sun sensor. The recalibrations will then be automatically used in the EXOSAT Observatory. This list of recalibrated pointing positions will, in the next month, be circulated to all EXOSAT observers (together with the mission log). In the meantime, observers wanting to derive accurate positions should contact the observatory.

J. Osborne
L. Angelini

5. References

1. EXOSAT Express No. 12, p.53, Aug. 1985.
2. FOT Handbook Section 7.1.7.3.
3. EXOSAT Express No.4, p.34, April 1984.
4. FOT Handbook Section 3.8.3.3.
5. Ritter, H. Astron. & Astrophys. Supp.Ser. 57, 185 (1985).
6. UCL UV Star Catalogue - see Cornocham, D. CDS Bull. 17,1979
7. Bradt, H. & McClintock J. (1983) Ann.Rev.Astron. & Astrophys. 21, 13
8. Veron-Catty, M. & Veron, P. (1985). ESO Scientific Report No. 4.
9. Clements, E. (1981). M.N.R.A.S. 197, 829.
10. Hewitt, A. & Burbridge, G. (198057-Ap.J.Suppl. 43, 57.
11. Argyle, R. (1983). IAU Circ. No. 3897.

Figure 1: Misalignment Calibration Check

fig1 description above

Figure 2: Distribution of Radial Position Errors

fig2 description above

TABLE 1 - ROLL MISALIGNMENT ERROR CHECK
2003+225 FIELD (A0 mv = 7-9) theta = 339 42'
cts x y RAobs* DECobs* ID RA+cat DEC+cat delta alpha
3 529 133.97 200.13 20 04 29.72 +22 34 06.23 HD 190946 20 04 30.04 +22 34 00.8 0.93
4 291 140.11 0.69 20 03 36.33 +22 39 07.37 HD 190750 20 03 34.34 +22 39 12.0 -2.13
5 321 374.86 0.98 20 04 00.00 +22 53 47.78 HD 190843 20 03 59.23 +22 53 56.4 -0.24
6 200 -207.86-68.97 20 02 42.67 +22 18 57.62 HD 190591 20 02 40.40 +22 18 42.9 0.86
UN1 223 482.00 -18.50 20 04 05.50 +23 00 55.83 HD 190865 20 04 02.85 +23 01 24.4 -1.06
PLEIADES FIELD (A0 - B8 mv = 2.9-7.5) theta = 12 49'
1 3445 10.44 -100.553 44 30.87 +23 57 11.41 HD 23630 3 44 30.42 +23 57 07.3 1.22
2 1312 -107.23 228.613 46 12.16 +23 54 23.18 HD 23850 3 46 11.02 +23 54 07.4 0.32
3 189 -34.66 248.45 3 46 13.04 +23 59 23.61 HD 23862 3 46 12.39 +23 59 07.4 0.22
4 1206 307.52 -373.043 42 53.81 +24 12 24.65 HD 23408 3 42 50.7 +24 12 46.7 0.39
5 945 407.17 -461.863 42 22.00 +24 17 34.23 HD 23338 3 42 13.56 +24 18 42.6 -0.43
6 343 463.92 -316.063 42 59.91 +24 23 25.23 HD 23432 3 42 55.36 +24 23 59.8 -0.14
7 943 -71.34 362.08 3 43 21.82 +23 47 58.52 HD 23480 3 43 21.18 +23 47 28.8 -0.57
8 86 170.62 333.92 3 46 24.28 +24 13 59.82 HD 23873 3 46 22.59 +24 13 46.7 -0.41
9 1160 117.51 -614.653 41 57.62 +23 56 26.03 HD 23302 3 41 54.05 +23 57 27.6 1.71
*uncorrected for preliminary pitch & yaw misalignment errors.
+ catalogue position from ref. 6.
TABLE 2
DATE cts x y RAobs DECobs theta delta beta delta gamma
VW Hyi (RA = 4h Dm 32s.3, DEC = -71° 25' 29" ref. 5)
340/83 42 -5.26 1.50 4 9 33.61 -71 25 18.28 081 13 4.55 11.55
126/84 452 -0.83 9.71 4 9 34.80 -71 25 39.77 289 11 -7.74 14.10
301/84 48580 30.51 29.81 4 9 29.61 -71 25 18.06 120 52 -5.42 15.99
337/83 62 -3.94 1.19 4 9 32.24 -71 25 17.77 084 29 -1.36 11.15
318/83 620 -2.37 -0.75 4 9 30.81 -71 25 21.81 102 52 -5.34 8.59
122/84 1105 5.04 -3.15 4 9 35.53 -71 25 30.78 291 56 -13.65 7.42
AM Her (RA = 18 14 58.6, DEC = +49 50 55 ref. 5)
222/83 170 1.15 -0.04 18 14 59.29 49 50 59.39 315 26 -7.81 1.67
068/84 146 1.42 0.27 18 14 57.28 49 50 51.79 165 06 -6.38 11.51
245/84 1200 2.33 1.53 18 14 59.53 49 51 04.05 336 11 -11.91 4.57
307/83 444 0.85 3.37 18 14 58.78 49 51 09.6 035 33 -10.87 9.91
214/84 20340 6.48 -0.99 18 15 00.15 49 50 59.91 307 21 -14.90 5.19
301/84 16510 31.54 32.93 18 14 59.40 49 51 08.76 029 33 -8.15 13.52
151/84 746 0.53 -5.46 18 14 59.02 49 50 45.90 244 59 -7.53 6.53
184/84 13670 10.28 -1.37 18 14 59.85 49 50 50.79 277 29 -11.44 5.76
272/84 14670 24.41 33.94 18 14 59.69 49 51 05.24 002 51 -9.70 11.04
264/84 23610 2.21 -87.49 18 14 59.11 49 51 04.46 354 25 -9.90 3.99
Her X-1 (RA = 16 56 01.68,DEC = 35 25 04.8 ref. 7)
217/83 64 0.91 0.11 16 56 2.08 35 25 07.88 328 39 -5.17 2.57
225/83 171 1.77 0.22 16 56 2.21 35 25 09.05 335 02 -6.59 4.08
061/84 7405 2.71 2.51 16 56 0.64 35 24 52.53 172 41 -13.79 11.05
071/84 151 0.97 2.52 16 56 0.76 35 24 57.88 181 21 -6.65 11.41
080/84 275 1.02 2.75 16 56 0.75 35 24 56.23 189 08 -6.66 12.59
096/84 3975 -2.80 10.34 10 56 0.66 35 24 53.28 202 49 -5.78 15.96
130/84 45520 1.91 1.79 16 56 1.93 35 24 50.87 238 40 -9.86 10.31
197/84 1859 -3.59 -1.18 16 56 2.34 35 25 00.90 310 24 -3.62 8.20
235/84 10700 2.12 -1.32 16 56 2.25 35 25 10.67 343 28 -7.61 5.01
270/84 4252 33.62 27.44 16 56 2.39 35 25 12.37 013 30 -5.34 10.21
DATE cts x y RAobs DECobs theta delta beta delta gamma
3C273 (RA = 12 26 33.2, DEC = +02 19 43 ref. 8)
351/83 1235 -2.46 4.05 12 26 32.24 02 19 43.57 156 07 -5.30 13.39
029/84 511 -1.65 3.72 12 26 32.16 02 19 39.55 158 42 -8.88 13.27
137/84 1003 0.45 0.25 12 26 34.01 02 19 51.14 332 44 -12.80 7.06
3C120 (RA - 4 30 31.61, DEC = +05 14 59.79 ref. 9)
228/83 741 28.40 -114.62 04 30 31.47 05 14 51.00 192 58 -8.10 4.01
044/85 491 0.95 148.82 04 30 31.86 05 15 11.09 012 26 -10.14 6.06
IRAS 1883+326 (2A = 1S' 33 11.97, DEC = +32 39 18.22 ref. 9)
187/85 573 24.45 30.84 18 33 12.53 32 39 06.34 277 50 -5.39 12.73
195/85 379 36.80 35.26 18 33 12.69 32 39 08.70 285 55 -6.13 11.65
204/85 167 33.16 25.51 18 33 12.72 32 39 13.71 297 16 -6.35 8.35
211/85 120 35.67 33.91 18 33 12.99 32 39 11.67 304 25 -6.93 12.45
211/85 240 35.80 26.21 18 33 13.05 32 39 17.38 304 25 -10.78 8.40
223/85 226 38.04 24.69 18 33 13.09 32 39 20.29 317 08 -11.14 8.96
233/85 360 30.46 32.16 18 33 13.10 32 39 19.10 326 41 -8.57 11.44
246/85 284 26.61 23.66 18 33 12.90 32 39 19.21 338 54 -5.15 10.60
256/85 391 31.32 35.81 18 33 13.25 32 39 20.62 347 17 -5.90 15.24
257/85 50 28.50 25.87 18 33 13.15 32 39 22.76 347 17 -7.71 13.54
273/85 227 27.19 33.63 18 33 12.89 32 39 20.96 000 57 -2.25 11.66
TABLE 3
NAME DATE cts x y theta RAobs DECobs RAcat DECcat REF. delta beta delta gamma
2223-052 152/84 13 -0.80 -8.70 201 35 22 23 11.21 -5 12 19.22 22 23 11.05 -5 12 17.0 10 2.96 1.36
1207+39 154/84 32 2.00 -2.72 329 03 12 08 01.07 39 41 10.46 12 08 01.06 39 41 01.8 9 -7.49 -4.35
1207+39 311/83 86 -3.04 2.01 131 39 12 08 00.87 39 41 03.09 12 08 01.06 39 41 01.8 9 -0.78 2.42
1207+39 323/83 28 -5.20 1.54 139 43 12 08 01.32 39 41 10.85 12 08 01.06 39 41 01.8 9 8.84 3.56
1207+39 109/84 122 -4.03 -3.85 299 41 12 08 01.00 39 41 04.40 12 08 01.06 39 41 01.8 9 -0.69 -2.60
1207+39 002/85 86 26.61 -37.88 167 50 12 08 00.89 39 40 49.99 12 08 01.06 39 41 01.8 9 -11.96 -0.57
MKN501 032/84 880 -38.37 33.41 148 10 16 52 11.96 39 50 19.88 16 52 11.73 39 50 26.0 10 -3.80 -5.48
MKN501 034/84 1260 -39.06 33.30 149 25 16 52 11.74 39 50 22.27 16 52 11.73 39 50 26.0 10 -3.15 -2.00
LMC X-4 291/83 2020 4.52 -74.55 149 09 5 32 47.57 -66 24 18.13 5 32 47.3 -66 24 13 7 -3.57 -4.02
LMC X-4 303/83 13 3.00 1.00 138 13 5 32 46.85 -66 24 19.28 5 32 47.3 -66 24 13 7 -6.48 -2.17
LMC X-4 116/84 40 -1.83 3.09 319 40 5 32 47.12 -66 24 13.58 5 32 47.3 -66 24 13 7 1.14 -0.45
SU UMa 077/84 184 -0.68 4.87 328 51 8 08 05.55 62 45 21.59 8 08 05.5 62 45 23 7 1.03 1.02
NGC3783 162/84 173 -2.05 -1.01343 18 11 36 32.79 -37 27 44.69 11 36 33.0 -37 27 40.9 8 4.35 -1.31
NGC5506 235/83 17 -8.42 -5.25 345 21 14 10 39.39 -2 58 32.27 14 10 39.13 -2 58 26.26 9 4.85 5.29
NGC5506 061/84 20 12.15 11.24 167 44 14 10 38.90 -2 58 32.93 14 10 39.13 -2 58 26.26 9 -7.25 1.95
EX Hya 035/84 4753 -4.58 8.16 147 10 12 49 42.31 -28 58 38.91 12 49 42.6 -28 58 40 5 -1.15 3.79
EX Hya 195/85 5116 36.11 35.04 335 34 12 49 42.82 -28 58 45.45 12 49 42.6 -28 58 40 5 3.77 4.88
SS Cyg 315/83 191 3.34 3.40 005 58 21 40 44.53 43 21 25.70 21 40 44.5 43 21 23 5 -2.65 0.61
SS Cyg 338/83 4426 1.64 4.58 025 34 21 40 44.95 43 21 22.80 21 40 44.5 43 21 23 5 2.30 4.34
VV Pup 036/84 4288 1.99 -1.71 067 34 8 12 51.52 -18 54 06.29 8 12 52.2 -18 54 02 5 -7.28 -7.65
Cyg X-1 142/84 3397 4.37 -5.47 213 14 19 56 29.12 35 03 52.37 13 56 28.87 35 03 55 7 -3.88 -1.13
Cyg X-1 189/84 4276 5.52 -2.79 256 49 19 56 29.14 35 03 56.83 19 56 28.87 35 03 55 7 -2.81 -2.54
Cyg X-2 263/83 10210 0.93 3.11 313 58 21 42 36.99 38 05 21.60 21 42 36.9 38 05 28 7 3.68 5.34
Cyg X-2 265/83 16110 0.13 2.86 316 09 21 42 36.76 38 05 20.45 21 42 36.9 38 05 28 7 6.59 4.04
V0332+53 332/83 32 5.77 0.07 288 49 3 31 15.44 53 00 29.18 3 31 14.9 53 00 25 11 -5.96 -2.39
3C390.3 153/84 26 -1.38 -5.50 239 19 18 45 39.19 79 43 09.74 18 45 37.6 79 43 6 9 -1.75 -5.39
0311-227 333/83 11560 2.28 1.58 069 27 3 11 59.65 -22 46 48.88 3 12 00 -22 46 47 5 -3.87 -3.46
E1405-227 084/84 2471 2.19 1.79 128 12 14 05 57.57 -45 03 08.79 14 05 58.2 -45 03 06 5 -6.97 1.94
AN UMa 102/84 3565 0.92 1.20 309 48 11 01 35.36 45 19 27.67 11 01 35.6 45 19 26 5 0.88 -2.90


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