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Instrument Science Report OSG-003

Transforming Non-COSTAR Aperture Positions to the New Vehicle Reference
M. Lallo, C. Cox. O. Lupie October 3, 1996

ABSTRACT A major effect of the on-orbit FGS to FGS re-alignment of day 105 1996, was the redefinition of the vehicle reference frame, (V1,V2,V3). In support of the plan to perform close-out calibrations using the GHRS and FOC without the COSTAR DOB, we have transformed these "Non-COSTAR" aperture positions of the affected SIs into the current frame. FOS non-COSTAR positions were also calculated to support any possible contingencies. We discuss that process, and compare the results to those predicted by a polynomial fit of aperture shifts resulting from the day 105 FGS-FGS re-alignment project.

1. Introduction
Both at the STScI and at GSFC, there exists software to accurately compute HST's pointing, based on knowledge of guidestar and target positions, and of focal plane geometry and internal FGS calibrations. Cox and Lallo (1994) wrote such an algorithm, and demonstrated that the STScI and GSFC codes produced identical results. GSFC/PASS provides a service for the STScI, using this algorithm to calculate pointing based on operational or, if desired, non-operational FGS to FGS alignment information. This allows us to determine the effect on the SI apertures produced by FGS-FGS alignment matrix changes. It was on this processing method that we based zero-points for the SI aperture positions following the day 105 (15 April) 1996 FGS-FGS realignment, and we again used this procedure to derive the needed non-COSTAR apertures. A Focal Plane Calibration Observation (Heptathlon) from April 1993 (pre-COSTAR) was used as the input observations. From these time periods the code used the guide star telemetry to calculate new aperture positions based on the current FGS-FGS alignment. This particular observation was chosen for a few important reasons. It was taken before the servicing mission so positional displacements due to COSTAR are not involved; the observation places targets on reference fiducials in the FOC, GHRS, and FOS; the obser-

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vation used the same guidestars for the three instruments, and the guidestar and target positions are well determined astrometrically, reducing error in the attitude calculation. Procedurally, accurate celestial coordinates are supplied for the guidestars and target, and the code determines the target's corresponding V2,V3 positions, during the time period in question. The images are then examined to find the target star's offset with respect to the reference point, in order to determine the V2,V3 position of the aperture reference. Once updated positions for the SIs' apertures in question were found, the same delta can be applied to other apertures on the same plate; the angular distances in the FOV between apertures within an SI plate are small, and neglecting rotation over this scale produces differences only at the milliarcsecond level. FOS blue and red sides were computed independently, as were the HRS LSA and SSA. A small correction of 0.15° is also made to the angle relating each SI's coordinate system to the V2,V3 frame, which has been shifted. In the operational SIAF aperture file, part of the Project Data Base (PDB), the science instruments with and without COSTAR are treated as distinct. This allows us to implement these updates without any impact on current operations. This procedure should be completed by the time of this ISR's release. Serving as an independent check against gross errors, a bi-linear polynomial was derived from the SI shifts calculated for the April 1996 re-alignment. This polynomial relates V2,V3 positions before and after the re-alignment. There is no reason to believe that a linear fit is adequate but we found fitting errors less than 50 mas in the data (COSTAR-affected FOC, GHRS and FOS.). These points lie only in the +V2 half of the focal plane and therefore, to update the non-COSTAR values, we are relying on aperture positions directly calculated by the GSFC/PASS pointing code, rather than on extrapolation across the field of view from this fit. However, we found agreement to within a few tenths of an arcsecond between extrapolated and calculated positions. See table 1.

2. Results
Table 1 lists the V2,V3 PDB pre-COSTAR positions for the apertures in the old vehicle frame, the computed numbers for the new frame, the values predicted from the fit derived from earlier data, and the differences. In updating the PDB, we use the calculated values. The calculated minus predicted is 0.4'' for GHRS. FOC and FOS are under 0.25''. Given the input apertures' pre-COSTAR positional uncertainty, error budget in the image analyses, small errors in the pointing determination, as well as the possibility of positional changes between the time of the pre-COSTAR input observations and SM97, we expect these aperture determinations to be good to within 1.0''. Figure 1 graphically represents the results of the polynomial fit over the field of view based on the positions of the COSTAR-affected FOS, GHRS, and FOC apertures. Comparing the newly determined non-COSTAR aperture positions in the current frame to the polynomial is interesting, since the non-COSTAR calculations could probe errors result-

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ing from the extrapolation to the -V2 half. In the figure, vectors represent the shifts which transforms a position in the old frame to the new. Largest vectors within the field of view (observed in outer edge of +,+ quadrant) are ~1.7 arcsec long. Calculated shifts for the non-COSTAR SI general positions are 0.8, -1.1 (FOC), -0.5, 0.6 (GHRS), and 0.2, 0.2 (FOS), derived from table 1. These can be easily qualitatively compared to the fit.

3. References
Cox, C., M. Lallo, 1994, A Multipurpose Pointing Analysis Tool. OSG Instrument Science Report SOB-94-02-15

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Table 1. Transformed Aperture Positions
Instrument & Aperture Name FOC F96 HRS lsa HRS ssa FOS 4.3 blu FOS 4.3 red V2,V3 PDB (old frame)
+338.785 +191.701 -228.600 -234.400 -225.940 -237.060 -129.097 +160.202 -169.607 +119.377

V2,V3 Calculated (new frame)
+339.597 +190.601 -229.051 -233.881 -226.420 -236.500 -128.883 +160.428 -169.450 +119.890

V2,V3 Predicted from fit.
+339.55 +190.81 -229.41 -234.03 -226.76 -236.70 -128.69 +160.40 -169.35 +119.67

Calculated minus Prediction
+0.047 -0.209 +0.349 +0.149 +0.340 +0.200 -0.193 +0.028 -0.100 +0.220

Figure 1: Polynomial fit over field of view, showing the transformation to the post-day 105 vehicle reference. Vectors represent the offset which transforms a position in the old frame to the new. Largest vectors within field of view (observed in outer edge of +,+ quadrant) are 1.7 arc-sec long. Calculated shifts for the general non-COSTAR SI positions are 0.8, -1.1 (FOC), -0.5, 0.6 (GHRS), and 0.2, 0.2 (FOS). Figures derived from table 1.

V3

arc-sec

FOC F96 FOS bl FOS rd COSTAR FOC F96

GHRS COSTAR FOSrd COSTAR FOSbl COSTAR GHRS

V2

arc-sec

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