Astrometric Precision and Accuracy

with HST FGS 3 in the Position Mode

A.L. Whipple, B. McArthur, Q. Wang, W.H. Jefferys,

G.F. Benedict, A.M. Lalich, P.D. Hemenway, E. Nelan,

P.J. Shelus, and D. Story

The University of Texas at Austin

where x, y denote the observed position within the FGS field of view, x', y' denote the corrected position, and the numerical values of the coefficients a_ij and b_ij must be determined by calibration. Gravity release, outgassing of the graphite-epoxy structures, and post-launch adjustment of the HST secondary mirror required that the final determination of the OFAD coefficients a_ij and b_ij be made by an on-orbit calibration.

Since there was no star field that was large enough and for which the relative positions of the stars were known to the level of a millisecond of arc, the positions of the stars had to be estimated simultaneously with the distortion parameters. This was accomplished during a nineteen orbit calibration, executed on 10 January 1993. Only FGS number 3 was calibrated in this way. The data were analyzed to estimate the relative star positions, the pointing and roll of the telescope during each orbit, the magnification of the telescope, the OFAD polynomial coefficients, and several parameters that describe the star selector optics inside the FGS. A complete description of that calibration, the analysis of the data, and the results are given in Jefferys et al. (1994).

Just prior to the 1993 OFAD calibration, a series of one orbit long-term stability tests (LTSTAB) was initiated. An LTSTAB is run approximately once per month and consists of a single pointing from the spring 1993 OFAD calibration or its fall orientation counterpart. The LTSTAB is sensitive to scale and low order distortion changes. The LTSTAB series immediately showed that the scale measured by the FGS was changing with time. The most obvious indication of this change was the large increase with time in the post-fit residuals from a solution that solved for constant sets of star positions, star selector parameters, and OFAD parameters (Fig.1a). The amount of scale change is too large to be due to true magnification changes in the HST optical telescope assembly. These changes may be due to water desorption in the graphite-epoxy components within the FGS. This scale- like change is very well modeled by a change in the star-selector-A effective lever arm. In response to our early experience with these tests we modified our model to incorporate a time dependent rA (Whipple et al. 1993). Figure 1b shows the effect Fig. 2. Differences (post-pre) between pre-servicing mission OFAD and the post-servicing OFAD with rotation, scale, and shift removed. of including the time dependentterm in the analysis of the OFAD and LTSTAB data. The residuals from the fit are decreased from as much as 50 mas in the x and 10 mas in y if is left constant (Fig. 1a) to about 10 mas in both coordinates when is allowed to vary with time (Fig. 1b). Ten milliseconds of arc is still about five times larger than our goal for the OFAD calibration.

Fig. 1. Post-fit residuals from solutions that simultaneously fit the data from the 1993 OFAD, 1994 -OFAD, and all LTSTAB calibration tests. Note the significant improvement achieved by successive model modifications. (a) 5th order polynomial and star selector parameters held to values derived from 1993 OFAD. (b) 5th order polynomial, rho_B, and k_A held fixed to 1993 OFAD values, separate values of rho_A estimated for each epoch of calibration data. (c) 1992 through 1994 data reduced with 5th order polynomial, rho_B, and k_A held fixed to 1993 OFAD values, 1994 to 1995 data reduced with 5th order polynomial, rho_B, and k_A fit to 1994 -OFAD, separate values of rho_A estimated for each epoch of calibration data. (d) 1992 through 1994 data reduced with 5th order polynomial, rho_B, and k_A held fixed to 1993 OFAD values, 1994 to 1995 data reduced with 5th order polynomial, rho_B, and k_A fit to 1994 -OFAD, separate values of rho_A and 3rd order polynomial coefficients estimated for each epoch of calibration data. (e) Same as (d) but with the removal from the x component of all data of a four frequency Fourier series that was fit to the 1993 OFAD data.

The HST servicing mission in December 1993 required that the secondary mirror of the telescope be adjusted to optimize the performance of the refurbished instruments. This caused a change in the FGS OFAD due in part to the effects of the spherical aberration of the telescope, uncorrected at the FGS during the servicing mission. This change can be seen clearly in Fig. 1b. A five orbit -OFAD was performed on 27 April 1994 to restore the OFAD calibration to the 1993 level. Significant changes in the OFAD, in addition to the scale-like changes and at the level of 10 mas, were found (Fig. 2). Figure 1c shows the improvement in the residuals from the fit to the OFAD and LTSTAB data when two sets (one pre- servicing mission and one post-servicing mission) of coefficients a_ij, b_ij in Eq. (1) are estimated. The root-mean-square of the residuals is reduced to about 6 mas in both axes.

The LTSTAB tests have revealed continued changes in the FGS. In addition to the scale changes, we have begun to note higher order distortion changes. These changes manifest themselves as something that looks like a radial scale change and is fairly well modeled by changes in the third order terms in Eq. (1). This is illustrated in Fig. 3 which compares two post-servicing OFAD polynomials, one of which was fit to the 1994 five orbit calibration and the other of which had only the third order coefficients adjusted to fit the 1995 day 170 LTSTAB data. Additionally, the LTSTAB data taken in the fall orientation (which is rolled 180° from the spring orientation) have never fit as well as the spring data. This has led us to experiment with time dependent coefficients for the third order terms in the Fig. 3. Differences 1994.117-LTSTAB 1995.170) between the 3rd order distortions estimated from the post-servicing mission -OFAD and those estimated from a spring 1995 LTSTAB orbit with rotation, scale, and shift removed. OFAD polynomial. Estimating the third order coefficients for each epoch of calibration data further reduces the residuals from the fit to the OFAD and LTSTAB calibrations to about 3 mas in both axes although the residuals for the data taken in the fall orientation are still higher than the corresponding spring data (Fig. 1d).

We have also recently discovered a systematic signature in the residuals from the analysis of the 1993 OFAD calibration. This appears as a very distinctive curve in the x component residuals as a function of position angle in the FGS field of view (Fig. 4). The curve cannot be modeled by the fifth order polynomial. We have used a four frequency Fourier series to remove this effect. The size of this effect, in an RMS sense over the entire field of view of the FGS, is about one millisecond of arc. However, the peak-to-peak values near the center of the field of view can be as large as 6 mas. The addition of these terms to our model has reduced the residuals from the OFAD and LTSTAB calibrations to about 2 mas in x (Fig. 1e). The residuals in the y axis are unchanged at about 3 mas. The source of this unexpected distortion is not known but it may be due to the way the FGS responds to the spherically aberrated HST beam. This component of the distortion appears to be very stable with time.

On the basis of two and a half years of monitoring the distortions in FGS 3 we have concluded that at the level of a few milliseconds of arc, the optical field angle distortion in HST FGS 3 changes with time. These changes can be monitored and modeled by continuing the LTSTAB tests. There remains some dichotomy between the OFAD calibration data taken in the spring and that taken in the fall. A likely explanation for this is that the y components of the distortions are not adequately sampled by the spring telescope pointings. A new , in the fall orientation, is planned for November 1995. Fig. 4. Residuals from the 1993 OFAD calibration in the x axis (a) without and (b) with a four frequency Fourier series removed.

The cross filter test provided us with three high quality data sets in three positions in the FGS 3 field of view (Fig. 5). The data were analyzed in several ways, all of which gave similar results. Eleven settings were made using two filters on the same star, alternating between the F583W and the F5ND filters, within one observation set. The analysis took the difference between successive measurements through one filter and through the other filter as a single data point, to correct for any uncompensated spacecraft and/or FGS-to-FGS drift. Thus, 11 differences were obtained within each observation set. The data had been pipelined and de-drifted prior to analysis. Table I gives the results. The sigmas are the standard deviations of the means, and are probably smaller than realistic estimates of the external errors. Still, the difference between the F5ND filter and the F583W filter is significant in both x and y. In y, the measurements are consistent to within 1 millisecond of arc. The difference in x appears to be field dependent. We have settled on a piece-wise sub-field correction, dividing the FGS 3 field of view roughly in thirds and applying the x correction determined from the calibration data for that third.

Therefore, we conclude that we have measured a significant cross filter position shift in both x and y coordinates, and that applying that calibration significantly improves the FGS measurements made when both F5ND and F583W filters are used in the same observation set.

An on-orbit test was designed and conducted in December 1991. Due to excessive spacecraft jitter (from a combination of the original solar arrays and insufficient damping in the telescope pointing control system) and insufficient knowledge of the OFAD, the results were inconclusive. A similar test was carried out in December 1994. Preliminary analyses have failed to detect any measurable lateral color signature. We continue detailed reanalyzes of these data, motivated both by pre-launch predictions and by a fortuitous observation of a very blue stellar flare on Proxima Centauri (a very red star). A position shift observed during the flare indicates that lateral color may remain an important source of systematic error.

- Bradley, A., Abramowicz-Reed, L., Story, D., Benedict, G., and W. Jefferys: 1991, 'The Flight Hardware and Ground System for Hubble Space Telescope Astrometry', PASP 103, 317

- Benedict, G.F., Nelan, E., McArthur, B., Story, D., van Altena, W., Ting-Gao, Y., Hemenway, P.D., Shelus, P.J., Whipple, A.L., Franz, O.G., Fredrick, L.W., and R.L. Duncombe: 1993, 'Periodic Low-Amplitude Variations in the Brightness of Proxima Centauri', PASP 105, 487- 493

- Ftaclas, C., Nonnenmacher, A., Weindling, F., Story, D., and E. Nelan: 1993, 'Hubble Space Telescope Fine-Guidance-Sensor Transfer Function and its Impact on Alignment and Guidance', Ap. Opt. 32, 1696

- Jefferys, W.J., Whipple, A., Wang, Q., McArthur, B., Benedict, G.F.,
Nelan, E., Story, D, and L. Abramowicz-Reed: 1994, 'Optical Field Angle
Distortion Calibration of FGS 3' in J.C. Blades and S.J. Osmer, ed(s).,
*Calibrating Hubble Space Telescope*, Space Telescope Science Institute, Baltimore, 353-374.

- Whipple, A., Jefferys, W., Wang, Q., McArthur, B., Benedict, G.F.,
Nelan, E., Story, D., and L. Abramowicz-Reed: 1994, 'Maintaining the FGS
3 OFAD Calibration with the Long-Term Stability Test' in J.C. Blades and
S.J. Osmer, ed(s).,
*Calibrating Hubble Space Telescope*, Space Telescope Science Institute, Baltimore, 375-379