Position Mode Calibrations and Error Sources
FGS science data is processed at three distinct levels: the exposure, the visit, and the epoch. Each of these levels is subject to different sources of error. Table 5.1 summarizes the accuracies of Position Mode calibrations. Most of the errors listed are statistical. Multi-epoch observations reduces the impact of these errors in the science data.
Table 5.1: FGS1r Position Mode Calibration and Error Source Summary
| Type of Calibration Correction |
Pre-Calibration Error Extent |
Calibration Error
(mas) |
Comments |
Exposure Level Calibration Corrections: |
| Average background and detector noise |
|
|
Serendipitously acquired during the FGS IFOV servo slew to the target; ~215 cts/sec in each PMT; used to adjust for position centroid errors. |
| Star Selector Encoder fine bit errors |
|
|
Correction applied in the SSA,B->X,Y conversion. |
| Centroid errors |
|
|
Apply median filter. |
| Relative PMT sensitivity |
|
|
Analysis removes PMT mismatch effect; used to adjust for position centroid errors. |
| Differential velocity aberration |
|
|
Depends on HST velocity vector and target geometry, ephemeris errors and alignment calibration. Correction applied during post-observation processing. |
| Relative distortion across FOV (OFAD) |
|
|
STScI calibration in filter F583W. |
| Lateral color correction |
for  (B-V) = 1 |
|
No corrections applied. Calibration planned for FGS1r. |
| Cross filter calibration |
|
|
Relative positional shifts are calibrated for filters F583W and F5ND at pickle center. |
Visit Level Calibration Corrections: |
| HST jitter |
|
|
Correction derived from guide star motion. Large jitter excursions could cause loss of lock or corrupt a data set; disqualify outliers. |
| Drift |
5-20 mas: two GS FineLock. 12-60 mas: one GS + gyro roll control |
|
Special observing strategy for check stars; Drift models derived from check star motion and applied to target data. |
Epoch-Level Calibration Corrections: |
| Temporal evolution of OFAD and plate scale. |
|
|
Long-term stability monitor program: update OFAD coefficients and FGS star selector calibration. |
Position Mode Exposure Level Calibrations
The corrections and calibrations described below are applied by the FGS Calibration Pipeline.
Star Selector Encoder Fine Bit Errors
The star selector rotation angles are read as 21 bit integers. The 7 least significant bits (LSBs) are read by an optical resolving device that was calibrated during the manufacturing process. The size of the calibrated correction is about 1 mas with a residual of about 0.1 mas. Errors in the 14 most significant bits (MSBs) are absorbed by the OFAD calibration.
Position Centroiding
The location of a star in the FOV during a Position Mode observation is determined by identifying the median of the 40 Hz SSA or SSB samples (while the target is being tracked in FineLock). The median measurement is robust against most spacecraft jitter, short-interval transients and telemetry dropouts. If faint targets (V > 16.0) are observed, the photometric noise results in a large noise equivalent angle. Spacecraft jitter and photometric noise contribute to the standard deviations about the median of up to 2 mas per axis for V < 14.5 and up to 3 mas per axis for V > 15.0. However, the repeatability of the centroid measurement (over smaller intervals of the exposure) is the true assessment of the precision of the measurement, typically 0.7 mas and 1.5 mas for targets where V < 14.5 and V > 15.0 respectively.
PMT Sensitivities and Position Centroid Adjustment
The effect of PMT sensitivity on FGS observations is discussed in Appendix 1. In order to accommodate the differences between the two PMTs along each axis, the FGE computes an average difference (DIFF) and average sum (SUM) of their photometric response to the star over the first few FESTIMES in the WalkDown. These values are used in the calculation of the Fine Error Signal. The results are accurate for bright (V < 14.0) objects but become unreliable for fainter targets, a result of the short integration period and increasingly noisy photon statistics. The pipeline gathers photometric data over the entire WalkDown (typically 80 times as many samples) to achieve a better signal-to-noise and more reliable values of DIFF and SUM. These are used to recompute the Fine Error Signal and adjust the (x,y) centroids in post-observation data reduction.
Differential Velocity Aberration
Differential velocity aberration arises as a result of small differences in the angle defined by the HST velocity vector and the line of sight to targets in the FGS FOV. The HST PCS guides for zero differential velocity aberration (DVA) at one position in the FOV. The positions of targets elsewhere in the FOV must be corrected for DVA. Calibration errors in the relative alignment of the FGSs, catalog position errors of the guide stars, and ephemeris errors all contribute-though negligibly-to the errors in the differential velocity aberration correction. The actual adjustment to the target's positions can be as large as ± 30 mas (depending on the target and velocity vector geometry) but are corrected by post-observation data processing to an accuracy of ±0.1 mas.
Optical Field Angle Distortion (OFAD) Calibration
Field angle distortion introduces errors in the measurement of the relative angular separation of stars at varied positions across the FGS FOV. The distortion errors originate from:
- Radial distortions induced by the Ritchey-Chretian design of the OTA.
- Manufacturing irregularities in the FGS/OTA optical train.
- The optical reader produces errors in the 14 most significant bits of the 21-bit Star Selector A and B encoder values.
The distortion is independent of target magnitude, color, or exposure time, and depends only on the location of the object in the FGS FOV. The Space Telescope Astrometry Science Team (STAT) has calibrated the optical field angle distortion (OFAD) in FGS3 and maintained this calibration (the OFAD has a slow time dependence). The data for calibrating FGS1r became available in December 2000 and the analysis of those observations is underway (by the STAT) at the time of this writing. However, using FGS3 to infer FGS1r potential distortion, we expect - on average - 500 mas distortion across the FOV. This effect is represented by two fifth-degree two-dimensional polynomials. Post-calibration residual errors are typically 
mas throughout most of the FOV. The FGS3 OFAD residuals are plotted in Figure 5.3 for illustration. See the HST Data Handbook for additional information. The OFAD calibration of FGS1r is a part of the FGS calibration plan.
We expect smaller OFAD residuals for FGS1r (compared to FGS3) due to the design of the calibration test. The FGS3 data were acquired at a time when the roll of HST was restricted to be within 30 degrees of nominal for the date of the observations. The FGS1r test executed when the target field (M35) was close to the "anti-sun" position, i.e., when HST could be rolled over a full 360 degrees. Figure 5.1 shows an overlay of the pointings used for the FGS3 calibration, while Figure 5.2 shows the same for the FGS1r calibration. Clearly, the distortions should be more apparent in the FGS1r test, allowing for an optimal calibration (compared to the FGS3 test).
Figure 5.1: Overlay of the pointings used for the FGS3 OFAD calibration
Figure 5.2: Overlay of pointings used for the FGS1r OFAD calibration
Figure 5.3: FGS3: Residuals of OFAD Calibration in the X-axis (top panel) and Y-axis (bottom panel).
Lateral Color
The five-element corrector group (see box in Figure 2.1) is a collection of refractive elements tasked with the removal of astigmatism and the final of the beam. It's refractive properties introduce subtle changes to angle of propagation of the beam to a degree which depends on the spectral color of the source. This change causes the apparent position of the star in the FOV to shift slightly, an effect referred to as lateral color. The positional error introduced by lateral color is thought to be relevant only when comparing the relative positions of two targets of extreme colors: a color difference of (B - V) = 1 between two targets could introduce a ±1 mas positional error. An in-orbit assessment of lateral color associated with FGS1r was performed in December 2000, and the analysis is pending. Please check the FGS Web Site for more details.
Position Mode Visit Level Calibrations
Jitter
Significant enhancements to the HST pointing control system and the replacement of the original solar arrays have reduced quiescent vehicular jitter to 2-4 mas. Although small for most HST science applications, the jitter must be removed from astrometry data.
Since astrometric measurements are made sequentially, relating the measurements to one another requires a mapping of each measurement onto a fixed common reference that defines the visit. Guide star positional data, also telemetered at 40 Hz, are used to define jitter characteristics over the course of the visit. In this way, low frequency jitter (on time scales of minutes) can be removed from the target data.
High frequency, large-excursion jitter, most often a result of the transition to and from orbital day and night, ranges from 5 to 150 mas in amplitude and lasts for several seconds to several minutes. If particularly frenzied, the large jitter can cause total or temporary loss of lock of the guide stars. An example of the jitter during the onset of a day/night transition is shown in Figure 5.4. The large vibrations increase the standard deviations of FineLock tracking in the three FGSs by up to a factor of eight over the pre-transition values. Fortunately, such instances are rare.
The overall residual from the "de-jittering" process is only ~ 0.1 mas, the small value testifying to the advantages of using a median filter in the centroid computation and to the excellent pointing of the HST.
Figure 5.4: FGS2 Guide Star Motion at the Onset of a Day/Night Transition
Drift
FGS drift was discussed in Chapter 7 with regards to observation strategy, i.e., the use of check stars to track apparent motion of the FOV during the visit so it can be removed during post-observation processing. There are two different classes of drift, depending on whether one or two FGSs guided the HST during the visit. With two FGSs guiding, drift is identified as a slow but correlated wander of the targets observed more than once during the visit. The amount of drift appears to be related to the intensity of the bright Earth entering the telescope during target occultations. Accordingly, the drift is highest for targets in HST's orbital plane (~ 10 mas) and lowest for those at high inclination (~ 2 mas).
When only one FGS is used to guide the telescope, the drift is typically 20 mas over the course of the visit. The single guide star controls the translational motion of the spacecraft while the HST roll axis is constrained by the gyros. Gyro-induced drift around the dominant guide star ranges from 0.5 to 5 mas/sec, and is typically of order 1 mas/sec. Note the gyro drift is a spacecraft roll, and does not represent the translational motion of a target at the FGS (which will typically be ~0.01mas/sec). Over the course of a visit, the roll drift error measured by the astrometer can build up to 40 mas or more (but is typically less than 20 mas).
Regardless of the size of the drift, it can be characterized and removed by applying a model to the check star motions, provided the visit includes a robust check star strategy: a check star observation every 5-6 minutes (described in Chapter 7). At a minimum, two check stars measured three times each are needed to model translational and rotational drift.
Cross Filter Calibrations
For a target star (or any reference stars) brighter than V = 8.0 to be included as part of an FGS observation, it must be observed with the neutral density attenuator F5ND. As a result of the differing thicknesses of F583W and F5ND, and possibly a wedge effect between the two filters, the measured position of the bright target in the FOV will shift relative to the (fainter) reference stars. A cross-filter calibration is required to relate these observations, as relative positional shifts may be as high as 7 mas. Also, further evidence from FGS3 indicates these shifts are field dependent. If the effect is uncorrected, a false parallax will occur between the science and reference targets as the star field is observed at different orientations in the FOV. Since it would be prohibitive to calibrate the cross-filter effect as a function of field location, FGS1r cross-filter calibrations will be restricted to the center of the FOV. For reference, the uncertainty after the FGS3 cross-filter calibration is ~0.5 mas.
Position Mode Epoch-Level Calibrations
Plate Scale and Relative Distortion Stability
For FGS3, the plate scale and OFAD exhibits a temporal dependence on an average time scale of ~4 months and a size of several tens of milliarcseconds (predominately, a scale change). The evolution of the FGS3 OFAD revealed that the variability is probably due to the slow but continued outgassing (even after 10 years!) of the graphite epoxy structures in the FGS. A long-term stability monitoring test is executed bi-monthly to help measure and characterize the distortion and relative plate scale changes and thus update the OFAD. Post-calibration residuals are on average ±1 mas along the X-axis and Y-axis. Better performance (of order ± 0.5 mas) is achieved in the central region of the FOV.
The FGS1r Position Mode stability was coarsely monitored during Cycle 7. Large scale changes in its S-Curve, attributed to outgassing effects, show that the instrument was unstable (for high accuracy astrometry) during its first year in orbit, as expected. In early 1998 the evolution slowed, and by April 1998 FGS1r's S-curves fully stabilized; a major prerequisite for the OFAD calibration was met.
The OFAD and lateral color calibrations were to have been performed during cycle 8 when the target field was at anti-sun and HST would not be roll constrained. Unfortunately this coincided with and was pre-empted by the Servicing Mission 3a. Rather than perform the calibrations under less favorable, roll-constrained conditions, STScI decided to defer the observations until December 2000, when the target field again has an anti-sun alignment.
The science data that has accumulated since the beginning of cycle 8 will be re-processed once the OFAD calibrations are in hand. Any temporal evolution since the beginning of cycle 8 can be back-calibrated away by use of the long term monitoring observations that have been executing all along. Check the FGS web pages for updates with regard to the OFAD calibrations.
Errors Associated with Plate Overlays
The errors associated with several of the corrections described above will not manifest themselves until data from individual visits are compared. The most dominant source of Position Mode error are the OFAD and changes in the plate-scale. The derivation of a plate scale solution is described in the HST Data Handbook. In general, for regions near the center of the pickle, residuals are smaller than 1 mas if the reference star field is adequately populated.
