This section contains a discussion of the detailed corrections that are applied to Position mode FGS astrometry data by calfgsa and calfgsb. A flowchart is provided in Figure 3.3 to help illuminate data processing with calfgsb (please see the flowchart given by Figure 3.1 for an overview of calfgsa related processing of Position Mode data)

3.5.1 Processing Individual Observations

Position Mode pipeline processing for each individual observation in the visit executes the following steps:

1. Inspection of the flags/status bits to locate the data fields recording:
   

   -The slew of the IFOV to the target’s location.

   -The WalkDown to FineLock.

   -The FineLock tracking (FineLock/DataValid) of the target.

2. Computing the centroid of the IFOV, taken to be the median of the instantaneous (x, y) positions during the FineLock/DataValid interval, in the astrometer as well as the guide star positions in the guiding FGSs. Standard deviations about these centroids are also computed.
3. Updating the HST state vector, specified in the header files for the beginning of the observation, so that it is accurate for the temporal midpoint of the FineLock/DataValid interval.
4. Gathering photon statistics on:
   -PMT background during the slew to the target.
   -PMT data taken during the Walkdown to FineLock (FL) while the IFOV was still far (>0.1") from interferometric null. (These data can be used to calculate SUM and DIFF values more accurately than those computed at the start of the WalkDown, as they are based on up to 80 times more samples.)
   -PMT data taken while FGS was in FL/DV. (These data are averaged to compute the points on the S-curves of both axes which the FGS's microprocessor determined to be the true interferometric null. These values should be approximately the same as the DIFF and SUM computed by the FGS’s microprocessor at the start of the WalkDown).
5. Applying the DIFF and SUM corrections to both axes of only the astrometry data in order to locate the true interferometric null. This algorithm determines the slope of the fine error signal near interferometric null as a function of position in the pickle, using a library of reference S-curves, the target magnitude, making use of the background data computed above, and the difference in the photomultiplier averages computed during the WalkDown and the FineLock/DataValid intervals. This correction tends to be small for bright stars (V < 13.5) but can be as large as 5 mas for faint (V > 15) stars.
6. Converting the raw telemetry encoder positions to instantaneous (x, y) detector coordinates using several parameters, such as the star selector lever arm lengths, and offset angles. The lever arm and offset angle are known to vary in time. They are monitored by an ongoing program called the Long Term Stability Monitor (LTSTAB) which executes multiple times a year. The values applied in the pipeline are determined by interpolation of the LTSTAB results.
7. Correcting the (x, y) centroids in the astrometer for Optical Field Angle Distortions (OFAD).
8. Correcting distortions in the astrometer arising from the pickoff mirror and aspheric mirror.
9. Removing differential velocity aberration from the (x, y) centroids using the updated HST state vector, a JPL Earth ephemeris, HST's V1 RA and DEC, the V3 roll, and the V2,V3 position of the alignment point. This correction is applied to both the astrometer FGS and the guide star FGSs.

The pipeline produces output files that log these corrections, the associated standard deviations about the centroids, and the photometry averages from the four PMTs. calfgsa performs the majority of these corrections. However, corrections 6 through 8 are re-done by calfgsb which uses the most up to date value of coefficients for the OFAD correction and the star selector angles to (x, y) conversion (contained in reference files not accessed by calfgsa).

At this point no further processing on the individual observations are possible. The next step is to combine the measurements of the individual targets to correct for Position Mode-mode jitter and FGS drift.

3.5.2 Visit level processing

The goal of this segment of the pipeline (within calfgsb) is to map all of the positional measurements of the individual targets onto a fixed but arbitrary coordinate system. It involves Position Mode de-jittering and application of the drift correction.

Position Mode De-jittering

The pipeline accounts for spacecraft jitter during the visit by establishing a fixed but arbitrary reference frame determined by the (x, y) centroids of the guide stars (within the guiding FGSs) from the first exposure in the observing sequence. The HST pointing control system uses the position of the dominant guide star to fix HST's translational position and that of the roll guide star to fix HST's orientation. The output products of the pipeline processing of the individual observations include the (x, y) centroids of the guide star positions evaluated over the same time interval as the astrometer centroids. During the course of the visit any change in the (x, y) centroids of the dominant guide star within its FGS is interpreted to be HST translational jitter and is removed from both the astrometer and the guide star maintaining HST roll. Next, any motion of the roll guide star with respect to the dominant guide star perpendicular to the line between them is interpreted as uncompensated roll of HST about the dominant guide star. The pipeline then removes this roll from the astrometry data. Typically the size of the de-jittering correction is less than a millisecond of arc when averaged over the visit but can be as large as 3–5 mas for any given observation (eg., when HST transits from orbital night to orbital day).

De-jittering is not performed at a 40 Hz rate because that would introduce noise into the dataset. Instead the time-averaged centroids of the guide stars are computed for the same time interval that the astrometer was in FineLock/DataValid. The positions of the guide stars in the first exposure, corrected for differential velocity aberration, define the reference frame for the remainder of the visit. So, for example, if the dominant guide star (x, y) centroids measured during the Nth astrometry observation differed from those in the first observation by (dx, dy) = (1 mas,1 mas), then the appropriate conversion to dV2,dV3 is applied to the roll star and the astrometer's local (x, y) centroids. This procedure creates a fixed but arbitrary coordinate system for the entire visit.

Position Mode Drift Correction

After the FGS data have been de-jittered, there will remain an apparent motion of those astrometry targets which were observed more than once within the observing sequence. These check stars provide the data required for the drift correction, which assumes that the astrometer is a rigid body which both translates and rotates in the HST focal plane during the course of the visit and corrects the measured positions of the stars in the visit for contamination by this motion.

The time-tagged positions of the check stars are used to generate a model for this drift, and the time-tagged positions of all the stars in the visit are adjusted by application of the model. Three separate models can be applied:

• Linear: Translation only, no rotation.
• Quadratic: Translation only, no rotation.
• Linear and roll: Translation and rotation.

The choice of model depends upon the number of check stars available and the number of times each is observed. Clearly if there is only one check star in the visit the rotation model cannot be applied. Also, if check stars are not observed frequently enough (three times or more), the quadratic models might not be reliable. The pipeline applies all three models, providing three sets of corrected centroids to the data. It is the responsibility of the user to decide which set is the best. The output of the fitting program includes fit residuals and χ². Inspecting these values is the best way to determine which model yielded the best result.

The size of the drift correction is typically 2 to 6 mas under two-FGS guidance. The amount of drift appears to be related to the intensity of the bright Earth projected down the V1 boresight during target occultations. This intensity, and hence check star drift (generally), is highest for targets in HST’s orbital plane and lowest for those at high inclination.

When only one FGS is used for guiding, the telescope is not roll-constrained. Under such circumstances the check stars can reveal very large motions, up to 60 or 70 mas over the course of the orbit (5 to 10 mas is more typical). Nevertheless, this drift can be successfully removed from the astrometry data, provided the proposal contained an adequate check star scenario. For example, the overlay of the plates from two separate Position Mode visits, each measuring ~ 20 stars in an astrometric star field distributed throughout the pickle yielded an rms residual of about 1 mas, even though one of the visits had one-FGS guiding and check-star drifts on the order of 30 mas.