13.3 Resolving Structure with TRANSFER Mode

Routine pipeline processing of TRANSFER mode data, discussed in Chapter 11 is confined to locating the individual scans within the data files, editing out bad data, and computing guide star centroids and standard deviations during each scan. Otherwise TRANSFER mode observations have always been processed interactively rather than through a pipeline, which is why we discuss them here as a form of FGS data analysis. In the near future the pipeline will be upgraded to perform extensive data reductions on TRANSFER mode observations (see Chapter 11) in order to support the mixed-mode approach, which combines TRANSFER mode observations with POSITION mode observations made in the same visit. More specifically, the pipeline modifications will enable the results from TRANSFER mode observations to be used along with the POSITION mode observations in the construction of virtual plates. The ultimate goal is to support the scientific determination of parallaxes, proper motions, and reflex motions due to dark companions of multi-star systems resolvable with the FGS.

13.3.1 FGS Response to a Binary

The wavefront of a point source at the face of a Koester prism is colliminated, coherent, polarized, and characterized by a propagation vector. As the instantaneous field of view of the FGS scans across the target, the tilt of the wavefront varies and the PMTs register different relative intensities. Plotting the position of the IFOV along the scan path against the normalized difference of the PMTs thus reveals the characteristic S-curve of the FGS (see "S-curves" on page 9-8).

If the source is a double star, then its wavefront at the face of the Koester prism will have two components, each coherent with itself but incoherent with respect to the other. Two propagation vectors characterize this wavefront and the angle between them is directly related to the angular separation of the stars on the sky. As the FGS's IFOV scans across the object, each component of the wavefront generates its own S-curve, whose modulation is diminished by the non-interfering background contribution from the other component. The interferometric null for each star occurs at a different point along the scan path, so the resulting relationship between the position of the IFOV along the scan path to the normalized difference of the PMTs depends upon both the separation of the stars and their relative brightnesses. To demonstrate this effect, Figure 13.4 shows the FGS 3 y-axis S-curves of several synthetic binary systems with a variety of angular separations and relative intensities.

Figure 13.4: Effect of Double Stars on S-curve

The modulation and morphology of its point-source S-curves ultimately determines the resolving power of the FGS. Figure 13.5 diagrammatically demonstrates how the amplitude of the S-curve couples with the magnitude difference of the binary to determine the FGS's resolving power. It shows a synthetic binary star system with an angular separation of 50 mas on both the x and y axes of FGS 3, but at a variety of relative intensities. It is clear that as the magnitude difference increases, the resolving power of the FGSs along the x-axis becomes doubtful well before that of the y-axis. Note, however, that this separation and selection of magnitude differences was chosen solely for its visual impact. The data reduction algorithm would have no difficulty resolving the binary in Figure 13.5c.

13.3.2 TRANSFER Mode Data Reduction

1. Visual inspection of the S-curves from each scan to identify and disqualify those corrupted by vehicular jitter or data dropouts.
2. Dejittering of the astrometry data at 40 Hz using the instantaneous position of the dominant guide star in its FGS, if desired. (This step may requalify scans that would otherwise be deleted from further consideration.)
3. Cross-correlation of each scan, in order to detect any drift of the FGS across the sky during the course of the observation.
4. Shifting of each scan by the amount determined necessary in step (3) so that all scans are mapped to a common reference frame.
5. Binning and co-adding of the individual scans to generate a high signal to noise composite S-curve. Each step of the IFOV along each scan is placed into an appropriate bin, and then all entries in a given bin are averaged to produce the high S/N binned and co-added S-curve. See Figure 13.6.
6. Fitting of a piecewise third order polynomial fit to the binned and co-added S-curve.

If the observation under analysis is of a binary star system and the observer wishes to determine the angular separation and magnitude difference of its components, the following additional tasks are undertaken.

1. Selection of an appropriate set of reference S-curves from the calibration library on the basis of the target color (or colors) and the dates of observation of both the binary system and the calibration stars. These dates should be as close as possible to minimize the impact of temporal variations in FGS3.
2. Fitting the binary system's composite S-curves with the reference S-curves by iteratively determining the angular separation and magnitude difference. This fitting is done on both the x and y axis. The quality of the fit can be assessed by comparing the magnitude differences determined independently along each axis. On the other hand, if the observed target is an extended object, the GO will retrieve the appropriate reference S-curves from the calibration data base and use software tools appropriate for such an investigation.

   Whether the observation be of a calibration star, a binary system, or an extended source, STScI will be producing publically available software packages to support the analysis of these data. Please consult the STScI FGS Web pages for updates.

• Spacecraft jitter.
• FGS drift.
• Temporal variability of the S-curves.
• Wavelength dependence of the S-curves.
• Roll dependence of the FGS plate scale.

To obtain high signal-to-noise S-curves, the single scans must be cross-correlated, shifted, binned, and co-added. Any small, unaccounted for spacecraft motion that occurs during each scan will effectively blur the boundaries of the binning procedure, ultimately causing the co-added S-curve to suffer some loss of spatial resolution. This effect invariably occurs because even a 40 Hz de-jittering of an astrometry observation executed during the quietest of HST orbits will not escape the residual jitter introduced into the pointing control system by the guide stars' photometric noise. Thus, the maximum resolving power of an FGS in TRANSFER mode can not be better than about 1 mas. Figure 13.7 compares the S-curves from two single scans, one obtained during a nominally quiet HST pointing, and the other observed during a time of high spacecraft jitter.

Figure 13.7: Comparison of S-curves from Two Separate Scans during Same Observation

Proper cross correlation is relatively straightforward for bright objects (V < 13), but for fainter objects it becomes more difficult, just as binning and co-adding becomes all the more important. In such cases it might be advantageous to construct a drift model iteratively by time tagging the shifts determined by the cross-correlation procedure. Fitting of these shifts to a linear or quadratic drift model might align the individual S-curves more reliably than a procedure that depends solely on individual noisy scans. For bright stars with V < 13, drift in the FGS is estimated to degrade the resolution of TRANSFER mode observations by about 1 mas. For fainter stars, the degradation will increase significantly in a way that depends on details of HST's orbital environment during the visit. Recall from the discussion of drift on page 12-12 that its origin is not well understood. It is not repeatable, and its amplitude depends weakly upon the declination of HST's V1 axis. If a particular observation of a faint star (V > 15) was subject to typical drift of around 10 to 12 mas, then the estimated loss of angular resolution would be about 4 mas.

Temporal Variability of S-Curves

• Obtain reference standard star data at the time of the observation. (S-curves appear to remain stable over at least a few months.)
• Select from a library of calibration S-curves taken over the course of the cycle the one closest in time to the target observation.
• Determine a correction algorithm which interpolates in time between S-curves taken from the S-curve library. Calibration standards for multiple component systems with small separations and large magnitude differences may have to be observed in the same epoch as the target as part of the proposed observing program. For less constrained programs, selection of reference S-curves close in time to the observation should be adequate. The STScI Cycle 7 calibration program contains a monitoring program which will allow us to establish the size of the S-curve variability and to assess its time scale coarsely. We will determine whether or not we can derive a correction algorithm as these data accumulate. Figure 13.8 shows the variability of FGS 3's S-curves over a time period exceeding two years.

Figure 13.9: Effects of Star Color on FGS S-curves

This effect is believed to be due to a rotation of the Koester prism about the normal to its entrance face. The Cycle 7 calibration program incorporates a test that will be used to verify and fine-tune this model, and the results will be made generally available as an STSDAS calibration tool. Check the STScI FGS WWW pages for updates.