Fine Guidance Sensor Instrument Handbook for Cycle 14
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5.1 Position Mode Calibrations and Error SourcesChapter 5:
FGS Calibration Program
5.1.1 Position Mode Exposure Level Calibrations
5.1.2 Position Mode Visit Level Calibrations
5.1.3 Position Mode Epoch-Level Calibrations
5.2 Transfer Mode Calibrations and Error Sources
5.3 Linking Transfer and Position Mode
Observations
5.4 Cycle 13 Calibration and Monitoring Program
5.4.1 Active FGS1r Calibration and Monitoring Programs
5.5 Special Calibrations
This chapter describes FGS error sources, associated calibrations, and residual errors for Position, Transfer, and mixed (Position + Transfer) observing modes. A discussion of the FGS 1R calibration plan is included.
5.1 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.
Exposure level calibrations address the per observation errors. The visit level corrections address the errors after an entire orbit of astrometry data are combined The epoch-level corrections include the long term changes in scale and distortion of the instrument. The residuals after combining data from multiple visits include the plate overlays and, for example, the determination of an object's parallax and proper motion.5.1.1 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 A. 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. The analysis (by the STAT) was completed in June 2001. The distortion, on average about 500 mas across the FOV, is represented by two fifth-degree two-dimensional polynomials. Post-calibration residual errors are typically ~0.3 mas throughout most of the FOV. The OFAD calibration of FGS1r was part of the FGS1r commissioning calibration plan.
The OFAD residuals for FGS1r are smaller than those of 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. The freedom to rotate the field of view maximized the apparent effect of the distortions, making them more easily measured compared to the FGS3 test.
The accuracy of the astrometric catalog generated from ground based observations is insufficient for calibrating an FGS as a science instrument. As part of the OFAD calibration, it was necessary to derive an accurate star catalog. This requires that selected stars be observed at several HST pointings. In Figure 5.1 and Figure 5.2, the bold symbols denote stars that were observed as part of the calibration. For the FGS1r calibration, special care was taken to maximize the number of pointings which measured every star.
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
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 collimation of the beam. It's refractive properties introduce subtle changes to angle of propagation of the beam as a function of 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 relevant when comparing the relative positions of two targets of extreme colors: for example, a color difference of
(B - V) = 1 between two targets could introduce a ~1 mas positional shift. An in-orbit assessment of lateral color associated with FGS1r was performed in December 2000 and again in December 2001 (and will be repeated in December 2002). The results of these tests are available from the FGS web site.
5.1.2 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. Using the time dependent guide star centroids, low frequency jitter (on time scales of minutes) can be removed from the target data.
The pre-SM3B solar panels caused high frequency, large-excursion jitter, as HST transitioned to and from orbital day and night. These disturbances ranged in amplitude from 50 to 150 mas and lasted up to several tens of seconds. If particularly frenzied, a temporary or total loss of lock of the guide stars would result. An example of the jitter during the onset of a day/night transition is shown in Figure 5.3. 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 were rare.
With the new solar arrays installed during SM3B, the day/night disturbances no longer cause significant vehicle jitter. With the new arrays, HST jitter is characterized by two low amplitude (~5 mas) vibrational modes at 0.5 and 1.2 HZ. A larger, intermittent (and infrequent) disturbance of up to 100 mas persists, however. Fortunately HST's pointing control law damps this jitter away in about 10 seconds or less.
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 tracking of guide stars by the guider FGSs.
Figure 5.3: FGS2 Guide Star Motion at the Onset of a Day/Night Transition
This plot shows the relative position of a guide star in FGS2 along the HST V3 axis as a function of time. The large disturbance at about 157 seconds occurred as HST transitioned from orbit night into daylight. This was typical until the new solar panels were installed in March 2002 (SM3B). Significant jitter is no longer present at day/night or night/day transitions.
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.
5.1.3 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 milli arcseconds (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 preempted 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 analysis of the OFAD data were carried out as a "calibration out sourced" proposal led by members of the STAT from the University of Texas at Austin. The results of this calibration have been made available to STScI and reside as reference files used by the FGS calibration pipeline.
The science data that has accumulated since the beginning of cycle 8 can be fully calibrated with the OFAD calibration. Any temporal evolution since the beginning of cycle 8 is 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.5.2 Transfer Mode Calibrations and Error Sources
Table 5.2 summarizes Transfer mode sources of error and associated calibrations. Each entry is described in the subsections below.
A Transfer mode observation contains multiple scans of a target. To obtain optimal S/N values, the individual scans are cross-correlated, binned, and co-added. The reliability of this process is dominated by spacecraft jitter for targets with V < 14.5, and by photometric noise for fainter targets.
Background and Dark Subtraction
Targets fainter than V ~ 14.5 are increasingly affected by dark and background counts which reduces the amplitude of the S-Curve (since these contributions are not coherent with the light from the star. see Chapter 7). The instrumental dark counts have been measured as part of the STScI FGS calibration program (and are listed in Table 2.1). These values are needed for the analysis of data from Transfer mode observations of stars with V>14. Background measurements may also be needed if the star is embedded in significant nebulosity. These measurements must be made as part of the visit that observes the target. See example x.x for an example of how to obtain such data.
PMT Sensitivity Differences
Although individual PMT sensitivities in an FGS differ, these differences do not introduce a significant source of error in Transfer mode observations. Differences in the PMT response manifest themselves as a bias (offset) of the S-Curve. This bias is present in the calibration standard star S-Curves (the single stars) as well, and so the effect is neutralized when deconvolving the science target Transfer Function into its component single S-Curves (provided the spectral colors of the science and reference targets are well matched).
Jitter
Typically, quiescent vehicular jitter is about 2-4 mas in amplitude on timescales of minutes. With the solar panels installed in March 2002 during SM3B, the large 150 mas amplitude disturbances associated with the day/night orbital transitions of HST do not occur. Spacecraft jitter is removed by using the guide star centroids for quiescent times, or by eliminating intolerably corrupted scans or segments of scans from the co-addition process. For illustration, Figure 5.4 shows the effects of jitter on the FGS1r interferogram (single scan).
Figure 5.4: Effects of Jitter on an FGS1r S-Curve (single scan)
The quiescent scan (Figure 5.4a) shows features due to jitter - like the jump in S(y) around 0.03 arcsecond - which can be filtered out during post-observation processing. Unfortunately, the extreme effects of vehicle jitter on the S-Curve shown in Figure 5.4b cannot be corrected. Scans such as this are deleted from further consideration in the analysis. Note the small variations in the S-Curve's wings seen near the extreme edges of the plot (i.e., +/- 0.08") are due to photometric noise (the data presented in this example are from an observation of a bright V=9 star).
Drift
Drift is defined in Chapter 7, and its application to Position mode observations has been discussed earlier in this chapter. Drift is also apparent in Transfer mode observations but its removal from the raw data is straightforward; the cross-correlation of S-Curves, prior to binning and co-adding, automatically accounts for drift. Each individual S-Curve is shifted so that the particular feature of the S-Curve used for the cross correlation coincides with that of the fiducial S-Curve. However, the reliability of implicitly removing the drift is only as good as the accuracy of the cross correlation procedure, which becomes photon noise dominated for stars fainter than V=15 (i.e., cross correlation of scans is not reliable for V>15, hence drift can not be removed from such observations).
For bright stars with V < 13, FGS drift is estimated to degrade the resolution of Transfer mode observations by about 0.5 mas. For fainter stars, the degradation is worse. If an observation of a faint star (V > 15) was subject to typical drift (10 to 12 mas), then the estimated loss of angular resolution would be ~ 3 mas.
Instrumental Stability
Analysis of observations of resolved objects (i.e, binary systems or extended sources) involves the de-convolution of the observed transfer function using reference S-Curves of point sources. The repeatability, or temporal stability, of point-source S-Curves has a direct effect on the reliability (or accuracy) of the scientific result. FGS3 continued to demonstrate a variability of ~ 15% in its X-axis S-Curve (as determined from repeated observations of a standard star). This effectively rendered FGS3 unreliable for observing close (separations < 20 mas) binary systems. However, FGS1r has demonstrated repeatability at the 2% level, implying reliable measurements of binary systems down to 7 mas.
Figure 5.5 illustrates FGS3's persistent variability and FGS1r's stability over comparable timescales. Figure 5.5a shows FGS3's inherent variability in the S-Curves of the same point source over a 102-day span in 1997. Note this intrinsic variability in the instrument is indistinguishable from its interferometric response to a 15 mas binary with
m = 0.5 mag (when compared with a point-source, as shown in Figure 5.5c). In contrast, the stability of FGS1r (Figure 5.5b) easily permits detection of the 15 mas binary system (Figure 5.5d) when compared to a point-source. We note the "difference" seen in Figure 5.5d are due to systematic changes in the observed interferogram (i.e., the object is resolved), not random effects.
As was discussed in chapter 4, FGS1r has shown a slow "evolution" of its y-axis S-curve. This should not compromise the reliability of this instrument for observing close binary systems; STScI will continue to observe calibration standards in each cycle as needed so that GOs have access to calibration data appropriate of a given epoch.
Interferometric Response and Source Color
The morphology and amplitude of the S-Curve is sensitive to the spectral color of the source. The point-source reference S-Curve used for comparison to the observed fringes of a science target should match the color of the target to within
Figure 5.5: Temporal Stability: FGS3 v. FGS1r
The two plots at the top compare the fringes of FGS3 (left) and FGS1r (right) from observations of point sources taken at two different times. Clearly FGS3 shows significantly more variability than FGS1r. The plots in the bottom row compare the FGS3 and FGS1r fringes of a point source to that of a 15 mas binary. Given FGS3's temporal variability (top left plot), the detection of the binary (bottom left plot) is questionable, unlike the reliable detection by FGS1r.
The point-source calibration S-Curves are obtained only at the center of the FGS1r FOV. Other locations in the FOV are not routinely calibrated.
Table 5.3: Library of cycle 10 calibration point source S-curves
Transfer Mode Scale as a Function of HST Roll Angle
Testing of FGS1r during its commissioning in Cycle 7 revealed that the measured separation and position angle of the stars in a binary system is sensitive to the system's orientation relative to the interferometer axis and hence the HST roll angle. Over time, as a system is observed at a variety of HST roll angles, this introduces systematic errors into the derivation of the binary's apparent orbit. The error in the measured separation of the stars can be as large as ~ 1% of the true projected separations, so measurements of wide binaries are affected more than those of close systems. The effect is believed to be due to a small rotation error of the Koesters prism(s) about the normal to its entrance face.
During Cycle 9 a wide binary (KUI 83, component separation ~0.3") was observed with FGS1r in Transfer mode at three different HST roll angles (V3roll = 25, 43, 60 degrees). The measured total separation of the components was constant to about 1 mas, indicating that the scale is not dependent upon vehicle roll, in contradiction to the Cycle 7 results. STScI will monitor this aspect of FGS1r's performance, but at a low frequency (approximately every 2 to 3 years).
5.3 Linking Transfer and Position Mode
Observations
It is possible to use the FGS in both Transfer and Position mode during a given observing session (visit). As was mentioned in Section 3.4, by using Transfer mode observations to determine a binary system's true relative orbit, and using Position mode observations of nearby reference stars (and perhaps the binary as well) to determine the binary's parallax, the system's total mass can be derived. Furthermore, if the data are of sufficient quality, i.e., if the uncertainty in the position of each component with respect to the reference stars is small compared to the semi-major axis of the binary's orbit, then the motion of each component about the system's barycenter can be determined. From this information, the mass ratio, and hence the mass to luminosity ratio of each of the two stars, can be calculated.
Investigations of an extended source, such as a giant star, can also benefit from a combination of Transfer and Position mode observations. If the FGS in Transfer mode can resolve the disk and measure its angular size, and nearby stars are measured in Position mode to derive the object's parallax, then the physical size of the disk can be determined.
In order to achieve these scientific objectives, the Transfer mode data must be related to the Position mode data. If the binary is observable in Position mode, then it is straightforward to determine the offsets between the Position mode reference frame and Transfer mode positions. If the binary cannot be observed in Position mode, then the task of relating the Transfer data to the Position data is more complex.
Linking a Transfer mode observation of a binary system to Position mode observations of reference stars in the same visit requires that the x,y coordinates of each of the binary's components, derived from analysis of the Transfer function, be mapped onto the same x,y coordinate system as the Position mode observations (the visit level "plate"). This implies that all pertinent corrections and calibrations applied to Position mode data must be applied to the Transfer mode centroids, i.e., visit-level corrections for low frequency oscillations of the spacecraft's pointing, FOV drift, the OFAD, and the differential velocity aberration. The level of difficulty in accomplishing this task depends on the structure of the binary (i.e., the separation of the components and their relative brightness).
More information on analysis techniques can be found in the
HST Data Handbook.5.4 Cycle 13 Calibration and Monitoring Program
A short summary is given for each FGS1r calibration and monitoring observation included in the Cycle 13 calibration plan. For specific information, please refer to the STScI FGS web page (under the topic FGS and Calibration Plans") and to the HST Schedule and Program Information web page:
http://www.stsci.edu/hst/scheduling/program_information5.4.1 Active FGS1r Calibration and Monitoring Programs
- Prop 10386: Long Term Monitoring of FGS1r in Position mode
- The open cluster M35 will be observed six times per year to evaluate the stability of the FOV, plate scale, and optical field angle distortions (OFAD) in FGS1r. Products will include calibration database parameters which remove these effects in science data. Additional calibrations will be serendipitously performed as well, including (but not limited to) monitoring the FGS1r photometric calibration, lateral color (shift of a star's centroid as a function of spectral color due to FGS1r's refractive optics), and the F583W/F5ND cross filter calibration at several locations in the FOV.
- Prop 10387: Monitoring FGS1r's Interferometric Response as a Function of Spectral Color
- Unresolved stars of a variety of (B - V) colors will be observed in Transfer mode to calibrate the effect of color on a point-source S-Curve. In addition, each object will be observed in Position mode to help calibrate the POS/TRANS offset, and for the fainter stars, the F583W/F5ND cross filter offset, as a function of color. These data will provide the GO with a library of appropriate point-source templates. This proposal also monitors the temporal stability of the S-curves since the target list includes stars that have been observed in Cycles 8 and 9. The measurements from this proposal will be made at the center of the FGS FOV only.
5.5 Special Calibrations
The Cycle 13 calibration program will be defined a few months after the Phase II deadline for approved programs. It is expected that the same calibrations outlined here for recent cycles and the current Cycle 13 plan will be maintained for Cycle 14.
It is the intention of STScI to develop a calibration program that most effectively balances the needs of the community for obtaining excellent science results from the instrument with the limited resources available(e.g., a nominal limit of 10% time available for calibration). Common uses of the instrument will be fully calibrated.
In special circumstances proposers may wish to request additional orbits for the purpose of calibration. These can be proposed in two ways and should be for calibrations that are not likely to be in the core calibration programs. An example of a non-core calibration would be one that needs to reach precision levels well in excess of those outlined in Tables 5.1 and 5.2.
The first type of special calibration would simply request additional orbits within a GO program for the purpose of calibrating the science data to be obtained (see Section 4.3 of the CP). In this case the extra calibration would only need to be justified on the basis of the expected science return of the GO's program.
The second type of special calibration would be performed as a general service to the community via Calibration Proposals (Section 3.6 of CP). In this case the calibration observations should again be outside the core responsibilities of the FGS group to perform, and furthermore should be directed at supporting general enhancement of FGS capabilities with the expectation of separately negotiated deliverables if time is granted.
Proposers interested in obtaining either type of special calibration should consult with Instrument Scientists from the FGS Group via questions to the Help Desk at least 14 days before the proposal deadline in order to ascertain if the proposed calibrations would be done at STScI in the default program.
Observations obtained for calibration programs will generally be flagged as non-proprietary.
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