List of Figures Figure 1.1: FGS Interferometric Response (the "S-Curve") Figure 1.2: FGSs in the HST Focal Plane (Projected onto the Sky) Figure 1.3: FGS Star Selector Geometry Figure 2.1: FGS1r Optical Train Schematic Figure 2.2: Light Path from Koesters Prisms to the PMTs Figure 2.3: The Koesters Prism: Constructive and Destructive Interference. Figure 2.4: Full Aperture S-Curves of the Original FGSs Figure 2.5: Improved S-Curves for Original FGSs when Pupil is in Place Figure 2.6: FGS1r S-Curves in Full Aperture Across the Pickle Figure 2.7: FGS Proposal System and Detector Coordinate Frames Figure 2.8: FGS1r Filter Transmission Figure 2.9: PMT Efficiency Figure 3.1: Comparison: PC Observation v. FGS Observation Figure 3.2: Simulated PC Observations v. FGS Observations of a 70mas Binary Figure 3.3: Comparison of FGS1r and FGS3 Transfer Mode Performance Figure 3.4: Relative Orbit of the Low-Mass Binary System Wolf 1062 AB Figure 3.5: Mira-type variable with a resolved circumstellar disk Figure 3.6: Flare Outburst of Proxima Centauri as Observed with FGS3 Figure 3.7: Triton Occultation of the Star TR180 as Observed by FGS 3 Figure 4.1: Default FESTIME as a Function of V Magnitude for F583W FGS1r: NEA as a Function of Magnitude and FESTIME Figure 4.2: A Sample Visit Geometry Figure 4.3: .Binary S-Curves Generated from FGS1r X-Axis Data Figure 4.4: FGS1r (F583W) S-Curves: Single and Co-Added Figure 4.5: Evolution of S-curve morphology along the FGS1r Y-axis 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: FGS2 Guide Star Motion at the Onset of a Day/Night Transition Figure 5.4: Effects of Jitter on an FGS1r S-Curve (single scan) Figure 5.5: Temporal Stability: FGS3 v. FGS1r Figure 6.1: Example 1: Field of View at Special Orientation Figure 6.2: Example 2: Field of View at Special Orientation Figure 6.3: Example 3: Trans + Pos Mode Visits Figure 6.4: Example 4: Trans + Pos Mode Exposures Figure 7.1: CALFGSA Common Processing Tasks Figure 7.2: CALFGSA Transfer Mode Processing Tasks Figure 7.3: CALFGSB Position Mode Processing Figure A.1: Location of IFOV as FGS Acquires a Target Figure A.2: Offset of True Null from Sy= 0 Figure A.3: X,Y Position in Detector Space of FGS 3's IFOV During WalkDown to FineLock and Subsequent Tracking of a Star in FineLock Figure B.1: FGS1r S-Curves: Before and After AMA Adjustment Figure B.2: FGS1r S-Curves: First Six Months After AMA Adjustment Figure B.3: FGS1r S-Curves: Second Six Months After AMA Adjustment Figure B.4: Optimized FGS1r S-Curves Used in Angular Resolution Test Figure B.5: FGS1r Transfer Function: Change in Angular Separation of a Binary Figure B.6: FGS1r Transfer Function Amplitude w/ Binary Separation