Fine Guidance Sensor Instrument Handbook for Cycle 14
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2.1 The Optical TrainChapter 2:
FGS Instrument Design
2.1.1 The Star Selectors
2.1.2 The Interferometer
2.2 FGS Detectors
2.3 HST's Spherical Aberration
2.4 The FGS Interferometric Response
2.4.1 The Ideal S-Curve
2.4.2 Actual S-Curves
2.5 The FGS1r Articulated Mirror Assembly
2.6 FGS Aperture and Filters
2.6.1 FOV and Detector Coordinates
2.6.2 Filters and Spectral Coverage
2.7 FGS Calibrations
This chapter details the design of the FGS. The optical path, detectors, interferometric response, and the effect of optical misalignments and HST's spherical aberration on FGS performance are discussed in detail. Description of the apertures and available filters are provided.
2.1 The Optical Train
Each FGS comprises two orthogonal white-light, shearing interferometers, their associated optical and mechanical elements, and four S-20 photo-multiplier tubes (PMTs). For clarity, we divide the FGS optical train into two sections: The Star Selectors and The Interferometer..
2.1.1 The Star Selectors
A schematic view of the FGS optical train is shown in Figure 2.1. Light from the HST Optical Telescope Assembly (OTA) is intercepted by a plane pickoff mirror in front of the HST focal plane and directed into the FGS. The beam is collimated and compressed (by a factor of ~60) by an aspheric collimating mirror, and guided to the optical elements of the Star Selector A (SSA) servo assembly. This assembly of two mirrors and a five element refractive corrector group can be commanded to rotate about the telescope's optical axis. The corrector group compensates for designed optical aberrations induced by both the asphere and the HST Optical Telescope Assembly (OTA). The asphere contributes astigmatism, spherical aberration and coma to the incident beam. Aberrations from the OTA's Ritchey-Chretien design include astigmatism and field curvature.
After the SSA assembly, the beam passes through a field stop (not shown) to minimize scattered light and narrow the field of view. The four mirrors of the Star Selector B (SSB) assembly intercept and re-direct the beam to a fold flat mirror and through the filter wheel assembly. From there, the Articulating Mirror Assembly (AMA) reflects the beam onto the Polarizing Beam Splitter. Like the SSA, the SSB assembly rotates about a vector parallel to the telescope's optical axis. Together the SSA and SSB assemblies allow for the transmission to the polarizing beam splitter only those photons originating from a narrow region in the total FGS field of view. This area, called the Instantaneous Field of View (IFOV), is a 5 x 5 arcsec patch of sky, the position of which is uniquely determined by the rotation angles of both the SSA and SSB. The IFOV can be brought to any location in the full FOV and its position can be determined with sub-milliarcsecond precision (see Figure 1.3).
The AMA is an enhancement to the original FGS design. It allows for in-flight alignment of the collimated beam onto the polarizing beam splitter and therefore the Koesters prisms. Given HST's spherically aberrated OTA, this is an important capability, the benefits of which will be discussed in subsequent chapters.
Figure 2.1: FGS1r Optical Train Schematic
2.1.2 The Interferometer
The interferometer consists of a polarizing beam splitter followed by two Koesters prisms. The polarizing beam splitter divides the incoming unpolarized light into two plane polarized beams with orthogonal polarizations, each having roughly half the incident intensity. The splitter then directs each beam to a Koesters prism and its associated optics, field stops, and photomultiplier tubes. Figure 2.2 illustrates the light path between the Koesters prism and the PMTs.
The Koesters prisms are constructed of two halves of fused silica joined together along a coated surface which acts as a dielectric beam splitter. The dielectric layer performs an equal intensity division of the beam, reflecting half and transmitting half, imparting a 90 degree phase lag in the transmitted beam. This division and phase shift gives the Koesters prism its interferometric properties: the beam reflected from one side of the prism interferes constructively or destructively with the beam transmitted from the other side. The degree of interference between the two beams is directly related to the angle, or tilt, between the incoming wavefront's propagation vector and the plane of the dielectric surface.
Each Koesters prism emits two exit beams whose relative intensities depend on the tilt of the incident wavefront. Each beam is focussed by a positive doublet onto a field stop assembly (which narrows the IFOV to 5 x 5 arcsec). The focussed beams are recollimated by field lenses (after the field stop) and illuminate the photomultiplier tubes (PMT). The PMT electronics integrate the photon counts over 25 millisecond intervals.
The Koesters prism is sensitive to the angle of the incoming wavefront as projected onto its dielectric surface. To measure the true (non-projected) direction of the source, each FGS has two Koesters prisms oriented perpendicular to one another (and therefore a total of 4 PMTs).
Figure 2.2: Light Path from Koesters Prisms to the
PMTs
Small rotations of the star selector A and B assemblies alter the direction of the target's collimated beam, and hence the tilt of the incident wavefront with respect to the Koesters prisms. Figure 2.3 is a simplified illustration of Koesters prism interferometry. As the wavefront rotates about point b, the relative phase of the transmitted and reflected beams change as a function of angle
Figure 2.3: The Koesters Prism: Constructive and Destructive Interference.. When the wavefront's propagation vector is parallel to the plane of the dielectric surface (b-d) a condition of interferometric null results, and the relative intensities of the two emergent beams will ideally be equal. When
2.2 FGS Detectors
The FGS PMTs (four per FGS) are end-illuminated, 13 stage venetian blind dynode S-20 photon-counting detectors with an effective photocathode area of about 4 mm. The A and B channels for each FGS interferometric axis operate independently. The PMTs are sensitive over a bandpass of 4000-7000A, with an efficiency of ~ 18% at the blue and diminishing linearly to about 2% at the red end.
The FGS1r dark counts for each channel are given in Table 2.1.
Table 2.1: FGS1r Dark Counts
1Values based on an average of 40Hz PMT counts and associated standard deviations.
2.3 HST's Spherical Aberration
The interferometric response of the Koesters prism arises from the difference in optical path lengths of photons entering one side of the prism to those entering the other side (and therefore to the tilt of the wavefront). A photon transmitted by the dielectric surface within the prism is re-combined with one which has been reflected by the surface. Both of these photons were incident on the prism's entrance face at points equidistant from, but on opposite sides of, the dielectric surface. The degree to which they constructively or destructively interfere depends solely on their difference in phase, which by design, should depend only upon the wavefront tilt. Any optical aberration in the incident beam that does not alter the phase difference of the recombining beams will not affect the interferometric performance of the FGS. Such aberrations are considered to be symmetric.
No correction for the HST's spherical aberration is incorporated in the original or refurbished FGSs. Though the Koesters prisms are not sensitive to symmetric aberrations (e.g., spherical aberration), small misalignments in the internal FGS optical train shift the location of the beam's axis of tilt ("b" in Figure 2.2 and in Figure 2.3) effectively breaking the symmetry of the OTA's spherical aberration. This introduces an error in the phase difference of the re-combining photons and degrades the interferometric response.
With HST's 0.23 microns of spherical aberration, a decentering of the wavefront by only 0.25 mm will decrease the modulation of the S-Curve to 75% of its perfectly aligned value. If the telescope were not spherically aberrated (i.e., if the wavefront were planar) misalignments up to five times this size would hardly be noticeable. The impact of HST spherical aberration and the improved performance of FGS1r are discussed in the next sections.
2.4 The FGS Interferometric Response
FGS interferometry relates the wavefront tilt to the normalized difference of intensity between the two beams emerging from the Koesters prism (see Figure 2.3). As the tilt varies over small angles (as when the IFOV scans the target), this normalized intensity difference defines the interferogram, or "S-Curve", given by the relation,
Sx = (Ax - Bx) / (Ax + Bx),where Ax and Bx are the photon counts from PMTXA and PMTXB respectively, accumulated over 25 milliseconds intervals when the IFOV is at location x. The Y-axis S-Curve is defined in an analogous manner. Figure 1.1 shows an S-Curve resulting from several co-added scans of a point source.
Because the FGS is a white light, broad bandpass interferometer, its S-Curve is essentially a single fringe interferogram. The spectral incoherence of white light causes the higher order fringes to be strongly damped. Because the S-Curve is a normalized function, its amplitude is not sensitive to the target's magnitude provided the background and dark contributions to the input beam are relatively small. However, as fainter targets are observed (i.e., V
), the S-Curve's amplitude will be reduced (background and dark counts contributions are not coherent with light from the target). Usually the effect of dark + background is easily calibrated and therefore does not compromise the instrument's scientific performance in either Position or Transfer mode.
2.4.1 The Ideal S-Curve
The intensity of each beam exiting the Koesters prism is the integral of the intensity of each ray along the entire half-face of the prism. When the IFOV is more than 100 milliarcseconds (mas) from the location of the interferometric null, the PMTs of a given channel record nearly equal intensities since the re-combining beams are essentially incoherent over such large optical path differences (the photons constructively and destructively interfere at approximately the same rate). Closer to the interferometric null (at about +/- 40 mas from the null), a signal emerges as the Koesters prism produces exit beams of different relative intensities.
Maximum fringe visibility of the ideal S-Curve min/max extremes is 0.7, occurring at about -20 and +20 mas for the positive and negative fringe maxima, respectively. Thus the "peak-to-peak" amplitude is 1.4. An ideal S-curve is inverse symmetric about the central "zero point crossing". This crossing occurs when the wavefront's propagation vector is normal to the Koesters prism entrance face, a condition referred to as interferometric null (jargon derived from guide star tracking or Position mode observing for when a target's fine error signal has been nulled out).
2.4.2 Actual S-Curves
HST's Spherical Aberration
The characteristics of real S-Curves depend on several factors: the quality and fabrication of the internal optics, the relative sensitivity of the PMTs, the alignment of the internal optics, the filter in use, the color of the target, and the effect of the spherically aberrated HST primary mirror. Some of the effects can be removed during processing and calibration, while others limit the performance of the instrument.
Referring back to Figure 2.3, if the tilt axis is of the incident beam is not at point `b,' the beam is said to be decentered with respect to the Koesters prism. Given the presence of spherical aberration from the HST's misfigured primary mirror, the wavefront presented to the Koesters prism is not flat but has curvature. This greatly amplifies the effects of misalignments in the FGS optical train. A decentered spherically aberrated beam introduces a phase error between the re-combining transmitted and reflected beams, resulting in degraded S-Curve characteristics. The interferometric response (in filter F583W) of the 3 original FGSs are shown in Figure 2.4. Decenter emerges as morphological deformations and reduced modulation of the fringes. Of the original three FGSs, FGS3 was the only instrument with sufficient fringe visibility to perform as an astrometric science instrument.
Figure 2.4: Full Aperture S-Curves of the Original FGSs
The degrading effects due to the misalignment of an FGS with the spherically aberrated OTA can be reduced by masking out the outer perimeter of the HST primary mirror. This eliminates the photons with the largest phase error. The 2/3 PUPIL stop accomplishes this and restores the S-Curves to a level which allows the FGS to track guide stars anywhere in the FOV. Unfortunately, it also blocks 50% of the target's photons, so nearly a magnitude of the HST Guide Star Catalog is lost. Figure 2.5 shows the improvement of the S-Curve signature with the 2/3 PUPIL in place relative to the full aperture for the three FGSs. The PUPIL has been used for HST guiding since launch.
Figure 2.5: Improved S-Curves for Original FGSs when Pupil is in Place
Field Dependence and Temporal Stability of the S-Curves
The Star Selectors center the beam on the face of the Koesters prisms while varying the tilt of the wavefront. Errors in the alignment of either the SSA or SSB with respect to the Koesters prisms will decenter the beam on the face of the prisms. Since the servos rotate over large sky angles to bring the IFOV to different positions in the Field of View, misalignments of these elements result in field-dependent S-curves. For this reason, Transfer mode observations should be restricted to the center of the FGS FOV, the only location supported by observatory calibrations.
The S-Curve measurements in the original three FGSs indicated large decenters of the Koesters prisms in FGS1 and FGS2 and field dependency in FGS3. FGS1r also shows field dependence, as can be seen for three positions across the FGS1r FOV in Figure 2.6 (however, note that its x,y fringes are near ideal at the FOV center).
Temporal stability of S-Curves is also a concern. Monitoring of the FGS3 S-Curves along the X-axis showed the instrument suffered from variability of such amplitude that it could not be used to reliably resolve binary systems with projected X-axis separations less than ~ 20 mas. Conversely, FGS1r is far more stable. Its interferometric fringes show much less temporal variation, allowing the observer to confidently distinguish the difference between a point-source and a binary star system with a separation of 8 mas. This, in part, prompted the switch to FGS1r as the Astrometer for Cycle 8 and beyond.
Figure 2.6: FGS1r S-Curves in Full Aperture Across the Pickle
2.5 The FGS1r Articulated Mirror Assembly
FGS1r has been improved over the original FGS design by the insertion of the articulating mirror assembly (AMA) designed and built by Raytheon (formerly Hughes Danbury Optical Systems, currently BFGoodrich Space Flight Systems). A static fold flat mirror (FF3 in Figure 2.1) in FGS1r was mounted on a mechanism capable of tip/tilt articulation. This Articulating Mirror Assembly (AMA) allows for in-orbit re-alignment of the wavefront at the face of the Koesters prism. An adjustable AMA has proven to be an important capability since, given HST's spherical aberration, even a small misalignment degrades the interferometric performance of the FGS. On orbit testing and adjustment of the AMA were completed during FGS1r's first year in orbit. A high angular resolution performance test executed in May 1998 demonstrated the superiority of FGS1r over FGS3 as a science instrument. Therefore, FGS1r has been designated the Astrometer and has replaced FGS3 in this capacity. Information on the FGS1r calibration program can be found in Chapter 5 of this handbook.
The AMA has been adjusted to yield near-perfect S-Curves at the center of the FGS1r FOV, and an optimum compromise results for the remainder of the FOV. The variation of S-Curve characteristics across the FOV arises from "beam walk" at the Koesters prisms as the star selectors rotate to bring the IFOV to different locations in the FGS FOV. This field dependence does not necessarily impair FGS1r's performance as a science instrument, but it does restrict Transfer mode observations to the center of the FOV since it is the only location calibrated for that mode (Position mode is calibrated for the entire FOV).
2.6 FGS Aperture and Filters
2.6.1 FOV and Detector Coordinates
Figure 1.2 shows the HST focal plane positions of the FGSs as projected onto the sky. Figure 2.7 is similar, but includes the addition of two sets of axes: the FGS detector coordinate axes, and the POSTARG coordinate axes (used in the Phase II proposal instructions to express target offsets).
Each FGS FOV covers approximately 69 square arcmin, extending radially from 10 arcmin to 14 arcmin from the HST's boresight and axially 83.3 degrees on the inner arc and 85 on its outer arc. The IFOV determined by the star selector assemblies and field stops is far smaller, covering only 5 x 5 arcsec. Its location within the pickle depends upon the Star Selector A and B rotation angles. To observe stars, the star selector assemblies must be rotated to bring the IFOV to the target. This procedure is called slewing the IFOV.
The (X,Y) location of the IFOV in the pickle is calculated from the Star Selector Encoder Angles using calibrated transformation coefficients. Each FGS has its own detector space coordinate system, the (X,Y)DET axes, as shown in Figure 2.7. FGS2 and FGS3 are nominally oriented at 90 and 180 degrees with respect to FGS1r, but small angular deviations are present (accounted for in flight software control and data reduction processing). The FGS detector reference frame is used throughout the pipeline processing. The POS TARG coordinate axes, (X,Y)POS, should be used to express offsets to target positions in the Phase II proposal (Special Requirements column). See Chapter 5: Writing a Phase II Proposal for more details.
The approximate U2,U3 coordinates for the aperture reference position (default placement of a target) for each FGS and the angle from the +U3 axis to the +YDET and +YPOS Axis are given in Table 2.2. The angles are measured from +U3 to +Y in the direction of +U2 (or counterclockwise in Figure 2.7). Note that the FGS internal detector coordinate reference frame and the POS TARG reference frame have opposite parities along their respective X-axes.
Figure 2.7: FGS Proposal System and Detector Coordinate Frames
Table 2.2: Approximate Reference Positions of each FGS in the HST Focal Plane
(arcsec)
(arcsec)
2.6.2 Filters and Spectral Coverage
Filter Bandpasses
The filter wheel preceding the dielectric beam splitter in each FGS contains five 42mm diameter slots. Four of these slots house filters-F550W, F583W, F605W and F5ND-while the fifth slot houses the PUPIL stop. This stop helps restore the S-Curve morphology throughout the FOV of each FGS by blocking out the outer 1/3 perimeter of the spherically aberrated primary mirror. The filter selection for each FGS, their central wavelengths, and widths are listed in Table 2.3. The transmission curves (filters and PUPIL) are given in Figure 2.8. The PMT efficiency is given in Figure 2.9.
Figure 2.8: FGS1r Filter Transmission
Figure 2.9: PMT Efficiency
2.7 FGS Calibrations
For the most part, the calibration requirements of the current Cycle's GO science programs will be supported by STScI. For Position mode observations, this includes the optical field angle distortion (OFAD) calibration, cross-filter effects, lateral color effects, and the routine monitoring of the changes in distortion and scale across the FOV.
For Transfer mode, STScI will calibrate the interferograms (S-Curves) as a function of a star's spectral color. In addition, the S-Curves will be monitored for temporal stability.
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