9.2 FGS Design

9.2.1 FGS Optics

The direction of the exit ray depends upon the incoming beam's angle of incidence on the SSA assembly, and therefore the rotation position of SSA and the beam's point of origin on the aspheric mirror which is, in turn, determined by the angle between the spacecraft's optical axis (V1) and the position of the star on the sky.

After exiting the SSA assembly the ray encounters a field stop to minimize scattered light and to narrow the field of view. The four mirrors of the Star Selector B (SSB) assembly receive the ray and redirect it through the filter wheel assembly and a plane fold flat mirror (FF3) reflects it onto the polarizing beam splitter. Like the SSA assembly, the SSB assembly can be commanded to rotate within HST's focal plane. Together the SSA and SSB assemblies transmit to the polarizing beam splitter only those photons originating from a narrowly defined direction, masking out all but a small (5" x 5") area of sky.

The polarizing beam splitter divides the incoming unpolarized light into two linearly plane polarized beams with orthogonal polarizations, each having roughly half the incident intensity, and directs them to the two Koesters prisms and their associated optics, field stops, and photomultiplier tubes (see Figure 9.1). Each of the two output rays from the polarizing beam splitter fall upon the face of the appropriate Koesters prism.

The Koesters prisms are constructed of two halves of fused silica joined together along a surface coated to act as a dielectric beam splitter. The dielectric performs an equal intensity division, introducing a 90 degree phase difference between the reflected and transmitted portions of the beam, with the transmitted lagging the reflected. This division gives the Koesters prism its interferometric properties because the beam reflected from one side of the prism, when joined with the transmitted beam from the other side, constructively or destructively interferes to a degree depending upon the angle between the incoming wavefront and the entrance face. Each Koesters prism thus emits two collimated exit beams whose relative intensities depend upon the tilt of the incident wavefront. Each beam is then focused and passed through a field stop to illuminate the surface of a photomultiplier tube (PMT) which records the number of photons received during each 25 msec interval.

The collimated beam entering each Koesters prism can be characterized by a propagation vector. The Koesters prism senses the tilt of this incident wavefront only in the direction perpendicular to the plane of the dielectric surface. Small rotations of the star selector A and B assembles can change the direction of the propagation vector, and hence the tilt of the incident wavefront at the face of the Koesters prism. When the component of the wavefront's propagation vector perpendicular to the plane of the dielectric surface is zero, a condition of interferometric null results, and the relative intensities of the two emergent beams, measured by the PMTs, will ideally be equal. Meanwhile, the other Koesters prism is sensitive to the wavefront's tilt in the orthogonal plane.

Figure 9.1 schematically displays the important optical and mechanical components of an FGS. Each Koesters prism is sensitive to the tilt of the wavefront about an axis which is parallel to the face of the prism and in the plane of the dielectric beam splitter (the shaded area within each prism).

Figure 9.1: The FGS Optical Train

An (x,y) coordinate system maps the detector space of an FGS. The Koesters prisms are aligned such that one is sensitive to angular displacements along the x direction, the other along the y direction. Because each Koesters prism has two associated PMTs, each FGS has four PMTs in all. The two PMTs associated with the x-axis Koesters prism are labeled PMTXA and PMTXB. The other pair, associated with the y-axis Koesters prism, are labeled PMTYA and PMTYB.

The (x,y) location of the IFOV in the total FOV is determined from the rotation angles of the star selector A,B assemblies. Each FGS has its own detector space (x,y) coordinate system which maps into HST's (V1,V2,V3) coordinate system. FGS 2, and FGS 3 are nominally oriented at 90, and 180 degrees with respect to FGS 1, but small angular deviations are present. The FGS-to-FGS alignment matrix in the onboard flight software accounts for these deviations. Figure 9.2 and Figure 9.3 show the FGSs and their coordinate systems in the HST focal plane.

Figure 9.2: FGS Field of View (pickle) the HST Focal Plane with Local (x,y) Coordinate System Related to HST (V2,V3) System.

Figure 9.4: Emergent Beams from Koesters Prism and Photo-multiplier Tubes. The Koesters prism is sensitive to the tilt of the wavefront about an axis normal to the page and intersecting point B.

Figure 9.5: Internal Reflection and Transmission of the Beam Entering the Koesters Prism on the AC Face

S_x = (A_x - B_x) / (A_x + B_x)

where A_x is the photon count from PMTXA (accumulated over 25msec), and B_x is the count from PMTXB. The y-axis S-curve is computed in a similar way. Figure 9.6 shows the S-curves for the x and y axes observed near the center of the field of view of FGS 3. When the IFOV is more than 100 mas from the location of interferometric null, the PMTs of a given channel record nearly equal intensities. But closer to the interferometric null a signal emerges as the Koesters prism produces beams of different relative intensities. The so-called zero point crossing between the +/- peaks of the S-curve ideally occurs at interferometric null. Note however, that the relative sensitivities of the PMTs and the optical paths traversed by the beam after emerging from the Koesters prism are not identical, and therefore, the zero point crossing may not occur exactly at the interferometric null. (This effect is accounted for in the data reduction process.) Because a one-to-one relationship exists between the rotation angles of the Star Selector A and Star Selector B assemblies and the x,y detector space coordinates, the values of these rotation angles at interferometric null can be used to measure the position of the star in x,y detector space.

Figure 9.6: FGS 3 S-Curves of Upgren69 in F583W at (x,y) = (0,0)

An FGS will display degraded S-curve performance when the collimated beam is not well centered on the face of the Koesters prism. In addition, given the presence of spherical aberration due to the misfigured primary mirror, the wavefront presented to the Koesters prism is not flat but has curvature, a fact that greatly amplifies the effects of optical misalignments. Specifically, a decentered beam in the presence of spherical aberration gives rise to coma and astigmatic aberrations, resulting in degraded S-curve characteristics.

The source of the field dependency is thought to be beam walk originating from a misalignment of the star selector B assembly with respect to the Koesters prism that changes as a function of SSB rotation angle. The Star Selectors center the beam on the face of the Koesters prisms while varying the tilt of the wavefront. If there is a clocking error in the alignment of SSB and the Koesters prism, the beam will not remain centered as SSB rotates, resulting in field dependency. Furthermore, if the amount of decentering changes with time, its effects must be monitored in order to calibrate the science data properly. The S-curve measurements in the original three FGSs indicated large decenters of the Koesters prisms in FGS 1 and FGS 2 and strong field dependency in FGS 3.

Figure 9.7 shows that the S-curves of FGS 1 and FGS 2 are not adequate for astrometric science. Only FGS 3 has S-curves with signal-to-noise ratios sufficient for precise astrometry.

Figure 9.7: Full-Aperture X and Y Axis S-curves of Original Three FGSs -Measured at the Center of Each FGS Field of View

The FF3 has been adjusted to yield near perfect S-curve performance at the center of FGS 1R's pickle. And although the S-curves of FGS 1R show field dependency, it is not as extreme as that in FGS 3. Therefore, with excellent S-curves at pickle center and improved performance (relative to FGS 3) everywhere else, FGS 1R is potentially the best astrometric science instrument onboard HST. Figure 9.9 and Figure 9.10 compare the S-curves from three positions in the pickle of FGS 3 with those from FGS 1R.

Figure 9.9: Field Dependency of FGS3 Across the Pickle