1 Calibration of Complex Instrument Systems Using the HST Fine Guidance Sensor Example July 20, 2005 Yale Astrometry Workshop

2 Who are we?

3 Topics The Goals Overview of an HST Fine Guidance Sensor (FGS) Error Budgets and Modeling Error Sources On-orbit Calibrations

4 The Goals The two priority goals for HST Astrometry with an FGS were: 1.Perform relative positional astrometry (POS Mode) to 2.8 mas, rms 2.Improve on orbital element information and mass estimates of binary and multi-body star systems (TRANS Mode) This presentation concentrates on goal #1.

5 FGS Overview HST contains three Fine Guidance Sensors (FGS) –Two of three FGS’s are required for guidance One controls vehicle pitch and yaw The second controls vehicle roll –The third is used as a scientific instrument used for astrometry Hubble’s focal plane Courtesy:

6 FGS Overview Interferometer Star Selector Assembly Filter Wheel POM Collimating Asphere (cell only visible) PMTs Latch

7 FGS in Danbury

8 FGS at KSC

9 FGS Overview Guidance Each FGS Has 42 precisely aligned precision optical elements Guidance to 14.5 mv star 2.8 mas rms positional accuracy Probability of acquisition greater than 98% Astrometric Science Acquires stars to 18 mv Used in the discovery of extra solar planets Used to determine the mass of extra solar planets

10 FGS Overview Collimator and Field Selection Optics The FGS has two main optical subassemblies –Collimator and field-selection optics (two Star Selectors) scan the FGS FOV and re-orient the collimated beam onto the interferometer –Two Koesters prism white-light interferometers and their PMTs, sense wavefront tilt (pointing error) in X and Y. Interferometer portion of FGS

11 FGS Overview Collimator and Field Selection Optics Collimator Star /Selectors portion of the FGS takes a target from the FGS pick-off mirror, collimates the light and re-orients the beam onto the interferometer From Collimating Asphere

12 FGS Overview Collimator and Field Selection Optics The combination of Star Selector A and B (SSA and SSB) rotation allows for target accessibility across the entire FGS FOV 6.77 degrees X, asec Y, asec   Lever arms  A =  B : scan in azimuthal direction  A = -  B : scan in radial direction FGS FOV in object space

13 FGS Overview Collimator and Field Selection Optics Star Selector B X, asec Y, asec   Lever arms  A =  B : scan in azimuthal direction  A = -  B : scan in radial direction FGS FOV in object space = 6.77 degrees B Star Selector Collimated beam from Star Selector A AA BB R

14 FGS Overview Collimator and Field Selection Optics in which, R is the radial projection on the FGS FOV, Φ is the azimuth angle measured from X = 0 to R, and M is the magnification The Star Selector parameters are used to generate the following coordinates:

15 FGS Overview Collimator and Field Selection Optics Star Selector Readout Method –Each Star Selector is associated with a 21-bit optical encoder. –The word (or bit pattern) is divided into a most significant bit (MSB) and least significant bit (LSB) to obtain the star location in servo angle space.

16 FGS Overview Collimator and Field Selection Optics Potential Error Sources Uncompensated opto-mechanical distortion can cause errors in the relative position measurements of stars Possible contributors to opto-mechanical distortion: –Pick-off mirror, asphere, and upper and lower folds of SSA occur prior to collimated space. Local tilts (figure error) in each surface need to be examined in amplitude and frequency to assure no negative impact on upper level performance number. – SSA and SSB zero point (  A and  B in previous chart) uncertainty must be examined to assure no negative impact on Astrometry performance –SSA and SSB deviation angles (  A and  B, lever arms in previous chart) uncertainty must be examined to assure no negative impact on performance

17 FGS Overview Collimator and Field Selection Optics Potential Error Sources Uncompensated encoder errors may also cause errors in the relative position measurements of stars. Encoder errors that should be investigated include: –Repeatability in MSB patterns on the encoder –Repeatability of LSB patterns on the encoder –Encoder wobble Filter wedge in the FGS filters have a DC component and a dispersive effect (lateral color)

18 FGS Overview The Interferometer S-curve produced in one axis (ideal modulation 1.4) Tracking signal – Proportion gain obtained from the linear region

19 FGS Overview The Interferometer Photomultiplier Tubes CB A Koester's Prism S- curve A R B R C T B T A T C R B R B T /4 delay A T = transmitted wavefront A R = reflected wavefront Incoming Wavefront A B

20 FGS Overview The Interferometer Pointing error causes interferometric fringes to appear in pupil image Fringes nulled with no pointing error Fringes appear with pointing error: -signal increases in one PMT, decreases in other

21 FGS Overview The Interferometer The measured level of intensity, as sensed by each photomultiplier tube, is a function of wavefront tilt. The resulting signal modulation at one value of wavefront tilt is: The signal resulting from Q as a function the wavefront tilt in milliarcseconds is the S-curve

22 FGS Overview The Interferometer

23 FGS Overview The Interferometer Error Sources Possible contributors to distortion errors include: –PMT mismatch which contribute to lateral color –Temporal changes in pupil alignment as the FGS desorbs moisture (eventually stabilizes) Errors in photometric calibration include: –Temporal changes in field stop alignment from desorption (eventually stabilization occurs) Contributors to S-curve signal degradation include: –Pupil misalignment at Koester’s prism –Field dependent misalignment of pupil to Koester’s prism –Refurbished FGSs contain an actuated fold mirror for on-orbit re- alignment

24 FGS Overview Modes of Operation for Astrometry Searching for a target star (FGS visual magnitude range: 18 to 9 ) Locking on to the chosen star interferometrically Star Selectors generate patterns with feedback from error signals

25 FGS Overview Modes of Operation for Astrometry POS Mode –Lock onto target and integrate on linear region of S-curve –Used for measuring relative star positions TRANS Mode (Transfer Scan, S-curve) –Center up and scan through the target several times –Used for computing orbital elements and mass. Co-add and smooth 10 S-curves

26 Error Budgets Error budgets (or performance estimates) are assembled prior to and during design phase –They are updated as the design progresses –They are updated after on-orbit calibration The top level Astrometry budget is presented. –Source are assumed to be independent and therefore RSS’d. This presentation places emphasis on portions of the calibration entry 2.8Astrometry Error (mas) 0.74Dominant Guide Star 1.22Secondary Guide Star 0.53SSM/PCS 2.04Astrometry Star 0.59OTA/OCS 1.03Calibration

27 Error Budgets* * HST STR-20 HST 32-KB Astrometry Error Budget

28 Distortion Calibration Sources of distortion –OTA/FGS optical design (some residual distortion exists) –Manufacturing uncertainties Conic constant uncertainties –OTA –Asphere –Five element corrector group Alignment uncertainties –Optical alignments –Clocking and deviation angle errors in SSA and SSB –Figure error in optical elements prior to collimated space Pick-off Asphere SSA upper and lower folds –Encoder induced distortion Least significant bit repeatability of FOV Most significant bit repeatability over FOV

29 Method of Calibration (for Distortion) How do we characterize the distortion? –Mathematical function –Subtraction maps Mathematical Function –If possible use a function with the following characteristics Find a function that characterizes (at least) the distortion and is stable for least squares fits Find a function that requires minimizes computations. Use an orthogonal polynomial Distortion team used an X,Y based polynomial that was requested for PCS use.

30 Distortion Calibration How well does the polynomial fit the distortion signature? 1.Generate design distortion at various locations in the FGS FOV and fit the data to the polynomial 2.Measure the distortion and fit the data to the polynomial. 3.Model the distortion effects from manufacturing uncertainties and fit the data to the polynomial. 4.Repeat steps 1 through 3 with noise added to the data.

31 Distortion Calibration (The Polynomial) Uncompensated (design) telescope distortion is about 5 arseconds over the FGS FOV it fits well to a radially symmetric polynomial to a few tenths of a milliarcsecond (mas) –Field dependent magnification is a radial function in the aligned case –X,Y are local FGS coordinates Uncompensated optical misalignments can be as large as 28 mas and therefore, must be considered in the function. With misalignments and tilt terms (figure error) in the elements, radial symmetry is perturbed and the resulting polynomial produces a better overall fit

32 Distortion Calibration (Polynomial Verification - Optics) Wavefront tilt terms (figure) in the pick-off, asphere, and upper and lower fold mirrors were measured and converted to x,y tilts in mas surface terms in object space The tilts in x and y were modeled with the two 11 term polynomials, yielding a residual of about 0.55 mas (for all elements) Uncertainties in optical alignment and conics were modeled and fit to the polynomials to an accuracy of about 0.3 mas Tilt term locations on the asphere

33 Distortion Calibration (Polynomial Verification – Encoder Errors) The accuracy in the MSB (14 bit word) of the optical encoder was measured for each star selector. –The angles were converted to x,y local FGS object space –The polynomial characterized the 14- bit error to about 0.4 mas The LSB (7-bit fine word) was measured at several locations in the FGS FOV. –The angles were converted to x,y local FGS object space –The variations were of high spatial frequency and could not be characterized with the distortion polynomial. A look-up table was produced for the 7- bit error. –Error in budget reflect repeatability of measurements to about 0.22 mas 14-bit error in encoder 14-bit Error 7-bit Error

34 Distortion Calibration (Polynomial Verification – Encoder Errors) Star Selector clocking and deviation angles were not adequately characterized by the distortion polynomial - residuals were about 30 mas. –Solution: solve for the parameters in the least squares function (Loss Function) –With a similar expression in Y. X and Y are local FGS coordinates in terms of direction cosines and the subscripts, I and j refer to the i th star in the j th frame. – X and Y are functions of the Star Selector clocking and deviations angle –The manufacturing uncertainties for Star Selector clocking and deviation angles were modeled in the “Star Selector Equations”, converted to X,Y and characterized via least squares techniques The process was repeated with noise added (Gaussian jitter for the spacecraft and Poisson noise for the target star)

35 Distortion Calibration On-orbit Calibration Once all error sources are known and characterized in the Loss Function, simulate an on-orbit calibration for distortion by 1. Distorting star positions in the FGS FOV 2. Adding noise to the distorted star location Solve for the true star positions. Distorted positions in “+”

36 Distortion Calibration On-orbit Calibration For on-orbit calibrations use the overlapping plate method in which the relative star positions are invariant from one rotation of the FGS FOV to the next. Use of calibrated star fields (calibrated plate) is a good starting point, but the distortion algorithm actually improves on the plate accuracy (relative position accuracy). The following LOSS function was produced for the on-orbit calibration of the FGSs:

37 Distortion Calibration On-orbit Calibration the LOSS Function Algorithm team included HST Astrometry Team, Goodrich, CSC, MSFC, and GSFC

38 Distortion Calibration On-orbit Calibration Get adequate distortion information and coverage over the FGS FOV with 25 to 30 stars observed per frame (orbit) Utilize 10 to 20 frames (orbits) at different orientations to gather data. FGS/HST orientations for distortion calibration Courtesy B. McArthur et al, HST Calibration Workshop 2002

39 During data reduction, remove known errors from observed stars, prior to performing the least squares fit. Use the best starting values in the Loss Function Schedule stability checks every 3 to 4 months to determine changes and update the distortion parameters. FGS Met Positional Requirements Distortion Calibration On-orbit Calibration

40 Additional calibrations performed on the collimator/field selection optics portions of the FGS include: –Magnification 1.Use the calibrated plate angular separations from star pairs for the intermediate solution and a known asteroid trajectory for the high accuracy solution. 2.Solve for the following equation in both cases: 3.Iterate between magnification and distortion to converge to the best solution –Cross Filter Calibration 1.To remove the effects of filter wedge observe the change in location of a star of known color magnitude as the filter type changes. 2.Repeat the test for several stars covering a wide range of color magnitudes –Lateral Color A Mention of Additional On-orbit Calibrations

41 The most important calibration performed on the interferometer portion of the FGS is S-curve optimization –The OTA wavefront, g-release and desorption degrade the ground optimized S-curve –Align the pupil to the face of the Koester’s prism with a mechanized fold flat 3. Photometric calibration is performed but stabilizes after field stop motion (due to desorption) ends. A Mention of Additional Calibrations Optimized S-curve Ground to orbit change

42 Calibration Results Courtesy of Lowell Observatory Franz/Wasserman Fits to GL473 star system

43 Summary While the FGS is a complicated instrument its error sources were identified and calibration procedures were modeled and well understood. The calibration process and results led to significant scientific discoveries and improvements in astrometric measurements. FGS Science includes: –The measurement of the precise mass of the planet Gliese 876 –FGS resolves the discrepancy between Hipparcos distance estimates to Pleiades and older measurements –Measurement of the diameters of a special class of pulsating star called Mira variables, which rhythmically change size. The results suggest these gigantic, old stars aren't round but egg-shaped. –Astrometry of two high--velocity stars –Binary star orbital elements –Discovery of multi-body systems