1 calibration of complex instrument systems using the hst fine guidance sensor example july 20, 2005...

1

Calibration of Complex Instrument Systems Using the HST Fine Guidance Sensor Example

July 20, 2005

Yale Astrometry Workshop

2

Who are we?

Hubble Space Telescope

SIRTF IR Telescope

SPITZERHST FGSs

• Infrared Telescope Technology Testbed

• All Be Low Mass Optical System for SIRTF Mission

Chandra

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: www.STScI.edu

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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 planetsPICKOFFMIRROR

CORRECTORGROUP

STAR SELECTORB, K-MIRROR

FOLD FLAT #3

STARSELECTORA

ASPHERICCOLLIMATOR

FILTER

FOLDFLAT#4

BEAMSPLITTERAND KOESTERSPRISM

DOUBLETLENS

PINHOLELENSASSY.

STARSELECTORMIRRORS

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FGS OverviewCollimator 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.

PICKOFFMIRROR

CORRECTORGROUP

STAR SELECTORB, K-MIRROR

FOLD FLAT #3

STARSELECTORA

ASPHERICCOLLIMATOR

FILTER

FOLDFLAT#4

BEAMSPLITTERAND KOESTERSPRISM

DOUBLETLENS

PINHOLELENSASSY.

STARSELECTORMIRRORS

Interferometer portion of FGS

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• 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

SSA SSBFF3

FF4

Pick-offmirror

Koesters prism

FoldedV1 axis

V1 axis

FGS Asphere

SSA SSBFF3

FF4

Pick-offmirror

Koesters prism

FoldedV1 axis

V1 axis

FGS Asphere

From Collimating Asphere

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• The combination of Star Selector A and B (SSA and SSB) rotation allows for target accessibility across the entire FGS FOV

SSA

SSB

6.77 degrees

0

500

1000

-1000 -500 0 500 1000

X, asec

Y,

as

ec

Lever arms

A = B : scan in azimuthal directionA = -B : scan in radial direction

FGS FOV in object space

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• Star Selector B

0

500

1000

-1000 -500 0 500 1000

X, asec

Y,

as

ec

Lever arms

A = B : scan in azimuthal directionA = -B : scan in radial direction

FGS FOV in object space

=6.77 degrees

B Star Selector

Collimated beam from Star Selector A

A

B

R

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)sin(*)M

Rsin(Y

)cos(*)M

Rsin(X

)Rsin(*)sin(

)Rcos(*)cos()cos(cosa

)cos(*)sin(*)sin()cos(*)cos(cosaR

A

ABA

ABbAbA

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:

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• 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.

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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

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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)

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FGS Overview The Interferometer

X Axis Koester'sPrism

PolarizingBeam

SplittingCube

Y Axis Koester'sPrism

X axis polarizedbeam

Fold Flat 4

Fold Flat 5

Fold Flat 6YB Axis

Achrom aticCondenser

Lens YB


Lens YA


Lens XB


Lens XA

Y axis polarizedbeam

FoldFlat 6

XA Axis

FoldFlat 6

XB Axis

FoldFlat 6

YA Axis

Y A

Y B

XB SensitiveAxis

XA SensitiveAxis

YA SensitiveAxis

YB SensitiveAxis

YB InsensitiveAxis

YA InsensitiveAxis

XA InsensitiveAxis

X A

XB InsensitiveAxis

X B

Definitions of Field Stop Position Directions

+

+ +

+

+

+

+

+

CollimatedBeam fromFold Flat 3

FGS Interferometer Optical Path

View looking intothe interferometer

IS

IS

Dome

Interferom eter

+ Y

+X

FGS

Pick-offM irror

Assem bly

C Latch

Input fromTelescope

YAPM T

YBPM T

XBPM T

XAPM T

Field Stops&

Doublets

XB

YA

XA

YB

9-22-00 R .W .

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

S-curve produced in one axis

(ideal modulation 1.4)

Tracking signal – Proportion gain obtained from the linear region

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Photomultiplier

Tubes

C B A

Koester's Prism

S-curve

AR

BR

CT

BT

ATCR

BR

BT

/4 delay

AT = transmitted

wavefront

AR = reflected

wavefront

Incoming Wavefront

A B

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• 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

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• 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:

QA B

A B

The signal resulting from Q as a function the wavefront tilt in milliarcseconds is the S-curve

-0.800

-0.600

-0.400

-0.200

0.000

0.200

0.400

0.600

0.800

-300.0 -200.0 -100.0 0.0 100.0 200.0 300.0

x (milliarcseconds, object space)

Q (n

o di

men

sion

)

pointing control around null crossing

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FGS Koester’s prism interferometers can function well, even with spherical aberration, as long as optical alignment is within tolerance required for the aberration.

Ideal alignment of OTA pupil image to Koester’s prism interferometer

Pupil

1 mm misalignment of OTA pupil image to Koester’s prism interferometer

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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

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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

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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.

-0.800

-0.600

-0.400

-0.200

0.000

0.200

0.400

0.600

0.800

-300.0 -200.0 -100.0 0.0 100.0 200.0 300.0

x (milliarcseconds, object space)

Q (n

o di

men

sion

)

pointing control around null crossing

Co-add and smooth 10 S-curves

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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

2.8 Astrometry Error (mas)

0.74 Dominant Guide Star

1.22 Secondary Guide Star

0.53 SSM/PCS

2.04 Astrometry Star

0.59 OTA/OCS

1.03 Calibration

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Error Budgets*

Calibration (mas)

0.95 Jitter 0.36 Plate Scale

0.09 Star Selectors 0.42 Filter0.03 Noise0.09 Granularity 0.87 Distortion

0.63 Detector Noise 0.03 HST Optics0.36 Photon noise 0.02 Design0.04 Dark Current 0.30 Manufacture0.33 Background0.00 Cosmic Radiation 0.55 FGS Optics

0.00 Design (included above)0.71 Thermal 0.55 Manufacture

0.03 Pickoff Mirror0.01 Transfer Function Comp 0.22 Asphere

0.05 Lower Fold1.80 Non-Averaging 0.03 Upper Fold

0.41 Corrector Group0.22 Star Selectors

0.22 Fine Bits 0.44 Star Selectors0.01 Rotation Axis

0.03 Thermal (slue) 0.44 Encoder Errors (Coarse Bits)

0.31 Thermal Orb-Orb 0.42 Pointing Errors During Distortion Calibration

1.74 Chromatic Tilt

0.27 Spectral Mismatch

Astrometry Star (mas) 1.032.04

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

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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

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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.

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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.

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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

22222

22222

)()(

and

)()(

yxybyxyayMY

yxbxyxxaxMX

yxbyxbybyxbyxbybxbybxbyxbxybY

yxayxaxayxayxayaxayaxayxaxaX

441

3223

505

221

212

303

330

202

2201101

414

2332

550

221

212

303

330

202

2201110

and

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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

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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

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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 ith star in the jth 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)

BB

AA

BB

AA

ijm

ijl

lmlmijij

xxxxyxaxxF

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Distortion CalibrationOn-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.

-1

1

3

5

7

9

11

13

15

-10 -8 -6 -4 -2 0 2 4 6 8 10

Distorted positions in “+”

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• 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:

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Distortion CalibrationOn-orbit Calibration the LOSS Function

MATRIX ROTATION THE OF COMPONENTS THE ARE ETC R ,R

EQUATIONS SELECTOR STAR THE OF SDERIVATIVE PARTIAL ARE YYYY

XXXX

EACH) TERMS (11 SPOLYNOMIAL DISTORTION THE ARE YXB AND YXA

SCORRECTION ICRELATIVIST ARE ~ AND ~ ,

~WHERE

POSITION STAR TRUE

~)1(R~)1(R

~)1(R

YYYYYXBY

~)1(R~)1(R

~)1(R

XXXXYXAX

.

.

.

~)1(R~)1(R

~)1(R

YYYYYXBY

~)1(R~)1(R

~)1(R

XXXXYXAX

:OFAD FOR CONDITION OF EQUATIONS VECTOR THE

XY,XX

BB

11A

A

11B

B

11A

A

11

BB

11A

A

11B

B

11A

A

11

MIJ

L MIJLM

MIJ

L M

LIJLM

1IJ1IJ1IJ

IJYZIJYYIJYXBB

IJA

A

IJB

B

IJA

A

IJMIJ

L MIJLMIJ

IJXZIJXYIJXXBB

IJA

A

IJB

B

IJA

A

IJMIJ

L M

LIJLMIJ

11YZ11YY11YXBB

11A

A

11B

B

11A

A

11M11

L M

L11LM11

11XZ11XY11XXBB

11A

A

11B

B

11A

A

11M11

L M

L11LM11

Algorithm team included HST Astrometry Team, Goodrich, CSC, MSFC, and GSFC

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• 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

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• 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


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

)MRcos(*)MRcos()cos(*)MRsin(*)MRsin()cos( 1j

1iji

1j

1iij

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

• Ambiguous values along sensitive direction both depicted as stops

FGS IFOV: OVERLAP OF STOPS

42

Calibration Results

Courtesy of Lowell Observatory Franz/Wasserman

Fits to GL473 star system

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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

1 calibration of complex instrument systems using the hst fine guidance sensor example july 20, 2005...

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