Transcript FTS Training - Yale University

Yale Astrometry Workshop
Calibration of Complex Instrument Systems Using
the HST Fine Guidance Sensor Example
July 20, 2005
1
Who are we?
Hubble Space Telescope
Chandra
HST FGSs
SIRTF IR Telescope
SPITZER
• Infrared Telescope
Technology Testbed
• All Be Low Mass
Optical System for
SIRTF Mission
2
Topics
• The Goals
• Overview of an HST Fine Guidance Sensor (FGS)
• Error Budgets and Modeling Error Sources
• On-orbit Calibrations
3
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.
4
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
5
FGS Overview
Collimating Asphere
(cell only visible)
PMTs
Interferometer
Latch
Filter Wheel
Star Selector Assembly
6
POM
FGS in Danbury
7
FGS at KSC
8
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
9
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
10
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
FF4
Koesters prism
FF3
V1
axis
Folded
V1 axis
SSA SSB
FGS Asphere
Pick-off
mirror
11
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
1000
6.77 degrees
Y, asec
SSA
QB
500
Lever arms
QA
0
-1000
-500
0
500
1000
X, asec
FGS FOV in object space
DQA = DQB : scan in azimuthal direction
DQA = -DQB : scan in radial direction
SSB
12
FGS Overview
Collimator and Field Selection Optics
•
Star Selector B
Collimated beam from
Star Selector A
1000
Y, asec
=6.77 degrees
B
500
QB
R
Lever arms
0
-1000
-500
A
0
R1
QA
POINT 18
SSA PUPIL
R2
500
1000
X, asec
R3
R4
FGS FOV in object space
DQA = DQB : scan in azimuthal direction
DQA = -DQB : scan in radial direction
REFLECTED V1
AXIS
13
B Star Selector
FGS Overview
Collimator and Field Selection Optics
The Star Selector parameters are used to generate the following coordinates:
R  a coscos( A ) * cos( b )  sin( A ) * sin( b ) * cos(Q B  Q A )
 cos( B )  cos( A ) * cos(R ) 
  Q A  a cos

sin( A ) * sin(R )


R
X  sin( ) * cos()
M
R
Y  sin( ) * sin()
M
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
14
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.
15
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 (QA and QB 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
16
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)
17
FGS Overview
The Interferometer
FGS Interferometer Optical Path
XB
PMT
Definitions of Field Stop Position Directions
YA
XB
XB Insensitive
Axis
+
+
Field Stops
&
Doublets
XA
XA
PMT
XA Insensitive
Axis
YA Sensitive
Axis
+
XB
+
XB Sensitive
Axis
YA
PMT
YA
YA Insensitive
Axis
+
View looking into
the interferometer
+
XA Sensitive
Axis
XA
YB
YB Sensitive
Axis
YB
PMT
+
YB Insensitive
Axis
Achromatic
Condenser
Lens XB
+
S-curve produced in one axis
(ideal modulation 1.4)
Fold
Flat 6
YA Axis
0.8
YB
Achromatic
Condenser
Lens YA
0.6
0.4
Fold
Flat 6
XB Axis
0.2
0
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
Achromatic
Condenser
Lens XA
-0.2
Fold
Flat 6
XA Axis
X Axis Koester's
Prism
-0.4
-0.6
X axis polarized
beam
-0.8
Tracking signal –
Proportion gain obtained
from the linear region
Fold Flat 4
Polarizing
Beam
Splitting
Cube
Dome
Input from
Telescope
Interferometer
IS
+Y
IS
+X
FGS
Y Axis Koester's
Prism
Y axis polarized
beam
Fold Flat 5
Collimated
Beam from
Fold Flat 3
Achromatic
Condenser
Lens YB
Fold Flat 6
YB Axis
C Latch
Pick-off
Mirror
Assembly
18
FGS Overview
The Interferometer
Incoming Wavefront
C
B
A
AT = transmitted
wavefront
AR = reflected
Koester's Prism
wavefront
CR
CT
AT
BR
BT BT
AR
BR
l/4 delay
A
Photomultiplier
B
Tubes
S-curve
19
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
20
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
0.600
Q (n o d im e n s io n )
AB
Q
AB
0.800
0.400
pointing control around
null crossing
0.200
0.000
-0.200
-0.400
-0.600
-0.800
-300.0
-200.0
-100.0
0.0
100.0
200.0
x (m illiarcseconds, object space)
300.0
21
FGS Overview
The Interferometer

FGS Koester’s prism interferometers can function well, even with
spherical aberration, as long as optical alignment is within
tolerance required for the aberration.
Pupil
Ideal alignment of OTA pupil image
to Koester’s prism interferometer
1 mm misalignment of OTA pupil image
to Koester’s prism interferometer
22
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 realignment
23
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
24
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
Q (n o d im e n s io n )
•
0.400
pointing control around
null crossing
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 (m illiarcseconds, object space)
Co-add and smooth 10 S-curves
25
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
26
Error Budgets*
2.04
Astrometry Star (mas)
0.95 Jitter
1.03
Calibration (mas)
0.36 Plate Scale
0.09
0.03
0.09
Star Selectors
Noise
Granularity
0.36
0.04
0.33
0.00
Detector Noise
Photon noise
Dark Current
Background
Cosmic Radiation
0.63
0.71
Thermal
0.01
Transfer Function Comp
0.42 Filter
0.87 Distortion
0.03
0.02
0.30
0.55
0.00
0.55
1.80 Non-Averaging
0.22
0.22
Star Selectors
Fine Bits
0.03
Thermal (slue)
0.31
Thermal Orb-Orb
1.74
Chromatic Tilt
0.27
Spectral Mismatch
0.44
0.01
0.44
0.42
HST Optics
Design
Manufacture
FGS Optics
Design
(included above)
Manufacture
0.03
Pickoff Mirror
0.22
Asphere
0.05
Lower Fold
0.03
Upper Fold
0.41
Corrector Group
Star Selectors
Rotation Axis
Encoder Errors (Coarse Bits)
Pointing Errors During Distortion Calibration
27
* HST STR-20 HST 32-KB Astrometry Error Budget
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
28
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.
29
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.
30
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)
X  M x  a x ( x 2  y 2 )  bx( x 2  y 2 ) 2
and
– Field dependent magnification is
a radial function in the aligned case
– X,Y are local FGS coordinates
Y  My  a y ( x 2  y 2 )  by ( x 2  y 2 ) 2
•
•
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
X  a10 x  a11 x y  a20 x 2  a02 y 2  a30 x 3  a03 y 3  a12 x y 2  a21 x 2 y  a50 x 5  a32 x 3 y 2  a14 x y 4
and
Y  b01 xy b11 x y  b20 x  b02 y  b30 x  b03 y  b12 x y  b21 x y  b05 y  b23 x y  b41 x y
2
2
3
3
2
2
5
2
3
4
31
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)
•
Tilt term locations on the asphere
Uncertainties in optical alignment
and conics were modeled and fit to
the polynomials to an accuracy of
about 0.3 mas
32
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 14bit 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 7bit error.
– Error in budget reflect repeatability of
measurements to about 0.22 mas
14-bit Error
14-bit error in encoder
7-bit Error
33
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)
xFij  xij   alm x l ij y m ij 
lm
x
x
x
x
 A 
 B 
QA 
QB
 A
 B
Q A
Q B
– 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)
34
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
15
13
11
9
7
5
•
Solve for the true star
positions.
3
1
-1
-10
-8
-6
-4
-2
0
2
4
6
8
10
Distorted positions in “+”
35
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:
36
Distortion Calibration
On-orbit Calibration the LOSS Function
THE VECTOR EQUATIONS OF CONDITION FOR OFAD :
X 11
X 11
X 11
X 11
~
~ 

L
M
~
X 11   A LM X 11 Y11   A   B  Q QA  Q QB  R XX (1) 11  R XY (1)11  R XZ (1) 11 
L M
A
B
A
B




Y

Y

Y

Y
~
~ 
L
M
11
11
11
11
~
Y11   B LM X 11 Y11   A   B  Q QA  Q QB  R YX (1) 11  R YY (1)11  R YZ (1) 11 
L M
A
B
A
B


.



.
  TRUE STAR POSITION
.



X IJ
X IJ
X IJ
X IJ
~
~ 
X 
L
M
~
A LM X IJ YIJ 
A 
B 
QA 
QB  R XX (1)  IJ  R XY (1) IJ  R XZ (1)  IJ
 IJ 

 A
 B
Q A
Q B
L M


YIJ
YIJ
YIJ
YIJ
~
~


M
~
YIJ   B LM X IJ YIJ   A   B  Q QA  Q QB  R YX (1)  IJ  R YY (1) IJ  R YZ (1)  IJ 
L M
A
B
A
B


WHERE
~
~ AND ~
IJ 1 , 
 IJ 1 ARE RELATIVISTIC CORRECTIONS
IJ 1
 A
L
M
LM
X LIJ YIJM AND  B LM X IJ YIJM ARE THE DISTORTION POLYNOMIALS (11 TERMS EACH)
L
M
X 11
X 11
X 11
X 11
A 
B 
QA 
QB
 A
 B
Q A
Q B
Y11
Y
Y
Y
A  11  B  11 QA  11 QB ARE PARTIAL DERIVATIVES OF THE STAR SELECTOR EQUATIONS
 A
 B
Q A
Q B
R XX , R XY, ETC ARE THE COMPONENTS OF THE ROTATION MATRIX
37
Algorithm team included HST Astrometry Team, Goodrich, CSC, MSFC, and GSFC
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
38
Distortion Calibration
On-orbit Calibration
•
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
39
A Mention
of
Additional On-orbit Calibrations
•
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:
cos(Qij )  sin(Ri M1 ) * sin(R jM1 ) * cos(i   j )  cos(Ri M1 ) * cos(R jM1 )
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
40
A Mention
of
Additional Calibrations
•
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.
Optimized S-curve
Ground to orbit change
FGS IFOV: OVERLAP OF STOPS
Photometric calibration is
performed but stabilizes after
field stop motion (due to
desorption) ends.
41
• Ambiguous values along sensitive direction both depicted as stops
Calibration Results
Fits to GL473 star system
42
Courtesy of Lowell Observatory Franz/Wasserman
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
43