Transcript Project Manager Presentation to the TMT Board

Evaluation of Astrometry Errors
due to the
Optical Surface Distortions
in
Adaptive Optics Systems and Science Instruments
Brent Ellerbroeka, Glen Herriotb, Ryuji Suzukic, and Matthias Schoecka
aTMT
Observatory Corporation, bNRC Herzberg, cNational Astronomical Observatory of Japan
Adaptive Optics for Extremely Large Telescopes 3
Florence, Italy
May 28, 2013
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Presentation Outline
Current astrometry requirements and error budget for
TMT
Objectives of this exercise
Simplified model for astrometric observations
Simplified modeling assumptions
Summary of analytical results
Application to NFIRAOS+IRIS for TMT
Summary and future plans
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Astrometry Requirements for TMT
[REQ-1-ORD-3650] NFIRAOS shall enable precise differential
astrometry measurements,
– where one-dimensional time-dependent rms astrometric positional
uncertainties, after fitting distortion measured with field stars, and over a
30 arcsecond field of view
– shall be no larger than 50 µ-arcseconds in the H band for a 100s
integration time.
– Errors should fall as t-1/2.
– Systematic one-dimensional rms position uncertainties shall be no
more than 10 µas.
[REQ-1-ORD-3652] The AO system should provide sufficient
calibration information to not degrade the astrometric capabilities
beyond the limits set by the atmosphere.
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Astrometry Error Budget Organization for TMT
Reference catalogue errors
Atmospheric refraction correction
Other atmospheric effects
Opto-mechanical errors:
–
–
–
–
–
–
–
–
–
More than 30
(currently 34) terms
grouped in 5
categories
Telescope optics calibration
–
Guide probe position
Imager calibration
Optical surface calibration Driven by optical–
surface errors in
Rotator calibration
IRIS and NFIRAOS
Quasi-static errors
Stuck actuators, diffraction spikes
–
Vibrations
Coupling with other effects
Focal plane errors
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Organization
derived in part from
MICADO budget
Values of many
terms are scenariodependent
Many terms remain
work in progress
4
Objectives of this Exercise
Develop engineering formulas for estimating astrometry
errors due to optical surface errors in instruments and
AO systems
– Intended as a practical tool to support development of error
budgets and optical surface specifications
Apply to current optical designs and surface
specifications for IRIS + NFIRAOS to confirm that TMT
astrometry requirements can be met
Begin to iterate designs and surface specifications as
necessary…
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Observing Sequence Model
Distortion
Calibration
w/ Ref. Grid
Distortion
map, postfocal optics
• Quasi-static error #1 • Quasi-static error #2
• Boresight error #2
• Boresight error #1
• Field rotation or dither
Distortion
Calibration
w/ Stars
+
-
S
Science
Exposure #1
Distortion
map, prefocal optics
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+
+
S
-
+
+
-
Calibration by
Field Stars
Science
Exposure #2
S
-
Position
Measurement #1
S
S
Position
Measurement #2
Differential
Position
Measurement
6
Modeling assumptions
Optical surface errors
Random, with shift-invariant statistics
 Defined by PSDs
Induced wavefront errors
Linear sum of contributions from “phase screens”
at each surface
Resulting image distortion
RMS best-fit tilt to exit pupil wavefront
Random boresight errors
Normally distributed in 2 dimensions
Intentional field-of-view
offset or rotation
Linear displacement of optical path through some
or all optical surfaces
Distortion calibration by
reference sources/stars
Measures image distortion map up to the Nyquist
rate defined by reference source spacing
Distortion calibration by
field stars
Removes low-order (polynomial) modes of image
distortion map
Other simplifying
assumptions
Circular, unobscured aperture
Circular field-of-view
Circularly symmetric error PSDs
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Formulation of Results
Mean-square error a sum of contributions from each surface:
Tip/Tilt
Low-order Mode
2


 i2
i filter
Error
removal filter
PSD
For quasi-static errors
  2
 i2     
 D   
2
2
2
2
4 J 2 (D )  M (m  1) J m 1 (2b) 
1  

 d  i ( ) D Translation

b
m

0


filter
For dither/rotation errors (random boresight errors similar)
  2
 i2     
 D   
2
2
2
 M (m  1) J m 1 (2b) 2 
4 J 2 (D )

 d  i ( ) D 2  2 J 0 2hi 1  m0

b


For calibration errors
  2
 i2  2   
 D   
2
Domain of aliasing
2
4 J 2 (D )
d


(

)
i
  ( 2hi d )1
D
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8
Optical Train Schematic for NFIRAOS (Facility AO
System) + IRIS (Near IR Imager/Spectrograph)
TMT
Distortion
Calibration via Stars
NFIRAOS Windows
(Reference Source Grid)
Rotates in IRIS
Coordinate System
NFIRAOS Optics
(Rotation Bearing)
IRIS Window
Distortion
Calibration via
Reference Sources
IRIS Optics
Focal Plane
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TMT+NFIRAOS Optical Layout
2-5: Input windows
1,16: Input/output focus
7,9,10,14: OAPs
8,11: DMs
12: Science beamsplitter
15: Instrument selection fold
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(Initial) NFIRAOS Optical Surface
Specifications
Developed based upon overall
NFIRAOS wavefront error
budgets
– Science field
– Off-axis guidestars
– Compensation by NFIRAOS
deformable mirrors permitted
Values specify transmitted
wavefront errors over surface
clear aperture with tip/tilt/focus
removed
Power law error PSD specified
– p=-2.5
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Total
Win 1 (-191.1 km)
76.5 nm RMS
Win 2 (-198.2 km)
30.9 9.0
31.0 5.5
OAP1 (49.2 km)
25.1
OAP2 (-36.6 km)
24.6
OAP3 (35.2 km)
24.9
Sci B/S (-9.7 km)
27.5
OAP4 (-43.6 km)
24.3
Inst. Fold (-85.2 k m)
27.1
Uniform tolerance of 25 nm RMS
assumed for initial astrometry budgeting
Input window specifications tightened as
needed to achieve astrometry budget
11
IRIS Imaging Channel
(ApT Collimator + TMA Camera)
Entrance window
Fold mirror
Detector
Camera TMA
Collimator lens
Pupil
NFIRAOS focal plane
Filter
Fold mirror Collimator lenses ADC
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IRIS Optical Surface Specifications
Surf.
Name
DA,
m
h,
km
PSD ,
pwr nm
#
Surf.
Name
DA,
m
h,
km
PSD ,
pwr nm
1
Win f
0.10
2890
2.30
2.8
13
ADC 1f
0.10
-19.8
2.12
3.2
2
Win b
0.10
2520
2.29
2.7
14
ADC 1c 0.10
-21.5
2.12
0.7
3
Col 1f
0.12
1290
2.23
2.6
15
ADC 1b 0.10
-22.8
2.12
4
4
Col 1b
0.12
1190
2.22
2.6
16
ADC 2f
-25.7
2.12
4
5
Fold 1
0.12
895
2.21
10.6
17
ADC 2c 0.10
-27
2.12
0.7
6
Fold 2
0.12
156
2.15
9.6
18
ADC 2b 0.10
-28.7
2.12
3.2
7
Col 2f
0.12
63.5
2.14
6.9
19
Filt. F
0.08
-61.5
2.12
2.0
8
Col 2b
0.12
61
2.14
6.9
20
Filt. B
0.08
-63.5
2.12
2.0
9
Col 3f
0.12
50.8
2.13
2.1
21
Cam 1
0.16
-171
2.14
9.7
10
Col 3b
0.12
47.3
2.13
2.1
22
Cam 2
0.16
-370
2.16
10.0
11
Col 4f
0.12
45.3
2.13
2.2
23
Cam 3
0.24
-620
2.17
10.5
12
Col 4b
0.12
40.2
2.13
2.2
#
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Distortion Calibration Errors vs.
Reference Source Spacing
Calibration Error, m arc sec
100.0
All optics except
NFIRAOS Windows
Spacing of 0.7 arc
sec yields 5 m arc sec
error
10.0
NFIRAOS windows,
original specs
Errors too large!
NFIRAOS windows,
revised specs
1.0
Spacing of 5 arc sec
yields 6 m arc sec
error
0.1
0.1
1.0
Source Spacing arc sec
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10.0
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Distortion Calibration Error
Contribution by Surface
NFIRAOS windows, original specs
Calibration Error, m arc sec
NFIRAOS windows, revised specs
Fold
mirror 1
IRIS input
window
Camera
mirrors 2
and 3
Collimator
lens 1
Surface number in optical train
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Field-averaged differential distortion, m arc sec
Differential Image Distortion Due to
Iris/NFIRAOS Rotation
1000
Red: Original window tolerances
Blue: Revised tolerances
Solid: Global tip/tilt calibration using reference stars
Dashed: Plate scale calibration
Fourier model
approximates field
rotation by a global
translation:
100
10
1.0
0.1
1.0
Line-of-sight shift in NFIRAOS, arc sec
10.0
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Sensitivities for Quasi-Static DM Figure
Errors on DM11.2 in NFIRAOS
10.0
Sensitivity, mas/nm
1.0
0.1
0.01
0.001
0.0001
0.001
0.01
0.1
Spatial frequency, cycles/m
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1.0
D=30m
30” FoV
11.2 km DM
conjugate range
0.5m actuator
pitch
Max. sensitivity
of ~2.5 mas/nm
with global tip/tilt
calibration
~0.15 with plate
scale calibration
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Summary
A Fourier model for evaluating the magnitude of image distortions due
to optical surface errors has been applied to develop astrometry error
budget terms for observations with IRIS+NFIRAOS on TMT
Results are preliminary, but confirm intuition and are encouraging:
– Calibration of static distortions to 5-7 m arc sec is feasible, but…
Tolerances on surfaces near focal planes are tight
Even so, many references sources are needed
IRIS optical design may be iterated to adjust surface conjugates
– As with K-mirrors, a consistent image rotator angle must be used for
repeated observations of the same field
– Image distortion due to quasi-static errors on DM11.2 are small, provided
that overall plate scale changes can be calibrated using reference stars
Further modeling/simulation is planned to using more realistic models
of static errors, calibration procedures, quasistatic errors, etc.
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Acknowledgements
The TMT Project gratefully acknowledges the support of the TMT partner institutions.
They are
–
–
–
–
–
–
the Association of Canadian Universities for Research in Astronomy (ACURA),
the California Institute of Technology
the University of California
the National Astronomical Observatory of Japan
the National Astronomical Observatories and their consortium partners
And the Department of Science and Technology of India and their supported institutes.
This work was supported as well by
–
–
–
–
–
–
–
–
the Gordon and Betty Moore Foundation
the Canada Foundation for Innovation
the Ontario Ministry of Research and Innovation
the National Research Council of Canada
the Natural Sciences and Engineering Research Council of Canada
the British Columbia Knowledge Development Fund
the Association of Universities for Research in Astronomy (AURA)
and the U.S. National Science Foundation.
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