brent ellerbroek a , glen herriot b , ryuji suzuki c , and matthias schoeck a

Evaluation of Astrometry Errorsdue to the

Optical Surface Distortionsin

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 3Florence, ItalyMay 28, 2013

TMT.AOS.PRE.13.087.REL01AO4ELT3, Florence, 05/28/13

1

Presentation Outline

Current astrometry requirements and error budget for TMTObjectives of this exerciseSimplified model for astrometric observationsSimplified modeling assumptionsSummary of analytical resultsApplication to NFIRAOS+IRIS for TMTSummary and future plans


2

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.


3

4

Astrometry Error Budget Organization for TMT

Reference catalogue errorsAtmospheric refraction correctionOther atmospheric effectsOpto-mechanical errors:– Telescope optics calibration– Guide probe position– Imager calibration– Optical surface calibration– Rotator calibration– Quasi-static errors– Stuck actuators, diffraction spikes– Vibrations– Coupling with other effects

Focal plane errors

More than 30 (currently 34) terms grouped in 5 categories– Organization

derived in part from MICADO budget

– Values of many terms are scenario-dependent

– Many terms remain work in progress

Driven by optical surface errors in

IRIS and NFIRAOS


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 metBegin to iterate designs and surface specifications as necessary…

5TMT.AOS.PRE.13.087.REL01AO4ELT3, Florence, 05/28/13

Observing Sequence Model

6

Distortion Calibration w/ Ref. Grid

Distortion Calibration

w/ Stars

Distortion map, post-focal optics

Science Exposure #2

Science Exposure #1

Distortion map, pre-

focal optics

Position Measurement #1

Differential Position

Measurement

Position Measurement #2

• Quasi-static error #1• Boresight error #1

• Quasi-static error #2• Boresight error #2• Field rotation or dither

S S

S S

S

+ ++

+ +-

-

--

-

Calibration by Field Stars


Modeling assumptions

7

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 apertureCircular field-of-viewCircularly symmetric error PSDs


Formulation of Results

Mean-square error a sum of contributions from each surface:

For quasi-static errors

For dither/rotation errors (random boresight errors similar)

For calibration errors

8

i

i22

M

m

mii b

bJmDDJd

D 0

21

22

222 )2()1(1)(4)( 2

M

m

miii b

bJmhJDDJd

D 0

21

0

22

222 )2()1(1222)(4)( 2

1)2(

22

222 )(4)( 22

dh iii D

DJdD

Domain of aliasing

Translation filter

Error PSD

Tip/Tilt filter

Low-order Mode removal filter


Optical Train Schematic for NFIRAOS (Facility AO System) + IRIS (Near IR Imager/Spectrograph)

9

TMT

NFIRAOS Windows

(Reference Source Grid)

NFIRAOS Optics

IRIS Window

IRIS Optics

Focal Plane

(Rotation Bearing)

Rotates in IRIS Coordinate System

Distortion Calibration via Stars

Distortion Calibration via

Reference Sources


TMT+NFIRAOS Optical Layout

10

2-5: Input windows1,16: Input/output focus7,9,10,14: OAPs8,11: DMs12: Science beamsplitter15: Instrument selection fold TMT.AOS.PRE.13.087.REL01

AO4ELT3, Florence, 05/28/13

(Initial) NFIRAOS Optical Surface Specifications

Developed based upon overall NFIRAOS wavefront error budgets– Science field– Off-axis guidestars– Compensation by NFIRAOS

deformable mirrors permittedValues specify transmitted wavefront errors over surface clear aperture with tip/tilt/focus removedPower law error PSD specified

– p=-2.5

Total 76.5 nm RMSWin 1 (-191.1 km) 30.9

Win 2 (-198.2 km) 31.0

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

TMT.AOS.PRE.11.123.REL01AO4ELT, Victoria, September 26 2011

11

Uniform tolerance of 25 nm RMS assumed for initial astrometry budgeting

9.05.5

Input window specifications tightened as needed to achieve astrometry budget

NFIRAOS focal plane

Entrance window

Collimator lens

Fold mirror

Fold mirror Collimator lenses

Pupil

ADC

Filter

Camera TMADetector

IRIS Imaging Channel(ApT Collimator + TMA Camera)


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 0.10 -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 2.213


14

Distortion Calibration Errors vs. Reference Source Spacing

All optics except NFIRAOS Windows

Spacing of 0.7 arc sec yields 5 m arc sec error

NFIRAOS windows, original specs

Errors too large!NFIRAOS windows, revised specs

Spacing of 5 arc sec yields 6 m arc sec error

Source Spacing arc sec0.1 10.01.0

Cal

ibra

tion

Err

or, m

arc

sec

0.1

1.0

10.0

100.0


Distortion Calibration Error Contribution by Surface

15

Surface number in optical train

Cal

ibra

tion

Err

or, m

arc

sec Camera

mirrors 2 and 3

NFIRAOS windows, original specs

NFIRAOS windows, revised specs

IRIS input window Collimator

lens 1

Fold mirror 1


Differential Image Distortion Due to Iris/NFIRAOS Rotation

Fourier model approximates field rotation by a global translation:

16Line-of-sight shift in NFIRAOS, arc sec0.1 10.01.0Fiel

d-av

erag

ed d

iffer

entia

l dis

torti

on, m

arc

sec

1.0

100

10

1000Red: Original window tolerancesBlue: Revised tolerancesSolid: Global tip/tilt calibration using reference starsDashed: Plate scale calibration


Sensitivities for Quasi-Static DM Figure Errors on DM11.2 in NFIRAOS

D=30m30” FoV11.2 km DM conjugate range0.5m actuator pitchMax. sensitivity of ~2.5 mas/nm with global tip/tilt calibration~0.15 with plate scale calibration

17Spatial frequency, cycles/m1.00.10.010.001

1.0

10.0

0.1

0.01

Sen

sitiv

ity, m

as/n

m

0.001

0.0001


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 TMTResults 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 tightEven so, many references sources are neededIRIS 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.


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.


brent ellerbroek a , glen herriot b , ryuji suzuki c , and matthias schoeck a

Documents

boresight error

estimating astrometry

tmt astrometry requirements

development of error

nfiraos iris

iris nfiraos

field stars

field rotation