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Optical surface measurements for very large flat mirrors
Jim Burge, Peng Su, and Chunyu ZhaoCollege of Optical Sciences
University of Arizona
Julius YellowhairSandia National Laboratories
1
Introduction
We developed have techniques for measuring large flat mirrors
• Surface slope measurements– Electronic level – Scanning pentaprism slope measurments
• Vibration insensitive subaperture Fizeau interferometry
These are demonstrated on a 1.6-m flat, and are intrinsically scalable to much larger mirrors
2
Conventional Optical Testing of Large Flats
• Ritchey-Common test– Requires a spherical mirror larger than the flat– Difficult test to accomplish on a large scale– Requires a large air path
• Fizeau test with subaperture stitching– Commercial Fizeau interferometers are limited in size
(10-50 cm)– The accuracy of the test suffer as the size of the
subaperture becomes small compared to the size of the test mirror
– Vibration is difficult to control for large scale systems
• Skip flat test– Also performs subaperture testing at oblique angles– The accuracy of the test suffer as the size of the
subaperture becomes small
Flat surface
under test
Reference mirror
(spherical)
Fizeau interferometer
Large flat
Large flat
Return flat
Interferometer
Beam footprint
3
Measure slope variations with electronic levels
Measure slope difference between the two levels
Move across surface to measure slope variations to ~1 µrad
Use single axis or dual-axis levels
Correct for Earth curvature = 1/(4Mm) = 0.25 µrad/m
Slope measurement with scanning pentaprism test
• Two pentaprisms are co-aligned to a high resolution autocollimator • The beam is deviated by 90 to the test surface• Any additional deflection in the return beam is a direct measure of surface slope changes• Electronically controlled shutters are used to select the reference path or the test path• One prism remains fixed (reference) while the other scans across the mirror
• A second autocollimator (UDT) maintains angular alignment of the scanning prism through an active feedback control
Shutters
Autocollimator system
Fixed prism (reference )
Scanning prism
Feedback mirror
Mechanical supports
Coupling wedge
ELCOMAT(Measuring AC)
UDT(Alignment AC)
5
Coupling of Prism Errors into Measurements
Contributions to in-scan line-of-sight errors:
• First order errors (AC) are eliminated through differential measurements
• Second order errors affect the measurements (PP2, ACPP, ACPP)
• The change in the in-scan LOS can then be derived as:
Pentaprism motions:• Small pitch motion does not effect in-scan
reading (90 deviation is maintained)• Angle readings are coupled linearly for yaw
motion • Angle readings are coupled quadratically for
roll motion
rmsnrad182 PPPPACPPPPACPPPPLOS
Degrees of freedom defined
Auto-collimator
TS
AC
Scanning pentaprism
Test surface
x
y
z
: pitch
: yaw
: roll TS
AC PP
PPAC AC
6
Error Analysis for Scanning Pentaprism Test
Dominant error sources• 18 nrad rms : Errors from 0.1 mrad angular motions of the PP• 34 nrad rms : Thermal errors• 80 nrad rms : Errors from coupling lateral motion of the PP• 160 nrad rms : Random measurement errors from the AC
Combine errors ~ 190 nrad rms from one prism– Monte Carlo analysis showed we can measure a 2 m flat to 15 nm
rms of low-order aberrations assuming 3 lines scans and 42 measurement points per scan
On top of this, a fixed linear temperature gradient in the air will affect the data. We rely on air motion to mitigate this, causing noise that needs to be averaged.
7
Results for a 1.6 m FlatScanning mode(single line scan)
Power = 11 nm rms
Comparison to interferometer data
Use of data to determine power in the flat
Comparison of slope measurement with of interferometer data
Slope measurement comparison for 1.6-m flatE-levels and SPP
9
E-levels
245 nm rms
Scanning pentaprism
243 nm rms
Subaperture Fizeau interferometer
• Fizeau interferometry provides measurements with nm accuracy and excellent sampling
• Subaperture measurement allows reference to be smaller than the test part
• Combine subaperture data using overlap consistancy
Interference occurs here
Requires 8 subaperture measurements to get complete coverage
1.6 m test flat
1 m (8) subapertures
Large flat miror
1 m reference flat
Rotary air bearing table
10
Vibration insensitive Fizeau interferometry
• Simultaneous phase-shifting using polarization and polarizing elements• Orthogonal polarizations from the reference and test surfaces are combined
giving multiple interferograms with fixed phase shift
• The beams are circularity polarized to reduce the effect of birefringence
Large flat miror
1 m reference flat
Rotary air bearing table
LHC(B)
RHC(A)
Alignment mode
Software screen
Spots from the test surface
Spots from the reference surface
A B
A B
11
UA 1-m Fizeau interferometer
• Commercial instantaneous Fizeau interferometer (uses 2 circularly polarized beams)
• 1 m OAP collimates the light
• 1-m reference flat, supported semi-kinematically
• Mirror rotates under the Fizeau to get full coverage
Large flat miror
1 m reference flat
H1000 Fizeau interferometer
Fold flat
1 m illumination OAP
Rotary air bearing table
12
Reconstruction using modal methods or stitching
• Modal reconstruction– Represent the test mirror and reference mirror as set of modes
– Modulate the subaperture data through multiple rotations of the reference and test surfaces
– Solve for modal coefficients based on data
– Reference and test surface are both estimated to 3 nm rms – limited by repeatability of the measurements
• Subaperture stitching – Solve for bias and tilt of subaperture measurements based on consistency of
overlap regions.
– Maintains full resolution of subaperture measurement
– Errors from stitching are 2 nm rms
13
Support of 1-meter Reference Flat
• 1 m fused silica polished to 100 nm P-V
• Mechanically stable and kinematic mount held the reference flat– Three counter balanced cables attached to pucks bonded to the reference
flat surface– Six tangential edge support– Provide six equally spaced rotations and good position repeatability of the
reference flat
Bonded pucks and attached cables
Reference flat
Kinematic base
Upper support
Test flat Polishing
table
Reference Flat FEA Simulation
129 nm PV29 nm RMS
(nm) 75 59 43 27 11-6-22-38-54
184 nm PV42 nm RMS
Reference Flat Surface measurement (nm)
14[R. Stone]
[P. Su]
1.6-m flat mirrormeasured by subaperture Fizeau interferometer
Comparison of results from modal reconstruction and stitching– The same zonal features are observed in both
– The stitched map preserves higher frequency errors
– They agree for low order• But modal method solves for reference figure also
Flat Surface by Stitching Method - power/astigmatism removed
100 200 300 400 500 600 700 800
100
200
300
400
500
600
700
800 0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Reconstruction by stitchingModal reconstruction
6 nm rms after removing power & astigmatism 7 nm rms after removing power & astigmatism15
[P. Su] [R. Spowl]
Measuring larger flat mirrors
• Larger mirrors require more subapertures– 2.7-m flat– Two positions for interferometer, rotate test flat
Even larger flat mirror : TMT M3
Measurement of 3.5 x 2.5 m TMT flat simulated with 18 subapertures
Noise modeled at 3 nm rms subaperture with 25 cm correlation length
Monte Carlo simulation with different noise, alignment in each subaperture
Layout of subapertures Typical measurement noise
3 nm rms
Example for TMT M3 data stitching
M3 Subaperture example: 3nm
M3 stitched map: 6.4nm rms
M3 low order error from fitting: 3.8nm rms
M3 residual from fit: 5.2nm rms. (3 nm rms after removing global tilt)
Monte Carlo analysis for TMT M3
• 3 nm rms noise plus tilt and bias per subaperture• 18 subapertures for complete measurement
Mode 1 2.9 nm rms
Mode 2 2.4 nm rms
Mode 3 1.4 nm rms
Mode 4 1.1 nm rms
Mode 5 1.4 nm rms
Mode 6 0.8 nm rms
Mode 7 0.8 nm rms
Mode 8 0.8 nm rms
Mode 9 0.5 nm rms
Mode 10 0.8 nm rms
RSS for all modes: 4.6 nm rms
Residual from fitting all modes 3 nm rms
4.6 nm rms for all modes
3 nm rms residual
Conclusions
• We have developed methods and have implemented hardware for measuring flat mirrors that are – Accurate to few nanometers– Efficient to perform– Naturally scalable for measuring mirrors many meters
in diameter