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

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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