Optical surface measurements for very large flat mirrors Jim Burge, Peng Su, and Chunyu Zhao College of Optical Sciences University of Arizona Julius Yellowhair Sandia 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 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 (  PP 2,  AC  PP,  AC  PP ) 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 Degrees of freedom defined Auto- collimator  TS  AC Scanning pentaprism Test surface x y z  : pitch  : yaw  : roll  TS  AC  PP  PP  AC  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 Flat Scanning 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 flat E-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 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 PV 29 nm RMS (nm) nm PV 42 nm RMS Reference Flat Surface measurement ( nm ) 14 [R. Stone] [P. Su]

1.6-m flat mirror measured 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 Reconstruction by stitching Modal reconstruction 6 nm rms after removing power & astigmatism7 nm rms after removing power & astigmatism 15 [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

Monte Carlo analysis for TMT M3 3 nm rms noise plus tilt and bias per subaperture 18 subapertures for complete measurement 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