1 Design and analysis for interferometric measurements of the GMT primary mirror segments J. H. Burge a,b, L. B. Kot a, H. M. Martin a, R. Zehnder b, C. Zhao b University of Arizona a Steward Observatory b College of Optical Science

2 GMT Primary mirror In the telescope, primary mirror is 25 meter diameter, f/0.7 made from seven 8.4-m segments Optical shape of the segments 36 m radius of curvature 14,500 µm aspheric departure

3 Issues for GMT testing Accuracy of the optical testing is critical to GMT. The ability to correctly manufacture the optical surface on the primary segments depends on the ability to accurately measure the shape. We polish the surface, selectively wearing down the glass, until our optical test tells us that the surface is finished. UA has great experience in optical metrology for large, fast mirrors. The geometry of the GMT primary segments provides a new challenge. We will measure the GMT segments using interferometry to give a high-resolution map of the surface errors. We will augment the interferometry with other measurements to ensure accurate knowledge of the surface.

4 Optical testing of GMT segments Heritage (LBT) GMT Axisymmetric Test optics at ~20 meters Light from optical test is only 200 mm diameter near the test optics – allows direct measurement of test system No Axisymmetry Light path defined by GMT is much larger (~3.5 meters across at the top of our tower) Test optics ~1.4 mm aspheric departure ~14 mm aspheric departure Test wavefront defined to match aspheric shape of mirror 20 m roof

5 LBT testing State of the art for large mirrors 8.4-m f/1.1 Use interferometer and null lenses Calibrate null lens using small Computer Generated Hologram Exploit axisymmetry for optics, and test procedures Null lens assembly 23 cm Computer Generated Hologram Calibrates null corrector to ~10 nm accuracy

6 Interferometric optical test Components 3.75 m mirror, “fold sphere” folds the light path and provides much of the aspheric correction 75 cm mirror provides most of remaining correction Computer generated hologram provides high order correction and alignment references Vibration insensitive interferometer GMT segment 0.75 m sphere interferometer computer-generated hologram GMT segment Interferometer CGH 3.75-m fold sphere tilted 14.2° 25 meters 600 µm wavefront created by CGH CGH pattern (every 400th line) 75-cm mirror Axis of parent ellipsiod Fold sphere center of curvature

7 Alignment for optical test Laser tracker Place alignment CGH at intermediate focus Provides wavefront test Provides reference for alignment 1.Align CGH, small mirror using CGH references and metering rods (~10 µm tolerances) 2.Use CGH at intermediate focus. Use this to verify alignment, and to define alignment for 3.75-m sphere 3.Use laser tracker to define position of 3.75-m mirror with respect to CGH (100 µm tolerance) 4.Measure GMT segment position with laser tracker (200 µm tolerance) Additional cross-checks provide redundancy and improved accuracy. Interferometer at the center of curvature of fold sphere Real time measurement of shape Reference for locating the mirror Uses laser reflection from reference targets Angles + radial distance are measured to determine position of target Accurate to ~50 µm for this application

8 Analysis for test optics parallels operation in telescope In operation we will 1.Install mirror segments using coarse mechanical measurements 2.Measure wavefront using star light 3.Move mirror segments to optimize wavefront: translate in radial direction rotate about segment center (clocking) 4.Bend mirrors to correct other shape errors, including power The analysis of the test optics simulates the same operations.

9 Optimal use of alignment, active optics Coupling of bending modes and alignment aberrations for off axis mirror. Power, astigmatism, and coma can be eliminated by combination of alignment and forces But out of infinite number of combinations that do this, only one is optimum in terms of minimizing correction forces and residual error. Low-order aberrations have very different stiffness. Bending power requires 3 x greater force than astigmatism. We have developed methodology of optimizing alignment and bending that minimizes the required force For 0.5 mm radial shift and adjusting pointing, wavefront gets 0.81 µm rms power 0.55 µm rms astigmatism 0.05 µm rms coma 0.02 µm rms trefoil

10 Error analysis for alignment of test optics 1.For each alignment degree of freedom, perturb according to its expected tolerance and simulate the system in Zemax. 2.Calculate resulting shape error in mirror segment 3.Simulate the optimal alignment in telescope 4.Separate remaining wavefront error: Low order errors that will be corrected by bending – this includes power. Determine the applied force and the residual error from bending. Higher order errors that cannot be corrected by bending. 5.Use RSS to find net forces and structure functions for higher order shape errors. Also perform Monte Carlo analysis to see statistics of likely errors.

11 Error analysis for optical test

12 Structure function for residual (uncorrected) errors Structure functions of residual errors were computed The limitations from testing are very small compared to the 0.17 arcsec specification

13 Test tower at Steward Observatory Mirror Lab Existing tower New tower New tower 28 meters tall, 80 tons of steel floated on 400 ton concrete pad accommodates other UA projects (LBT, LSST) lowest resonance of 4.8 Hz with 9 ton 3.75-m fold sphere + cell

14 GMT test layout in new test tower

15 Tower details 6.5m test optics 8.4m test optics Folding deck (for interference with 8.4m test optics) Folding deck (for interference with 6.5m test optics) GMT off-axis test optics Crane, laser tracker and fold sphere access deck

16 Measurement of center segment The center segment can be measured by tilting the fold sphere to point straight down, then a small computer generated hologram will compensate the residual errors. 50 mm CGH compensates only 20µm aspheric departure Cone defined by light from outer edge of mirror Vibration insensitive interferometer Cone defined by light from edge of central hole

m fold sphere Lightweight borosilicate blank (3300 kg) Hangs from “Active” support, allowing some force adjustment based on in situ measurement Support actuators, with trim adjustment Cast in UA spinning oven

18 10 cm CGH 50 cm mirror 1.7-m primary mirror Off-axis piece of f/0.7 parent 15 cm lens <10 µm alignment tolerances Successful 1/5 scale prototype, used for 1.7 m NST primary mirror (R. Zehnder and C. Zhao)

19 Metrology details for 1.7-m test -- CGH 10 segments create 8 wavefronts. Main CGH creates the testing wavefront. The annular CGH aligns the substrate to the interferometer. 3 segments create a crosshair and 1 segment creates a clocking line to align the NST mirror to the test optics. 4 circular CGHs send beams to align the lateral positions of the 4 balls mounted on the surface of the fold sphere. Main CGH Substrate alignment CGH CGH creating clocking line 3-segment CGH creating crosshair 4 CGHs creating beams for spherical mirror alignment

20 Alignment of prototype system Uses combination of CGHs and mechanical metrology Provides experience base for GMT Ball at focus Ball at mirror CGH Metering rod w/ LVDTs Lens Spherical mirror ~1 m

21 Results from prototype system Good interferograms (image distortion is corrected in software) Big optomechanical system is stable NST mirror figure 32 nm rms

22 Other tests for GMT Scanning pentaprism system – Scan collimated laser beams across the surface and measure reflected light at prime focus. Laser Tracker surface measurements – Use second laser tracker + reference systems to measure segment surface point-by-point directly Shear test – Use the fact that the segments are symmetric about the parent axis. Rotate the segment about this axis. Separate segment errors from testing errors by measuring which errors move with the segment. See poster by Burge et al., “Alternate surface measurements for GMT primary mirror segments”, 6:00 in this conference Tuesday, May 30.

23 Scanning pentaprism test Collimated source Parent optical surface GMT segment CCD array at prime focus Fixed reference prism/beamsplitter Scanning prism on linear stage Optical axis for parent asphere Scans collimated laser beam across the pupil Pentaprism insures that the beam maintains it angle Measure slope errors using CCD at prime focus

24 Integration of pentaprism test CCD at GMT focal point GMT segment Tilted rail with scanning pentaprism Operational 3-rail system for 6.5-m collimator We need scans at 0°, 45°, 90°, and 135° to determine focus, coma, astigmatism, trefoil. Slope measurements of 1 µrad allow corroboration of low order GMT figure errors

25 Surface measurements with laser tracker SMR (sphere-mounted retroreflector) Retroreflector for interferometer and PSD (position sensing detector) Assemblies in 4 places at edge of mirror Laser Tracker and Interferometers

26 Summary Optical testing requirements for GMT PM segments push the state of the art for metrology. We take the challenge very seriously and we have initiated a robust program to develop the required technologies and to provide redundancy. Key items are underway. Demolition of the current tower starts in June and the new tower will be installed within 6 months. The mold for the 3.8-m fold sphere casting is being manufactured. This mirror will be cast in the spinning oven over the summer. The engineering is continuing. The mirror segment is now being processed. We will have hardware in ~1 year.