1. Use of a commercial laser tracker for optical alignment James H. Burge, Peng Su, Chunyu Zhao, Tom Zobrist College of Optical Sciences Steward Observatory University of Arizona

2. Laser Tracker: Optical coordinate measuring machine Projects a laser beam. Use two-axis gimbals to track the reflection from a corner cube Measure 3-space position: –Two pointing angles –Radial distance ADM (Absolute Distance Measurement) DMI (Distance measuring interferometer) SMR – Sphere Mounted Retroreflector Software converts from spherical coordinates What is a Laser Tracker? (Faro)

3. Laser tracker components

4. Leica Geosystems (Switzerland) FARO (USA) API (USA) 14” 21” 34” Three manufacturers of Laser Trackers

5. Laser tracker accuracy Assume advertised performance (all values are 2  Define z as line of sight direction for tracker Uncertainty in position using ADM is For other directions, use vector projection  a z x Lz Lz (Out of plane,  y, behaves the same as  x.) Radial: Lateral

6. Calibration of laser tracker Distance Measuring Interferometer gives < 0.1 µm/m accuracy –Typically limited by air temperature (1°C gives 1 µm/m error.) Tracker repeatability is typically < 1 µm/m for all dimensions The tracker can be calibrated for specific measurements using the DMI. –Radial : use DMI mode, moving the tracker ball –Lateral : use a second tracker in DMI mode So it is possible to get micron level accuracy –Need thermal control –Control of geometry –Careful calibration –Average out noise

7. Special advantages of the laser tracker Can achieve micron accuracy (so can CMM) Portable Measure over very large distances Can use optical tricks –Measure through fold mirrors –Measure through windows –Measure angles

8. New Solar Telescope Big Bear Solar Observatory Off axis Gregorian, f/0.7 parent

9. Use tracker to align mirrors in telescope Declination axis Secondary mirror with SMRs at known positions wrt aspheric parent 1.7-m primary mirror with SMRs at known positions wrt aspheric parent Laser tracker Has view to all SMRs

10. Measurement of NST secondary mirror Interferometer Ellipsoidal Secondary mirror Return sphere (CoC at F2) Focus 1 for ellipsoid Focus 2 for ellipsoid Laser tracker SMRs Located by return into interferometer Optical table Flat mirror

11. Measurement of angle with tracker Actual ball position (uncertainty  a 2,  b 2 ) Apparent ball position  a 1 ) Unique line connecting the position of the ball with the position of its mirror image: length = L The plane of the mirror is defined by - the line that connects the ball with its image - a point midway between the two balls Uncertainty in direction of flat mirror (defined by its normal) a2 a2  Uncertainty in mirror position b b b2 b2 b1b1

12. Test of tracker through fold mirrors Use high quality 12” flat mirror. Compare SMR measurements (actual and apparent). Calculate mirror normal Measure mirror surface directly by touching the mirror with the SMRs The two methods agree to within the 1 arcsec stability of the mirror

13. Measurement of object’s 3D orientation Fix 2 mirrors to the object at known angles Determine mirror normal directions using the tracker Determine objects 3D orientation in space

14. Definition of mirror angles 4 measurements : 2 normals, 2 DoFs each We get no information about rotation about the mirror’s normal 3 unknowns (three space orientation) Use least squares fit

15. Sensitivity vs angle between mirrors Sensitivity for determining object’s 3-space orientation from measuring two mirrors as a function of the angle between the mirrors Inverse sensitivity, normalized Defined as ratio Uncertainty in determination of object’s orientation Uncertainty in angular measurements

16. Interferometric testing primary mirror segments for the Giant Magellan Telescope GMT segment Spherical mirror 3.75 m diameter Tested in situ from floor M2 0.75 m diameter CGH 130 mm diameter Interferometer 23 m Sam

17. Reference CGH PSM aligned to M2 Interferometer for GMT measurements CGH M2 Insert a CGH to test system 8.4 m diam off axis segment for Giant Magellan Telescope 3.8-m sphere Use laser tracker to measure position of 3.8-m mirror wrt wavefront created by Sam Sam

18. Defining CGH orientation in tracker coordinates Invar plate 1.Fix mirrors, CGH, and SMRs to stable plate 2.Measure mirror orientation wrt CGH 3.Measure mirror normals with laser tracker CGH Prisms, used to fix reflective faces SMRs, used to give position

19. Measure mirror normals wrt CGH Pivot Linear grating on CGH substrate Autocollimator Rhomboid

20. Use of laser tracker for system alignment Laser tracker CGH with flats SMR, seen directly and in reflection

21. Using tracker through window Actual SMR position Apparent SMR position Use Snell’s law at interfaces for angles Radial distance must include glass: Measure the window carefully Correct for it to determine actual SMR position

22. Test of tracker looking through window An SMR was measured directly at ~1 m 1 cm thick window was inserted between the tracker and the SMR The apparent SMR position was measured with the tracker This was corrected for the refraction of the window These tests showed agreement to 20 ppm, which is consistent with the noise levels of this test

23. Conclusion The laser tracker is great for general purpose metrology It has some special capabilities that make it especially useful for optical alignment –Follows the light through fold mirrors –Can be calibrated to very high accuracy –Can be used for measuring angle as well as position –Can be used to measure through a window