Use of a commercial laser tracker for optical alignment

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. What is a Laser Tracker? 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 (Faro)

3. Laser tracker components

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

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

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 Secondary mirrorwith SMRs at known positions wrt aspheric parent Declination axis Laser trackerHas view to all SMRs 1.7-m primary mirrorwith SMRs at known positions wrt aspheric parent

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

11. Measurement of angle with tracker Db2 Actual ball position(uncertainty Da2, Db2) Da2 Unique line connecting the position of the ball with the position of its mirror image: length = L Db a Apparent ball position (Da1) Db1 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) Uncertainty in mirror position

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 eachWe 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 orientationfrom measuring two mirrors as a function of the angle between the mirrors Inverse sensitivity, normalized Defined as ratio Uncertainty in angular measurements Uncertainty in determination of object’s orientation

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

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

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

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

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

21. Using tracker through window Apparent SMR position Use Snell’s law at interfaces for angles Radial distance must include glass: Actual SMR position 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