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

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)

Laser tracker components

• Leica Geosystems (Switzerland)• FARO (USA)• API (USA)

14”14”

21”21”

34”34”

Three manufacturers of Laser Trackers

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

22

22

10 0.4

18 3

z

z

m

m

m

m

L

L

z

x y

For other directions, use vector projection

2 2cos sina z x

a

z

x

Lz

(Out of plane, y, behaves the same as x.)

Radial:

Lateral

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

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

New Solar Telescope

Big Bear Solar Observatory

Off axis Gregorian, f/0.7 parent

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 trackerHas view to all SMRs

Measurement of NST secondary mirror

Interferometer Ellipsoidal Secondary

mirror

Return sphere(CoC at F2)

Focus 1 for ellipsoid Focus 2 for ellipsoid

Laser trackerSMRs

Located by return into

interferometer

Optical table

Flat mirror

Measurement of angle with tracker

Actual ball position(uncertainty a2, b2)

Apparent ball position

a1)

Unique line connecting the position of the ball

with the position of its mirro

r 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

2 21 2a a

L

2 21 2

2

b bb

Uncertainty in mirror position

b

b2

b1

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

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

Mirror 1

Mirror 2

SMR 2

SMR 1

Object to be measured

Laser tracker

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

x

y

z O

A

B

Mirror 1

Mirror 2

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 determination of object’s orientation

Uncertainty in angular measurements

Interferometric testing primary mirror segments for the Giant Magellan Telescope

GMT segment

Spherical mirror3.75 m diameterTested in situ from floor

M20.75 m diameter

CGH130 mm diameter

Interferometer

23 m

Sam

Reference CGH

PSM PSM aligned to M2aligned to M2

Interferometer forInterferometer forGMT measurementsGMT measurements

CGH

M2

Insert a CGH to test Insert a CGH to test systemsystem

8.4 m diam off axis segment for8.4 m diam off axis segment forGiant Magellan TelescopeGiant Magellan Telescope

3.8-m sphere3.8-m sphere

Use laser tracker to measure position of 3.8-m mirror wrt wavefront created by Sam

SamSam

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

Measure mirror normals wrt CGH

Pivot

Linear grating on CGH substrate

Autocollimator

Rhomboid

Use of laser tracker for system alignment

Laser tracker

CGH with flats

SMR, seen directly and in reflection

Using tracker through window

Actual SMR position

Apparent SMR position

Use Snell’s law at interfaces for angles

Radial distance must include glass: i iOPD t n

Measure the window carefully

Correct for it to determine actual SMR position

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

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