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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
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
(Faro)
• Software converts from spherical coordinates
Laser tracker components
Three manufacturers of Laser Trackers
• Leica Geosystems (Switzerland)
• FARO (USA)
• API (USA)
34”
21”
14”
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
 m 
z  102   0.4  Lz 
 m 
2
 m 
x  y  182   3  Lz 
 m 
x
Lz
2
a
q
z
For other directions, use vector projection
a 
 z cosq )   x sin q )
2
(Out of plane, y, behaves the same as x.)
2
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
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
Measurement of NST secondary mirror
Return sphere
(CoC at F2)
Focus 1 for ellipsoid
Focus 2 for ellipsoid
Interferometer
SMRs
Located by return
into
interferometer
Laser tracker
Optical table
Flat mirror
Ellipsoidal
Secondary
mirror
Measurement of angle with tracker
b2
a2
b
Apparent ball
position
a
a1)
b1
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
Uncertainty in mirror position
(defined by its normal)
a12  a2 2
a 
L
b12  b2 2
b 
2
Actual ball position
(uncertainty a2, b2)
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
SMR 1
Object
to be
measured
Mirror 1
Mirror 2
SMR 2
Laser
tracker
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
x
A
Mirror 1
O

z
Mirror 2
y
B
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
angular
measurements
Uncertainty in
determination of
object’s orientation
Interferometric testing primary mirror segments
for the Giant Magellan Telescope
Spherical mirror
CGH
3.75 m diameter
Tested in situ from floor
130 mm diameter
M2
0.75 m diameter
23 m
Interferometer
Sam
GMT segment
Reference CGH
Insert a CGH to test
system
PSM
aligned to M2
3.8-m sphere
Sam
CGH
Interferometer for
GMT measurements
M2
Use laser tracker to measure position of 3.8-m
mirror wrt wavefront created by Sam
8.4 m diam off axis segment for
Giant Magellan Telescope
Defining CGH orientation in
tracker coordinates
1. Fix mirrors, CGH, and SMRs to stable plate
2. Measure mirror orientation wrt CGH
3. Measure mirror normals with laser tracker
Invar plate
SMRs,
used to give
position
CGH
Prisms, used to fix
reflective faces
Measure mirror normals wrt CGH
Autocollimator
Rhomboid
Pivot
Linear grating on
CGH substrate
Use of laser tracker for system alignment
CGH with flats
Laser tracker
SMR, seen
directly and in
reflection
Using tracker through window
Use Snell’s law at interfaces for angles
Radial distance must include glass: OPD 
t n
i i
Apparent SMR
position
Actual SMR
position
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