Use of a commercial laser tracker for optical alignment James H. Burge, Peng Su, Chunyu Zhao, Tom...
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Transcript of Use of a commercial laser tracker for optical alignment James H. Burge, Peng Su, Chunyu Zhao, Tom...
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