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Absolute Calibration of Null Correctors Using Dual-Computer-
Generated Holograms (CGHs)
Proteep Mallik, Jim Burge, Rene Zehnder, College of Optical Sciences, University of Arizona
Alexander PoleshchukInstitute for Automation, Novosibirsk, Russia
AOMATT, Chengdu, ChinaJuly 8-12, 2007
Outline• Introduction
– Null Test of Asphere– Calibration of Null Corrector
• Computer-generated Holograms (CGHs)– Fabrication– Accuracy of CGH
• Calibration of CGHs– Axisymmetric and non-axisymmetric errors
• Absolute Testing of Aspheres– Quadrant and superimposed CGHs
• Measurements Using Quadrant CGHs• Test System for CGH and Null Lens Calibration• Conclusions and Future Work
Null Test of Asphere (for a mild asphere)
interferometer
interferometer
Without Null Lens
With Null Lens
Null lens
Calibration of Null Lens
Primary Mirror (asphere) CGH
Null Lens
• Use CGH to calibrate null lens
• CGH reflects wavefront as if from primary mirror
• Excellent accuracy, limited by– Substrate flatness– Pattern errors
Why Use CGH?• CGH can be made more accurately than the null lens• But CGH cannot test mirror itself
– Must control ray angles and phase• Perform cascading test
– Use CGH to calibrate null lens– Use null lens to measure aspheric mirror
Paraxial Focus Plane
200mm diameter caustic
Wavefront fit ~0.030 rms (~19nm) f/0.85 aspheric
mirror
Fabrication of Computer-generated Holograms (CGHs)• Pattern written onto glass with laser writer
• Chrome on glass
Poleshchuk, App. Opt. 1999
Rings placed every λ/2 OPD
0 20 40 60 80 100 12010
0
101
CGH Linespacing
CGH Position (mm)
Log
Spa
cing
(um
)
CGH Design
-2500 -2000 -1500 -1000 -500 0 500 1000 1500 2000 2500-100
-80
-60
-40
-20
0
20
40
60
80
100Mirror Mapping Onto CGH
Mirror Position (mm)
CG
H P
ositi
on (
mm
)
-100 -80 -60 -40 -20 0 20 40 60 80 100-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0x 10
4 OPD at CGH
CGH Position (mm)
OP
D in
wav
es
How mirror maps onto CGH
Wavefront (OPD) at CGH
Spacing of lines on CGH
Example from a 220mm CGH to test a 4-meter f/0.85 parabola
•Leads to mapping error
•Needs to be corrected
Grid of rays at object plane
Grid of rays at CGH plane
x’ → ρ → a.ρ3
y’ → θ → θ’
CGH Distortion
Accuracy of CGH• Null lens corrects for aspheric departure, leaving
10 – 20 nm rms• CGH can measure null lens to oaccuracy of 3 – 6
nm rms• CGHs have been used as the “gold standard” for
numerous big mirrors at UA– 8.4-m LBT primary mirrors, f/1.1– Four 6.5-m mirrors, f/1.25 – Three 3.5-m mirrors f/1.5-f/1.75– MRO 2.4-m primary f/2.4And dozens of smaller mirrors for UA and for industry
Accuracy of CGH
4.61.738RSS
1.43210Wavelength (ppm)
2.02Chrome thickness variation (nm rms)
3.20.005Substrate figure (rms waves)
2.60.03Hologram distortion (μm rms)
0.9210.2Hologram distortion (μm scale)
Figure (nm rms)SA (nm rms)dK (ppm)ValueError Term
4.61.738RSS
1.43210Wavelength (ppm)
2.02Chrome thickness variation (nm rms)
3.20.005Substrate figure (rms waves)
2.60.03Hologram distortion (μm rms)
0.9210.2Hologram distortion (μm scale)
Figure (nm rms)SA (nm rms)dK (ppm)ValueError Term
Asphere CGH (Discovery Channel Telescope primary test)
D = 4.2-meter, f/2 parabola
CGH calibration for DCT test is accurate to
1.7 nm rms for low order spherical aberration
4.6 nm rms for other irregularity
Roadmap to <1 nm rms calibrationSeparate forms of error, measure each one
– Substrate errors• Measure flatness errors directly
– Pattern distortion errors• Use multiple holograms on the same substrate. One
hologram is used for null lens calibration. The other is used to calibrate the line pattern irregularity
– Non-axisymmetric errors • Measure these using rotation
Calibration of CGHNon-axisymmetric Errors
• Calibrate by rotating CGH
• Rotate CGH to N azimuthal positions– i.e., Nθ = 3600
– This removes all errors except of the form kNθ, where k = 1, 2, 3...
(Evans and Kestner, App. Opt. 1996)
• The residual error is axisymmetric error
Coma 00
Coma Rotated to 1800
Astigmatism
Evans and Kestner, App. Opt. 1996
Calibration of CGHNon-axisymmetric Errors
N = 2•Coma is a 1 θ error
•Astigmatism is a 2θ error
•Rotating coma by 1800 and averaging removes error
•Rotating astigmatism similarly doesn’t do any thing
3θ term remains
For case with errors up to 5θ
Rotate to 3 positions
and average
•Zernike terms up to 5θ introduced
•Position clocked by 3 1200 rotations
AB
•All error terms except the 3θ term averages out
N = 3
Calibration of CGHNon-axisymmetric Errors
Evans and Kestner, App. Opt. 1996
CGH-writer Errors•Spoke-like pattern comes from wobble of writer table
•Radial phase error comes from errors in radial coordinate
εaxisym(θ) = constantεnonaxisym(r) = constant
CGH writer Writing head
Written line
Pattern Distortion• Simultaneously write two CGH patterns
– Asphere, used for null lens calibration– Sphere, can be measured directly to high accuracy
• Writer errors will affect both patterns• Measure the sphere, from this determine CGH error and
make correction
Substrate Error• Make zero-order (undiffracted) wavefront measurement• Non-axisymmetric component removed by rotations
Calibration of CGHAxisymmetric Errors
Methods of Encoding CGHs• Separate quadrants of CGH into spherical and aspherical parts
Spherical Prescription
Aspheric PrescriptionQuadrant Hologram
• Complex superposition of spherical and aspherical patterns
Aspherical Prescription
Spherical Prescription
Superposed Hologram
(Reichelt, 2003)
Wavefront Errors in Sphere
r
W
Line Spacing for Sphere
r
S/
r = W*S/
* =
÷ =Line Spacing for Asphere
r
S/
W = r*/S
W
Wavefront Errors in Asphere
rr
r
Line Spacing Errors in Asphere
r
r
Line Spacing Errors in Sphere
Calibration of CGHAxisymmetric Errors
These are the same in
CGH coordinates!
Make correction to null lens test
CGH Distortion Correction
•D is distortion mapping function
•D does not change amplitude of ΔW
Fabricated Quadrant-CGHs•Reference rings are for scaling and distortion correction
•1 and 3 are aspheric, 2 and 4 are spherical quadrants
Sphere-asphere quadrants
1
4
3
2
220mm quadrant-CGH
Quadrant-CGHSubstrate Quality
a
b
220mm quadrant-CGH
220mm substrate
Substrate test
Demonstration – using two spheresSphere 1 R = 59mm
8.1 nm rms Sphere 2 R = 67 mm
7.0 nm rms
Radial portion of Sphere 1 3.8 nm rms
Radial portion of Sphere 2
3.2 nm rms
Notice the 2 nm zone at r=12.3 mm
In both patterns!
Calculation of CGH error for separate quadrants
CGH errors here match to ~0.01 µm rms for radial line distortion Wavefront effects will match to < 2 nm rms!
0 4 8 12 16radial position in m m
-0.2
-0.18
-0.16
-0.14
-0.12
-0.1
CG
H r
adia
l er
ror
in µ
m Sphere 1
Sphere 2
Null Lens Calibration Stand
• Facility at U of A• Test stand assembled• Automated motion control• Can be used to test large
null lenses and CGHs
interferometer
CGH
Null lens
3m
Primary mirror
Null lens test stand
Null lens
CGH
Interferometer
Assembled Test Stand
Alignment•Align interferometer to spherical alignment mirror
•Remove spherical mirror
•Interferometer is now aligned to null lens
•Align CGH to interferometer
Spherical alignment mirror•Kinematically mounted on top of null lens cell
Mirr
or R
oC
CGH
•Mounted on kinematic stage
•Stage has all 6 degrees of freedom
Null lens
Interferometer•Align to mirror
•Has 5 degrees of freedom
Superposed CGH Principle of Superposition
1 21 2 1 2
i iRU U U A e A e
1/ 22 2
Re ImR R RA U U
Complex field, UR, is sum of fields U1 and U2
S. Reichelt, H.J. Tiziani, Opt. Comm. 2003
1 21 2 1 2
i iRU U U Ae A e
where,
Imarctan
ReR
RR
U
U
For a binary phase profile:
, 0
/ 2, 0
0, 0
R
R
R
ΦB =
Superposed CGH Preliminary Design 1-D
0 100 200 300 400 500 600 700 800 900 10000
5
10
15
20
25
30
35
40
45
0 100 200 300 400 500 600 700 800 900 1000-4
-3
-2
-1
0
1
2
3
4
0 100 200 300 400 500 600 700 800 900 10000
0.2
0.4
0.6
0.8
1
OPD from 2 spheres
Sphere 1
Sphere 2
Unwrapped OPD
1-D binary superposed pattern
Issues:
•Determine minimum line width
•Cross-talk between orders
Conclusions/Future Work
• Analyze data from large, 220mm CGHs• Complete design of superposed CGHs• Make measurements using superposed CGHs on DCT
primary• Calibrate null lens in test stand to better than 1 nm rms
surface error• Use system for future CGH and null tests of large optics
Acknowledgements
• Parts for test stand fabricated at ITT, Rochester• CGHs fabricated by Dr. Poleshchuk• Research funded in part by NASA/JPL and DCT• Staff and scientists at our large optics facility
Thanks!