Transcript Null lens - The University of Arizona College of Optical Sciences

Absolute Calibration of Null
Correctors Using Dual-ComputerGenerated Holograms (CGHs)
Proteep Mallik, Jim Burge, Rene Zehnder,
College of Optical Sciences, University of Arizona
Alexander Poleshchuk
Institute for Automation, Novosibirsk, Russia
AOMATT, Chengdu, China
July 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)
Without
Null
Lens
With
Null
Lens
interferometer
Null lens
interferometer
Calibration of Null Lens
• Use CGH to calibrate
null lens
• CGH reflects wavefront
as if from primary mirror
• Excellent accuracy,
limited by
– Substrate flatness
– Pattern errors
Null Lens
Primary Mirror (asphere)
CGH
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
200mm
diameter
caustic
Wavefront fit ~0.030l rms
(~19nm)
Paraxial Focus
Plane
f/0.85 aspheric
mirror
Fabrication of Computer-generated
Holograms (CGHs)
• Pattern written onto glass
with laser writer
• Chrome on glass
Rings
placed
every λ/2
OPD
Poleshchuk, App. Opt. 1999
CGH Design
Mirror Mapping Onto CGH
100
How mirror
maps onto
CGH
CGH Linespacing
80
60
40
CGH Position (mm)
Example from a 220mm
CGH to test a 4-meter
f/0.85 parabola
20
0
-20
-40
-60
1
10
-80
Log Spacing (um)
-100
-2500 -2000 -1500 -1000
4
0
-500
0
500
Mirror Position (mm)
1000
1500
2000
2500
OPD at CGH
x 10
-0.5
OPD in waves
-1
0
10
0
20
40
60
80
CGH Position (mm)
100
120
Spacing of lines on CGH
Wavefront (OPD) at CGH
-1.5
-2
-2.5
-3
-3.5
-100
-80
-60
-40
-20
0
20
CGH Position (mm)
40
60
80
100
CGH Distortion
•Leads to mapping
error
Grid of rays at
object plane
•Needs to be
corrected
x’ → ρ → a.ρ3
y’ → θ → θ’
Grid of rays at
CGH plane
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/2.4
And dozens of smaller mirrors for UA and for industry
Accuracy of CGH
Asphere CGH (Discovery Channel Telescope primary test)
D = 4.2-meter, f/2 parabola
Error Term
Value
dK (ppm)
SA (nm rms)
Hologram distortion (μm scale)
0.2
21
0.9
Hologram distortion (μm rms)
0.03
2.6
Substrate figure (rms waves)
0.005
3.2
Chrome thickness variation (nm rms)
2
2.0
Wavelength (ppm)
10
RSS
32
1.4
38
1.7
Figure (nm rms)
CGH calibration for DCT test is accurate to
1.7 nm rms for low order spherical aberration
4.6 nm rms for other irregularity
4.6
Roadmap to <1 nm rms calibration
Separate 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 CGH
Non-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
Calibration of CGH
Non-axisymmetric Errors
N=2
Coma
00
•Coma is a 1 θ error
Coma
Rotated
to 1800
•Astigmatism is a 2θ error
•Rotating coma by 1800 and
averaging removes error
•Rotating astigmatism
similarly doesn’t do any thing
Astigmatism
Evans and Kestner, App. Opt. 1996
Calibration of CGH
Non-axisymmetric Errors
N=3
For case
with errors
up to 5θ
3θ term
remains
Rotate to 3
positions
and
average
A
•Zernike terms up to 5θ introduced
•Position clocked by 3 1200 rotations
B
•All error terms except the 3θ term
averages out
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
εnonaxisym(r) = constant
εaxisym(θ) = constant
Writing head
CGH writer
Written line
Calibration of CGH
Axisymmetric Errors
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
Methods of Encoding CGHs
• Separate quadrants of CGH into spherical and aspherical parts
Spherical Prescription
Quadrant Hologram
Aspheric Prescription
(Reichelt, 2003)
• Complex superposition of spherical and aspherical patterns
Spherical
Prescription
Superposed Hologram
Aspherical
Prescription
Calibration of CGH
Axisymmetric Errors
Line Spacing for Sphere
Wavefront Errors in Sphere
S/l
DW
r
Line Spacing Errors in Sphere
Dr
*
r
=
r
Dr = DW*S/l
Line Spacing Errors in Asphere
Dr
r
Line Spacing for Asphere
÷
Wavefront Errors in Asphere
S/l
=
DW
r
r
DW = Dr*l/S
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
220mm quadrant-CGH
1
2
4
3
Quadrant-CGH
Substrate Quality
a
220mm
substrate
b
220mm quadrant-CGH
Substrate test
Demonstration – using two spheres
Sphere 1 R = 59mm
8.1 nm rms
Sphere 2 R = 67 mm
7.0 nm rms
Notice the 2 nm zone
at r=12.3 mm
Radial portion of Sphere 1
3.8 nm rms
Radial portion of Sphere 2
3.2 nm rms
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!
CGH radial error in µm
-0.1
-0.12
Sphere 1
Sphere 2
-0.14
-0.16
-0.18
-0.2
0
4
8
12
radial position in mm
16
Null Lens Calibration Stand
interferometer
•
•
•
•
Facility at U of A
Test stand assembled
Automated motion control
Can be used to test large
null lenses and CGHs
Null lens
3m
CGH
Interferometer
Null lens
test stand
Assembled Test Stand
Null lens
Primary mirror
CGH
Alignment
•Align interferometer to
spherical alignment mirror
•Remove spherical mirror
Interferometer
•Align to mirror
•Has 5 degrees of
freedom
Mirror RoC
•Interferometer is now
aligned to null lens
•Align CGH to interferometer
Spherical alignment mirror
•Kinematically mounted on top of null lens cell
Null lens
CGH
•Mounted on kinematic stage
•Stage has all 6 degrees of
freedom
Superposed CGH
Principle of Superposition
Complex field, UR, is sum of
fields U1 and U2
U R  U1  U 2  A1ei1  A2 ei2
U R U1 U 2  A1ei1  A2ei2
where,

 

1/ 2
2
2

AR  Re U R   Im U R  


 Im U R  
 R  arctan 

 Re U R  
For a binary phase profile:
ΦB =
 , R  0
 / 2,  R  0
0,  R  0
S. Reichelt, H.J. Tiziani, Opt. Comm. 2003
Superposed CGH
Preliminary Design 1-D
OPD from 2 spheres
Unwrapped OPD
45
4
40
3
35
2
Sphere 1
30
1
25
0
20
Sphere 2
-1
15
10
-2
5
-3
0
0
100
200
300
400
500
600
700
800
900
-4
1000
0
100
200
300
400
500
600
700
800
900
1
Issues:
•Determine minimum line
width
•Cross-talk between
orders
0.8
1-D binary
superposed pattern
0.6
0.4
0.2
0
0
100
200
300
400
500
600
700
800
900
1000
1000
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!