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!