1. 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 Poleshchuk Institute for Automation, Novosibirsk, Russia AOMATT, Chengdu, China July 8-12, 2007

2. 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

3. Null Test of Asphere (for a mild asphere) interferometer Without Null Lens With Null Lens Null lens

4. 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

5. 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

6. 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

7. CGH Design 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

8. Leads to mapping error Needs to be corrected Grid of rays at object plane Grid of rays at CGH plane x’ → ρ → a.ρ 3 y’ → θ → θ’ CGH Distortion

9. 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

10. Accuracy of CGH 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

11. 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

12. Calibration of CGH Non-axisymmetric Errors Calibrate by rotating CGH Rotate CGH to N azimuthal positions –i.e., Nθ = 360 0 –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

13. Coma 0 0 Coma Rotated to 180 0 Astigmatism Evans and Kestner, App. Opt. 1996 Calibration of CGH Non-axisymmetric Errors N = 2 Coma is a 1 θ error Astigmatism is a 2θ error Rotating coma by 180 0 and averaging removes error Rotating astigmatism similarly doesn’t do any thing

14. 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 3 120 0 rotations A B All error terms except the 3θ term averages out N = 3 Calibration of CGH Non-axisymmetric Errors Evans and Kestner, App. Opt. 1996

15. CGH-writer Errors Spoke-like pattern comes from wobble of writer table Radial phase error comes from errors in radial coordinate ε axisym (θ) = constantε nonaxisym (r) = constant CGH writer Writing head Written line

16. 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 CGH Axisymmetric Errors

17. Methods of Encoding CGHs Separate quadrants of CGH into spherical and aspherical parts Spherical Prescription Aspheric Prescription Quadrant Hologram Complex superposition of spherical and aspherical patterns Aspherical Prescription Spherical Prescription Superposed Hologram (Reichelt, 2003)

18. Wavefront Errors in Sphere r WW Line Spacing for Sphere r S/  r =  W*S/ * = ÷ = Line Spacing for Asphere r S/  W =  r* /S WW Wavefront Errors in Asphere r r rr Line Spacing Errors in Asphere r rr Line Spacing Errors in Sphere Calibration of CGH Axisymmetric Errors These are the same in CGH coordinates! Make correction to null lens test

19. CGH Distortion Correction D is distortion mapping function D does not change amplitude of ΔW

20. 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

21. Quadrant-CGH Substrate Quality abab 220mm quadrant-CGH 220mm substrate Substrate test

22. Demonstration – using two spheres Notice the 2 nm zone at r=12.3 mm In both patterns!

23. 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!

24. 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

25. Primary mirror Null lens test stand Null lens CGH Interferometer Assembled Test Stand

26. 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 Mirror RoC CGH Mounted on kinematic stage Stage has all 6 degrees of freedom Null lens Interferometer Align to mirror Has 5 degrees of freedom

27. Superposed CGH Principle of Superposition Complex field, U R, is sum of fields U 1 and U 2 S. Reichelt, H.J. Tiziani, Opt. Comm. 2003 where, For a binary phase profile: Φ B =

28. Superposed CGH Preliminary Design 1-D OPD from 2 spheres Sphere 1 Sphere 2 Unwrapped OPD 1-D binary superposed pattern Issues: Determine minimum line width Cross-talk between orders

29. 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

30. 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!