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Download Null lens - The University of Arizona College of Optical Sciences
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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 A1ei1 A2ei2 U R U1 U 2 A1ei1 A2ei2 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!
