A Path to Freeform Optics. Kyle Fuerschbach University of Rochester Jannick Rolland University of Rochester Kevin Thompson Synopsys

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1 A Path to Freeform Optics Kyle Fuerschbach University of Rochester Jannick Rolland University of Rochester Kevin Thompson Synopsys

2 Role of Non-Symmetric/Freeform Surfaces in Optical Systems Design Packaging is a driving constraint during optical design Non-symmetric surfaces provide new degreesof-freedom for achieving shrinking space requirements Minimize number of elements Tilted/Decentered geometries

3 Deployment of Optical Systems Spheres Symmetric Aspheres Off-Axis Conics φ Polynomials Freeform Shapes Surface Shape s-7's* 198's Active Research Optical Design 189 s-7s Late 9's (DARPA) Active Research Active Research Surface Fabrication 189 5* 198's 7 Active Research Surface Testing Evolution Active Research Active Research Active Research Future Research Telescope Assembly Evolution Evolution Active Research Active Research Future Research *Recently (5) it has been demonstrated that power series aspheres are mathematically unstable and new surface formulation has been proposed.

4 -Polynomial Surface Type A surface whose departure from a sphere Varies with radial distance from center Varies with clocking angle Frequency of N cycles per roundtrip in the aperture Sag of optical surface is no longer limited to be rotationally symmetric Additional degree(s) of freedom Surface can correct for asymmetric aberrations (i.e. coma) within an optical design

5 Surface Conic surface with FRINGE Zernike overlay z c k c j 1 C j Z j Sag Sag w/o Base Conic

6 Optical Design Tools Nodal Aberration Theory (NAT) Foundation for behavior of ANY optical imaging system with a circular or near circular (within ~3%) pupil There are NO new aberrations Aberrations have a new dependence in field Nodes are zeros of aberration Full Field Display Computes Zernike coefficients Throughout FOV over grid of points Displays coefficients Magnitude/Orientation

7 Non-Symmetric Surfaces in NAT Two places for non-symmetric surfaces to lie At the stop surface Beam footprint for all fields fills stop All fields are influenced by non-symmetric surface equally Result is field-constant contribution to aberration function Away from the stop surface Beam footprint is different for each field Each field is influenced differently by non-symmetric surface Result is both field-constant and field-dependent contributions to aberration function

8 Example: Zernike 3 rd Ord. Spherical Beam Footprint incident on Z 3rd Spher surface Generates Z 3rd Spher, Z 3rd Coma, Z 3rd Astig and low order 1λ Z 3rd Spher Beam Footprint BF Minus PST/TLT/PWR & Z 3rd Spher BF Minus PST/TLT/PWR & Z 3rd Spher /Z 3rd Coma

9 Example: Zernike 3 rd Ord. Coma Beam Footprint incident on Z 3rd Coma surface Generates Z 3rd Coma, Z 3rd Astig and low order 1λ Z 3rd Coma Beam Footprint BF Minus PST/TLT/PWR & Z 3rd Coma

10 Example: Zernike 3 rd Ord. Astigmatism Beam Footprint incident on Z 3rd Astig surface Generates Z 3rd Astig and low order 1λ Z 3rd Astig Beam Footprint BF Minus PST/TLT/PWR & Z 3rd Astig

11 Design Example F/1.9, 1 FFOV Low Cost LWIR Imager Micro-Bolometer 3x pixel resolution, 5µm pitch Uncooled Does not need accessible exit pupil Requires fast system F/# Drives up spherical volume of system Compact Geometry Large input port in small spherical volume Unobscured

12 11:5:1 Y Field Angle Potential On-Axis Solution 1:1:5 NPP Solution RMS wavefront error less than < λ/5 over 1 FFOV 1% Obscured k Sec =.5 k Ter =.3 9-Jun-11 Diffraction = 1µm RMS WAVEFRONT ERROR Minimum =.877 Maximum =.388 Average =.313 Std Dev =..5waves (1. nm) k Pri = MM 1.71 MM Scale: Jun-11

13 11:5:59 11:5:59 11:5:59 Aberration Contributions Diffraction 1µm Z 3rd Astig 1 diagonal FFOV Z 3rd Coma = Z 3rd Spher Zernike Polynomial 9-Jun-11 Z Ellip. Coma Z Obl.Spher. Z 5th Spher FRINGE ZERNIKE PAIR Z5 AND Z Minimum =.1957e-5 Maximum =.1188 Average =.53 Std Dev =.317.5waves (1. nm) Zernike Polynomial 9-Jun-11 FRINGE ZERNIKE PAIR Z7 AND Z8 Minimum =.11e-5 Maximum = Average =. Std Dev =.13.5waves (1. nm) Zernike Polynomial 9-Jun-11 FRINGE ZERNIKE COEFFICIENT Z9 Minimum = Maximum = -.13 Average = -.17 Std Dev =.198.5waves (1. nm)

14 Creating an Unobscured System Off-axis in aperture? Shape of primary prohibitive Off-axis in field? Need to use large field angles Tilt the surfaces? 1:1: MM Scale: Jun-11

15 Tilting the Surfaces? To date, most solutions have been offset in aperture and/or field Invoking φ-polynomial surfaces has created for truly off-axis designs with high performance

16 1:37:3 1:37:35 1:37:35 Tilt the Surfaces (On-Axis) Astigmatism Node Z 3rd Astig Z 3rd Coma Z 3rd Spher ynomial FRINGE ZERNIKE PAIR Z5 AND Z 1:37:35 Minimum =.1957e-5 Maximum =.81 Average =.8757 Std Dev = Jun-11.5waves (1. nm) FRINGE ZERNIKE PAIR Z5 AND Z 1 diagonal FFOV Minimum =.1957e-5 Maximum =.81 Average =.8757 Std Dev =.838 FRINGE ZERNIKE PAIR Z7 AND Z8 Minimum =.11e-5 Maximum =.1889 Average =.77 Std Dev =.913 FRINGE ZERNIKE COEFFICIENT Z9 Minimum = Maximum =.91 Average =.155 Std Dev = Jun-11.5waves (1. nm) 8-Jun-11.5waves (1. nm) 8-Jun-11.5waves (1. nm) 5. MM

17 1::1 1::1 1:: Tilt the Surfaces (5% Tilt) Z 3rd Astig Z 3rd Coma Z 3rd Spher ynomial FRINGE ZERNIKE PAIR Z5 AND Z 1:: Minimum =.19 Maximum = 8.53 Average = Std Dev = Jun-11 3waves (1. nm) FRINGE ZERNIKE PAIR Z5 AND Z Minimum =.19 Maximum = 8.53 Average = Std Dev = 1.31 FRINGE ZERNIKE PAIR Z7 AND Z8 Minimum = 1.99 Maximum =.33 Average =.18 Std Dev =.979 FRINGE ZERNIKE COEFFICIENT Z9 Minimum = -.81 Maximum =.1387 Average =.378 Std Dev =.3 8-Jun-11 3waves (1. nm) 8-Jun-11 3waves (1. nm) 8-Jun-11 3waves (1. nm) 5. MM

18 1:5: 1:5: 1:5: Tilt the Surfaces (5% Tilt) Z 3rd Astig Z 3rd Coma Z 3rd Spher ynomial FRINGE ZERNIKE PAIR Z5 AND Z 1:5: Minimum =.19 Maximum = 8.53 Average = Std Dev = Jun-11 3waves (1. nm) FRINGE ZERNIKE PAIR Z5 AND Z Minimum =.978 Maximum = 1.38 Average = 9.98 Std Dev = 3.91 FRINGE ZERNIKE PAIR Z7 AND Z8 Minimum = 3.7 Maximum = Average =.879 Std Dev =.591 FRINGE ZERNIKE COEFFICIENT Z9 Minimum = Maximum =.373 Average =.8957 Std Dev =.17 8-Jun-11 3waves (1. nm) 8-Jun-11 3waves (1. nm) 8-Jun-11 3waves (1. nm) 5. MM

19 1:5:8 1:5:8 1:5:8 Tilt the Surfaces (75% Tilt) Z 3rd Astig Z 3rd Coma Z 3rd Spher ynomial FRINGE ZERNIKE PAIR Z5 AND Z 1:5:8 Minimum =.19 Maximum = 8.53 Average = Std Dev = Jun-11 3waves (1. nm) FRINGE ZERNIKE PAIR Z5 AND Z Minimum =.57 Maximum = 3.57 Average = Std Dev = 5.73 FRINGE ZERNIKE PAIR Z7 AND Z8 Minimum = 5.37 Maximum = 1.8 Average = 7.9 Std Dev = 1.91 FRINGE ZERNIKE COEFFICIENT Z9 Minimum = -1. Maximum =.8559 Average =.1991 Std Dev =.3 8-Jun-11 3waves (1. nm) 8-Jun-11 3waves (1. nm) 8-Jun-11 3waves (1. nm) 5. MM

20 1:: 1::7 1::7 Tilt the Surfaces (1% Tilt) Z 3rd Astig Z 3rd Coma Z 3rd Spher ynomial FRINGE ZERNIKE PAIR Z5 AND Z 1::7 Minimum =.19 Maximum = 8.53 Average = Std Dev = Jun-11 3waves (1. nm) FRINGE ZERNIKE PAIR Z5 AND Z Minimum = Maximum = Average = 9.83 Std Dev = FRINGE ZERNIKE PAIR Z7 AND Z8 Minimum = Maximum = Average = Std Dev = 5.38 FRINGE ZERNIKE COEFFICIENT Z9 Minimum =.885 Maximum = Average =.387 Std Dev =. 8-Jun-11 3waves (1. nm) 8-Jun-11 3waves (1. nm) 8-Jun-11 3waves (1. nm) 5. MM

21 Recovering the Performance With tilted mirrors for unobscured system Nearly constant field aberrations within 1 FFOV True for low & high order terms Negligible effect on spherical aberration

22 Design Strategy I Use φ-polynomials at stop surface to remove field-constant contributions to the aberration function

23 1:8: 1:8: 1:8:1 1:8:3 11:1:1 On-Axis Full Tilt Z 3rd Astig Z 3rd Coma Z 3rd Spher X Field Angle in Object Space - degree 7-Jun-11 FRINGE ZERNIKE PAIR Z5 AND Z Minimum =.58 Maximum = 8.5 Average =.377 Std Dev = waves (1. nm) RMS WAVEFRONT ERROR Minimum =.98 Maximum = 1.37 Average =.731 Std Dev =.17 7-Jun-11 FRINGE ZERNIKE PAIR Z7 AND Z8 Minimum = Maximum = Average = Std Dev =.3 1waves (1. nm) RMS WAVEFRONT ERROR FIELD ANGLE IN OBJECT SPA 7-Jun-11 1waves (1. nm) Z Ellip. Coma Z Obl.Spher. RMS WFE 7-Jun-11 7-Jun-11 Minimum = Maximum = 1.39 FRINGE ZERNIKE COEFFICIENT Average Z9= 11.9 FIELD ANGLE IN OBJECT Std Dev SPACE =.313 Minimum =.198 Maximum = Average =.7 Std Dev =.3 1waves (1. nm) 1waves (

24 1:8: 1:8: 1:8:1 1:8:3 11:1:1 On-Axis Full Tilt Z 3rd Astig Z 3rd Coma Z 3rd Spher Use these polynomials on stop surface X Field Angle in Object Space - degree 7-Jun-11 FRINGE ZERNIKE PAIR Z5 AND Z Minimum =.58 Maximum = 8.5 Average =.377 Std Dev = waves (1. nm) RMS WAVEFRONT ERROR Minimum =.98 Maximum = 1.37 Average =.731 Std Dev =.17 7-Jun-11 FRINGE ZERNIKE PAIR Z7 AND Z8 Minimum = Maximum = Average = Std Dev =.3 1waves (1. nm) RMS WAVEFRONT ERROR FIELD ANGLE IN OBJECT SPA 7-Jun-11 1waves (1. nm) Z Ellip. Coma Z Obl.Spher. RMS WFE 7-Jun-11 7-Jun-11 Minimum = Maximum = 1.39 FRINGE ZERNIKE COEFFICIENT Average Z9= 11.9 FIELD ANGLE IN OBJECT Std Dev SPACE =.313 Minimum =.198 Maximum = Average =.7 Std Dev =.3 1waves (1. nm) 1waves (

25 11:15:59 11:15:59 11:15:59 11:1:1 11:1:1 Optimized Design with Strategy I Z 3rd Astig Z 3rd Coma Z 3rd Spher X Field Angle in Object Space - degree 7-Jun-11 FRINGE ZERNIKE PAIR Z5 AND Z Minimum =.753 Maximum =.8 Average =.393 Std Dev =.838 1waves (1. nm) RMS WAVEFRONT ERROR Minimum =.98 Maximum = 1.37 Average =.731 Std Dev =.17 7-Jun-11 FRINGE ZERNIKE PAIR Z7 AND Z8 Minimum =.9157 Maximum =.57 Average =.187 Std Dev = waves (1. nm) RMS WAVEFRONT ERROR FIELD ANGLE IN OBJECT SPA 7-Jun-11 1waves (1. nm) Z Ellip. Coma Z Obl.Spher. RMS WFE 7-Jun-11 7-Jun-11 Minimum =.98 Maximum = 1.37 FRINGE ZERNIKE COEFFICIENT Z9 Average =.731 FIELD ANGLE IN OBJECT Std SPACE Dev =.17 Minimum =.179 Maximum =.999 Average =.53 Std Dev = waves (1. nm) 1waves (

26 Design Strategy II Use φ-polynomials away from stop surface to counteract field dependent aberrations

27 11:17:15 11:17:15 11:17:15 11:17:18 11:17:18 Optimized Design with Strategy I Z 3rd Astig Z 3rd Coma Z 3rd Spher X Field Angle in Object Space - degre 7-Jun-11 FRINGE ZERNIKE PAIR Z5 AND Z Minimum =.753 Maximum =.8 Average =.393 Std Dev =.838 1waves (1. nm) RMS WAVEFRONT ERROR Minimum =.98 Maximum = 1.37 Average =.731 Std Dev =.17 7-Jun-11 FRINGE ZERNIKE PAIR Z7 AND Z8 Minimum =.9157 Maximum =.57 Average =.187 Std Dev = waves (1. nm) RMS WAVEFRONT ERROR X Field Angle in Object Space FIELD - ANGLE degreesin OBJECT SP Z 7-Jun-11 1waves (1. nm) Ellip. Coma Z Obl.Spher. RMS WFE 7-Jun-11 7-Jun-11 Minimum =.98 Maximum = 1.37 Average =.731 FRINGE ZERNIKE COEFFICIENT Z9 Std Dev =.17 Minimum =.179 Maximum =.999 Average =.53 Std Dev = waves (1. nm) 1waves (

28 11:17:15 11:17:15 11:17:15 11:17:18 11:17:18 Optimized Design with Strategy I Z 3rd Astig Z 3rd Coma Z 3rd Spher Use this polynomial on Tertiary X Field Angle in Object Space - degre 7-Jun-11 FRINGE ZERNIKE PAIR Z5 AND Z Minimum =.753 Maximum =.8 Average =.393 Std Dev =.838 1waves (1. nm) RMS WAVEFRONT ERROR Minimum =.98 Maximum = 1.37 Average =.731 Std Dev =.17 7-Jun-11 FRINGE ZERNIKE PAIR Z7 AND Z8 Minimum =.9157 Maximum =.57 Average =.187 Std Dev = waves (1. nm) RMS WAVEFRONT ERROR X Field Angle in Object Space FIELD - ANGLE degreesin OBJECT SP Z 7-Jun-11 1waves (1. nm) Ellip. Coma Z Obl.Spher. RMS WFE 7-Jun-11 7-Jun-11 Minimum =.98 Maximum = 1.37 Average =.731 FRINGE ZERNIKE COEFFICIENT Z9 Std Dev =.17 Minimum =.179 Maximum =.999 Average =.53 Std Dev = waves (1. nm) 1waves (

29 11::5 11::5 11::5 11::53 11:17:18 Optimized Design with Strategy II Z 3rd Astig Z 3rd Coma Z 3rd Spher X Field Angle in Object Space - degr 7-Jun-11 FRINGE ZERNIKE PAIR Z5 AND Z Minimum =.5 Maximum = 1.7 Average =.77 Std Dev =.351 1waves (1. nm) RMS WAVEFRONT ERROR Minimum =.98 Maximum = 1.37 Average =.731 Std Dev =.17 7-Jun-11 FRINGE ZERNIKE PAIR Z7 AND Z8 Minimum = Maximum =.313 Average = Std Dev = waves (1. nm) RMS WAVEFRONT ERROR X Field Angle in Object Space FIELD - degrees ANGLE IN OBJECT SP Z 7-Jun-11 1waves (1. nm) Ellip. Coma Z Obl.Spher. RMS WFE 7-Jun-11 7-Jun-11 Minimum =.1173 Maximum =.353 Average =.587 FRINGE ZERNIKE COEFFICIENT Z9 Std Dev = Minimum = Maximum = Average = Std Dev = waves (1. nm) 1waves (

$wavefront error at a λ = 1 µm of less than λ/5 over 1 FFOV Secondary 8 Primary Diffraction = Limit @ 1µm$

30 Final Optimized Solution With further implementation of design strategies I & II Reach solution with RMS wavefront error at a λ = 1 µm of less than λ/5 over 1 FFOV Secondary 8 Primary Diffraction = 1µm Tertiary

31 Fabrication Secondary mirror has been diamond turned by II-VI Infrared Inc.

32 Metrology 1:1:17 1:1:17 Acceptance testing/characterization configuration for the secondary mirror Deformable Mirror (Coma) Pupil Imager Output of Interferometer Offner Null (Spherical) Tilted Geometry (Astigmatism) Mirror Under Test 75. MM XZ

33 Metrology 1:1:17 1:1:17 Acceptance testing/characterization configuration for the secondary mirror Deformable Mirror (Coma) Pupil Imager Output of Interferometer Offner Null (Spherical) β Tilted Geometry (Astigmatism) Mirror Under Test 75. MM XZ

34 Metrology 1:1:17 1:1:17 Acceptance testing/characterization configuration for the secondary mirror Deformable Mirror (Coma) Pupil Imager Output of Interferometer Offner Null (Spherical) Tilted Geometry (Astigmatism) Mirror Under Test 75. MM XZ

35 Metrology 1:1:17 1:1:17 Acceptance testing/characterization configuration for the secondary mirror Deformable Mirror (Coma) Pupil Imager Output of Interferometer Offner Null (Spherical) Tilted Geometry (Astigmatism) Mirror Under Test 75. MM XZ

36 Summary φ-polynomial Surfaces: Allow for off-axis optical designs with high performance When located at stop surface will remove fieldconstant contributions to the aberration function When located away from stop surface will counteract field dependent aberrations Can be fabricated with current technologies in the infrared Testing configurations are realizable

37 We thank: Acknowledgements Frank J. Horton Research Fellowship National Science Foundation (EECS-1179) II-VI Foundation II-VI Corporation for fabrication support Synopsys for the student license of CODE V

38 1:19:3 1:19:3 1:19: 1:3:3 Aberrations of Final System Diffraction Z 3rd Astig 1 diagonal FFOV Z = 3rd Coma 1µm Z 3rd Spher FRINGE ZERNIKE COEFFICIENT Z1 Minimum = Maximum =.15 Average =.113 Std Dev =.1918 X Field Angle in Object 15-Jun-11 Space - degrees.1waves (1. nm) Zernike Polynomial 15-Jun-11 Z Ellip. Coma Z Obl.Spher. Z 5th Spher FRINGE ZERNIKE PAIR Z5 AND Z Minimum =.8515 Maximum =.989 Average =.375 Std Dev =.155.1waves (1. nm) Zernike Polynomial 15-Jun-11 FRINGE ZERNIKE PAIR Z7 AND Z8 Minimum =.337 Maximum =.1 Average =.55 Std Dev = waves (1. nm) Zernike Polynomial 15-Jun-11 FRINGE ZERNIKE COEFFICIENT Z9 Minimum = Maximum =.1155 Average = -.11 Std Dev =.817.1waves (1. nm)

Freeform, φ-polynomial Optical Surfaces: Optical Design, Fabrication and Assembly. Kyle Fuerschbach. Submitted in Partial Fulfillment of the

Freeform, φ-polynomial Optical Surfaces: Optical Design, Fabrication and Assembly by Kyle Fuerschbach Submitted in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Supervised