Tutorial: Design, Fabrication, and Testing of Aspheric Surfaces

1. Tutorial:Design, Fabrication, and Testing of Aspheric Surfaces Chia-Ling Li College of Optical Sciences, University of Arizona Dec. 12. 2013

2. Outline • Introduction • Design • Mathematical representation of aspherical surfaces • Aspheric shape design guide • Tolerances for aspherical optical elements • Fabrication • Testing • Profilometry • Interferometry in reflection • Interferometry in transmission • Summary

3. Introduction

4. What is an aspherical surface? • The aspheric surface means not spherical. • It can be thought as comprising a base sphere and an aspheric cap. Aspherical surface Aspherical cap Spherical base surface

5. Why is it important? • It can correct aperture dependent aberrations, like spherical aberration. • It can correct field dependent aberrations, like distortion and field curvature. • It can reduce lens weight, make optical systems more compact, and in some cases reduce cost. • Fewer elements are needed in a system with aspherical surfaces: making systems smaller, lighter and shorter.

6. Design

7. Mathematical representation of aspherical surfaces Q-Type Asphere: Even Asphere: Polynomial: Zernike Standard Sag

8. Aspheric shape design guide • When designing an aspheric surface, some surface shapes should be avoided because they could increase the manufacture difficulty and the cost. • The slope of the aspheric departure often has a larger impact on manufacturing difficulty than the amplitude of the asphere. Kreischer Optics, Ltd., “Aspheric Design Guide”

9. Tolerances for aspherical optical elements (1) http://www.optimaxsi.com/capabilities/aspheres/

10. Tolerances for aspherical optical elements (2) ISO 10110 • 3/4(0.8/0.4) :a sag error of 4 fringes (@ λ = 546 nm), a total irregularity of 0.8 fringes, and a rotational symmetric irregularity of 0.4 fringes • 4/ : tolerance for the tilt angle • B. Braunecker, etc., “Advanced Optics Using Aspherical Elements”, SPIE ebook, 2008.

11. Fabrication

12. Different process technologies • http://www.optimaxsi.com/capabilities/aspheres/ • B. Braunecker, etc., “Advanced Optics Using Aspherical Elements”, SPIE ebook, 2008.

13. The manufacturing cost of different materials • Crystals: CNC machining or diamond turning • Glasses:CNC machining or precision molding • Polymers: injection-molding • B. Braunecker, etc., “Advanced Optics Using Aspherical Elements”, SPIE ebook, 2008.

14. Classical optics fabrication • The actual production sequence is iterative; several steps must be taken between surface shaping and measurement before the required accuracy level is achieved. • B. Braunecker, etc., “Advanced Optics Using Aspherical Elements”, SPIE ebook, 2008.

15. The characteristic features of each process step • B. Braunecker, etc., “Advanced Optics Using Aspherical Elements”, SPIE ebook, 2008.

16. Moore Nanotech® 350FGUltra-Precision Freeform® Generator • Five-axis CNC machining • Used for on-axis turning of aspheric and toroidal surfaces; slow-slide-servo machining (rotary ruling) of freeform surfaces; and raster flycutting of freeforms, linear diffractives, and prismatic optical structures • Workpiece Capacity: 500mm diameter x 300mm long • Programming Resolution: 0.01 nm linear / 0.0000001º rotary • Functional Performance: Form Accuracy (P-V) ≤ 0.15µm / 75mm dia, 250mm convex aluminum sphere. http://www.nanotechsys.com/

17. Testing

18. Profilometer - 2D map • It is less accurate than an interferometer. • It can measure almost any surface. • Multiple profilometer traces can map the surface more accurately. • Measurement certainty is ~0.1 µm at best. • Limit: slope<40°, sag<25mm • http://www.optimaxsi.com/capabilities/aspheres/

19. Stitching interferometry-3D map • Measure overlapping smaller patches • Use phase shifting interferometry for individual measurements • Calculate the final surface height map by stitching all the patches Annular ring stitching Sub-aperture stitching • Part is moved in Z to focus on different annular zones. • Limit: surface departure from a sphere <800μm • Part is moved in Z, tip, and tilt to focus on different patches. • Limit: surface departure from a sphere <650μm • http://www.optimaxsi.com/capabilities/aspheres/

20. Null testing in reflection Computer generated hologram, CGH Spherical null lens Spherical wavefront Aspherical wavefront • Part specific • Takes time and money • Limit: surface departure from a sphere <100μm • Part specific • Takes time and money • Surface departure from a sphere can be high. • http://www.optimaxsi.com/capabilities/aspheres/

21. Null testing in transmission • Field is less than ±5°. • Limit: surface departure from a sphere <100μm • http://www.optimaxsi.com/capabilities/aspheres/

22. Flexible measurement technique • Many wavefronts simultaneously impinge onto the surface under test. • It’s rapid, flexible and precise. • Wide dynamic range in the asphericities is allowed. • Special calibration is needed. MA=microlens array; PA=point source array; M=source selection mask • C. Pruss, E. Garbusi and W. Osten, “Testing Aspheres”, Optics & Photonics News, pp. 25-29, Apr. 2008.

23. Summary • Aspheres, which are designed to null out a unique set of aberrations, are specified using the aspheric equation. • A suitable manufacturing method is chosen according to the lens materials and the required accuracy. • There are many metrology options, with selection driven by surface departure, form error and cost objectives.

24. Thank you!