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

2. Outline Introduction Design Fabrication Testing Summary
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.
Spherical base surface
Aspherical surface
Aspherical cap

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:
Find best asphere
When optimizing an optical system that uses a higher order aspheric surface, more field points are necessary.
Higher order aspheres improve performance in diamond turned optics and molded optics with little or no increase in cost or complexity.
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)

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
computer controlled polishing (CCP), fluid jet polishing, magnetorheological finishing (MRF), and ion beam figuring (IBF)
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® 350FG Ultra-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 / º rotary
Functional Performance: Form Accuracy (P-V) ≤ 0.15µm / 75mm dia, 250mm convex aluminum sphere.

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

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

20. Null testing in reflection
Spherical null lens
Computer generated hologram, CGH
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.

21. Null testing in transmission
Field is less than ±5°.
Limit: surface departure from a sphere <100μm

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 , Apr

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!