Tutorial:Design, Fabrication, and Testing of Aspheric Surfaces

Chia-Ling LiCollege of Optical Sciences, University of Arizona

Dec. 12. 2013

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

Outline

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Introduction

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The aspheric surface means not spherical.

It can be thought as comprising a base sphere and an aspheric cap.

What is an aspherical surface?

Spherical base surface

Aspherical surfaceAspherical

cap

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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.

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Design

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Mathematical representation of aspherical surfaces

Even Asphere:

Polynomial:

Q-Type Asphere:

Zernike Standard Sag 6

Aspheric shape design guide

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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”

Tolerances for aspherical optical elements (1)

8http://www.optimaxsi.com/capabilities/aspheres/

Tolerances for aspherical optical elements (2)

9B. Braunecker, etc., “Advanced Optics Using Aspherical Elements”, SPIE ebook, 2008.

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

ISO 10110

Fabrication

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Different process technologies

11B. Braunecker, etc., “Advanced Optics Using Aspherical Elements”, SPIE ebook, 2008.http://www.optimaxsi.com/capabilities/aspheres/

The manufacturing cost of different materials

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Crystals: CNC machining or diamond turning Glasses: CNC machining or precision

molding Polymers: injection-moldingB. Braunecker, etc., “Advanced Optics Using Aspherical Elements”, SPIE ebook, 2008.

The actual production sequence is iterative; several steps must be taken between surface shaping and measurement before the required accuracy level is achieved.

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Classical optics fabrication

B. Braunecker, etc., “Advanced Optics Using Aspherical Elements”, SPIE ebook, 2008.

The characteristic features of each process step

14B. Braunecker, etc., “Advanced Optics Using Aspherical Elements”, SPIE ebook, 2008.

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.

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Moore Nanotech® 350FGUltra-Precision Freeform® Generator

http://www.nanotechsys.com/

Testing

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Profilometer - 2D map

17http://www.optimaxsi.com/capabilities/aspheres/

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

Stitching interferometry-3D map

18http://www.optimaxsi.com/capabilities/aspheres/

Measure overlapping smaller patches Use phase shifting interferometry for individual

measurements Calculate the final surface height map by stitching all the

patchesAnnular 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

Spherical null lens

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Null testing in reflectionComputer generated hologram, CGH

http://www.optimaxsi.com/capabilities/aspheres/

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.

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Null testing in transmission

http://www.optimaxsi.com/capabilities/aspheres/

Field is less than ±5°. Limit: surface departure from a sphere <100μm

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.

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Flexible measurement technique

C. Pruss, E. Garbusi and W. Osten, “Testing Aspheres”, Optics & Photonics News, pp. 25-29, Apr. 2008.

MA=microlens array; PA=point source array; M=source selection mask

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.

Summary

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Thank you!

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