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

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

Introduction

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

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.

Design

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

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”

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

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.

Fabrication

Different process technologies computer controlled polishing (CCP), fluid jet polishing, magnetorheological finishing (MRF), and ion beam figuring (IBF) http://www.optimaxsi.com/capabilities/aspheres/ B. Braunecker, etc., “Advanced Optics Using Aspherical Elements”, SPIE ebook, 2008.

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.

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.

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

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 / 0.0000001º rotary Functional Performance: Form Accuracy (P-V) ≤ 0.15µm / 75mm dia, 250mm convex aluminum sphere. http://www.nanotechsys.com/

Testing

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/

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/

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

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

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.

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.

Thank you!