Chia-Ling Li
College 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
1
2


The aspheric surface means not spherical.
It can be thought as comprising a base
sphere and an aspheric cap.
Aspherical
cap
Aspherical
surface
Spherical
base surface
3




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.
4
5
Q-Type Asphere:
Even Asphere:
Polynomial:
Zernike
Standard Sag
6


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”
7
http://www.optimaxsi.com/capabilities/aspheres/
8
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.
9
10
http://www.optimaxsi.com/capabilities/aspheres/
B. Braunecker, etc., “Advanced Optics Using Aspherical Elements”, SPIE ebook, 2008.
11



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.
12

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.
13
B. Braunecker, etc., “Advanced Optics Using Aspherical Elements”, SPIE ebook, 2008.
14





http://www.nanotechsys.com/
Five-axis CNC machining
Used for on-axis turning of aspheric
and toroidal surfaces; slow-slideservo 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.
15
16





http://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
17



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


Part is moved in Z to
focus on different
annular zones.
Limit: surface departure
from a sphere <800μm
http://www.optimaxsi.com/capabilities/aspheres/
Sub-aperture stitching


Part is moved in Z,
tip, and tilt to focus
on different
patches.
Limit: surface
departure from a
sphere <650μm
18
Spherical null lens
Spherical
wavefront



Computer generated hologram, CGH
Aspherical
wavefront
Part specific
Takes time and money
Limit: surface departure
from a sphere <100μm
http://www.optimaxsi.com/capabilities/aspheres/



Part specific
Takes time and money
Surface departure from a
sphere can be high.
19


Field is less than ±5°.
Limit: surface departure from a sphere <100μm
http://www.optimaxsi.com/capabilities/aspheres/
20




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.
21



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.
22
23