Bonnet Polishing and Fluid Jet Polishing
Zeeko., Ltd. Richard Freeman
1.

Introduction

1.1 The need for free-form surfaces
The capability of producing free-form surfaces – surfaces not
limited to regular forms constrained by symmetry – opens up newvistas for optical designers. Such surfaces introduce newdegrees of freedom into the optical design optimization process.
This opens the door for imaging solutions with improved
performance, and/or reduced complexity, lower mass andsmaller package size. In illumination applications, free-form
surfaces permit the spatial distribution of illumination to be tuned
far more effectively than could be achieved with regular asphericsurfaces. The challenges have been how to manufacture,measure, and test such surfaces. This paper presents some
useful steps in this direction.
1.2 Free-form polishing technologyTM[1-12]
CNC polishing process
has two
Zeekos’s Precessions
principal functions – to remove surface and sub-surface damage
from a ground part, and then to correct the form. The process
operates by scanning a local spot of removal across the global
surface, varying the spot size and dwell-time (or, in practice, thetraverse-rate) to concentrate removal more on the areas that are
too high than those that are too low. Several removal processes
are currently available – inflated membrane (“bonnet”) based[13]
polishing, fluid-jet polishing , and a family of hybrid “grolishing”[10]
processes intermediate between polishing and grinding.
The form-correction software requires three key pieces of input
information, i) the target form, ii) the measured form, or formerror, and iii) the tool influence function i.e. the local imprint leftby the tool operating on a single site on the surface. A numerical
optimization method is then used to define the optimum dwelltime map on the surface to correct the form error. Because of
the inherent complexity of the surface chemistry and physics ofpolishing at the nano-scale, 100% predictability of removal isnever achieved; there is always a residual error. Therefore, theprocess is iterative, requiring cycles of metrology and material
removal to converge on the final target form.
1.3 The importance of metrology data
The total time required depends critically on the convergence
rate of the process. Key factors affecting convergence are thecorrect interpretation of the metrology data, the quantitative
accuracy and repeatability of the metrology, and the integrity of
the geometric relationship between the coordinate frame of themetrology data and that of the machine-tool. Specific problems
that have been encountered with different metrology devices andformats are given in the next section.
1.4 Specific metrology issues
Interferometers and optical wavefront sensors–
ambiguity of height being referred to the surface
or the reflected-wavefront (factor of two or four
depending on the setup)–
ambiguity of sign in XY plane (upside-down or
mirror image)–ambiguity in magnification and orientation ofinterferometer data–geometric distortion in the XY plane of theinterferometer data–difficulties locating fiducials on the wavefront
image–
slope limitations causing whole areas to be
irresolvable

Profilometers and CMMs
setting accurate and reliable datum points whenmeasuring in 3D
compensating for thermal drift occurring over thescanning period
compensating mechanical and geometricalissues, such as tilt and decentering when using arotary stage with a profilometer
These problems can become severe for aspheric surfaces, andextreme for free-forms surfaces. Further complications arise
when the metrology data needs to be registered with CAD design
data as well as with the machine-tool coordinate frame. Datafusion or stitching in the spatial or spatial-frequency domain
between different metrology devices also introduces its own
problems of maintaining integrity across the fused data set.
1.5 The generality of the problem
The authors grasped that these issues are not unique to specificpolishing technology, but are encountered in numerous other
iterative manufacturing processes requiring metrology input,
which are generally combined to produce a single component:
precision grinding
precision diamond turning
ion beam deposition or removal
Reactive atomic plasma technology (RAPT)This evident need for standardization and a holistic approach tohandling metrology data led us over a period of time to develop
software tools addressing these various issues. It became
apparent over time that these tools could be gathered into asingle toolkit application, dedicated to solving metrology issues
and orientated toward precision and ultra precision
manufacturing processes.
2.

Metrology Toolkit Software

2.1 Metrology devices
Surface texture analysis is an area of metrology that has been
extensively studied, and is covered by many commercial
software applications supporting a wide range of scanning andimaging instruments. Large-scale dimensional analysis (formerror) however, has not received such intensive coverage andfew alternatives are available to exploit the potential capability ofmetrology instruments to support form-control on general freeform shapes.
The main measurements solutions for measuring free-forms arelisted below, with their advantages and limitations:
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-

CMMs
o pros: can measure and fit most free-form
shapes, provided a CAD file of the part isavailable and 3D software exists for the
instrument.
o cons: highest accuracy only ~1um (Zeiss
UPMC), machine with 3D software often
costly3D Scanners (laser triangulation)o pros: can measure and fit most free-form
shapes, if suitable software is available,
low cost
o cons: low accuracy ~10um, thus notsuitable for imaging optics

-

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-

Profilometerso pros: good sensitivity in Z direction(<=100nm) when used in 2D mode on
rotationally symmetrical shapeso cons: raster scanning causes the stylus todeflect slightly because of Y slope
component. Rolling ball algorithm
compensates only for X slope, thus
making raster-scan suitable only for nearflat shapes[14]
Nanomefos
o pros: designed to achieve 10nm range
accuracyo cons: still in development, restricted rangeof measurable shapes (limited deviationfrom a best fit sphere)
UA3P (Panasonic)
o pros: ability to raster or spiral scan freeform shapes, stated accuracy <=100nm
o cons: cost of machine + software

2.2 The advent of the metrology toolkit
The software solutions presently available for measuring freeform shapes are lacking any interfacing with precision
manufacturing equipment.
The Metrology Toolkit was thus developed to facilitate the fittingof form error from a wide variety of instruments and enable theinterfacing with precision manufacturing equipment. The
following considerations were taken into account in the design ofthe software:compatibility with free-form definition methods
compatibility with a wide range of measuring
instruments
compatibility with a wide range of manufacturingmachine tools
functionality allowing correctly to format andprocess data sets-differential equations describing the function of
the optical component
CAD file containing a combination of primitives
and b-splines

In order to unify the handling of free-form surfaces, the use of[15]
non-uniform rational b-splines (NURBS ) was adopted. The
Metrology Toolkit features a surface editor that allows defining
free-forms in any of the above formats, and then automaticallyconverts the surface into a NURBS object. Additionally, many
modern CNC controllers offer the ability to feed tool paths directly[8,16], which offers increased process control andin NURBS format
accuracy.
2.5 Metrology instruments compatibility
Metrology data is generally expressed in one of the following
formats:
linearly or non-linearly spaced XYZ arrays orvectors (profilometers, interferometers)
scattered or randomly distributed point clouds(scanners, CMMs)
Certain distributions, such as profilometer data, may be linear in
spherical coordinates rather than Cartesian. When projected toCartesian the distribution may no longer be linear, with thetransformation breaking down entirely at the edge of ahemisphere. However, all distributions are special cases of thegeneral random point cloud distribution. The Toolkit algorithms
were implemented to solve this general case, and are thus
compatible with any more-specific distribution (some code
optimizations were subsequently performed to speed-up
calculations whenever certain distribution properties aredetected). Data fusion of different metrology sources is also
possible thanks to this approach.
2.6 Manufacturing equipment support
Most precision manufacturing equipment relies on software
generating G-Code CNC files that are fed to a numericalcontroller (Fanuc, Bosch, Siemens, Cranfield). The Toolkit canmake modifications directly to the G-Code, enabling integration
without the need to modify the equipment’s original software.
Through an iterative approach, machine systematic errors can becompensated and form error reduced.
2.7 Processing and formatting functionality
The Toolkit integrates various processing and formatting
functions enabling expression of the data in an intelligible way to
manufacturing equipment and/or user.
data sets can be referenced to part design withfunctions that retrieve and create fiducials
simple geometrical transformations are available:
mirror, offset, tilt and rotate
incomplete or corrupted data sets can be resampled,
trimmed,de-noised,smoothed,
interpolated and extrapolated
datum points can be converted to deviation datausing the aspheric and free-form fit functions
several data sets can be fused to create new
point clouds

FIGURE 1. Metrology Toolkit integration diagram.
2.4 Free-form definition methods
Free-form shapes are commonly defined in the following formats:analytically: section of a primitive shape (sphere,
cylinder, ellipsoid, toroid…) combined with apolynomial
expressionz = P(x,y)
numerically: XYZ array or point cloud derived
from numerically solving a system of partial

3. Case Study 1 – Manufacturing a free-form optic
A practical experiment to demonstrate the integration of thesoftware in a manufacturing environment was conducted, using aprecision grinder and the Precessions process to produce a freeform optic. The measurement device used throughout thisexperiment was a Zeiss UPMC CMM.

29.7µm. The cylindrical component was almost entirely removed,
and the amplitude of the see-sawing effects was greatly reduced.

FIGURE 2. Free-form optic inside Zeeko polisher.

The part was then polished using the Precessions corrective
polishing software, to remove surface and sub-surface damage
while further improving the form error PV. The Toolkit could
export the error map to Precessions, were it was analyzed
against the influence of the polishing process in use, to produce
a polishing tool path with varying speed and spot properties.

The part was first ground with a spiral tool path that had been
derived from the theoretical design. The optical surface was thenmeasured on the CMM and the Toolkit was used to fit the datum
points to the design in order to produce a deviation map (error
map).

FIGURE 5. Final error after Precessions runs: 2.54µm.

FIGURE 3. Original grinding error: 180µm PV.
The error map showed 180µm PV of deviation on the clear
aperture, with a main cylindrical component and an underlying
see-sawing effect. This error map was used within the Toolkit to
apply compensations on the grinder’s G-Code CNC file. The partwas then re-ground and re-measured.

After two Precessions runs the form error was reduced to 2.5um
PV. This clearly demonstrated the capability of the Toolkit
successfully to interpret the data from the CMM, and convert it
into useful compensations for the grinding and polishingprocesses. Limiting factors to reaching sub-micron form error
were found to be:
accuracy of CMM measurement (~1um)
density of CMM data (2mm data points spacing)
shortest grind ripples would have required the useof fluid jet polishing or grolishing, not available forthis project4.

Case Study 2 – Overcoming metrology limitations withdata fusion and distortions compensation
An experiment was carried out to demonstrate the usefulness ofdata fusion, and the capability of the Toolkit to deal with spatial
distortions. A 190mm diameter parabolic concave mirror was
ground on a precision grinder, and pre-polished on a Zeeko IRP
polishing machine. The mirror was then measured with a Zygo
interferometer in double pass mode using an auto-collimation flat
mirror.

FIGURE 6. Double pass setup using flat reflector.
FIGURE 4. Grinding error after compensation: 29.7µm.
The measurement analysis in the Toolkit showed that thiscompensation reduced the PV of the error from 180µm down torun improved the form error sufficiently for the mirror to beresolvable on the interferometer up to a diameter of 190mm.
However, further Precessions runs seemed to reach an
improvement barrier at 150nm PV of form error, the surface
features showing peak-to-peak distances equal or smaller than
6mm. An investigation was carried out to ensure that
Precessions was asked to correct the ‘right error’ at the ‘rightlocation’. A literature survey revealed that optical errors ininterferometers can include imaging distortions and ray-mapping[17]
errors . In order to characterize the distortions associated with
our double pass setup, six sets of three fiducials were placed on
the surface, to calibrate a succession of six diameters spanning
an interval from 62mm to 164mm.

FIGURE 7. Visible area: 160mm.
The interferometer could resolve fringes up to a diameter of
160mm, while the clear aperture extended to 185mm.
Measurements of the mirror on a Form Talysurf profilometer
revealed that slopes in the region beyond 160mm were severe,due to the presence of a ‘lip’ defect.

FIGURE 9. Three fiducials calibrate one diameter.

FIGURE 8. 2D profiles reveal problematic area.

The Toolkit was able to register each set of fiducials as aseparate diameter calibration. Plotting the camera resolution, asa percentage of the value at 164mm against the diameter span,
showed as much as 3% of variation. On a 190mm diameter
mirror, this variation would amount to 3mm of radial inaccuracy inthe localization of peaks and valleys.

While the profilometer data could be used to correct this edge
defect, its lower accuracy and density would have degraded theprecision of measurement in the area visible on theinterferometer. The Toolkit could address this issue by stitching
together the interferometer and profilometer data sets through aprioritizing algorithm.

FIGURE 10. Camera resolution variation.
The Toolkit fiducialisation functions enabled us to take into
account all six calibrations, and rescale non-linearly the error
map in the XY domain. The morphed error map was thenexported to Precessions, and a further corrective run was
attempted.

FIGURE 9. Toolkit fuses data sets into a single map.
Additionally, the merged error map contained the residual
spherical power, missing in the interferometer measurement but
present in the profiles. Using this error map, a single Precessions

5. “The Precessions process for efficient production of aspheric
optics for large telescopes and their instrumentation”, D.D.
Walker, A.T.H. Beaucamp , R.G. Bingham, D. Brooks, R.
Freeman , S.W. Kim, A. King, G. McCavana , R. Morton , D.
Riley, J. Simms , Proc. SPIE Astronomical Telescopes andInstrumentation Meeting, Hawaii, 2002, Vol. 4842, pp73-84
6. ‘The ‘Precessions’ Tooling for Polishing and Figuring Flat,
Spherical and Aspheric Surfaces’, D.D. Walker, D. Brooks, A.
King, R. Freeman, R. Morton, G. McCavana, S-W Kim , Optics
Express, Published by Optical Society of America on
http://www.opticsexpress.org/, Vol. 11, issue 8, 2003, pp958-964

FIGURE 11. Precessions achieves 40nm PV (lambda/15) using
the morphed error map.
The 150nm PV barrier was overcome, and a single corrective runbrought the global form error to 40nm (lambda/15) over the full
185mm clear aperture. This process was successfully repeatedon several dozen parts, with global form error consistently
brought to less than 60nm PV, which demonstrated the capabilityof the Toolkit accurately to fuse data sources, and compensate
mapping distortions.
5.

Discussion and Conclusion

This paper has illustrated the practical importance of considering
metrology as an integral part of the process-loop for
manufacturing aspheric and free-form optics. There are pitfalls inall methods of testing optical surfaces, but we have found thatthese pitfalls are substantially amplified in components with freeform surfaces, and surfaces with high local or global slopes. We
have shown the importance of proper mathematical descriptionsof the surface. We have also emphasized the need for a rigorous
approach to handling the metrology data, and to consider how
the surface-description and metrology data relate to the machine
tool used to correct measured errors. Specific software tools
have been described that can greatly assist the manufacturing
process-chain, with relevance to several different processes.
6.

References

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