Directly milling a small parabolic aluminum mirror

This is one of those projects that originally started as a paper draft, never really became its own publication and then ended up being buried as a manufacturing Appendix in a later manuscript on ghost imaging with free electron-photon pairs. Since the mirror itself and the workflow may still be useful to others, it is probably more useful as a blog article than as another half-finished manuscript fragment that remains unpublished.

What a research group at the TU Wien needed was a small parabolic mirror that fits onto a custom transmission electron microscope sample holder and still places its focus into the sample region. That sounds harmless until one looks at the available space: the mirror had to fit into the narrow polepiece region, had to leave a hole for the electron beam, had to collect light efficiently and ideally had to work from the visible into the UV and IR as well.

Luckily a friend at the Institute of Production Engineering, Forming and Environmental Technology had access to an amazing machine.

⚠️ Author’s Note / Disclaimer: This is a personal blog article about the journey of milling these mirrors. It is not associated with the institutions at which the manufacturing or measurements took place.

• Why one would mill such a mirror at all
• The geometry and constraints of the mirror
• How FreeCAD and the optics workbench helped
• Why the Krause and Mauser Praezoplan is interesting
• Material tests and the actual milling process
• What the finished mirror looked like in practice

Why not just Grind and Polish it?

When people hear “optical mirror”, the default expectation is usually some combination of grinding, lapping and polishing. That is of course the classical route and for many optical components it is still the correct one. The problem is that this mirror was neither large nor mechanically convenient. It was tiny, strongly curved, had to include a beam hole and had to be integrated into a very constrained mechanical environment.

The target geometry was a miniature parabolic mirror for cathodoluminescence photon extraction inside a TEM. The mirror had to sit on top of a custom holder and collect photons emitted close to the eucentric sample position. At the same time the electron beam still had to pass through the mirror body without distortion. This makes the geometry much more awkward than a simple standalone optical element on a bench with accessible curvature.

For such a geometry, directly machining the optical surface becomes a reasonable option. If the machine and tool are good enough, one can generate the shape directly instead of first creating a near-net form and then trying to reach the final surface by a separate polishing process on a feature that is tiny and impossible to access. And the specifications of our milling system suggested it could produce surface qualities better than grinding.

The Basic Geometry

The mirror was designed around the space available on the sample holder (that was of course also designed by myself) in the microscope polepiece region. The focal length was set to about $750 \mu m$, the overall height was about $1.7\mathrm{mm}$, the width about $4.37\mathrm{mm}$ and a $300 \mathrm{\mu m}$ beam hole had to be included for the electron beam path. The resulting numerical aperture was roughly $\mathrm{NA} \sim 0.58$.

This is the type of component where small geometric errors start to matter. One cannot just design the nice optical shape and afterwards think about mounting. The slot for fastening, the beam hole, the holder outline and the mirror contour all influence each other.

The mounted assembly looked as follows:

To allow mounting and manual transverse adjustment, the mirror body received a slot and was fixed using an $\mathrm{M}1.6 \times 0.35$ screw. This is not the most elegant mount in the world, but it is compact, practical and easy to integrate into a custom holder. If one wants to go one step further one should reduce stresses in the mount and make it more reproducible, but it was sufficient for our application for now.

Design and Raytracing in FreeCAD

One aspect that is worth highlighting explicitly is that the whole geometry was designed with open source tools. The mirror itself was modeled in FreeCAD, which provides a practical parametric CAD workflow without relying on proprietary software for the design stage. For this project the important part was not only CAD but also optical sanity checking. FreeCADs optics workbench allowed me to perform raytracing directly on the model and check if the mirror still behaved sensibly once the very non-ideal holder geometry around it was included.

That mattered because the mirror is not used as a clean standalone textbook paraboloid in empty space. It sits on a surface, close to surrounding structures, and small shifts in sample position or mechanical alignment matter immediately. Doing a few quick simulations on the actual CAD geometry is much better than hand-waving about ideal rays.

The design workflow was therefore fairly direct:

• Create the constrained geometry in FreeCAD
• Model also the mechanical and optical environment (not shown in this blog article due to patent and confidentiality reasons)
• Use the CAD geometry itself for basic optical raytracing
• Export the final shape as STEP
• Hand over the resulting model to (closed source) CAM (Siemens NX due to specific needs of the control system of the mill) for generating the toolpaths (we are also playing around trying to get a CAM postprocessor working for FreeCAD though)

Especially for small custom optics this open workflow is practical. One does not have to switch between isolated tools, make a handstand converting between formats, think about the non-modelable environment in the given simulation tool and much more just to answer design questions.

Why the Praezoplan 300 matters

The central machine for the whole exercise was a Krause and Mauser Praezoplan 300 at the Institute of Production Engineering and Photonic Technologies. The relevant point here is its machine architecture. It uses an area-guided XY system with aerostatic guides, which helps to avoid the usual stacking of axis errors and reduces friction, wear and stick-slip effects.

According to the referenced machine characterization, the system reaches positioning repeatability down to the tens-of-nanometers range and micrometer level absolute positioning with its measurement system. This is what makes direct milling of highly curved precision surfaces on such a machine technically plausible.

The final surface was generated with a monocrystalline diamond ball end mill manufactured by Paul Horn GmbH. That combination matters: the machine needs the positioning quality, but the tool edge quality, that is near perfect for monocrystalline diamonds, is equally important once one wants the surface itself to become optical grade.

The following photo shows the cutter. People seeing this for the first time may ask why this is a ball cutter - if one imagines the tool to rotate the outer curve resembles the surface of the sphere.

And here is one of the SEM shots of the cutting edge that was later used to determine the effective tool curvature more precisely:

This is another detail that is worth mentioning: the workflow was not “trust the nominal tool diameter and hope for the best”. The tool geometry was inspected via electron microscopy, traced and fed back into the machining preparation.

In addition we also tuned the curve with focused ion beam milling - a residue of a first experiment can be seen on the top of the cutter in the above image (the black dot is a hole, that has been milled as a test with a Gallium ion beam).

Material Choice and Machining

The mirror material was chosen to be aluminum because the intended optical use was broadband and aluminum is still a very practical reflector from the UV into the IR. In addition it is compatible with the diamond tool used for machining and it was simple to source. And in the end the second best option for our application would have been Rhodium or Platinum - we all wish financing in science would be better but even then this would be way over the top as wrough material.

Before committing to the final mirror, a few alloy tests were done on flat surfaces. The candidates included 6060, 5083, 6082 and 7075. Somewhat surprisingly, the softer 6060 turned out to be the better compromise for this application. The harder alloys are mechanically attractive in many contexts and we actually expected them to perform better, but here the softer material behaved more favorably during machining. Counterintuitively the larger amount of plastic smearing helped to smooth some microstructural surface errors rather than making the optical finish worse.

The actual process was roughly:

Roughing with $4\mathrm{mm}$ and $2\mathrm{mm}$ carbide flat end mills from Holex / Hoffmann Group

Drilling the beam hole with a generic $0.3\mathrm{mm}$ carbide drill

Semi-finishing with a $2\mathrm{mm}$ full-radius carbide end mill, again from Holex / Hoffmann Group

Final finishing with a $1\mathrm{mm}$ full-radius monocrystalline diamond ball mill from Paul Horn:

The carbide tools had to be cleaned periodically to prevent chip build-up. For this purpose, a small sodium-hydroxide bath was placed on the same tailstock as the workpiece, outside the machining area. After every few toolpath lines, the machining cycle was paused and the cutter was moved into the bath, where it rotated slowly while soaking. It was then retracted, moved clear of the bath and spun at higher speed to remove residual liquid before the minimum-quantity lubrication was re-enabled and machining continued. This cleaning cycle was incorporated directly into the machining program, which made it possible to maintain reasonably consistent cutting conditions over the long finishing pass.

The CAM preparation itself was done in Siemens NX, mainly because this tool supports the actual machine and control system. The machine itself was operated via a Heidenhain control system. In addition, the SEM-based measurements of the diamond tool edge were fed back into the generated toolpaths instead of just trusting the nominal tool radius.

The milled part itself looked like this:

What came out in the end

For a quick practical check we measured the reflectance at $650nm$ using a small laser diode and a Thorlabs power meter:

In the visible range we expected roughly mid-80-percent reflectivity for a decent aluminum surface, and the measured result ended up in that ballpark. That is sufficient to show that direct milling produced a sufficiently reflective surface rather than merely something shiny.

The later experiments showed that the directly milled surface provided sufficient optical quality for the intended photon-collection and imaging application, although machining-induced roughness remained a measurable source of aberration. As shown in the publications in the references section, position space resolutions down to $1.19\mathrm{\mu m}$ have been achieved via a camera placed on the outside of the electron microscope.

The mounted mirror also survived the transition from interesting machined part to actual system component:

Of course the surface was not mathematically perfect. SEM inspection clearly showed the characteristic line-by-line structure left by machining as well as material-related texture from the alloy itself.

A note on open workflows

Another reason I wanted to write this down is that the project is also an example of an open engineering workflow being sufficient for real scientific hardware:

• FreeCAD for the constrained mirror geometry
• FreeCAD’s optics workbench for raytracing and alignment sanity checks
• Standard STEP export into the downstream CAM chain
• Custom Python postprocessing scripts to manipulate the generated machine code
• Measurement feedback from microscopy into the machining process

This is a reminder that open source tools are not restricted to hobby parts or simple brackets. If one understands the limitations and the interfaces between tools, they can also play a role in precision engineering workflows.

Conclusion

The interesting point of this project was not that a mirror was made from aluminum. People machine reflective aluminum parts all the time. The interesting part was that a very small, strongly curved paraboloidal mirror, constrained by an electron-beam aperture, a custom TEM sample holder and very little available space, could be manufactured directly without relying on a conventional grinding and polishing workflow.

For that to work, four things had to line up:

• A geometry that was designed around the real mechanical constraints instead of an idealized optical sketch
• A precision machine platform that is actually suited for this kind of surface generation
• A workflow that integrates CAD, simple simulation, CAM and measurement feedback without too much friction
• Metrology to determine tool parameters and machining results that could be fed back into the parameterization of the manufacturing process.

In this case the combination of FreeCAD, the optics workbench, SEM-based feedback and the Praezoplan with a diamond ball mill was sufficient to turn a mechanically challenging mirror geometry into a practical component.

It was also an example of what can happen when different research units and groups work together on a problem. In our case the combination of the electron microscopy / quantum optics side at the Atominstitut of TU Wien with the manufacturing science side was useful because it brought together the application constraints and optics knowledge and the required manufacturing and machining know-how. Collaborations of this type can produce components that would otherwise be difficult to realize within a single group.

It is the kind of small project that tends to disappear into appendices, while demonstrating impressively how unconventional manufacturing methods can open up applications that would otherwise be difficult to realize.

References

• A YouTube playlist containing machining videos that have been taken during this project.
• Machining references:
  • S. Jaumann and K. Wegener, PRÄZOPLAN: die aerostatisch flächig geführte Hochpräzisionsfräsmaschine , Wiener Produktionstechnik Kongress 2012. DOI: 10.3929/ethz-a-007598851
• Material References:
  • J. Bartl, Emissivity of aluminium and its importance for radiometric measurement, 2004.
• Software:
  • FreeCAD
  • C. Bergmann, OpticsWorkbench for FreeCAD
  • Siemens NX CAD/CAM software
• Hardware models:
  • Custom Tecnai G20 sample holder CAD model
• Tooling manufacturers:
  • Paul Horn GmbH
  • Holex / Hoffmann Group
  • Thorlabs
• Institutes related to the project:
  • USTEM electron microscopy facilities
  • Haslinger Lab
  • Atominstitut, TU Wien
  • Institute of Production Engineering, Forming and Environmental Technology
• Selected publications that were made possible with this mirror:
  • Ghost imaging with free electron-photon pairs
  • Experimental Verification of Electron-Photon Entanglement

This article is tagged: Hardware, CAD, FreeCAD, Optics, Physics, Experiment