# Process Control with Sub-Aperture Polishing

These tips and tools will help you use sub-aperture polishing systems effectively for a wider variety of materials.

As demand increases for aspherical optical elements, many optical fabrication shops are acquiring computer numerically controlled (CNC) sub-aperture polishing machines, which can produce a wide array of high-quality optics. Some of these optics would be impossible to manufacture using traditional techniques and materials, and they require different techniques to control the processes that achieve these results.

Sub-aperture polishing differs from conventional polishing in that the tool is not in contact with a large portion of the surface to be polished. The small contact patch creates additional process-control challenges, since minute material removal rate changes cannot be averaged across the optic. Changes in removal rate can be the result of a variety of effects, and they negatively impact the determinism of the system, causing imperfections in the optical surface.

## Sub-aperture process flow

Before understanding how to control a sub-aperture polishing process, one must comprehend the process flow. First, a sacrificial representative part is used to characterize the polishing rate. This is accomplished by bringing the tool in contact with the part for a known amount of time and measuring the resulting “dimple” where material was removed. This dimple, called the removal function, serves as the basis for deterministic figure correction that is performed later. It is one of the primary determinants of the validity of the figure-correction algorithms.

The next step for deterministic sub-aperture polishing is to establish what is known as the forward removal problem, which is formulated by simulating the tool path of the tool as it traverses the optic. The material removal is calculated using Preston’s equation (Eq. 1) and the corresponding forward removal problem (Eq. 2).

dh/dt=Cp PV (1)
RMvc=sc (2)

in which dh/dt is the material removal rate, Cp is Preston’s coefficient, P is the applied pressure, V is the relative tool velocity, RM is the removal matrix created by the tool path simulation, vc is the dwell time of the tool at each location, and sc is the material removal at each location. This forward removal problem is then inverted, and the inverse problem is solved to produce the desired surface, sc. The solution calculates how long the tool needs to stay at each location to correct the local figure error.

Calculated surface: (Top) Simulation of the figure correction with a 10 percent fluctuation of the removal function. (Bottom) Simulation of a figure correction with a non-fluctuating removal function.

## Process-control problems

In order for the deterministic figure correction algorithm to function properly, the removal characteristics of the polishing tool must not change considerably during the polishing run. Even a 10 percent change in the removal function can affect the figure-correction capability, as the figure on the right demonstrates.

Many causes may underlie an inconsistent removal rate, ranging from temperature change to slurry consistency. One of the most common causes of material removal changes is polishing tool wear. Some manufacturers of sub-aperture polishing systems have methods for mitigating this effect. For instance, in magneto-rheological finishing, engineers use a reservoir of fluid to minimize polishing rate changes. In UltraForm finishing, they reduce the tool wear rate by spreading the wear over a long belt of polishing material. Another approach is to remove less material per polishing pass. Although this technique is time-consuming, it works well because it spreads tool wear over multiple runs and allows the operator to adjust for removal rate changes in an efficient manner.

One removal rate control problem that is encountered with large-grain optical materials such as aluminum oxynitride (AlON) is grain highlighting. This is caused by polishing rates that change depending on the grain orientation of the material being polished. Using a stiffer polishing tool can help mitigate this effect. UltraForm finishing has removed grain highlighting on AlON using this stiff-tool technique.

## Diagnosing control problems

Determining the cause of an uncontrolled process problem can be difficult. Fortunately, there are metrics that can help. One of the most informative measurements of the material removal rate of the polishing tool is the measured removal function data. Changes in the removal function reflect modifications in the figure correction on the optical surface. For instance, one can attain much of the data used to determine the desired polishing parameters for grain highlighting removal by studying the polishing dimple that is created when a removal function is generated. This provides a rapid testing metric for a variety of parameters, including polishing tool hardness, polishing slurry and polishing tool speed.

Tracking the tool position as a function of time is another way to diagnose process-control problems. For instance, air pressure in the polishing shop may cycle at a specific frequency that causes the machine parameters to change slightly. These changes may be traced to correlate the pattern generated on the optical surface of the part to the shop air pressure cycles. Changes can then be made to reduce the effect of the environment.

## Conclusion

Sub-aperture polishing systems are very precise machines that enable the fabrication of shapes that would be too costly to produce using conventional techniques. These techniques also allow for a wider variety of materials to be effectively polished. With the proper process control techniques, these machines will enable engineers to consistently and rapidly manufacture complex surface geometries using fewer of the artisan techniques required for conventional polishing.

Scott Bambrick is a senior scientist at OptiPro in Ontario, N.Y., U.S.A. Mike Bechtold, Dave Mohring and Adam Farnung are also with OptiPro.

### References and Resources

>> F.W. Preston. “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol. 11, 214-56 (1927).
>> Fess et al. “UltraForm finishing processes for optical materials,” Optical Manufacturing and Testing VI, Proc. SPIE 5869, 0F1-0F6 (2005).
>> A.B. Shorey et al. “Magnetorheological finishing of large and lightweight optics,” Proc. SPIE 5533, 99-107 (2004).

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# Process Control with Sub-Aperture Polishing

These tips and tools will help you use sub-aperture polishing systems effectively for a wider variety of materials.