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In this paper we first contrast classical and CNC polishing techniques in regard to the repetitiveness of the machine motions. We then present a pseudo-random tool path for use with CNC sub-aperture polishing techniques and report polishing results from equivalent random and raster tool-paths. The random tool-path used – the unicursal random tool-path – employs a random seed to generate a pattern which never crosses itself. Because of this property, this tool-path is directly compatible with dwell time maps for corrective polishing. The tool-path can be used to polish any continuous area of any boundary shape, including surfaces with interior perforations.
©2008 Optical Society of America
1. Introduction
In craft polishing of aspheres, the optician typically uses two generic types of process to control form. One involves hand-use of small tools to target specific local errors or zones on the surface. This has a tendency to leave mid spatial frequency defects, due to the tool’s box-function-like imprint, the superposition of its paths, and to the varying mismatch between the surface of the tool over surface of the asphere. The second process is a smoothing operation (which also has capability to influence overall form), typically employing a larger (and often compliant) tool following a sweeping stroke such as a ‘W’ path over the work-piece. Combined with rotation of the work-piece and the vagaries of hand-work, smoothing can provide good randomization of the surface, albeit with some form-regression. For this reason, local figuring runs are often interspersed with smoothing. Motorized polishing spindles, if giving purely repetitive strokes, can tend to polish “Lissajous figures” into a surface. In a case familiar to the authors, pivoted polishing arms with epicyclic drives provided the lap-stroke, where one motor fed two main drive-gears which were different in pitch by one tooth. Clearly randomness or even pseudo-randomness is important, whether the tool is actuated manually, or by classical lapping machine.
Deterministic CNC polishing machines, such as the Precessions ™ process, operate in a fundamentally different manner. The influence function of the Precessions ™ sub-aperture tool is near-Gaussian, avoiding the effects of a box-function [1]. A measured influence function and surface error-map provide the input-date for computing a dwell-time map. This defines the optimum time the (overlapping) influence functions should spend at each location in a grid over the surface, in order to correct the error of form. The machine interprets this as a continuous motion at varying surface-speed along a regular path, where the integration of the surface speeds corresponds to the dwell-time map. This is directly applicable only where the path does not exhibit local cross-over points (e.g. spiral or raster), as very high machine accelerations and decelerations would be required to off-set the double-removal at local cross-overs. In the special case of a pair of crossed-rasters (with cross-overs at every intersection), the times in the dwell time map are halved, and executed as two distinct polishing runs.
A regular tool-path inevitably leaves repetitive signature in the surface, resulting from the superposition of the near-Gaussian influence functions over a range of parallel tracks in the spiral or raster. These features could typically be at the few-nanometer level. They can be revealed by white-light interferometry, and give characteristic spikes in the surface power spectral density plot at the raster or spiral spacing and its harmonics. Such signatures can cause unwanted diffraction effects in critical applications. The challenge is how to introduce elements of the randomness associated with classical smoothing into a deterministic CNC Gaussian small-tool process such as Precessions ™.
2. The unicursal path
A unicursal path is one that travels over the part without crossing. Spiral and rasters are examples of unicursal patterns. The unicursal random pattern satisfies the non-crossing criterion, and an example is given in Fig. 1, which also includes a tilted interferogram showing the resulting fringes after using the random tool path on a flat surface. It has many qualities that make it useful as a tool path for sub-aperture polishing techniques. The tool path can be used with any continuous region, including those with one or more interior perforations. The density of the pattern can be changed, as in Fig. 2, which is analogous to increasing or decreasing the spacing of a raster or spiral path. A completely different random pattern is produced every time the generation algorithm is run. Because this pattern never crosses itself, it can be used directly with a dwell time map to perform prescriptive corrective polishing and is integrated into Zeeko Ltd’s Precessions ™ software.
Fig. 1. Example of a unicursal random tool path and a tilted interferogram resulting from polishing with this tool path
3. Experimental results
All experimental polishing with the random tool path reported in this paper was carried out on Zeeko 7-axis CNC polishing machines using ZeekoTPG tool path generation software [2]. The experiments used the Zeeko Classic process, where the tool comprises a spinning, inflated bulged membrane (the ‘bonnet’), covered with a polyurethane polishing cloth and operating in the presence of cerium oxide polishing slurry. The bonnet is brought into contact with the surface of the part, and then advanced towards the part through a pre-calculated distance to compress the bonnet and create a defined polishing spot. The orientation of the H (tool-rotation) axis can be maintained at a defined inclination angle with respect to the local normal over the entire work-piece surface. Four successive passes over the surface are then performed, with the H axis precessed around the local-normal in four discrete steps of 90o. This gives an accumulated influence function which is near-Gaussian.
3.1 Comparison of surface texture due to raster and random tool paths
Two 35-mm diameter areas were polished on a flat pitch-polished BK7 glass sample using the tool paths shown in Fig. 3. This experiment was performed on a Zeeko IRP600 robotic polishing machine using the polishing parameters in Table 1. The pattern density of the random path was chosen to be equivalent to the raster spacing.
Table 1. Polishing Parameters
Surface texture measurements of each region, shown in Fig. 4, were carried out on an ADE Phase Shift MicroXAM stitching white light interferometer. The sample size on both measurements is 5.22 by 1.02 mm, with a resolution of 2.12 µm/pixel. Tilt was removed from both measurements.
A two-dimensional power spectral density (PSD) was calculated for a profile from each of these measurements. The PSD, in Fig. 6, shows the strong periodic features present in the raster polished sample are absent in the random polished region. The PSD was calculated using MicroXAM’s analysis software. First, a two-dimensional profile (Fig. 5) was extracted across each of the measurements in Fig. 4. The Fourier transform was calculated for each profile and plotted (Fig. 6) using Matlab.
The strongest peak in the raster PSD corresponds to the raster spacing of 0.35 mm (2.85 raster passes per mm). The periodic structure left by the raster polishing can be seen in the profile in Fig. 5, along with some noise across the entire profile. This noise is rendered into the smaller peaks seen in the PSD plot at the harmonics of the raster signal.
3.2 Removing raster marks using the random tool path
In a second experiment, a glass flat was first raster polished with parameters chosen to produce a periodic signature. This surface was then re-polished twice using a different random pattern each time. The machine parameters for all three polishing iterations, carried out on a Zeeko IRP200 robotic polishing machine, are shown in Table 2. Both the raster and random polishing patterns had a spacing of 0.35 mm.
Table 2. Polishing parameters
Figure 7 is a white light interferometry measurement of the surface after raster polishing. The region illustrated is 0.9 by 1.4 mm in size. Measurements were made using a Wyko NT2000 white light interferometer. Fig.s 8 and 9 show the surface after the first and second iteration of random polishing and statistics about the surface quality are presented in Table 3.
Table 3. Surface statistics
A two-dimensional profile across the sample region after each polishing process is shown in Fig. 10 and the PSD of these profiles in Fig. 11. The strong periodic feature can be seen in the original surface diminishes with each application of the random tool path.
4. Conclusions
In an experiment CNC post-polishing a pitch-polished surface, raster polishing gave the expected periodic structure due to the superposition of the parallel raster tracks. In contrast, the random unicursal tool path avoided introducing such periodic structure, resulting in surfaces with superior PSD characteristics where the principal peak and harmonics seen in the rastered surface were effectively suppressed. In a separate experiment, the random tool path was also successfully used to improve a surface with a strong pre-existing periodic structure. Work is in progress to integrate the random path with Zeeko’s Precessions software for corrective polishing. The property of the unicursal random path in attacking the edge of a part tangentially is also being explored with a view to improving edge-control.
The unicursal random path is not limited in its application to Precessions polishing. It is equally applicable to any process that scans a surface to give local material removal, local material deposition, or local modification of material characteristics. Relevant technologies include ablation from laser, fluid-jet, ion and reactive atomic plasma; deposition by sputtering; and modification by ion-implantation.
References and links
1. D. D. Walker, D. Brooks, A. King, R. Freeman, R. Morton, G. McCavana, and S-W Kim, “The ‘Precessions’ tooling for polishing and figuring flat, spherical and aspheric surfaces,” Opt. Express 11, 8, 958–964, (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-8-958. [CrossRef] [PubMed]
2. D. D. Walker, R. Freeman, R. Morton, G. McCavana, and A. Beaucamp, et.al. “Use of the ‘Precessions’ process for pre-polishing and correcting 2D & 2½D form,” Opt. Express 14, 11787–11795 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-24-11787. [CrossRef] [PubMed]
