The effect of polishing an optical workpiece with a polyurethane pad was studied in this paper, including material removal rate, surface roughness and subsurface damage. Usually, optical polishing pitch is applied to polish optical workpieces, but the material removal rate (MRR) of pitch is quite low, and polyurethane foam is thus substituted for polishing pitch. With the polyurethane pad a much higher MRR was obtained. Surface roughness and subsurface damage of workpieces were also examined. We were gratified to find that there was almost no subsurface damage in the workpieces manufactured with pad polishing and surface roughness was comparable to the result of pitch polishing. Finally, a hypothesis was proposed in an attempt to explain the result that workpieces were defect-free.
©2008 Optical Society of America
Polishing is a critical path to achieve optical surface during cold processing of optical glasses, the purpose of which is to shape the optical components to the desired form, to eliminate the damage, including surface and subsurface damage introduced by grinding, and to reduce the surface roughness which usually strongly influences the succeeding processes. At present, pitch, such as Gugolz pitch from Switzerland, is widely used in the polishing process, to accomplish the polishing step. Certain properties  of optical pitch make it superior to other materials for polishing, for instance, high accuracy in surface form (Peak-to-Valley<1λ, λ=632.8nm) and low surface roughness (<1nm) [2,3], however, the material removal rate (MRR) is not satisfying, around 2µm/h. Moreover, pitch-polishing can give rise to a hydrated deposition layer of about 1µm deep which will adhere to the surface of workpiece and conceal the remains of surface defects such as scratches or fractures to form subsurface damage [4–6]. Subsurface damage is partially or totally covered by the polishing deposition layer (Fig. 1), though the surface of the workpiece seems to be perfect. SSD will influence the laser-induced damage threshold of optics, imaging quality and so on [5–8].
Thus polyurethane was proposed to substitute for polishing pitch to manufacture optical components [9, 10]. Polyurethane was one of some materials which were suitable for polishing optical components. Polyurethane is characterized by pores and asperities which are contained in its body and surface (Fig. 2). This characterization facilitates the retention of slurry particles during the polishing process. Secondly, a high viscosity and relatively high softening temperature, which make rapid linear/angular velocity possible, are other outstanding properties compared with pitch [9–12]. To our pleasure, besides exhibiting excellent wear resistance and long life [9, 12], polyurethane can retain its surface figure for a quite long period without needing to be shaped and can produce batches of optical components with uniform surface form. In this work, the material removal rate, surface roughness and subsurface damage of a workpiece polished with a polyurethane lap were investigated, and defect-free optical workpieces were obtained.
GR-35 pad (Rhodes, Universal Photonics, USA), with a diameter of 44 inches and 0.05 inches thick, was chosen as polishing pad. Workpieces are a 330mm×330mm×10mm fused silica and a 330mm×330mm×40mm thick BK7,respectively. Experiments were conducted on a traditional single spindle polishing machine (III II-320, Russia) with a pitch lap and a custom designed high speed polishing machine (PPS100, North Tiger Company, China) with a polyurethane lap (Fig. 3).
Material removal rate was measured by measuring the thickness of the workpiece near each of four corners and each midpoint of four edges for square workpiece. As for a circular one, the measurement was conducted at the 3, 6, 9 and 12 o’clock position. The measurement was taken by applying a dial indicator (Mitutoyo, Japan) with a minimum scale value of one micron. The measurement was made by placing the workpiece on a round or square platen made of granite with the centers of workpiece and granite platen coinciding. The dial indicator was fixed on the Z2 axis of PPS100 which can move along Z direction with a resolution of one micron. Measurements were made every hour.
Examination for SSD was made by etching the workpiece in HF solution (wt1%) at room temperature 25°C. Etching was taken when scratches or fractures were polished out, that is, no defect was found in the surface of workpiece before etching. And the surface was observed with an optical microscope (TATA-400III, Japan) at 1000× magnification before and after chemical etching . Surface roughness was examined with an optical profiler (WYKO RST plus, USA) followed by microscopic observation.
Polishing processes were ended when scratches were speciously eliminated and no scratches were found with the microscope before chemical etching.
3. Results and discussion
3.1 Material removal rate (MRR)
According Preston’s theory , MRR, which can be written as MRR=kPv, is generally dominated by normal pressure, the difference of linear velocity between pad and workpiece, and other factors such as slurry flow rate, pH, temperature, and so on. The relationships of MRR with load and spindle rotary rate were evaluated respectively. The rotation rate of the workpiece is identical to that of the pad throughout the experiments. The results imply consistency with the Preston formula showing the MRR increases with the increase of normal load and rotation rate (Fig. 4).
Referring to Fig. 3, platen and workpiece can be driven independently, and presuming the angular velocities are Ω and ω, respectively. Given the distance R between the centers of the workpiece and platen, then the relative linear velocity between the polishing pad and the point A(r,θ) at workpiece coordinates is given by 
Therefore, if other parameters, pressure and flow rate of slurry, etc., are kept constant, the material removal rate at point A(r,θ) is deduced by substituting (1) into Preston equation as follows
In our experiments, the angular velocity of the platen is the same as that of the workpiece (i.e. Ω=ω). Substituting Ω=ω into (2), we can obtain the material removal rate MRR=kPRΩ, which relies on R and Ω, independent of r and θ. MRR will be proportional to P when other factors are constant, and so is the Ω dependence of MRR. This is supported by the results of experiments (Fig. 4).
Preston’s coefficient k is also calculated based on experimental data (Table 1) and the order of k is 10-12 m2/N for BK7, which is in accord with reported results, but coefficient k for fused silica is slightly larger than that in the literature [2,10]. This may result from the deformation of the workpiece which is more likely to take place when the sample is ultra thin such as the one used in our experiments. The deformed workpiece will engage better with the polyurethane pad, which will result in a greater number of active abrasives and thus a larger MRR and Preston’s coefficient .
Clearly, Preston’s coefficient k for BK7 is more than that for fused silica, that is, the MRR of BK7 is relatively greater compared with that of fused silica when polished under alike conditions. This can be understood without difficulty if one considers aspects of the glass polishing mechanism . Mechanical wear theory depicts that the harder the glass is, the smaller the MRR is. If so, the relationship may be represented in the expression k=MRR/PRΩ∝1/H, because fused silica is harder than BK7 , k for fused silica is smaller when other factors are the same. Our results, to some extent, verify the wear theory. On the other hand, the chemical corrosion theory can also be applied to explain our experimental results. BK7 glass consists of much more sodium oxide and potassium oxide than fused silica, and therefore is more easily corroded by slurry and water during the polishing operation, resulting a higher MRR, that is to say, the slopes of curves of BK7 are steeper than those of fused silica as shown in Fig. 4. Our experimental data is consistent with corrosion theory, too.
3.2 Surface and subsurface damage (SSD)
A scratch existed in the surface of workpiece before pitch polishing. We examined the scratch by naked eye every half a polishing hour until the scratch disappeared. The polishing process had lasted for 10 hours and the thickness of removed material was about 10µm when the scratch was eliminated. Following that, etching processes were conducted. When the depth of etching reached 200nm and 1000nm, topographies of the workpiece were observed with a microscope at 1000× magnification. Surface topographies of the workpiece were shown as follows (Fig. 5):
The result showed evidence that scratches in the workpiece surface were covered by some substance which was called the hydrated layer. A number of research papers investigating the mechanism of glass polishing have been published over the past decade. At present, chemical mechanical theory has been widely accepted [3–4]. The theory pointed out the chemical process was a key factor besides the mechanical effect during glass polishing. A layer formed on the surface of workpiece, which was softer than the bulk material, because of interactions among abrasive particles, the workpiece and polishing pitch. Then this layer was scraped by abrasive or the polishing pad so that new material was revealed and a hydrated layer formed again. Consequently, the material was removed from the surface of workpiece. During the scraping process, some lower regions, for instance scratches, will be filled with hydrated composite (Fig. 6). When chemical etching, scratches will be gradually revealed, though the surface of the workpiece seems to retain its integrity. When the thickness of removed material is large enough, scratches will ultimately disappear.
Similarly, there was an objective scratch in the surface of workpiece when the polyurethane polishing operation started. About 4 hours later, the surface was defect free. The workpiece was also etched 200nm and 1000nm in order to compare it with that of pitch polishing. The images were presented, too (Fig. 7).
On the contrary, scratches were not found after chemical etching in the workpiece polished with the polyurethane pad. We attributed it to deposition rate. Assuming that the deposition rate, erosion rate and abrasion rate, say DR, ER and AR, (Abrasion rate can be considered as the rate that the hydrated layer is abraded by slurry particles and pad asperities.) then MRR is equal to AR, and DR is equivalent to the difference of ER and AR, DR=ER-AR. In the pitch polishing process, ER is so large that there is not enough time for slurry particles or pad asperities to abrade the hydrate away from the surface of wokepiece, in other words, DR is greater than zero. Thus scratches will be covered by the hydrated layer. If the thickness of material removed is not large enough, the scratch still lie in the surface of workpiece, although the surface will look perfect. Only when material is sufficiently removed can scratches and SSD be completely eliminated. As for polyurethane pad polishing, AR is not less than ER, so the DR is almost zero, that is, the depth of the deposition layer is very thin and can be negligible. Scratches, therefore, will entirely vanish as long as we don’t find scratches in the surface of workpiece after pad polishing (Fig. 8).
To what depth does the workpiece need to be polished so that scratches are really eliminated in pitch polishing, and is the removed thickness equivalent to the depth of the deepest scratch? Further study is underway to answer these questions and, moreover, to find conditions under which AR will be no less than ER for pitch polishing.
3.3 Surface roughness (SR)
Surface roughness was also investigated. Surface roughness is almost unchanged, about 1.0nm, after HF etching in pad polishing. It is noteworthy that the value of SR became smaller when the polishing time increased. Values of SR, which were measured when the BK7 workpiece was polished for 10 hours and 60 hours, were 1.2nm and 0.9nm (300µm×300µm), respectively. The reason is that the size of slurry particles became smaller (Fig. 9).
From Fig. 9, it is seen most particles lie between 10µm and 60µm after being used 10 hours, whilst the size of 90% particles was less than 20µm in 60 hours. Note that there were two peaks at less than 1µm and more than 100µm, respectively. Particles larger than 100µm indicate contamination by impurities rather than agglomeration of slurry particles [3, 17].
The particle size dependence of SR, which was approximately equal to the cutting depth of the abrasive, is related to the abrasive size, hardness of workpiece and so on. The formulation can be written as follows 
Where: Ra is the mean value of surface roughness of polished workpiece, C is a constant influenced by surface conditions of polishing pad, Ep is the Young’s modulus of polishing pad, P is the downward pressure applied to the workpiece, Hw is the hardness of the workpiece and d is the mean size of slurry particles. Obviously, SR is proportional to particle size. This is supported by experiments [3,17]. Using different size abrasives, 500 mesh and 300 mesh size, SR values were tested to be 1.1nm and 1.3nm, in the first 10 hours. Equation (3) can be used to estimate SR, but it is difficult in calculating the accurate value of coefficient C, which should be fitted through experimental data. C can be estimated at 0.016 from our experimental data (Ra=1.3nm, Ep=3.5GPa , P=1.0kPa, Hw=5.6GPa , d=20 µm). The research team is proceeding with experiments for determining the coefficient C with more accuracy.
Polyurethane pad polishing yields a much higher MRR than a pitch polishing tool because of its excellent physical properties. The values of MRR for BK7 and fused silica reached approximately 10µm and 4µm, respectively. Therefore, surface damage can be rapidly eliminated within several hours; moreover, SSD will also be mitigated. This will be gospel for raising the laser-induced damage threshold of optics. In addition, a workpiece polished by polyurethane also exhibits satisfying surface roughness results, around 1nm, which meets the requirements of precision polishing. Consequently, the time needed for successive polishing stages will be markedly shortened. Lastly, it is easier to condition a polishing pad than a pitch polishing tool.
The authors would like to thank all reviewers for valuable suggestions and acknowledge financial support from Fine Optical Engineering Research Center (FOERC).
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