Development of major optical projects demands great amounts of freeform optics, which requires mass-production technology. The atmospheric pressure plasma processing (APPP) based on chemical etching shows the advantage of high efficiency in form generation. However, the surface texture gets deteriorated with roughness to 60 nm Ra. Bonnet polishing can achieve ultra-smooth surface texture using flexible inflated tool. In this study, a combined processing chain consisting of APPP and bonnet polishing was proposed, in which APPP plays a role in form generation and bonnet polishing plays a role in rapid surface smoothing. Firstly, the form generation using APPP and the surface finishing using bonnet polishing were analyzed. Then the form-preserving ability of bonnet polishing under various conditions, including polishing parameters and surface form characteristics, was investigated experimentally. Consequently, the influence of bonnet polishing on surface form change was analyzed. Two sinusoidal freeform surfaces with 5 mm and 16 mm spatial period were generated using APPP and then smoothed using bonnet polishing. The experimental results show that the polishing induced form change is smaller than 20 nm PV with roughness improved to 2 nm Ra, which verifies the feasibility of the combined processing chain.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
With additional degrees of freedom for optical application, freeform surfaces become highly significant in major projects, such as high-quality telescope , laser fusion project  and so forth. A large amount of freeform optics are required to be manufactured with high form accuracy, low sub-surface damage, ultra-smooth texture and high production efficiency . Together with these high-demanding requirements, the complex structure with small spatial period of freeform optics poses extremely challenge to optical fabrication technology.
During the past decades, many researchers and organizations have been attracted to this subject and developed various advanced optical fabrication technologies. Bonnet polishing was proposed in the Optical Science Laboratory at University College London and has been commercialized by Zeeko Ltd . Walker et al. investigated various aspects of bonnet polishing, such as tool path generation , surface texture finish  and edge control , which proved excellent optical fabrication capability of this technology. Cao et al. built a multi-scale removal model and surface generation model of bonnet polishing [8,9], and then proposed the swing precess bonnet polishing (SPBP) method  and model-based self-optimization method to generate complex freeform surfaces . However, the typical spot size of bonnet polishing is relatively large, which is not suitable for creating surface structure with spatial period down to several millimeters. Magnetorheological Finishing (MRF) was firstly invented by the team of William Kordonski and developed by QED company , in which the material removed is based on shear stress under magnetic field. Since the spot length ranges from several to tens millimeters, MRF shows enormous advantage in reducing low, mid and high-spatial frequency errors on freeform surfaces with high precision and low surface roughness [12–14]. In addition, fluid jet polishing (FJP) and ion beam figuring (IBF) are developed to fabricate freeform surfaces [15,16]. In term of material removal mechanism, the mechanical process, such as plough, fracture or bombardment, plays a major role in the above machining methods.
Recently, reactive plasma processing techniques under atmospheric pressure are being developed, including plasma jet machining (PJM) , plasma chemical vaporization machining (PCVM) , reactive atom plasma technology (RAPT) , atmospheric pressure plasma processing (APPP)  and arc-enhanced plasma machining (AEPM) . Depending on versatile machining modes, the size of influence function can be varied in a large range between 0.1 mm  and 25 mm , which is suitable to fabricate freeform surfaces with complex structure. Arnold et al. adopted a small plasma jet of 0.42 mm to generate the sinusoidal structure with 0.5 mm spatial period and ‘Mona Lisa’ image on SiO2 surface . Takino et al. proposed a figuring method with constant velocity to create a 12 mm × 12 mm non-axisymmetric mirror with a maximum depth of approximately 3 μm [23,24]. Recently, APPP was developed to fabricate 330 mm × 330 mm continuous phase plate with complex surface structure in two modes with high efficiency .
However, it has been found that the ultra-smooth surface quality is deteriorated after reactive plasma processing and the additional surface finishing method should be introduced. Paetzelt et al. proposed plasma jet polishing (PJP) based on thermal effect of plasma jet, in which the material on surface redistributes to a smooth morphology. PJP was implemented prior to PJM to remove subsurface damage and improve roughness to 2 nm RMS. However, PJP is not suitable for finishing large aperture optics due to the low finishing rate with 1 cm2/min [26,27]. Mori et al. combined the PCVM and elastic emission machining (EEM) to fabricate X-ray optics with atomic surface quality. In the combined process, the figure correction in larger spatial period was carried out using PCVM with high efficiency and the surface finishing in spatial period lower than 500 μm was realized by EEM [28,29]. Though the EEM is capable to smooth surface excellently to 0.1 nm RMS, the machining spot area is only 100 μm × 1 mm, which is more appropriate for smoothing small optics. Besides, soft polishing were introduced after PJM to improve surface quality to 0.6 nm RMS roughness .
The previous research has demonstrated the capability of reactive plasma processing for fabricating freeform optics and the necessity of introducing additional surface finishing method. To fabricate complex freeform optics with high quality, a combined processing chain, which can mixes the strength of APPP and the additional surface finishing method, needs to be studied. Since the surface finishing is realized through contact polishing process, there comes up a question whether the surface form generated by reactive plasma processing will be altered by polishing or not. If it does not, how much form change may the polishing method introduce? In terms of freeform optics, the contact condition between polishing tool and substrate can be more complicated due to the complex surface structure.
According to the analysis above, a combined processing chain for complex freeform surfaces based on APPP and bonnet polishing is studied in this work. The principle of the combined processing chain is proposed. The ability of form generation and surface finishing in this processing chain are analyzed in Section 2. Then, the form-preserving capability of bonnet polishing is investigated experimentally in Section 3. Next, the freeform sinusoidal surfaces are fabricated to evaluate the form-preserving capability and the combined processing chain in Section 4. Finally, the conclusion is summarized in Section 5.
2. Combined processing chain for complex freeform surfaces
2.1 Concepts of combined processing chain
Figure 1 shows the schematic diagram of the combined processing chain. The fabrication process of complex freeform surfaces is divided into two steps, which are form generation and surface smoothing. APPP, an atmospheric chemical etching technique, is used to generate surface form with high efficiency. Compared with conventional polishing method, the material removal of APPP is realized through chemical etching and the material removal rate is not limited by tool size, contact zone size or rotatory speed. Thus, APPP is able to generate complex surface form with small structure efficiently. However, the ultra-smooth surface texture cannot be obtained using APPP due to the isotropic chemical etching process. Then the post polishing is to be used in the second step to achieve a smooth surface, in which the form change after polishing is expected as small as possible. To accomplish this aim, a compliant polishing tool that can contact local surface completely is desired. Therefore, the bonnet polishing is introduced to achieve form-preserving surface smoothing. Thus, the processing chain combines the advantages of high removal efficiency of APPP and surface finishing capability of bonnet polishing.
2.2 Surface form generation using APPP
Figure 2(a) describes the removal mechanism of APPP. Fluoride gas together with other assistant gas is introduced into the plasma torch and excited by radio frequency (RF) power. Then the reactive fluorine plasma jet is produced, which can be regarded as a tool for material removal. The reactive species in plasma jet react with silica-based material, such as fused silica, silicon carbide, silicon etc. Since the reaction product is volatile at room temperature, the material removal is realized.
Figure 2(b) shows the APPP machine tool used in this study. The reactive plasma machining system includes a 13.56 MHz power supply, a gas mass flowmeter, a plasma torch and a numerical control system. The substrate is placed on the ground electrode moving with X-Y stage, while the plasma torch is installed on the Z axis. The processing parameters used in this study are shown in Table 1.
The plasma jet can be seen as particle current including reactive chemical energy, thermal energy and dynamics energy. When impinging on the substrate, the energy are transferred into the substrate and the total energy distribution on substrate influences the chemical reaction rate. Thus, a Gaussian shape removal spot is realized, shown in Fig. 2(a). According to previous research, the generation capability of a influence function for a specific spatial period structure can be evaluated by Eq. (1) [16,31].
The principle of freeform surface generation using APPP is based on computer-controlled optical surfacing (CCOS) method. The desired surface is inverted at first and the actual removal can be obtained by adding additional material removal. Then, the dwell time is calculated using de-convolution algorithm. Consequently, the plasma torch scans on the substrate with various dwell time to create the freeform surface.
Due to the nature of pure chemical etching, the surface after APPP is affected by the initial surface and subsurface condition. Thus, the ultra-smooth surface cannot be achieved only using APPP. Figure 4(a) shows photography of polished fused silica machined by APPP. After APPP, there leaves a machining footprint on surface, which is consistent with the desired material removal of the sinusoidal surface. As shown in Fig. 4(a), the footprint affects the optical performance of the substrate. Figure 4(b) shows the surface texture after APPP measured by Ametek Taylor Hobson CCI 3000, which is a typical morphology etched by plasma. Generally, the surface roughness after APPP reaches 10-60 nm Ra under different conditions, which cannot satisfy optical application.
2.3 Surface finishing using bonnet polishing
For surface finishing, the bonnet polishing is conducted after APPP. To realize form-preserving polishing, the compliant bonnet tool is used in this study, instead of semi-rigid bonnet tool . As shown in Fig. 3, the polishing tool is an inflated spherical membrane covered with polishing cloth. The membrane, made of rubber layer and fiber mesh, can only sustain tension force and deform a little outward. Under compression force, the bonnet surface can deform inward easily. These characteristics make bonnet tool in this paper flexible to match local surface . The bonnet rotation axis is inclined to the local surface at a certain angle, called precess angle. With different precess angle, the relative velocity in contact area varies. The required polishing spot size can be obtained by a given offset with a certain tool radius. In addition, the polishing contact pressure can be altered by adjusting inflated pressure. A Zeeko IRP 600 machine tool with 7 axes was used in this study, shown in Fig. 3.
The most principal operation mode of bonnet polishing is form-correction, in which the bonnet tool scans on the substrate with various feed rate calculated from error map. On the other hand, the pre-polishing mode is conducted with a constant feed velocity, which is used to remove sub surface damage or obtain smooth surface after grinding . For prototype segments of European Extremely Large Telescope (E-ELT), both modes were deployed. Notably, the ground surface feature in the spatial frequency range of 0.5-0.29 /mm cannot be removed totally after long time of pre-polishing . This removal characteristics are adverse to production of the segments, and ‘grolishing’ was developed to remove the mid-spatial-frequency errors [34,35]. Fortunately, this mid-spatial-frequency form-preserving capability is suitable for finishing of complex freeform in this study. So that the pre-polishing mode is used to accomplish surface finishing after form generation using APPP.
Figure 4(c) shows the surface texture after bonnet polishing with roughness improved from 17.52 to 1.73 nm Ra, which verifies the surface finishing ability of bonnet polishing. The polishing parameters in the experiment are listed in Table 2. The substrate in Fig. 4(a) is 60 × 60 × 3 mm3 and the bonnet polishing process took about 25 minutes. More generally, the surface texture processed by APPP can be easily smoothed after material removal of about 1000 nm using bonnet polishing. With regard to the whole combined processing chain, the surface form change after bonnet polishing becomes a significant issue, which can bring great affect on final form accuracy.
3. Experimental study on form-preserving capability of bonnet polishing
To evaluate the form-preserving ability of the bonnet polishing quantitatively, ripple structures with different spatial period and peak-valley (PV) values were prepared using APPP. Note that, the generated ripple structures provide the evidence of form generation ability of APPP. Then, the substrates were smoothed using bonnet polishing under various conditions. The substrate is 100 × 100 × 3 mm3 made of fused silica. The surface form before and after bonnet polishing was measured using Fisba μPhase 2 HR interferometer.
Figure 5 describes the schematic of form-preserving polishing experiments and Table 3 shows the experimental details. The experiments were divided into 2 groups. In experiments group P1-P3, the influence of polishing parameters, such as bonnet inner pressure, polishing cloth and polishing direction on form change was studied. Two polishing directions were defined based on the direction of bonnet polishing axis and the axis of the ripple structure, shown in Fig. 5. In addition, the form change of different ripple structures was studied in experiments group S1-S4. The other parameters are same as those in Table 2.
3.1 The form change after bonnet polishing
Figure 6 shows the ripple structure with 5 mm spatial period before and after bonnet polishing. It can be seen that the bonnet polishing keeps the main characteristics of the ripple structure with PV decreasing slightly. Furthermore, the power spectrum density (PSD) analysis is conducted, shown in Figs. 6(c) and 6(d). There is an obvious peak at 0.216 /mm spatial frequency, which corresponds to the spatial period of the ripple structure. In addition, the decrease of PSD amplitude at 0.216 /mm spatial frequency indicates that the surface form changes in height direction.
To evaluate the form change visually, the profiles of the ripple structures were calculated and plotted in Fig. 7. The PV of ripple structures before and after bonnet polishing are defined as and . It is straightforward to find that the PV of ripple structures decreases after polishing. The PV decrease per 1 μm polishing removal depth is calculated and defined as the form change, . In addition, the change ratio after polishing is expressed as:
3.2 The influence of bonnet polishing parameters on surface form change
Figure 8 represents the results of experiments group P1 and P2, in which the spatial periods of ripple structures are 2.8 mm and 5 mm respectively. For these two experiments groups, regardless of the types of polishing cloth and the PV of ripple structures, the form change after polishing keeps constant with different inner pressure from 0.3 to 1.2 bar. These results indicate that the inner pressure has no influence on the form-preserving capability. Normally, the bonnet stiffness increases when inner pressure rises, consequently the material removal rate increases. Therefore, the higher inner pressure can be used for form-preserving polishing after APPP to speed up the whole processing chain.
Comparing the results using different polishing cloth in Fig. 8, the form change when using polyurethane is more significant than that using uninap, which can also be proved in the following experiments. The difference can be explained by the different elastic modulus of polishing cloth. The uninap has a smaller elastic modulus than polyurethane, it can deform more easily under the same load. When contacting ripple structures, the uninap is able to conform peaks and valleys with relatively uniform pressure distribution. Therefore, the removal rates at peaks and valleys are closer to each other, leading to less form change after polishing. On the other hand, the removal rate using polyurethane is higher than uninap, which provides an advantage in finishing efficiency when the induced form change is acceptable.
Figure 9 shows the form change using different polishing directions. It is found that the polishing direction has no effect on form change when using polyurethane and uninap. According to previous study, the surface texture after bonnet polishing can be further improved by 4 different precess directions . Therefore, the surface finishing in the combined processing chain can be conducted at four-step precession mode, without introducing additional form change.
3.3 The form change of different ripple structures after polishing
Figure 10 shows the correlation between the form change and the PV value of ripple structures when the spatial periods are 2.8 mm, 5 mm, 10 mm and 15 mm, which correspond to experiments groups S1, S2, S3 and S4. Based on least square method, the linear fitting equation is also obtained. Two types of polishing cloth were used in these experiments and the results are represented respectively.
For the experiments using uninap, the form changes are different as the spatial period varies from 2.8 to 15 mm. When the spatial periods are 2.8 mm and 5 mm shown in Figs. 10(a) and 10(b), the form change increases linearly with increasing PV of ripple structures. When the spatial periods are 10 mm and 15 mm, although the PV of ripple structures is larger, there is no obvious increase of the form change. Moreover, the slope of fitting equation decreases with increase of spatial period, which means that the bonnet polishing causes larger form change on ripple structures with smaller spatial period.
For the experiments using polyurethane, the relationship between the form change and the PV of ripple structures is more apparent. When the spatial periods are 2.8 mm, 5 mm and 10 mm, there is a significant linear correlation between the form change and the PV of ripple structures. Note that, the maximum form change is above 50 nm, which is much larger than that using uninap. When the spatial period is 15 mm, the form change shows no apparent increase with increasing PV of ripple structure and only fluctuates at about 6 nm.
According to Eq. (2), the change ratio is calculated. It is found that the change ratio with different PV of ripple structures is almost the same. Then the average change ratio is obtained shown in Fig. 11. For results using polyurethane, the average change ratio decreases with spatial period from 15% to 2%. When uninap is used, the average change ratio reaches maximum 2.4% at 2.8 mm spatial period. With larger spatial period, the average change ratio fluctuates at about 1%, showing an excellent form-preserving capability.
3.4 Analysis of the form-preserving capability
To achieve high efficiency in form-preserving polishing, the processing parameters can be optimized depending on surface form characteristics. Based on results in Section 3.2, higher inner pressure can be used for high smoothing efficiency. Considering the influence of surface structure characteristics, Fig. 12 summarizes the form change rules based on the fitting linear relationship in Section 3.3. The form change is influenced by the original PV and the spatial period of surface structures. When the polishing parameters are determined, the spatial period and structure PV show influence on form change in two aspects. The influence map are separated into two zone shown in Fig. 12. In zone A, the structure PV has primary affect on form change. As the spatial period becomes larger, shown in zone B, the structure PV has no affect on form change. In this zone, the form change keeps at a low level under 20 nm, which shows excellent form-preserving capability. Specifically, when the spatial period is down to about 5 mm, the surface structure can still be preserved after bonnet polishing using uninap.
In another respect, Fig. 12 provides a criterion to choose the optimal processing parameter for form-preserving polishing. For example, a freeform surface with 6 mm spatial period and 1200 nm PV is required to be finished within 20 nm form change. According to Fig. 12, the form change will be in the range of 10 nm to 20 nm when uninap is used. If the polyurethane is used, the form change will be over 40 nm. Thus, the uninap should be chosen to accomplish surface finishing.
4. Verification of the combined processing chain
To verify the combined processing chain as well as the form-preserving ability, two sinusoidal surfaces were generated using APPP, and then finished using bonnet polishing. The first one has 5 mm spatial period and 1200 nm PV. According to Fig. 12, it is found that the uninap is more suitable to obtain a better form-preserving result. The second one has 16 mm spatial period and about 1600 nm PV. The form change can be controlled less than 20 nm using uninap or polyurethane, and the polyurethane was used. The other polishing parameters are the same as those in Table 2.
Figures 13 and 14 show the measurement results before and after bonnet polishing. After registration of the measurement results, the form change maps were obtained. For the sinusoidal surface with 5 mm spatial period, the material removal of bonnet polishing is about 1.2 μm and the roughness improves from about 25 nm to 2.1 nm Ra. As shown in Fig. 13(c), the form change map shows a low spatial frequency error, which may be caused by non-uninform removal of polishing process. Even so, the form change still keeps less than 20 nm PV. For the sinusoidal surface with 16 mm spatial period, the material removal is about 0.8 μm. The PV of form change map is smaller than 20 nm and the roughness is improved from about 30 nm to 2.3 nm Ra. These results show strong evidence of the form-preserving capability of bonnet polishing. Such smaller form change introduced by bonnet polishing can be neglected in the whole processing chain. Therefore, the practicability of the combine processing chain has been proved.
In order to fabricate freeform optics with high efficiency and ultra-smooth surface, APPP and bonnet polishing were combined to utilize the strength of form generation and surface finishing respectively. The principle of the combined processing chain was proposed and discussed. APPP is able to generate freeform surfaces with spatial period down to 2 mm and the bonnet polishing can smooth surface texture with roughness improved from about 60 nm to 2 nm Ra. Furthermore, different ripple structures were polished to evaluate the form change induced by bonnet polishing. The experimental results indicate that the polishing cloth has a significant affect on form-preserving capability, instead of inner pressure and polishing direction. In addition, the form change induced by bonnet polishing increases with larger PV and smaller spatial period of ripple structures. Two freeform sinusoidal surfaces with 5 mm and 16 mm spatial period were generated using APPP and smoothed using bonnet polishing, with form change less than 20 nm PV and roughness improved to about 2 nm Ra. Overall, these results verify the feasibility of the combined processing chain, which provides a productive fabrication method for freeform optics.
National Natural Science Foundation of China (No. 51175123); National Science and Technology Major Project (No. 2013ZX04006011-205).
The author would like to thank the China Scholarship Council (CSC) for its financial support in studying at University of Huddersfield, the National Facility for Ultra Precision Surfaces, North Wales, UK.
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