Open Access
Add to BibSonomyAbstract
Formation of subsurface damage has an inseparable relationship with microscopic material behaviors. In this work, our research results indicate that the formation process of subsurface damage often accompanies with the local densification effect of fused silica material, which seriously influences microscopic material properties. Interestingly, we find ion beam sputtering (IBS) is very sensitive to the local densification, and this microscopic phenomenon makes IBS as a promising technique for the detection of nanoscale subsurface damages. Additionally, to control the densification effect and subsurface damage during the fabrication of high-performance optical components, a combined polishing technology integrating chemical-mechanical polishing (CMP) and ion beam figuring (IBF) is proposed. With this combined technology, fused silica without subsurface damage is obtained through the final experimental investigation, which demonstrates the feasibility of our proposed method.
© 2016 Optical Society of America
1. Introduction
Since subsurface damage (SSD) is a critical factor influencing the performance and usage of optical components, the fabrication and measurement requirements for subsurface quality are becoming ever more stringent with the development of modern high-performance optical systems. In some application fields, the specifications of subsurface quality even approach to the physical limit, especially during the fabrication process of high power laser optics and lithography optics. In the high power laser facilities, the optical components need resist the laser irradiation at a fluence about 10J/cm2 [1–3 ]. Considering SSD is an important initiator of laser-induced damage, damage-free machining in the full-area coverage is required to produce high damage threshold optics. Additionally, in the field of optics, probably the most stringent specifications for surface accuracy and smoothness are made on lithography optics that nanometer or even sub-nanometer magnitudes are required for these parameters [4, 5 ]. To fabricate such high-precision optics, material removal unit should be at the atomic/molecular level and the existing SSD would seriously influence the atomic/molecular material removal process. Consequently, the detection and control technologies for SSD are of great importance during the fabrication process of high-performance optics.
Fused silica, with advantages of excellent optical performances and material homogeneity, is an important material candidate for high-performance optical devices. Its typical application is used for high power laser optics and lithography optics [6–8 ]. However, surface/subsurface damage of fused-silica optics would be easily induced during traditional polishing process. Since the material structure of fused silica consists of a large amount of void space in addition to the volume occupied by silicon and oxygen atoms, the void space will decrease when subjected to sufficiently large compressive stresses [9–11 ]. In response, the fused silica material would densify permanently accompanying with the nanoscale material behaviors. During this process, various surface/subsurface damages, such as microscopic scratch and crack, would be generated. From the material structure view, fused silica optics without subsurface damage is very difficult to be obtained during the traditional polishing.
Various methods are developed to remove the SSD generated during the grinding and the traditional polishing, such as HF etching technique [12, 13 ] and magnetorheological polishing (MRF) [14–16 ]. Besides, the researchers also successfully reveal the embedded SSD through using these technologies to remove the surface layer. There is intense research under way to reduce SSD by weakening the mechanical effect and simultaneously strengthening chemical effect in the fabrication of low-damage optics. However, since the subsurface damage exhibits the characteristics of nanometer scale and shape diversity during the fine polishing process, there exist more or less difficulty for these above technologies to fabricate or measure such low-damage fused silica optics. On one hand, although the chemical processing methods can avoid the polishing load and restrain the local densification effect, the chemical reaction products would be remained on the optical surface and cover the subsurface damage. On the other hand, some contact processing methods, including MRF, the macroscopic damage would be effectively restrained, because only small stress is generated during the polishing process. However, these contact methods involve hard abrasive particle in contact with the surface material, where the nanoscale damage would be induced by the mechanical effect. Consequently, it is difficult for the current methods to maintain the original morphology of the subsurface and even accompany with the formations of the subsurface damage or hydrolysis layer, which would seriously influence the detection of nanoscale damage and the fabrication for damage-free optics.
The purpose of this work is to investigate the detailed subsurface damage measurement and efficient damage-free fabrication of fused silica optics assisted by ion beam sputtering. From the microscopic material behavior perspective, the formation process of subsurface damage often accompanies with the local densification effect, which would lead to the variation of microscopic material properties. We find that IBS is very sensitive the local densification of the fused silica material and this nanoscale phenomenon can characterize more detailed subsurface damages. Additionally, a polishing technique combining CMP and IBF is proposed to control the local densification effect and the formation of subsurface damage. Through the final experimental investigation, fused silica optics without subsurface damage is obtained with this combined technique.
2.Theoretical details
2.1 Microscopic densification phenomenon
For these materials comprised by the same particles, their physical properties would be seriously influenced by the configuration and internal structure of the material particles. In the majority of SiO2 materials, the Si atom shows tetrahedral coordination, with four oxygen atoms surrounding a central Si atom. These material forms involve tetrahedral SiO4 units linked together by shared vertices in different arrangements. Crystalline quartz material possesses a regular network structure through the connectivity of these tetrahedral units and its density is 2.65 g/cm3. Whereas the network structure of fused silica is unregular and it belongs to an amorphous material with a density of 2.2 g/cm3. The difference in density can be ascribed to the arrangements of tetrahedral units and the lengths of Si-O bonds, where the Si-O bond length in fused silica is greater than the Si-O bond length in crystalline quartz. From the material structure view, fused silica consists of massive void space in addition to the volume occupied by silicon and oxygen atoms, and the changes of the tetrahedral arrangement and the reduction of the void space would induce the variation of the microscopic material properties.
Obviously, the particle arrangement would be disarranged and the void space will decrease when subjected to sufficiently large compressive stress, leading to the permanent densification [Fig. 1(b) ]. Previous researches indicated that fused silica will densify permanently at a pressure of about 2 GPa and achieve densification saturation at 12 GPa with densification as large as 20% [9–11 ]. In traditional polishing, the local pressure at the nanoscales, between the abrasive particles and the surface material of fused-silica, can easily reach these values [9], so the plastic deformation is involved during the material removal process.
For the unique material structure, fused silica will easily densify permanently and various surface/subsurface damage, such as microscopic scratch, would be generated. Figure 2 shows the common scratch defects generated during the polishing, where the various structure types would be attributed to the different mechanical effects. In Fig. 2(c), we can observe continuous type scratch formation on the surface, where the mechanical effect of the polishing abrasive gives priority to continuous cutting effect in the material removal process [Fig. 2(a)]. When the rolling cutting effect of the abrasive is brought into this process [Fig. 2(b)], the microscopic structure type would be changed to Hertzian type scratch [Fig. 2(d)]. Additionally, with the combined action of these two mechanical effects, mixed type scratch will be exhibited on the polished surface. Defects, such as the above mentioned scratches, would be hidden below the surface because of the redeposition of the hydrolysis substance and therefore subsurface damages are generated. These damages whether on surface or in subsurface layer can be characterized by the change of the microscopic material physical properties resulting from the local densification.
Fig. 2 Analysis of mechanical effect on fused silica surface and common microscopic scratches generated during the traditional polishing. First Row: (a) sketch map of continuous cutting effect and (b) sketch map of rolling cutting effect. Second row: AFM images of (c) continuous type scratch; (d) Hertzian type scratch; (e) mixed type scratch.
2.2 Ion beam sputtering characteristic
Low-energy (≤1000eV) IBS technology possesses the advantage of atomic material removal capability, where the IBS involves bombarding a material surface with a low-energy particles beam and the kinetic energy is transferred through complex collision process [17]. This process utilizes physical sputtering effect to remove surface material with noncontact method, and therefore problems that exist in traditional figuring processes, such as pressure load and hydrolytic substance, disappear naturally.
Based on Sigmund’s sputtering theory [18, 19 ], the material removal rate is proportional to the power deposited on the material surface, where the primary factors related to material removal rate are ion energy, beam current density and material properties. Under the fixed sputtering conditions, the removal rate at the macroscales would be an invariant constant for these materials with high homogeneity. From the descriptions in the section 2.1, fused silica material at the nanoscales, however, always densifies during traditional polishing and exhibits an anisotropic surface with various material properties. During the IBS, the local sputtering rate would be influenced by the local densification effect. In response, the contribution of material properties to sputtering rate cannot be ignored at microscopic scale and the sputtering rate v(x, y) need be redefined as a variable:
Where J is beam current density; Mt is the molar weight of the bombarded material; ρt(x,y) is the local material density; NA is Avogadro number; Y(x,y) is local sputtering yield of the corresponding point (x,y) and can be given by:
Where Ub(x,y) is local banding energy of surface material; Cm is the parameter of differential scattering cross section; ε is the total deposited energy of a single incidence ion; σ is the average depth of ion incidence; and α and β are the Gaussian parameters of the distribution parallel and perpendicular to the beam direction, respectively.
Substituting Eq. (2) to Eq. (1), we can know that the local sputtering rate v(x,y) is mainly determined by material density ρt(x,y) and local banding energy Ub(x,y) for these materials comprised by the same particles, such as fused silica and crystalline quartz that are the two structural forms of SiO2 material. Overall, the sputtering rate is inversely proportional to the material density ρt(x,y) and banding energy Ub(x,y) under the fixed sputtering conditions:
From Eq. (3), we can know that IBS at microscopic scales has an inseparable relationship with nanoscale material behaviors. Corresponded to the surface/subsurface damages shown in Fig. 2, Fig. 3 illustrates the surface morphologies usually observed in our IBS experiments that the concave scratches vanish and the emergence of nanowall structures is clearly seen on the surface. It is obvious that the observed emerged nanowalls evolve from the initially existing defects generated during the pre-polishing process. Interestingly, based on Sigmund’s sputtering theory, the original scratches would become deeper because of the depression being eroded faster than protrusion [18, 19 ], but the observed experimental phenomenon are against this theory. These nanoscale phenomena validate that the densification-dependent sputtering would seriously influence and even dominate the morphology evolution process during the IBS of fused silica.
Fig. 3 IBS of densified fused silica material related to these defects described in Fig. 2. The AFM images in first row indicate the convex morphologies after IBS: (a) continuous type nanowall, (b) bilateral type nanowall and (c) convex nanowall corresponded to the Hertzian type scratch. Second row indicates the estimated mechanical effects during the formations of the initially existing damages before IBS: (d) compressive stress, (e) lateral compressive stress and (f) rolling compressive stress.
Additionally, the mechanical effects during the formations of the initially existing damages also can be simply estimated based on the generated convex nanostructures during the subsequent IBS. The continuous type nanowall [Fig. 3(a)] shows that the compressive stress of continuous cutting would dominate the material removal process during pre-polishing and the densification layer generated below the polishing particle [Fig. 3(d)]. When the compressive stress of continuous cutting is located on the bilateral areas of the polishing particle [Fig. 3(e)], the densification layer will distribute on the bilateral areas and this defect would transform to bilateral type nanowall after IBS [Fig. 3(b)]. Similarly, during the IBS the densification layer [Fig. 3(f)] formed from the rolling cutting process will induce the convex nanowall [Fig. 3(c)] corresponded to the Hertzian type defect.
Summarized from the above theoretical analysis and IBS experiments, we can find that the densification-dependent sputtering seriously influences the IBS process. Subjected to mechanical effect during the traditional polishing, fused silica material exhibits obvious local densification phenomenon. The local material densification results in the difference of sputtering rate at the nanoscales during the subsequent IBS and induces the surface/subsurface defects evolve to convex nanostructures. The theoretical analysis and experimental results show that the densification-dependent sputtering dominates morphology evolution during the IBS, which would make IBS as promising technology for revealing the subsurface damage.
3. Measurement experiments of subsurface damage
All sputtering experiments are performed in our self-developed IBS systems [20] under the bombardment of Ar+ ions at normal incidence, where the processing conditions are fixed at ion energy E ion = 800 eV and beam current J ion = 30 mA. For these experiments, fused silica (from Corning Inc.) samples with material bulk density ρ t = 2.2 × 103kg/m3 are prepared by different polishing conditions to various original components. To observe the surface morphology, atomic force microscopy (AFM, Bruker Dimension Icon) in ScanAsyst mode is used to investigate the microscopic morphology evolution on fused silica surfaces. In addition, the elastic modulus at the nanoscale is measured by AFM in PeakForce QNM (Quantitative Nanomechanical Mapping) mode using a DNISP probe (handcrafted natural diamond nanoindenting tip), which can simultaneously provide detailed surface morphology and elastic modulus images of within the measured area.
3.1 Measurement of microscopic densification
For investigation of the local densification effect and its influence on morphology evolution, experiments are performed on a sample that is pre-polished by traditional parallel-polishing method. This sample is polished by 2.5μm diamond abrasive, where the loaded pressure is 0.25 bars and the polishing time is about 60 min. Figure 4(a) shows that obvious microscopic scratches with different width and depth, generated during the diamond abrasive polishing, exist on the material surface. Subsequently, an ion beam (5.0 mm FWHM) is raster scanned within the central area.
Fig. 4 Measurement results of surface morphology and elastic modulus distribution: (a) Original surface morphology; (b) Sketch map of measurement method; (c) Surface morphology after IBS; (d) The corresponding elastic modulus distribution.
To investigate the material properties, elastic modulus at the nanoscale is measured by AFM, and the fundamental mechanism of this method is shown in Fig. 4(b). Firstly, nanoindentation experiments are made at the scattered points of the measured areas to obtain the corresponding load-depth curves. Then, the nanoscale elastic modulus at every point is calculated based on these nanoindentation curves and therefore the distribution within the whole measured areas can be obtained. With this method, the detailed surface morphology and elastic modulus images corresponded to the measured areas can be given simultaneously.
Since the penetration depth of the AFM probe is very small and the defects are usually covered by the surface hydrolysis layer, the AFM experiment for elastic modulus is implemented in a randomly selected area machined by the IBS. Concerning the final surface morphology in Fig. 4(c), AFM image indicates that the emerged nanowalls, l AB and l CD, and the two residual scratches, l EF and l GH, exist on the surface after removing material of 120 nm depth. Accordingly, in Fig. 4(d), we can clearly find that the elastic modulus within these corresponding nanowall and scratch areas are obviously larger than that of other areas. Known from the experimental results, the materials within surface/subsurface damage areas easily densify during the traditional polishing, where the difference of material property at nanoscale makes the fused silica material exhibits an anisotropic characteristic. As a result, these microscopic material behaviors seriously influence the morphology evolution during the subsequent IBS process, which validate the theoretical analysis described in the section 2.
3.2 Measurement results of nanoscale subsurface damage
To validate the measurement capability for nanoscale subsurface damage, comparative experiments are performed on a sample with IBS technique and HF etching technique. This fused silica sample with a diameter of Ø100mm is firstly processed by parallel-polishing. The 2.5μm diamonds are chosen as polishing abrasives to remove the coarse subsurface damages generated during the grinding and simultaneously provide small damages for this sample. Then, the subsequent pre-polishing process is divided into two steps. The objective of the first step is to rapidly remove the vast majority of the existing surface/subsurface damages and reduce the thickness of the damage layer. In this step, the sample is polished by 2.5μm CeO2 loose abrasive under the loaded pressure of 0.25 bars. The second step is mainly applied to further remove these damages, where the sample is polished by 0.5μm CeO2 loose abrasive without loaded pressure and this abrasive of a very low slurry concentration is used to control the material removal rate within a low level. After these pre-polishing processes, the surface quality is effectively improved with the surface roughness value down to about 0.15nm RMS. The most importance is that some hydrolysis substances are generated from the chemical reaction of CeO2 abrasive and SiO2 material, and the therefore the residual nanoscale damages will be hidden in the subsurface and no obvious microscopic surface defects can be observed.
In the comparative experiments, the area of this sample is equally divided into two parts. The measurement experiments of subsurface damage are made on these two areas with IBS method and HF etching method, respectively. Figure 5 (a) shows a taper polished by the IBS, where the depth of the taper is detected by interferometer and the points to be measured are marked at the different material removal depth. After removing material of 40nm depth, Fig. 5(b) illustrates that no material damage can be observed on the surface, implying that there is no subsurface damage existing in this material layer. When the material removal depth is further increased, the slight nanowall structures protrude from the surface after 60 nm depth material being removed, resulting in the nanoscale damages gradually exhibit on the surface [Fig. 5(c)]. With the material removal depth increased to 80nm, obvious protuberant nanowalls can be clearly observed in the AFM image of Fig. 5(d). The experimental results indicate that the IBS can effectively reveal the nanoscale subsurface damages based on the influence of densification effect on microscopic morphology evolution, which validates the feasibility of our proposed measurement method for more detailed subsurface damages.
Fig. 5 Measurement results of nanoscale SSD measured with the assistance of IBS: (a) Taper machined by IBS; (b)-(d) Microscopic morphology after the removal depth increasing from 40nm, 60nm to 80nm.
When the material removal depth is increased from 40nm to 80nm, experimental results in Fig. 6 , however, show that damage morphologies has never emerged on the surface during the HF etching technique. These results indicate that no subsurface damage has been detected. Two factors would be responsible for these experimental results. On one hand, the HF etching technique possesses the removal capability for surface/subsurface defects, especially for the nanoscale martial damages, which make this method hard to maintain the original status of the subsurface damages. On the other hand, since HF etching utilizes the chemical reaction between the hydrofluoric acid and the SiO2 material to remove the surface, the chemical reaction products would redeposit on the optical surface and the nanoscale damages are covered with this hydrolysis layer.
Fig. 6 Microscopic morphology after removing different material depth (a) 40nm, (b) 60nm and (c) 80nm with HF etching method.
Summarized from the above comparative experiments, the formation process of surface/subsurface damages often accompany with the material densification effect, which seriously influences the nanoscale material properties. Additionally, the IBS is very sensitive to this microscopic material behavior and can really reveal nanoscale subsurface damages. This nanosacle phenomenon distinguishes IBS technique as a promising detection technology for the more detailed subsurface damages.
4. Damage-free fabrication experiment
The above researches show that microscopic densification effect can be identified as an important material behavior during the formation process of subsurface damage. An effective approach to control the subsurface damage is to avoid the occurrence of the densification effect through weakening the mechanical effect and strengthening the chemical effect during the polishing process. Consequently, a combined technique integrating CMP and IBF technologies is proposed to fabricate damage-free fused silica optics. In our proposed method, the CMP step can effectively avoid the densification effect occurs in the material removal process and simultaneously remove the surface/subsurface damage. Then, an IBF step is used to remove the hydrolysis layer deposited on the surface.
To validate the feasibility of this combined technique, an experiment is implemented on a fused silica sample, whose aperture is Ø80mm and thickness is 1mm. In the first step, the sample is polished by the CMP, and the chosen loose polishing abrasive is 0.5μm CeO2 particles. For ensuring the sufficient material removal, polishing time of three hours is taken to completely eliminate the surface/subsurface damages. During this polishing process, we slowly dilute the polishing abrasive through adding the deionized water to gradually avoid the contact of the abrasive particles and the surface material. The sample is nearly polished with pure water during the final 45 min. Subsequently, an ion beam is raster scanned within an appointed area of a dimension of 30mm × 30mm, where the used ion energy is 800eV and the material removal depth is about 100nm. To avoid the influence of the sputtered particles generated in IBF process, a fused silica sheet is applied to cover these areas that are not expected to be machined by the IBF.
In order to more detailedly display the subsurface quality, cross-sectional transmission electron microscopy (JEM-2100F, produced by JEM Inc., Japan) experiments are taken within these areas that are machined or unmachined by the IBF, respectively. Figure 7(a) shows a cross-sectional sample with a dimension of 30μm × 10μm that is firstly prepared by the focused ion beam (FEI-200 THP, produced by FEI Inc., America) and then the central area of this sample is thinned by an ion beam thinner.
Fig. 7 Cross-sectional HRTEM image showing surface/subsurface of fused silica: (a) fused silica sample after ion beam thinning; (b) Hydrolysis layer formed during CMP that an obvious interface is observed; (c) damage-free machining is obtained by IBF; (d) the TEM image of subsurface.
Due to belonging to amorphous material, the detailed atomic structure of fused silica cannot be imaged by the TEM, whereas the nanoscale interface would be clearly distinguished when the adjacent areas comprised by the materials of different properties. TEM image in Fig. 7(b) shows that no subsurface damages and material densification phenomenon can be observed, where the arrangement of the material particles within the subsurface layer is very uniform after the CMP process. Although an obvious hydrolysis layer of about 7nm thickness [Fig. 7(b)], generated during the CMP step, exhibits on the surface, this hydrolysis layer is effectively removed during the IBF step [Fig. 7(c)]. Compared with the TEM image of the further deeper subsurface [Fig. 7(d)], the arrangement of the material particles approaches to the uniformity from the surface to the subsurface and the damage-free optics is obtained after the IBF. With this combined technology, fused silica without subsurface damage is obtained through the experimental investigation, which demonstrates the feasibility of our proposed method.
5. Conclusion
Formation process of subsurface damage often accompanies with the material densification effect, which seriously influences the nanoscale material properties. Through theoretical analysis and experimental researches, we find that the IBS is very sensitive to this material behavior and can effectively reveal the subsurface damages. This nanoscale phenomenon makes IBS technique as a promising detection technology for the nanosacle subsurface damages. Additionally, a combined polishing technology using CMP and IBF is proposed to fabricate the damage-free fused silica optics. The final experiments indicate that fused silica optics without subsurface damage is obtained with this combined technology, which effectively improves the subsurface quality.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (No. 91023042 and 91323302) and the Ministry of Science and Technology “973” Plan (No. 2011CB013200).
References and links
1. R. Laheurte, P. Darnis, N. Darbois, O. Cahuc, and J. Neauport, “Subsurface damage distribution characterization of ground surfaces using Abbott-Firestone curves,” Opt. Express 20(12), 13551–13559 (2012). [CrossRef] [PubMed]
2. J. Neauport, C. Ambard, P. Cormont, N. Darbois, J. Destribats, C. Luitot, and O. Rondeau, “Subsurface damage measurement of ground fused silica parts by HF etching techniques,” Opt. Express 17(22), 20448–20456 (2009). [CrossRef] [PubMed]
3. J. Bude, P. Miller, S. Baxamusa, N. Shen, T. Laurence, W. Steele, T. Suratwala, L. Wong, W. Carr, D. Cross, and M. Monticelli, “High fluence laser damage precursors and their mitigation in fused silica,” Opt. Express 22(5), 5839–5851 (2014). [CrossRef] [PubMed]
4. W. Liao, Y. Dai, X. Xie, and L. Zhou, “Microscopic morphology evolution during ion beam smoothing of Zerodur® surfaces,” Opt. Express 22(1), 377–386 (2014). [CrossRef] [PubMed]
5. M. Weiser, “Ion beam figuring for lithography optics,” Nucl. Instrum. Methods Phys. Res. B 267(8–9), 1390–1393 (2009). [CrossRef]
6. J. L. Ladison, J. F. Ellison, D. C. Allan, D. R. Fladd, A. W. Fanning, and R. Priestley, “Achieving low wavefront specifications for DUV lithography: impact of residual stress in HPFS fused silica,” Proc. SPIE 4346, 1416–1423 (2001). [CrossRef]
7. N. Shen, J. D. Bude, and C. W. Carr, “Model laser damage precursors for high quality optical materials,” Opt. Express 22(3), 3393–3404 (2014). [CrossRef] [PubMed]
8. N. I. Chkhalo, S. A. Churin, A. E. Pestov, N. N. Salashchenko, Y. A. Vainer, and M. V. Zorina, “Roughness measurement and ion-beam polishing of super-smooth optical surfaces of fused quartz and optical ceramics,” Opt. Express 22(17), 20094–20106 (2014). [CrossRef] [PubMed]
9. K. Xin and J. C. Lambropoulos, “Densification of fused silica: effects on nanoindentation,” Proc. SPIE 4102, 112–121 (2000). [CrossRef]
10. H. M. Cohen and R. Roy, “Densification of glass at very high pressure,” Phys. Chem. Glasses 6, 149–161 (1965).
11. T. Rouxel, H. Ji, J. P. Guin, F. Augereau, and B. Ruffle, “Indentation deformation mechanism in glass: densification versus shear flow,” J. Appl. Phys. 107(9), 094903 (2010). [CrossRef]
12. J. Neauport, C. Ambard, P. Cormont, N. Darbois, J. Destribats, C. Luitot, and O. Rondeau, “Subsurface damage measurement of ground fused silica parts by HF etching techniques,” Opt. Express 17(22), 20448–20456 (2009). [CrossRef] [PubMed]
13. T. I. Suratwala, P. E. Miller, J. D. Bude, W. A. Steele, N. Shen, M. V. Monticelli, M. D. Feit, T. A. Laurence, M. A. Norton, C. W. Carr, and L. L. Wong, “HF-based etching processes for improving laser damage resistance of fused silica optical surfaces,” J. Am. Ceram. Soc. 94(2), 416–428 (2011). [CrossRef]
14. J. A. Randi, J. C. Lambropoulos, and S. D. Jacobs, “Subsurface damage in some single crystalline optical materials,” Appl. Opt. 44(12), 2241–2249 (2005). [CrossRef] [PubMed]
15. T. Suratwala, L. Wong, P. Miller, M. D. Feit, J. Menapace, R. Steele, P. Davis, and D. Walmer, “Sub-surface mechanical damage distributions during grinding of fused silica,” J. Non-Cryst. Solids 352(52–54), 5601–5617 (2006). [CrossRef]
16. J. C. Lambropoulos, Y. Li, P. Funkenbusch, and J. Ruckman, “Non-contact estimate of grinding subsurface damage,” Proc. SPIE 3782, 41–50 (1999). [CrossRef]
17. T. W. Drueding, T. G. Bifano, and S. C. Fawcett, “Contouring algorithm for ion figuring,” Precis. Eng. 17(1), 10–21 (1995). [CrossRef]
18. R. M. Bradley and J. M. E. Harper, “Theory of ripple topography induced by ion bombardment,” J. Vac. Sci. Technol. A 6(4), 2390–2395 (1988). [CrossRef]
19. P. Sigmund, “Theory of sputtering. I. Sputtering yield of amorphous and polycrystalline targets,” Phys. Rev. 184(2), 383–416 (1969). [CrossRef]
20. M. Xu, Y. Dai, X. Xie, L. Zhou, and W. Liao, “Structure optimization and fabricating capability analysis of an ion-beam machine for a subnanometer optical surface,” Appl. Opt. 54(27), 8055–8061 (2015). [CrossRef] [PubMed]
