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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 19 — Sep. 17, 2007
  • pp: 12197–12205
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Subsurface damage in precision ground ULE® and Zerodur® surfaces

X. Tonnellier, P. Morantz, P. Shore, A. Baldwin, R. Evans, and D.D. Walker  »View Author Affiliations


Optics Express, Vol. 15, Issue 19, pp. 12197-12205 (2007)
http://dx.doi.org/10.1364/OE.15.012197


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Abstract

The total process cycle time for large ULE® and Zerodur® optics can be improved using a precise and rapid grinding process, with low levels of surface waviness and subsurface damage. In this paper, the amounts of defects beneath ULE® and Zerodur® surfaces ground using a selected grinding mode were compared. The grinding response was characterised by measuring: surface roughness, surface profile and subsurface damage. The observed subsurface damage can be separated into two distinct depth zones, which are: ‘process’ and ‘machine dynamics’ related.

© 2007 Optical Society of America

1. Introduction

A possible production improvement is to achieve a grinding process that is capable of producing better shaped surfaces having less subsurface damage and at higher material removal rates. To achieve this production capability a new ultra precision large optics grinder [3

3. P. Shore, P. Morantz, X. Luo, X. Tonnellier, R. Read, and R. May-Miller, “Design philosophy of the ultra precision big optix “BoX” machine,” Proc. Landamap , 200–209 (2005).

] - BoX® - has been developed at Cranfield University. A 5-axis Holroyd Edgetek grinding machine with a dedicated fixture has been used in advance in order to validate the BoX® grinding mode. The grinding forces and power [4

4. X. Tonnellier, P. Shore, X. Luo, A. Baldwin, P. Morantz, T. Jin, and D. Stephenson, “Wheel wear investigations when precision grinding of optical materials using the BoX® grinding mode,” Proc. 5th High Speed Machining , 177–186 (2006).

] as well as the wheel wear [5

5. X. Tonnellier, P. Shore, X. Luo, P. Morantz, and A. Baldwin, “High performance grinding studies on optical materials suitable for large optics,” Proc. 2nd CIRP High Performance Cutting (2006).

] induced by this particular grinding mode were previously discussed.

The purpose of the work described in this paper has been to establish the level of subsurface damage (SSD) in ULE® and Zerodur® using different material removal rates. A comparison of surface roughness and SSD qualities, for ULE® and Zerodur®, is provided in association with grinding parameters.

2. Theoretical details

2.1 Brittle materials

Ductile or brittle fracture mode grinding [6

6. I. Inasaki, “Grinding of Hard and Brittle Materials,” CIRP Annals 36/2, 463–471 (1987). [CrossRef]

] can be used to machine brittle materials such as Zerodur® and ULE®. Ductile mode grinding has been reported to give low SSD [7

7. T. G. Bifano, T. A. Dow, and R. O. Scattergood, “Ductile regime grinding - A new technology for machining brittle materials,” J. Eng. Ind. 113/2, 184–189 (1991). [CrossRef]

]. However, achievable material removal rate is low, as for example the critical depth of cut is ~50 nm on Zerodur® [8

8. P. Shore, P. McKeown, S. Impey, and D. Stephenson, “Surface and near surface conditions of “ductile” mode ground Zerodur,” Proc. 8th Int. Prec. Eng. Seminar , 365–368 (1995).

]. Higher manufacturing rates are supported using micro brittle fracture grinding. However, the brittle mode leaves surface and subsurface damage on ground surfaces.

An efficient grinding process requires optimisation of the grinding parameters to reduce the level of SSD. Micro fracture mechanisms that lead to SSD in brittle materials have been extensively investigated by Lawn [9

9. B. Lawn, Fracture of Brittle Solids (Cambridge University Press1975).

]. Median cracks commence and propagate with increase of indentation load. With indentation unloading, the median cracks close and lateral cracks grow towards the surface. These fracture mechanisms result in surface and subsurface defects.

2.2 Subsurface damage evaluation

In order to measure the extent of subsurface cracks, different non-destructive and destructive measurement methods have been developed. Some non-destructive subsurface inspection techniques [16

16. H. K. Tonshoff, E. Brinksmeier, and F. Hetz, “Detection of microcracks,” CIRP Annals 36/2, 545–552 (1987).

], such as ultrasonic Rayleigh wave measurement, have proved successful for information and qualification of significant and deep cracks. Destructive methods have proved to be more successful for detecting micron and sub-micron scale fractures. Cross-sectional transmission electron microscope (TEM) analysis has shown good results for detection of sub-micron scale defects in glasses and crystals [17

17. K. E. Puttick, C. Jeynes, L. Whitmore, M. R. Rudman, M. Yamasaka, P. Shore, and A. E. Gee, “Surface damage in nanoground silicon,” Proc. IMECH , 49–51 (1992).

]. This TEM process is however time consuming and less appropriate for large defects in multi-phase advanced ceramics. Repetitive polish, etch and optical microscopy have been widely employed to observe SSD in ground glasses [18

18. M. J. Ball, N. A. Murphy, and P. Shore, “Electrolytically assisted “ductile” mode diamond grinding of BK7 and SF10 optical glasses,” Proc. SPIE 1573, 30–38 (1991). [CrossRef]

]. A variant of this repetitive polish and etch method [19

19. X. Sun, D. J. Stephenson, O. Ohnishi, and A. Baldwin, “An investigation into parallel and cross grinding of BK7 glass,” Prec. Eng. 30/2, 145–153 (2006). [CrossRef]

] is a “wedge” polishing approach which simplifies assessment of how defect density relates to depth beneath the ground surface [20

20. X. Tonnellier, P. Shore, X. Luo, P. Morantz, A. Baldwin, R. Evans, and D. D. Walker, “Wheel wear and surface/subsurface qualities when precision grinding optical materials,” Proc. SPIE 6273, 627308 (2006). [CrossRef]

].

Two terms were employed to describe the subsurface damage level. The majority of subsurface cracks cluster together near the surface and terminate at a characteristic ‘cluster depth’. A small minority of cracks propagate deeper beneath the surface. The ‘single last fracture depth’ is usually much deeper than the cluster depth and corresponds to the deepest penetration of such cracks into the sample [12

12. P. P. Hed and D. F. Edwards, “Optical glass fabrication technology 2: Relationship between surface roughness and subsurface damage,” Appl. Opt. 26/21, 4677–4680 (1987). [CrossRef]

].

3. Experimental details

3.1 Specimens and grinding equipment

Zerodur® and ULE® specimens used in these tests were 100 mm×100 mm×20 mm.

Table 1. Material properties [21, 22]

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Tests were carried out on a Holroyd Edgetek 5-axis superabrasive grinding machine. A fixture was added on the grinding table so that the material blank can be tilted at 70° to the horizontal (the grinding spindle axis is horizontal). The fixture recreates the 20° wheel tilt angle employed on the BoX® machine and employs a vacuum system to hold the test samples in place (Fig. 1).

Fig. 1. (a). Holroyd Edgetek 5 axis machine and b) grinding set-up used

Three diamond abrasive resin bonded cup grinding wheels, FEPA 6V5, were used to perform ‘rough’, ‘semi finish’ and ‘finish’ cuts. Wheel details are given in Table 2. A nickel electroplated wheel with 181µm diamond grit size was employed to true and form the grinding wheels’ cross sections to a 300mm radius.

Table 2. Grinding wheels specifications

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The wheels were balanced in-situ using a Schenk dynamic balancing system. Before each cut, the wheel was ‘dressed’ by plunging into a dressing stick. The coolant employed throughout was a water based fluid with 2% Dowel. To achieve a relatively laminar flow, the pressure was set to 2 Bar. A slot nozzle design was chosen to provide ‘laminar like’ flow over the large engagement zone. All tests used a 30m/s grinding speed (vs). The surface roughness and surface waviness of specimens were assessed using a Form Talysurf profilometer. The stylus used was a 2µm radius conisphere diamond. The values of surface roughness (Ra) and surface profile (Pt) parameters were used to characterise the surface quality.

3.2 Grinding mode and grinding parameters

The grinding mode used in these tests (Fig. 2) corresponds to the BoX® grinding mode [3

3. P. Shore, P. Morantz, X. Luo, X. Tonnellier, R. Read, and R. May-Miller, “Design philosophy of the ultra precision big optix “BoX” machine,” Proc. Landamap , 200–209 (2005).

]. This type of grinding mode has previously been described in the use of the Large Optical Generator [23

23. R. E. Parks, “Two approaches to generating Free-Form optics,” Proc. ASPE 04 Winter Top. , 88–93 (2004).

] as well as the grinding of aspherical optical components [24

24. T. Kuriyagawa, M. S. S. Zahmaty, and K. Syoji, “A new grinding method for aspheric ceramic mirrors,” J. Mater. Process. Technol. 62/4, 387–392 (1996). [CrossRef]

].

Fig. 2. (a). Grinding mode, b) Semi finish surface (Zerodur®)

In that particular grinding mode, the surface profile corresponds to the ‘scallop height’. The profile is associated with wheel cutting radius (Rc) and the feed per step (fr). Table 3 shows the grinding parameters employed for the tests carried out.

Table 3. Grinding parameters

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4. Results

4.1 Surface geometry results

The surface profile (Pt) was measured perpendicular to the grinding direction. The results are reported in Table 4.

Table 4. Surface Responses

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The values show good correlation with equations developed for other processes of surface generation [25

25. C. F. Cheung and W. B. Lee, “Modelling and Simulation of Surface Topography in Ultra-Precision Diamond Turning,” Proc. IMECH 214/6, 463–480 (2000). [CrossRef]

]. For the finish cut, the profile value is noticeably influenced by the errors, particularly in respect of scallop to scallop height consistency. Examination of a Form Talysurf profile [5

5. X. Tonnellier, P. Shore, X. Luo, P. Morantz, and A. Baldwin, “High performance grinding studies on optical materials suitable for large optics,” Proc. 2nd CIRP High Performance Cutting (2006).

] shows that the bottoms of each ground cusp are distributed around the average surface line by approximately 2 µm p-v. This is as a result of error motion of the grinding machine’s axes at these high force levels; this effect is at least partially a function of static and dynamic stiffness of the machine. The difference between ULE® and Zerodur® is important when considering surface roughness ‘along vw but less significant for the surface profile.

4.2 Subsurface damage assessment

4.2.1 Surface preparation

Fig. 3. Finish cut using D46 a) Zerodur® b) ULE®

Using a ‘wedge’ polishing and surface etching approach, the SSD was evaluated using an optical microscope. Grooves were polished using a Zeeko IRP polishing machine in line with the grinding direction and corresponding to the bottom of the scallop where the ground surface is at its lowest point. The depth of the wedge was obtained using a profilometer. Etching of the polished ‘wedge’ was made using a HF/HCl solution on Zerodur® and a HF solution on ULE®. Etching rate on ground surfaces was established to choose an adequate and safe etching time. The etching times were set to 10 and 30 seconds which removes approximately 1µm and 0.5µm depth on Zerodur® and on ULE® respectively.

Figure 4 shows an example of the SSD in a Zerodur® and ULE® sample after etching. Labels on zones in Fig. 4 indicate distance along the wedge in mm, then depth in µm. This technique permits examination of numerous depth zones in one operation. Examination of different depths in a single location would require a protracted iterative polish-etch cycle.

Fig. 4. Subsurface damage after etching – a) ULE® b) Zerodur®

The number of defects per mm2 relative to the depth below the ground surface has been analysed by visual microscopy. Identification of defects for counting was based on judgment. Where the degree of interconnect rendered counting difficult, the results have been omitted from the analysis – such results represent very shallow damage depths.

4.2.1 Measurement results

Figures 5(a)5(b) and Figs. 6(a)6(b) show the amount of SSD for two finish cuts on ULE® and Zerodur® using 25 µm and 46 µm grit wheels respectively. A similar graphing procedure was used for each SSD observation.

Fig. 5. Number of cracks per mm2 for different depths beneath ground surfaces - D25 wheel - a) ULE® b) Zerodur®

For both materials, the amount of defects decreases more rapidly using the finer grit size wheel, 25 µm. For example, in Fig. 5(a), the last crack in ULE® is observed at a depth of 6.5 µm using a D25 wheel, whereas in Fig. 6(a), the last crack appears at a depth of 14.5 µm.

Fig. 6. Number of cracks per mm2 for different depths beneath ground surfaces - D46 wheel - a) ULE® b) Zerodur®

As the last crack observation is difficult to make, the SSD level differs slightly between each groove and ground surface. It is interesting to note that the amount of defects per mm2 reduces dramatically before this last crack. The ‘cluster depth’ is significantly influenced by reducing the abrasive size. However, an influence of abrasive size on SSD in respect of the ‘single last fracture depth’ is not clearly apparent. By contrast, a relationship between ‘single last fracture depth’ and material type is indicated.

A small number of samples were investigated due to the time consuming process of analysis. For the finish cut using the D25 wheel, the process was repeated once for each material; with the D46 and D76 wheels, one sample was used for each. To improve these initial findings, further work will be carried out in order to obtain statistical data.

Table 5 shows the SSD measured relative to the grinding parameters used for ULE® and Zerodur®.

Table 5. Subsurface damage data results

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5 Discussion

The results show that the ‘single last fracture depth’ is deeper for Zerodur® than for ULE® when grinding with a D25 wheel, using the finish cut parameters. However, for all other conditions the subsurface damage found in ULE® is higher than in Zerodur®. This can be explained by relating the level of subsurface damage to the brittleness of the material. A crack is less likely to be created in ULE® but it is more easily propagated once the load becomes significant.

As Zhang [14

14. P. Shore, “Machining of optical surfaces in brittle materials using an ultra-precision machine tool,” PhD thesis, Cranfield University (1995).

] showed in ceramics, a lower brittleness value and higher grit size lead to higher SSD. However, the lower SSD level obtained for the rough cut using the 76 µm grit size wheel shows that there are other important parameters to look at when assessing SSD. The degree to which densification of ULE® influences both its brittleness value and its response to the finishing operation is not known at this stage.

By plotting the number of defects per mm2 against the distance from the surface using a logarithmic scale, two zones can be identified, see Fig. 7(b).

Fig. 7. ‘Process’ related and ‘Machine dynamics’ related zones (finish cut - D25) - a) ULE® b) Zerodur®

6 Conclusions

The purpose of this research is to reduce to a minimum the required time for any subsequent polishing process. A high material removal rate at 187.5mm3/s has been demonstrated using resin bonded diamond wheels on Zerodur® and ULE®.

Achieved surface roughness and subsurface damage levels using the finer grit wheel (D25) during finish cuts were 124 nm (Ra) and 6.6 µm respectively for ULE®. For Zerodur®, these results were 137 nm (Ra) and 9.5 µm respectively.

Acknowledgments

The authors would like to acknowledge project funding through the UK’s Joint Research Councils’ Basic Technologies programme and funding support from the McKeown Precision Engineering and Nanotechnology Foundation at Cranfield.

References and links

1.

R. Gilmozzi, “Science and technology drivers for future giant telescopes,” Proc. SPIE 5489, 1–10 (2004). [CrossRef]

2.

P. Shore and R. May-Miller, “Production challenge of the optical segments for extra large telescopes,” Proc. Int. Progress on Adv. Optics & Sensors , 25–30 (2003).

3.

P. Shore, P. Morantz, X. Luo, X. Tonnellier, R. Read, and R. May-Miller, “Design philosophy of the ultra precision big optix “BoX” machine,” Proc. Landamap , 200–209 (2005).

4.

X. Tonnellier, P. Shore, X. Luo, A. Baldwin, P. Morantz, T. Jin, and D. Stephenson, “Wheel wear investigations when precision grinding of optical materials using the BoX® grinding mode,” Proc. 5th High Speed Machining , 177–186 (2006).

5.

X. Tonnellier, P. Shore, X. Luo, P. Morantz, and A. Baldwin, “High performance grinding studies on optical materials suitable for large optics,” Proc. 2nd CIRP High Performance Cutting (2006).

6.

I. Inasaki, “Grinding of Hard and Brittle Materials,” CIRP Annals 36/2, 463–471 (1987). [CrossRef]

7.

T. G. Bifano, T. A. Dow, and R. O. Scattergood, “Ductile regime grinding - A new technology for machining brittle materials,” J. Eng. Ind. 113/2, 184–189 (1991). [CrossRef]

8.

P. Shore, P. McKeown, S. Impey, and D. Stephenson, “Surface and near surface conditions of “ductile” mode ground Zerodur,” Proc. 8th Int. Prec. Eng. Seminar , 365–368 (1995).

9.

B. Lawn, Fracture of Brittle Solids (Cambridge University Press1975).

10.

T. M. A. Maksoud, A. A. Mokbel, and J. E. Morgan, “Evaluation of surface and sub-surface cracks of ground ceramic,” J. Mater. Process. Technol. 88, 222–243 (1999). [CrossRef]

11.

J. C. Lambropoulos, “From abrasive size to subsurface damage in grinding,” Optical Fab. & Testing, OSA Technical Digest , 17–18 (2000).

12.

P. P. Hed and D. F. Edwards, “Optical glass fabrication technology 2: Relationship between surface roughness and subsurface damage,” Appl. Opt. 26/21, 4677–4680 (1987). [CrossRef]

13.

J. Franse, “Aspects of Precision Grinding,” PhD thesis, Technische Universiteit Eindhoven (1991).

14.

P. Shore, “Machining of optical surfaces in brittle materials using an ultra-precision machine tool,” PhD thesis, Cranfield University (1995).

15.

X. Tonnellier, P. Morantz, P. Shore, A. Baldwin, R. Evans, and D. D. Walker, “Subsurface damage caused during rapid grinding of Zerodur,” Proc. ISAAT07, (to be published).

16.

H. K. Tonshoff, E. Brinksmeier, and F. Hetz, “Detection of microcracks,” CIRP Annals 36/2, 545–552 (1987).

17.

K. E. Puttick, C. Jeynes, L. Whitmore, M. R. Rudman, M. Yamasaka, P. Shore, and A. E. Gee, “Surface damage in nanoground silicon,” Proc. IMECH , 49–51 (1992).

18.

M. J. Ball, N. A. Murphy, and P. Shore, “Electrolytically assisted “ductile” mode diamond grinding of BK7 and SF10 optical glasses,” Proc. SPIE 1573, 30–38 (1991). [CrossRef]

19.

X. Sun, D. J. Stephenson, O. Ohnishi, and A. Baldwin, “An investigation into parallel and cross grinding of BK7 glass,” Prec. Eng. 30/2, 145–153 (2006). [CrossRef]

20.

X. Tonnellier, P. Shore, X. Luo, P. Morantz, A. Baldwin, R. Evans, and D. D. Walker, “Wheel wear and surface/subsurface qualities when precision grinding optical materials,” Proc. SPIE 6273, 627308 (2006). [CrossRef]

21.

L. Matson, “CTE Tailored Materials for Hybrid Mirror Systems,” presented at the SOMTC Technology days, US, 17 Sept. 2003.

22.

M. Viens, “Fracture Toughness and Crack Growth of Zerodur,” (Technical Memo, 1990) http://handle.dtic.mil/100.2/ADA309969

23.

R. E. Parks, “Two approaches to generating Free-Form optics,” Proc. ASPE 04 Winter Top. , 88–93 (2004).

24.

T. Kuriyagawa, M. S. S. Zahmaty, and K. Syoji, “A new grinding method for aspheric ceramic mirrors,” J. Mater. Process. Technol. 62/4, 387–392 (1996). [CrossRef]

25.

C. F. Cheung and W. B. Lee, “Modelling and Simulation of Surface Topography in Ultra-Precision Diamond Turning,” Proc. IMECH 214/6, 463–480 (2000). [CrossRef]

OCIS Codes
(160.2750) Materials : Glass and other amorphous materials
(220.4610) Optical design and fabrication : Optical fabrication
(240.5770) Optics at surfaces : Roughness
(350.1260) Other areas of optics : Astronomical optics
(350.1820) Other areas of optics : Damage
(350.3850) Other areas of optics : Materials processing

ToC Category:
Materials

History
Original Manuscript: July 23, 2007
Revised Manuscript: September 7, 2007
Manuscript Accepted: September 8, 2007
Published: September 11, 2007

Citation
X. Tonnellier, P. Morantz, P. Shore, A. Baldwin, R. Evans, and D. D. Walker, "Subsurface damage in precision ground ULE® and Zerodur® surfaces," Opt. Express 15, 12197-12205 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-19-12197


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References

  1. R. Gilmozzi, "Science and technology drivers for future giant telescopes," Proc. SPIE 5489, 1-10 (2004). [CrossRef]
  2. P. Shore and R. May-Miller, "Production challenge of the optical segments for extra large telescopes," Proc. Int. Progress on Adv. Optics and Sensors, 25-30 (2003).
  3. P. Shore, P. Morantz, X. Luo, X. Tonnellier, R. Read, and R. May-Miller, "Design philosophy of the ultra precision big optix "BoX" machine," Proc. Landamap, 200-209 (2005).
  4. X. Tonnellier, P. Shore, X. Luo, A. Baldwin, P. Morantz, T. Jin, and D. Stephenson, "Wheel wear investigations when precision grinding of optical materials using the BoX® grinding mode," Proc. 5th High Speed Machining, 177-186 (2006).
  5. X. Tonnellier, P. Shore, X. Luo, P. Morantz, and A. Baldwin, "High performance grinding studies on optical materials suitable for large optics," Proc. 2nd CIRP High Performance Cutting (2006).
  6. I. Inasaki, "Grinding of Hard and Brittle Materials," CIRP Annals 36/2, 463-471 (1987). [CrossRef]
  7. T. G. Bifano, T. A. Dow, and R. O. Scattergood, "Ductile regime grinding - A new technology for machining brittle materials," J. Eng. Ind. 113/2, 184-189 (1991). [CrossRef]
  8. P. Shore, P. McKeown, S. Impey, and D. Stephenson, "Surface and near surface conditions of "ductile" mode ground Zerodur," Proc. 8th Int. Prec. Eng. Seminar, 365-368 (1995).
  9. B. Lawn, Fracture of Brittle Solids (Cambridge University Press 1975).
  10. T. M. A. Maksoud, A. A. Mokbel, and J. E. Morgan, "Evaluation of surface and sub-surface cracks of ground ceramic," J. Mater. Process. Technol. 88, 222-243 (1999). [CrossRef]
  11. J. C. Lambropoulos, "From abrasive size to subsurface damage in grinding," Optical Fab. & Testing, OSA Technical Digest, 17-18 (2000).
  12. P. P. Hed, and D. F. Edwards, "Optical glass fabrication technology 2: Relationship between surface roughness and subsurface damage," Appl. Opt. 26/21, 4677-4680 (1987). [CrossRef]
  13. J. Franse, "Aspects of Precision Grinding," PhD thesis, Technische Universiteit Eindhoven (1991).
  14. P. Shore, "Machining of optical surfaces in brittle materials using an ultra-precision machine tool," PhD thesis, Cranfield University (1995).
  15. X. Tonnellier, P. Morantz, P. Shore, A. Baldwin, R. Evans, and D. D. Walker, "Subsurface damage caused during rapid grinding of Zerodur," Proc. ISAAT07, (to be published).
  16. H. K. Tonshoff, E. Brinksmeier, and F. Hetz, "Detection of microcracks," CIRP Annals 36/2, 545-552 (1987).
  17. K. E. Puttick, C. Jeynes, L. Whitmore, M. R. Rudman, M. Yamasaka, P. Shore, and A. E. Gee, "Surface damage in nanoground silicon," Proc. IMECH, 49-51 (1992).
  18. M. J. Ball, N. A. Murphy, and P. Shore, "Electrolytically assisted "ductile" mode diamond grinding of BK7 and SF10 optical glasses," Proc. SPIE 1573, 30-38 (1991). [CrossRef]
  19. X. Sun, D. J. Stephenson, O. Ohnishi, and A. Baldwin, "An investigation into parallel and cross grinding of BK7 glass," Precis. Eng. 30/2, 145-153 (2006). [CrossRef]
  20. X. Tonnellier, P. Shore, X. Luo, P. Morantz, A. Baldwin, R. Evans, and D. D. Walker, "Wheel wear and surface/subsurface qualities when precision grinding optical materials," Proc. SPIE 6273, 627308 (2006). [CrossRef]
  21. L. Matson, "CTE Tailored Materials for Hybrid Mirror Systems," presented at the SOMTC Technology days, US, 17 Sept. 2003.
  22. M. Viens, "Fracture Toughness and Crack Growth of Zerodur," (Technical Memo, 1990) http://handle.dtic.mil/100.2/ADA309969
  23. R. E. Parks, "Two approaches to generating Free-Form optics," Proc. ASPE 04 Winter Top., 88-93 (2004).
  24. T. Kuriyagawa, M. S. S. Zahmaty, and K. Syoji, "A new grinding method for aspheric ceramic mirrors," J. Mater. Process. Technol. 62/4, 387-392 (1996). [CrossRef]
  25. C. F. Cheung, and W. B. Lee, "Modelling and Simulation of Surface Topography in Ultra-Precision Diamond Turning," Proc. Inst. Mech. Eng., ImechE Conf. 214/6, 463-480 (2000). [CrossRef]

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