Abstract

We figure optical surfaces by plasma chemical vaporization machining (CVM) with a pipe electrode, in which an rf plasma generated at the electrode tip under approximately atmospheric pressure moves over the surfaces. We propose a shaping method in which the movement of plasma on the surfaces can be determined. Flat and aspheric surfaces are successfully figured with the desired peak-to-valley shape accuracy of 0.1 µm. The root-mean-square roughness of the resultant surfaces is at the subnanometer level. These results confirm that the plasma CVM and the shaping method have the capability to fabricate optics with high accuracy.

© 2002 Optical Society of America

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  1. R. Aspden, R. McDonough, F. R. Nitchie, “Computer assisted optical surfacing,” Appl. Opt. 11, 2739–2747 (1972).
    [CrossRef] [PubMed]
  2. R. E. Wagner, R. R. Shannon, “Fabrication of aspherics using a mathematical model for material removal,” Appl. Opt. 13, 1683–1689 (1974).
    [CrossRef] [PubMed]
  3. D. J. Bajuk, “Computer controlled generation of rotationally symmetric aspheric surfaces,” Opt. Eng. 15, 401–406 (1976).
    [CrossRef]
  4. R. A. Jones, “Optimization of computer controlled polishing,” Appl. Opt. 16, 218–224 (1977).
    [CrossRef] [PubMed]
  5. A. S. Savel’ev, A. P. Bogdanov, “Automated polishing of large optical components with a small tool,” Sov. J. Opt. Technol. 52, 294–297 (1985).
  6. G. Doughty, J. Smith, “Microcomputer-controlled polishing machine for very smooth and deep aspherical surfaces,” Appl. Opt. 26, 2421–2426 (1987).
    [CrossRef] [PubMed]
  7. M. Negishi, M. Ando, M. Takimoto, A. Deguchi, N. Nakamura, “Studies of super-smooth polishing on aspherical surfaces,” Int. J. Jpn. Soc. Precis. Eng. 29, 1–4 (1995).
  8. L. D. Bollinger, C. B. Zarowin, “Rapid, nonmechanical, damage-free figuring of optical surfaces using plasma-assisted chemical etching (PACE). Part I. Experimental results,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. SPIE966, 82–90 (1988).
    [CrossRef]
  9. C. B. Zarowin, L. D. Bollinger, “Rapid, nonmechanical, damage free figuring of optical surfaces using plasma assisted chemical etching (PACE). Part II. Theory and process control,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. SPIE966, 91–97 (1988).
    [CrossRef]
  10. D. Bollinger, G. Gallatin, J. Samuels, G. Steinberg, C. Zarowin, “Rapid, noncontact optical figuring of aspheric surfaces with plasma-assisted chemical etching,” in Advanced Optical Manufacturing and Testing, L. R. Baker, P. B. Reid, G. M. Sanger, eds., Proc. SPIE1333, 44–57 (1990).
    [CrossRef]
  11. Y. Mori, K. Yamamura, K. Yamauchi, K. Yoshii, T. Kataoka, K. Endo, K. Inagaki, H. Kakiuchi, “Plasma CVM (chemical vaporization machining)—a chemical machining method with equal performances to conventional mechanical methods from the sense of removal rates and spatial resolutions,” in Proceedings of the Seventh International Precision Engineering Seminar (Butterworth-Heinemann, Stoneham, Mass., 1993), pp. 78–87.
  12. Y. Mori, K. Yamamura, K. Yamauchi, K. Yoshii, T. Kataoka, K. Endo, K. Inagaki, H. Kakiuchi, “Plasma CVM (chemical vaporization machining)—an ultra precision machining with high pressure reactive plasma,” Technol. Rep. Osaka Univ. 43, 261–266 (1993).
  13. H. Takino, N. Shibata, H. Itoh, T. Kobayashi, H. Tanaka, M. Ebi, K. Yamamura, Y. Sano, Y. Mori, “Computer numerically controlled plasma chemical vaporization machining with a pipe electrode for optical fabrication,” Appl. Opt. 37, 5198–5210 (1998).
    [CrossRef]
  14. G. Boehm, W. Frank, A. Schindler, A. Nickel, H. J. Thomas, F. Bigl, M. Weiser, “Plasma jet chemical etching—a tool for the figuring of optical precision aspheres,” in Proceedings of the Ninth International Conference on Production Engineering: Precision Science and Technology for Perfect Surfaces, Y. Furukawa, Y. Mori, T. Kataoka, eds., (The Japan Society for Precision Engineering, Chiyoda, Tokyo, 1999), pp. 231–236.

1998 (1)

1995 (1)

M. Negishi, M. Ando, M. Takimoto, A. Deguchi, N. Nakamura, “Studies of super-smooth polishing on aspherical surfaces,” Int. J. Jpn. Soc. Precis. Eng. 29, 1–4 (1995).

1993 (1)

Y. Mori, K. Yamamura, K. Yamauchi, K. Yoshii, T. Kataoka, K. Endo, K. Inagaki, H. Kakiuchi, “Plasma CVM (chemical vaporization machining)—an ultra precision machining with high pressure reactive plasma,” Technol. Rep. Osaka Univ. 43, 261–266 (1993).

1987 (1)

1985 (1)

A. S. Savel’ev, A. P. Bogdanov, “Automated polishing of large optical components with a small tool,” Sov. J. Opt. Technol. 52, 294–297 (1985).

1977 (1)

1976 (1)

D. J. Bajuk, “Computer controlled generation of rotationally symmetric aspheric surfaces,” Opt. Eng. 15, 401–406 (1976).
[CrossRef]

1974 (1)

1972 (1)

Ando, M.

M. Negishi, M. Ando, M. Takimoto, A. Deguchi, N. Nakamura, “Studies of super-smooth polishing on aspherical surfaces,” Int. J. Jpn. Soc. Precis. Eng. 29, 1–4 (1995).

Aspden, R.

Bajuk, D. J.

D. J. Bajuk, “Computer controlled generation of rotationally symmetric aspheric surfaces,” Opt. Eng. 15, 401–406 (1976).
[CrossRef]

Bigl, F.

G. Boehm, W. Frank, A. Schindler, A. Nickel, H. J. Thomas, F. Bigl, M. Weiser, “Plasma jet chemical etching—a tool for the figuring of optical precision aspheres,” in Proceedings of the Ninth International Conference on Production Engineering: Precision Science and Technology for Perfect Surfaces, Y. Furukawa, Y. Mori, T. Kataoka, eds., (The Japan Society for Precision Engineering, Chiyoda, Tokyo, 1999), pp. 231–236.

Boehm, G.

G. Boehm, W. Frank, A. Schindler, A. Nickel, H. J. Thomas, F. Bigl, M. Weiser, “Plasma jet chemical etching—a tool for the figuring of optical precision aspheres,” in Proceedings of the Ninth International Conference on Production Engineering: Precision Science and Technology for Perfect Surfaces, Y. Furukawa, Y. Mori, T. Kataoka, eds., (The Japan Society for Precision Engineering, Chiyoda, Tokyo, 1999), pp. 231–236.

Bogdanov, A. P.

A. S. Savel’ev, A. P. Bogdanov, “Automated polishing of large optical components with a small tool,” Sov. J. Opt. Technol. 52, 294–297 (1985).

Bollinger, D.

D. Bollinger, G. Gallatin, J. Samuels, G. Steinberg, C. Zarowin, “Rapid, noncontact optical figuring of aspheric surfaces with plasma-assisted chemical etching,” in Advanced Optical Manufacturing and Testing, L. R. Baker, P. B. Reid, G. M. Sanger, eds., Proc. SPIE1333, 44–57 (1990).
[CrossRef]

Bollinger, L. D.

C. B. Zarowin, L. D. Bollinger, “Rapid, nonmechanical, damage free figuring of optical surfaces using plasma assisted chemical etching (PACE). Part II. Theory and process control,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. SPIE966, 91–97 (1988).
[CrossRef]

L. D. Bollinger, C. B. Zarowin, “Rapid, nonmechanical, damage-free figuring of optical surfaces using plasma-assisted chemical etching (PACE). Part I. Experimental results,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. SPIE966, 82–90 (1988).
[CrossRef]

Deguchi, A.

M. Negishi, M. Ando, M. Takimoto, A. Deguchi, N. Nakamura, “Studies of super-smooth polishing on aspherical surfaces,” Int. J. Jpn. Soc. Precis. Eng. 29, 1–4 (1995).

Doughty, G.

Ebi, M.

Endo, K.

Y. Mori, K. Yamamura, K. Yamauchi, K. Yoshii, T. Kataoka, K. Endo, K. Inagaki, H. Kakiuchi, “Plasma CVM (chemical vaporization machining)—an ultra precision machining with high pressure reactive plasma,” Technol. Rep. Osaka Univ. 43, 261–266 (1993).

Y. Mori, K. Yamamura, K. Yamauchi, K. Yoshii, T. Kataoka, K. Endo, K. Inagaki, H. Kakiuchi, “Plasma CVM (chemical vaporization machining)—a chemical machining method with equal performances to conventional mechanical methods from the sense of removal rates and spatial resolutions,” in Proceedings of the Seventh International Precision Engineering Seminar (Butterworth-Heinemann, Stoneham, Mass., 1993), pp. 78–87.

Frank, W.

G. Boehm, W. Frank, A. Schindler, A. Nickel, H. J. Thomas, F. Bigl, M. Weiser, “Plasma jet chemical etching—a tool for the figuring of optical precision aspheres,” in Proceedings of the Ninth International Conference on Production Engineering: Precision Science and Technology for Perfect Surfaces, Y. Furukawa, Y. Mori, T. Kataoka, eds., (The Japan Society for Precision Engineering, Chiyoda, Tokyo, 1999), pp. 231–236.

Gallatin, G.

D. Bollinger, G. Gallatin, J. Samuels, G. Steinberg, C. Zarowin, “Rapid, noncontact optical figuring of aspheric surfaces with plasma-assisted chemical etching,” in Advanced Optical Manufacturing and Testing, L. R. Baker, P. B. Reid, G. M. Sanger, eds., Proc. SPIE1333, 44–57 (1990).
[CrossRef]

Inagaki, K.

Y. Mori, K. Yamamura, K. Yamauchi, K. Yoshii, T. Kataoka, K. Endo, K. Inagaki, H. Kakiuchi, “Plasma CVM (chemical vaporization machining)—an ultra precision machining with high pressure reactive plasma,” Technol. Rep. Osaka Univ. 43, 261–266 (1993).

Y. Mori, K. Yamamura, K. Yamauchi, K. Yoshii, T. Kataoka, K. Endo, K. Inagaki, H. Kakiuchi, “Plasma CVM (chemical vaporization machining)—a chemical machining method with equal performances to conventional mechanical methods from the sense of removal rates and spatial resolutions,” in Proceedings of the Seventh International Precision Engineering Seminar (Butterworth-Heinemann, Stoneham, Mass., 1993), pp. 78–87.

Itoh, H.

Jones, R. A.

Kakiuchi, H.

Y. Mori, K. Yamamura, K. Yamauchi, K. Yoshii, T. Kataoka, K. Endo, K. Inagaki, H. Kakiuchi, “Plasma CVM (chemical vaporization machining)—an ultra precision machining with high pressure reactive plasma,” Technol. Rep. Osaka Univ. 43, 261–266 (1993).

Y. Mori, K. Yamamura, K. Yamauchi, K. Yoshii, T. Kataoka, K. Endo, K. Inagaki, H. Kakiuchi, “Plasma CVM (chemical vaporization machining)—a chemical machining method with equal performances to conventional mechanical methods from the sense of removal rates and spatial resolutions,” in Proceedings of the Seventh International Precision Engineering Seminar (Butterworth-Heinemann, Stoneham, Mass., 1993), pp. 78–87.

Kataoka, T.

Y. Mori, K. Yamamura, K. Yamauchi, K. Yoshii, T. Kataoka, K. Endo, K. Inagaki, H. Kakiuchi, “Plasma CVM (chemical vaporization machining)—an ultra precision machining with high pressure reactive plasma,” Technol. Rep. Osaka Univ. 43, 261–266 (1993).

Y. Mori, K. Yamamura, K. Yamauchi, K. Yoshii, T. Kataoka, K. Endo, K. Inagaki, H. Kakiuchi, “Plasma CVM (chemical vaporization machining)—a chemical machining method with equal performances to conventional mechanical methods from the sense of removal rates and spatial resolutions,” in Proceedings of the Seventh International Precision Engineering Seminar (Butterworth-Heinemann, Stoneham, Mass., 1993), pp. 78–87.

Kobayashi, T.

McDonough, R.

Mori, Y.

H. Takino, N. Shibata, H. Itoh, T. Kobayashi, H. Tanaka, M. Ebi, K. Yamamura, Y. Sano, Y. Mori, “Computer numerically controlled plasma chemical vaporization machining with a pipe electrode for optical fabrication,” Appl. Opt. 37, 5198–5210 (1998).
[CrossRef]

Y. Mori, K. Yamamura, K. Yamauchi, K. Yoshii, T. Kataoka, K. Endo, K. Inagaki, H. Kakiuchi, “Plasma CVM (chemical vaporization machining)—an ultra precision machining with high pressure reactive plasma,” Technol. Rep. Osaka Univ. 43, 261–266 (1993).

Y. Mori, K. Yamamura, K. Yamauchi, K. Yoshii, T. Kataoka, K. Endo, K. Inagaki, H. Kakiuchi, “Plasma CVM (chemical vaporization machining)—a chemical machining method with equal performances to conventional mechanical methods from the sense of removal rates and spatial resolutions,” in Proceedings of the Seventh International Precision Engineering Seminar (Butterworth-Heinemann, Stoneham, Mass., 1993), pp. 78–87.

Nakamura, N.

M. Negishi, M. Ando, M. Takimoto, A. Deguchi, N. Nakamura, “Studies of super-smooth polishing on aspherical surfaces,” Int. J. Jpn. Soc. Precis. Eng. 29, 1–4 (1995).

Negishi, M.

M. Negishi, M. Ando, M. Takimoto, A. Deguchi, N. Nakamura, “Studies of super-smooth polishing on aspherical surfaces,” Int. J. Jpn. Soc. Precis. Eng. 29, 1–4 (1995).

Nickel, A.

G. Boehm, W. Frank, A. Schindler, A. Nickel, H. J. Thomas, F. Bigl, M. Weiser, “Plasma jet chemical etching—a tool for the figuring of optical precision aspheres,” in Proceedings of the Ninth International Conference on Production Engineering: Precision Science and Technology for Perfect Surfaces, Y. Furukawa, Y. Mori, T. Kataoka, eds., (The Japan Society for Precision Engineering, Chiyoda, Tokyo, 1999), pp. 231–236.

Nitchie, F. R.

Samuels, J.

D. Bollinger, G. Gallatin, J. Samuels, G. Steinberg, C. Zarowin, “Rapid, noncontact optical figuring of aspheric surfaces with plasma-assisted chemical etching,” in Advanced Optical Manufacturing and Testing, L. R. Baker, P. B. Reid, G. M. Sanger, eds., Proc. SPIE1333, 44–57 (1990).
[CrossRef]

Sano, Y.

Savel’ev, A. S.

A. S. Savel’ev, A. P. Bogdanov, “Automated polishing of large optical components with a small tool,” Sov. J. Opt. Technol. 52, 294–297 (1985).

Schindler, A.

G. Boehm, W. Frank, A. Schindler, A. Nickel, H. J. Thomas, F. Bigl, M. Weiser, “Plasma jet chemical etching—a tool for the figuring of optical precision aspheres,” in Proceedings of the Ninth International Conference on Production Engineering: Precision Science and Technology for Perfect Surfaces, Y. Furukawa, Y. Mori, T. Kataoka, eds., (The Japan Society for Precision Engineering, Chiyoda, Tokyo, 1999), pp. 231–236.

Shannon, R. R.

Shibata, N.

Smith, J.

Steinberg, G.

D. Bollinger, G. Gallatin, J. Samuels, G. Steinberg, C. Zarowin, “Rapid, noncontact optical figuring of aspheric surfaces with plasma-assisted chemical etching,” in Advanced Optical Manufacturing and Testing, L. R. Baker, P. B. Reid, G. M. Sanger, eds., Proc. SPIE1333, 44–57 (1990).
[CrossRef]

Takimoto, M.

M. Negishi, M. Ando, M. Takimoto, A. Deguchi, N. Nakamura, “Studies of super-smooth polishing on aspherical surfaces,” Int. J. Jpn. Soc. Precis. Eng. 29, 1–4 (1995).

Takino, H.

Tanaka, H.

Thomas, H. J.

G. Boehm, W. Frank, A. Schindler, A. Nickel, H. J. Thomas, F. Bigl, M. Weiser, “Plasma jet chemical etching—a tool for the figuring of optical precision aspheres,” in Proceedings of the Ninth International Conference on Production Engineering: Precision Science and Technology for Perfect Surfaces, Y. Furukawa, Y. Mori, T. Kataoka, eds., (The Japan Society for Precision Engineering, Chiyoda, Tokyo, 1999), pp. 231–236.

Wagner, R. E.

Weiser, M.

G. Boehm, W. Frank, A. Schindler, A. Nickel, H. J. Thomas, F. Bigl, M. Weiser, “Plasma jet chemical etching—a tool for the figuring of optical precision aspheres,” in Proceedings of the Ninth International Conference on Production Engineering: Precision Science and Technology for Perfect Surfaces, Y. Furukawa, Y. Mori, T. Kataoka, eds., (The Japan Society for Precision Engineering, Chiyoda, Tokyo, 1999), pp. 231–236.

Yamamura, K.

H. Takino, N. Shibata, H. Itoh, T. Kobayashi, H. Tanaka, M. Ebi, K. Yamamura, Y. Sano, Y. Mori, “Computer numerically controlled plasma chemical vaporization machining with a pipe electrode for optical fabrication,” Appl. Opt. 37, 5198–5210 (1998).
[CrossRef]

Y. Mori, K. Yamamura, K. Yamauchi, K. Yoshii, T. Kataoka, K. Endo, K. Inagaki, H. Kakiuchi, “Plasma CVM (chemical vaporization machining)—an ultra precision machining with high pressure reactive plasma,” Technol. Rep. Osaka Univ. 43, 261–266 (1993).

Y. Mori, K. Yamamura, K. Yamauchi, K. Yoshii, T. Kataoka, K. Endo, K. Inagaki, H. Kakiuchi, “Plasma CVM (chemical vaporization machining)—a chemical machining method with equal performances to conventional mechanical methods from the sense of removal rates and spatial resolutions,” in Proceedings of the Seventh International Precision Engineering Seminar (Butterworth-Heinemann, Stoneham, Mass., 1993), pp. 78–87.

Yamauchi, K.

Y. Mori, K. Yamamura, K. Yamauchi, K. Yoshii, T. Kataoka, K. Endo, K. Inagaki, H. Kakiuchi, “Plasma CVM (chemical vaporization machining)—an ultra precision machining with high pressure reactive plasma,” Technol. Rep. Osaka Univ. 43, 261–266 (1993).

Y. Mori, K. Yamamura, K. Yamauchi, K. Yoshii, T. Kataoka, K. Endo, K. Inagaki, H. Kakiuchi, “Plasma CVM (chemical vaporization machining)—a chemical machining method with equal performances to conventional mechanical methods from the sense of removal rates and spatial resolutions,” in Proceedings of the Seventh International Precision Engineering Seminar (Butterworth-Heinemann, Stoneham, Mass., 1993), pp. 78–87.

Yoshii, K.

Y. Mori, K. Yamamura, K. Yamauchi, K. Yoshii, T. Kataoka, K. Endo, K. Inagaki, H. Kakiuchi, “Plasma CVM (chemical vaporization machining)—an ultra precision machining with high pressure reactive plasma,” Technol. Rep. Osaka Univ. 43, 261–266 (1993).

Y. Mori, K. Yamamura, K. Yamauchi, K. Yoshii, T. Kataoka, K. Endo, K. Inagaki, H. Kakiuchi, “Plasma CVM (chemical vaporization machining)—a chemical machining method with equal performances to conventional mechanical methods from the sense of removal rates and spatial resolutions,” in Proceedings of the Seventh International Precision Engineering Seminar (Butterworth-Heinemann, Stoneham, Mass., 1993), pp. 78–87.

Zarowin, C.

D. Bollinger, G. Gallatin, J. Samuels, G. Steinberg, C. Zarowin, “Rapid, noncontact optical figuring of aspheric surfaces with plasma-assisted chemical etching,” in Advanced Optical Manufacturing and Testing, L. R. Baker, P. B. Reid, G. M. Sanger, eds., Proc. SPIE1333, 44–57 (1990).
[CrossRef]

Zarowin, C. B.

C. B. Zarowin, L. D. Bollinger, “Rapid, nonmechanical, damage free figuring of optical surfaces using plasma assisted chemical etching (PACE). Part II. Theory and process control,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. SPIE966, 91–97 (1988).
[CrossRef]

L. D. Bollinger, C. B. Zarowin, “Rapid, nonmechanical, damage-free figuring of optical surfaces using plasma-assisted chemical etching (PACE). Part I. Experimental results,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. SPIE966, 82–90 (1988).
[CrossRef]

Appl. Opt. (5)

Int. J. Jpn. Soc. Precis. Eng. (1)

M. Negishi, M. Ando, M. Takimoto, A. Deguchi, N. Nakamura, “Studies of super-smooth polishing on aspherical surfaces,” Int. J. Jpn. Soc. Precis. Eng. 29, 1–4 (1995).

Opt. Eng. (1)

D. J. Bajuk, “Computer controlled generation of rotationally symmetric aspheric surfaces,” Opt. Eng. 15, 401–406 (1976).
[CrossRef]

Sov. J. Opt. Technol. (1)

A. S. Savel’ev, A. P. Bogdanov, “Automated polishing of large optical components with a small tool,” Sov. J. Opt. Technol. 52, 294–297 (1985).

Technol. Rep. Osaka Univ. (1)

Y. Mori, K. Yamamura, K. Yamauchi, K. Yoshii, T. Kataoka, K. Endo, K. Inagaki, H. Kakiuchi, “Plasma CVM (chemical vaporization machining)—an ultra precision machining with high pressure reactive plasma,” Technol. Rep. Osaka Univ. 43, 261–266 (1993).

Other (5)

G. Boehm, W. Frank, A. Schindler, A. Nickel, H. J. Thomas, F. Bigl, M. Weiser, “Plasma jet chemical etching—a tool for the figuring of optical precision aspheres,” in Proceedings of the Ninth International Conference on Production Engineering: Precision Science and Technology for Perfect Surfaces, Y. Furukawa, Y. Mori, T. Kataoka, eds., (The Japan Society for Precision Engineering, Chiyoda, Tokyo, 1999), pp. 231–236.

L. D. Bollinger, C. B. Zarowin, “Rapid, nonmechanical, damage-free figuring of optical surfaces using plasma-assisted chemical etching (PACE). Part I. Experimental results,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. SPIE966, 82–90 (1988).
[CrossRef]

C. B. Zarowin, L. D. Bollinger, “Rapid, nonmechanical, damage free figuring of optical surfaces using plasma assisted chemical etching (PACE). Part II. Theory and process control,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. SPIE966, 91–97 (1988).
[CrossRef]

D. Bollinger, G. Gallatin, J. Samuels, G. Steinberg, C. Zarowin, “Rapid, noncontact optical figuring of aspheric surfaces with plasma-assisted chemical etching,” in Advanced Optical Manufacturing and Testing, L. R. Baker, P. B. Reid, G. M. Sanger, eds., Proc. SPIE1333, 44–57 (1990).
[CrossRef]

Y. Mori, K. Yamamura, K. Yamauchi, K. Yoshii, T. Kataoka, K. Endo, K. Inagaki, H. Kakiuchi, “Plasma CVM (chemical vaporization machining)—a chemical machining method with equal performances to conventional mechanical methods from the sense of removal rates and spatial resolutions,” in Proceedings of the Seventh International Precision Engineering Seminar (Butterworth-Heinemann, Stoneham, Mass., 1993), pp. 78–87.

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Figures (17)

Fig. 1
Fig. 1

Schematic of the computer numerically controlled plasma CVM device.

Fig. 2
Fig. 2

Schematic of the shaping method. (a) The bird’s-eye view and the cross-sectional view of the shape error to be removed. The error is approximated as a set of thin layers. (b) The shape accuracy after the process. (c) Plasma scanning to remove the thin layers. Plasma is scanned at a constant feed pitch and a constant feed rate.

Fig. 3
Fig. 3

Schematic of the determination of plasma paths. (a) Shape error before processing. (b) Areas A i,j to be removed and plasma paths. Areas A i,j with depth of ε are to be removed. Removal is carried out along the solid lines and halted along the dotted lines.

Fig. 4
Fig. 4

Initial shape error of the flat surface. ϕ, diameter.

Fig. 5
Fig. 5

Cross section of the removal shape when plasma is scanned along the path in the inset with the feed rate v of 4 mm/s.

Fig. 6
Fig. 6

Simulation result of the shape error of the flat surface after the correction process. ϕ, diameter.

Fig. 7
Fig. 7

Example of removal area A i,j on the flat surface; i=11 and j=1. Plasma paths are also schematically shown. ϕ, diameter.

Fig. 8
Fig. 8

Shape error of the flat surface after the correction process. ϕ, diameter.

Fig. 9
Fig. 9

Removal areas A i,j on the flat surface in the second correction process. Plasma paths are also schematically shown. ϕ, diameter.

Fig. 10
Fig. 10

Shape error of the flat surface after the second correction process. ϕ, diameter.

Fig. 11
Fig. 11

Schematic of the operation of the electrode and workpiece for the figuring of of a curved surface. Situation of removal of errors on area A i,j is shown.

Fig. 12
Fig. 12

Cross section of removal marks for various tilt angles of the electrode. The profiles are almost the same regardless of the angle.

Fig. 13
Fig. 13

Cross section of removal marks for various thicknesses of the workpieces. The profiles are almost the same regardless of thickness.

Fig. 14
Fig. 14

Initial shape error of the aspheric surface. ϕ, diameter.

Fig. 15
Fig. 15

Simulation result of the shape error of the aspheric surface after the correction process. ϕ, diameter.

Fig. 16
Fig. 16

Shape error of the aspheric surface after the correction processes. The process was repeated three times. ϕ, diameter.

Fig. 17
Fig. 17

Roughness of the aspheric surface after the correction processes. Ra and rms surface roughnesses are 0.30 and 0.37 nm, respectively.

Metrics