Abstract

Ultra-precision and ultra-smooth surfaces are vitally important for some high performance optical systems. Ion beam figuring (IBF) is a well-established, highly deterministic method for the final precision figuring of extremely high quality optical surfaces, whereas ion sputtering induced smoothing, or roughening for nanoscale surface morphology, strongly depends on the processing conditions. Usually, an improper machining method would arouse the production of nanoscale patterns leading to the coarsening of the optical surface. In this paper, the morphology evolution mechanism on a fused silica surface during IBF of high-slope optical components has been investigated by means of atomic force microscopy. Figuring experiments are implemented on two convex spherical surfaces by using different IBF methods. Both of their surface errors are rapidly reduced to 1.2 nm root mean square (RMS) after removing similar deep material, but their surfaces are characterized with obviously different nanoscale morphologies. The experimental results indicate that the ion incidence angle dominates the microscopic morphology during the IBF process. At near-normal incidence, fused silica achieves an ultra-smooth surface with an RMS roughness value Rq down to 0.1 nm, whereas nanoscale ripple patterns are observed at a large incidence angle with an Rq value increasing to more than 0.9 nm. Additionally, the difference of incidence angles on various machined areas would influence the uniformity of surface quality, resulting from the interplay between the smoothing and roughening effects induced by ion sputtering.

© 2013 Optical Society of America

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  1. R. A. Jones and W. J. Rupp, “Rapid optical fabrication with CCOS,” Proc. SPIE 1333, 34–43 (1990).
    [CrossRef]
  2. Y. Dai, H. Hu, X. Peng, J. Wang, and F. Shi, “Research on error control and compensation in magnetorheological finishing,” Appl. Opt. 50, 3321–3329 (2011).
    [CrossRef]
  3. C. Jiao, S. Li, and X. Xie, “Algorithm for ion beam figuring of low-gradient mirrors,” Appl. Opt. 48, 4090–4096 (2009).
    [CrossRef]
  4. T. W. Drueding, T. G. Bifano, and S. C. Fawcett, “Contouring algorithm for ion figuring,” Precis. Eng. 17, 10–21 (1995).
    [CrossRef]
  5. L. N. Allen and H. W. Romig, “Demonstration of an ion figuring process,” Proc. SPIE 1333, 22–23 (1990).
    [CrossRef]
  6. T. Arnold, G. Böhm, R. Fechner, J. Meister, A. Nickel, F. Frost, T. Hänsel, and A. Schindler, “Ultra-precision surface finishing by ion beam and plasma jet techniques—status and outlook,” Nucl. Instrum. Methods Phys. Res., Sect. A 616, 147–156 (2010).
    [CrossRef]
  7. C. Jiao, S. Li, X. Xie, S. Chen, D. Wu, and N. Kang, “Figuring algorithm for high-gradient mirrors with axis-symmetrical removal function,” Appl. Opt. 49, 578–585 (2010).
    [CrossRef]
  8. T. Haensel, A. Nickel, and A. Schindler, “Ion beam figuring of strongly curved surfaces with a (x,y,z) linear three-axes system,” in Frontiers in Optics 2008/Laser Science XXIV/Plasmonics and Metamaterials/Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2008), paper JWD6.
  9. Y. Dai, W. Liao, L. Zhou, S. Chen, and X. Xie, “Ion beam figuring of high slope surfaces based on figure error compensation algorithm,” Appl. Opt. 49, 6630–6636 (2010).
    [CrossRef]
  10. M. Weiser, “Ion beam figuring for lithography optics,” Nucl. Instrum. Methods Phys. Res., Sect. B 267, 1390–1393 (2009).
    [CrossRef]
  11. A. Keller, S. Facsko, and W. Moller, “The morphology of amorphous SiO2 surfaces during low energy ion sputtering,” J. Phys. 21, 495305 (2009).
    [CrossRef]
  12. D. Flamm, F. Frost, and D. Hirsch, “Evolution of surface topography of fused by ion beam sputtering,” Appl. Surf. Sci. 179, 95–101 (2001).
    [CrossRef]
  13. Y. Kurashima, S. Miyachi, I. Miyamoto, M. Ando, and A. Numata, “Evaluation of surface roughness of ULE substrates machined by Ar+ ion beam,” Microelectron. Eng. 85, 1193–1196 (2008).
    [CrossRef]
  14. H. Endo, T. Inaba, S. A. Pahlovy, and I. Miyamoto, “Low energy Xe+ ion beam machining of ULE substrates for EUVL projection optics-Evaluation of high-spatial frequency roughness,” Microelectron. Eng. 87, 982–984 (2010).
    [CrossRef]
  15. T. M. Mayer, E. Chason, and A. J. Howard, “Roughening instability and ion-induced viscous relaxation of SiO2 surfaces,” J. Appl. Phys. 76, 1633–1643 (1994).
    [CrossRef]
  16. A. Keller, S. Facsko, and W. Moller, “Evolution of ion-induced ripple patterns on SiO2 surfaces,” Nucl. Instrum. Methods Phys. Res., Sect. B 267, 656–659 (2009).
    [CrossRef]
  17. P. Sigmund, “Theory of sputtering. I. Sputtering yield of amorphous and polycrystalline targets,” Phys. Rev. 184, 383–416 (1969).
    [CrossRef]
  18. R. M. Bradley and J. M. E. Harper, “Theory of ripple topography induced by ion bombardment,” J. Vac. Sci. Technol., A 6, 2390–2395 (1988).
    [CrossRef]
  19. M. A. Makeev, R. Cuerno, and A.-L. Barabasi, “Morphology of ion-sputtered surfaces,” Nucl. Instrum. Methods Phys. Res., Sect. B 197, 185–227 (2002).
    [CrossRef]
  20. R. Schlatmann, J. D. Shindler, and J. Verhoeven, “Evolution of surface morphology during growth and ion erosion of thin films,” Phys. Rev. B 54, 10880–10889 (1996).
    [CrossRef]
  21. C. C. Umbach, R. L. Headrick, and K.-C. Chang, “Spontaneous nanoscale corrugation of ion-eroded SiO2: the role of ion-irradiation-enhanced viscous flow,” Phys. Rev. Lett. 87, 246104 (2001).
    [CrossRef]
  22. W. M. Tong and R. S. Williams, “Kinetics of surface growth: phenomenology, scaling, and mechanisms of smoothing and roughening,” Annu. Rev. Phys. Chem. 45, 401–438 (1994).
    [CrossRef]
  23. G. Carter and V. Vishnyakov, “Roughening and ripple instabilities on ion-bombarded Si,” Phys. Rev. B 54, 17647–17653 (1996).
    [CrossRef]

2011 (1)

2010 (4)

C. Jiao, S. Li, X. Xie, S. Chen, D. Wu, and N. Kang, “Figuring algorithm for high-gradient mirrors with axis-symmetrical removal function,” Appl. Opt. 49, 578–585 (2010).
[CrossRef]

Y. Dai, W. Liao, L. Zhou, S. Chen, and X. Xie, “Ion beam figuring of high slope surfaces based on figure error compensation algorithm,” Appl. Opt. 49, 6630–6636 (2010).
[CrossRef]

H. Endo, T. Inaba, S. A. Pahlovy, and I. Miyamoto, “Low energy Xe+ ion beam machining of ULE substrates for EUVL projection optics-Evaluation of high-spatial frequency roughness,” Microelectron. Eng. 87, 982–984 (2010).
[CrossRef]

T. Arnold, G. Böhm, R. Fechner, J. Meister, A. Nickel, F. Frost, T. Hänsel, and A. Schindler, “Ultra-precision surface finishing by ion beam and plasma jet techniques—status and outlook,” Nucl. Instrum. Methods Phys. Res., Sect. A 616, 147–156 (2010).
[CrossRef]

2009 (4)

M. Weiser, “Ion beam figuring for lithography optics,” Nucl. Instrum. Methods Phys. Res., Sect. B 267, 1390–1393 (2009).
[CrossRef]

A. Keller, S. Facsko, and W. Moller, “The morphology of amorphous SiO2 surfaces during low energy ion sputtering,” J. Phys. 21, 495305 (2009).
[CrossRef]

A. Keller, S. Facsko, and W. Moller, “Evolution of ion-induced ripple patterns on SiO2 surfaces,” Nucl. Instrum. Methods Phys. Res., Sect. B 267, 656–659 (2009).
[CrossRef]

C. Jiao, S. Li, and X. Xie, “Algorithm for ion beam figuring of low-gradient mirrors,” Appl. Opt. 48, 4090–4096 (2009).
[CrossRef]

2008 (1)

Y. Kurashima, S. Miyachi, I. Miyamoto, M. Ando, and A. Numata, “Evaluation of surface roughness of ULE substrates machined by Ar+ ion beam,” Microelectron. Eng. 85, 1193–1196 (2008).
[CrossRef]

2002 (1)

M. A. Makeev, R. Cuerno, and A.-L. Barabasi, “Morphology of ion-sputtered surfaces,” Nucl. Instrum. Methods Phys. Res., Sect. B 197, 185–227 (2002).
[CrossRef]

2001 (2)

C. C. Umbach, R. L. Headrick, and K.-C. Chang, “Spontaneous nanoscale corrugation of ion-eroded SiO2: the role of ion-irradiation-enhanced viscous flow,” Phys. Rev. Lett. 87, 246104 (2001).
[CrossRef]

D. Flamm, F. Frost, and D. Hirsch, “Evolution of surface topography of fused by ion beam sputtering,” Appl. Surf. Sci. 179, 95–101 (2001).
[CrossRef]

1996 (2)

R. Schlatmann, J. D. Shindler, and J. Verhoeven, “Evolution of surface morphology during growth and ion erosion of thin films,” Phys. Rev. B 54, 10880–10889 (1996).
[CrossRef]

G. Carter and V. Vishnyakov, “Roughening and ripple instabilities on ion-bombarded Si,” Phys. Rev. B 54, 17647–17653 (1996).
[CrossRef]

1995 (1)

T. W. Drueding, T. G. Bifano, and S. C. Fawcett, “Contouring algorithm for ion figuring,” Precis. Eng. 17, 10–21 (1995).
[CrossRef]

1994 (2)

W. M. Tong and R. S. Williams, “Kinetics of surface growth: phenomenology, scaling, and mechanisms of smoothing and roughening,” Annu. Rev. Phys. Chem. 45, 401–438 (1994).
[CrossRef]

T. M. Mayer, E. Chason, and A. J. Howard, “Roughening instability and ion-induced viscous relaxation of SiO2 surfaces,” J. Appl. Phys. 76, 1633–1643 (1994).
[CrossRef]

1990 (2)

L. N. Allen and H. W. Romig, “Demonstration of an ion figuring process,” Proc. SPIE 1333, 22–23 (1990).
[CrossRef]

R. A. Jones and W. J. Rupp, “Rapid optical fabrication with CCOS,” Proc. SPIE 1333, 34–43 (1990).
[CrossRef]

1988 (1)

R. M. Bradley and J. M. E. Harper, “Theory of ripple topography induced by ion bombardment,” J. Vac. Sci. Technol., A 6, 2390–2395 (1988).
[CrossRef]

1969 (1)

P. Sigmund, “Theory of sputtering. I. Sputtering yield of amorphous and polycrystalline targets,” Phys. Rev. 184, 383–416 (1969).
[CrossRef]

Allen, L. N.

L. N. Allen and H. W. Romig, “Demonstration of an ion figuring process,” Proc. SPIE 1333, 22–23 (1990).
[CrossRef]

Ando, M.

Y. Kurashima, S. Miyachi, I. Miyamoto, M. Ando, and A. Numata, “Evaluation of surface roughness of ULE substrates machined by Ar+ ion beam,” Microelectron. Eng. 85, 1193–1196 (2008).
[CrossRef]

Arnold, T.

T. Arnold, G. Böhm, R. Fechner, J. Meister, A. Nickel, F. Frost, T. Hänsel, and A. Schindler, “Ultra-precision surface finishing by ion beam and plasma jet techniques—status and outlook,” Nucl. Instrum. Methods Phys. Res., Sect. A 616, 147–156 (2010).
[CrossRef]

Barabasi, A.-L.

M. A. Makeev, R. Cuerno, and A.-L. Barabasi, “Morphology of ion-sputtered surfaces,” Nucl. Instrum. Methods Phys. Res., Sect. B 197, 185–227 (2002).
[CrossRef]

Bifano, T. G.

T. W. Drueding, T. G. Bifano, and S. C. Fawcett, “Contouring algorithm for ion figuring,” Precis. Eng. 17, 10–21 (1995).
[CrossRef]

Böhm, G.

T. Arnold, G. Böhm, R. Fechner, J. Meister, A. Nickel, F. Frost, T. Hänsel, and A. Schindler, “Ultra-precision surface finishing by ion beam and plasma jet techniques—status and outlook,” Nucl. Instrum. Methods Phys. Res., Sect. A 616, 147–156 (2010).
[CrossRef]

Bradley, R. M.

R. M. Bradley and J. M. E. Harper, “Theory of ripple topography induced by ion bombardment,” J. Vac. Sci. Technol., A 6, 2390–2395 (1988).
[CrossRef]

Carter, G.

G. Carter and V. Vishnyakov, “Roughening and ripple instabilities on ion-bombarded Si,” Phys. Rev. B 54, 17647–17653 (1996).
[CrossRef]

Chang, K.-C.

C. C. Umbach, R. L. Headrick, and K.-C. Chang, “Spontaneous nanoscale corrugation of ion-eroded SiO2: the role of ion-irradiation-enhanced viscous flow,” Phys. Rev. Lett. 87, 246104 (2001).
[CrossRef]

Chason, E.

T. M. Mayer, E. Chason, and A. J. Howard, “Roughening instability and ion-induced viscous relaxation of SiO2 surfaces,” J. Appl. Phys. 76, 1633–1643 (1994).
[CrossRef]

Chen, S.

Cuerno, R.

M. A. Makeev, R. Cuerno, and A.-L. Barabasi, “Morphology of ion-sputtered surfaces,” Nucl. Instrum. Methods Phys. Res., Sect. B 197, 185–227 (2002).
[CrossRef]

Dai, Y.

Drueding, T. W.

T. W. Drueding, T. G. Bifano, and S. C. Fawcett, “Contouring algorithm for ion figuring,” Precis. Eng. 17, 10–21 (1995).
[CrossRef]

Endo, H.

H. Endo, T. Inaba, S. A. Pahlovy, and I. Miyamoto, “Low energy Xe+ ion beam machining of ULE substrates for EUVL projection optics-Evaluation of high-spatial frequency roughness,” Microelectron. Eng. 87, 982–984 (2010).
[CrossRef]

Facsko, S.

A. Keller, S. Facsko, and W. Moller, “Evolution of ion-induced ripple patterns on SiO2 surfaces,” Nucl. Instrum. Methods Phys. Res., Sect. B 267, 656–659 (2009).
[CrossRef]

A. Keller, S. Facsko, and W. Moller, “The morphology of amorphous SiO2 surfaces during low energy ion sputtering,” J. Phys. 21, 495305 (2009).
[CrossRef]

Fawcett, S. C.

T. W. Drueding, T. G. Bifano, and S. C. Fawcett, “Contouring algorithm for ion figuring,” Precis. Eng. 17, 10–21 (1995).
[CrossRef]

Fechner, R.

T. Arnold, G. Böhm, R. Fechner, J. Meister, A. Nickel, F. Frost, T. Hänsel, and A. Schindler, “Ultra-precision surface finishing by ion beam and plasma jet techniques—status and outlook,” Nucl. Instrum. Methods Phys. Res., Sect. A 616, 147–156 (2010).
[CrossRef]

Flamm, D.

D. Flamm, F. Frost, and D. Hirsch, “Evolution of surface topography of fused by ion beam sputtering,” Appl. Surf. Sci. 179, 95–101 (2001).
[CrossRef]

Frost, F.

T. Arnold, G. Böhm, R. Fechner, J. Meister, A. Nickel, F. Frost, T. Hänsel, and A. Schindler, “Ultra-precision surface finishing by ion beam and plasma jet techniques—status and outlook,” Nucl. Instrum. Methods Phys. Res., Sect. A 616, 147–156 (2010).
[CrossRef]

D. Flamm, F. Frost, and D. Hirsch, “Evolution of surface topography of fused by ion beam sputtering,” Appl. Surf. Sci. 179, 95–101 (2001).
[CrossRef]

Haensel, T.

T. Haensel, A. Nickel, and A. Schindler, “Ion beam figuring of strongly curved surfaces with a (x,y,z) linear three-axes system,” in Frontiers in Optics 2008/Laser Science XXIV/Plasmonics and Metamaterials/Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2008), paper JWD6.

Hänsel, T.

T. Arnold, G. Böhm, R. Fechner, J. Meister, A. Nickel, F. Frost, T. Hänsel, and A. Schindler, “Ultra-precision surface finishing by ion beam and plasma jet techniques—status and outlook,” Nucl. Instrum. Methods Phys. Res., Sect. A 616, 147–156 (2010).
[CrossRef]

Harper, J. M. E.

R. M. Bradley and J. M. E. Harper, “Theory of ripple topography induced by ion bombardment,” J. Vac. Sci. Technol., A 6, 2390–2395 (1988).
[CrossRef]

Headrick, R. L.

C. C. Umbach, R. L. Headrick, and K.-C. Chang, “Spontaneous nanoscale corrugation of ion-eroded SiO2: the role of ion-irradiation-enhanced viscous flow,” Phys. Rev. Lett. 87, 246104 (2001).
[CrossRef]

Hirsch, D.

D. Flamm, F. Frost, and D. Hirsch, “Evolution of surface topography of fused by ion beam sputtering,” Appl. Surf. Sci. 179, 95–101 (2001).
[CrossRef]

Howard, A. J.

T. M. Mayer, E. Chason, and A. J. Howard, “Roughening instability and ion-induced viscous relaxation of SiO2 surfaces,” J. Appl. Phys. 76, 1633–1643 (1994).
[CrossRef]

Hu, H.

Inaba, T.

H. Endo, T. Inaba, S. A. Pahlovy, and I. Miyamoto, “Low energy Xe+ ion beam machining of ULE substrates for EUVL projection optics-Evaluation of high-spatial frequency roughness,” Microelectron. Eng. 87, 982–984 (2010).
[CrossRef]

Jiao, C.

Jones, R. A.

R. A. Jones and W. J. Rupp, “Rapid optical fabrication with CCOS,” Proc. SPIE 1333, 34–43 (1990).
[CrossRef]

Kang, N.

Keller, A.

A. Keller, S. Facsko, and W. Moller, “Evolution of ion-induced ripple patterns on SiO2 surfaces,” Nucl. Instrum. Methods Phys. Res., Sect. B 267, 656–659 (2009).
[CrossRef]

A. Keller, S. Facsko, and W. Moller, “The morphology of amorphous SiO2 surfaces during low energy ion sputtering,” J. Phys. 21, 495305 (2009).
[CrossRef]

Kurashima, Y.

Y. Kurashima, S. Miyachi, I. Miyamoto, M. Ando, and A. Numata, “Evaluation of surface roughness of ULE substrates machined by Ar+ ion beam,” Microelectron. Eng. 85, 1193–1196 (2008).
[CrossRef]

Li, S.

Liao, W.

Makeev, M. A.

M. A. Makeev, R. Cuerno, and A.-L. Barabasi, “Morphology of ion-sputtered surfaces,” Nucl. Instrum. Methods Phys. Res., Sect. B 197, 185–227 (2002).
[CrossRef]

Mayer, T. M.

T. M. Mayer, E. Chason, and A. J. Howard, “Roughening instability and ion-induced viscous relaxation of SiO2 surfaces,” J. Appl. Phys. 76, 1633–1643 (1994).
[CrossRef]

Meister, J.

T. Arnold, G. Böhm, R. Fechner, J. Meister, A. Nickel, F. Frost, T. Hänsel, and A. Schindler, “Ultra-precision surface finishing by ion beam and plasma jet techniques—status and outlook,” Nucl. Instrum. Methods Phys. Res., Sect. A 616, 147–156 (2010).
[CrossRef]

Miyachi, S.

Y. Kurashima, S. Miyachi, I. Miyamoto, M. Ando, and A. Numata, “Evaluation of surface roughness of ULE substrates machined by Ar+ ion beam,” Microelectron. Eng. 85, 1193–1196 (2008).
[CrossRef]

Miyamoto, I.

H. Endo, T. Inaba, S. A. Pahlovy, and I. Miyamoto, “Low energy Xe+ ion beam machining of ULE substrates for EUVL projection optics-Evaluation of high-spatial frequency roughness,” Microelectron. Eng. 87, 982–984 (2010).
[CrossRef]

Y. Kurashima, S. Miyachi, I. Miyamoto, M. Ando, and A. Numata, “Evaluation of surface roughness of ULE substrates machined by Ar+ ion beam,” Microelectron. Eng. 85, 1193–1196 (2008).
[CrossRef]

Moller, W.

A. Keller, S. Facsko, and W. Moller, “Evolution of ion-induced ripple patterns on SiO2 surfaces,” Nucl. Instrum. Methods Phys. Res., Sect. B 267, 656–659 (2009).
[CrossRef]

A. Keller, S. Facsko, and W. Moller, “The morphology of amorphous SiO2 surfaces during low energy ion sputtering,” J. Phys. 21, 495305 (2009).
[CrossRef]

Nickel, A.

T. Arnold, G. Böhm, R. Fechner, J. Meister, A. Nickel, F. Frost, T. Hänsel, and A. Schindler, “Ultra-precision surface finishing by ion beam and plasma jet techniques—status and outlook,” Nucl. Instrum. Methods Phys. Res., Sect. A 616, 147–156 (2010).
[CrossRef]

T. Haensel, A. Nickel, and A. Schindler, “Ion beam figuring of strongly curved surfaces with a (x,y,z) linear three-axes system,” in Frontiers in Optics 2008/Laser Science XXIV/Plasmonics and Metamaterials/Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2008), paper JWD6.

Numata, A.

Y. Kurashima, S. Miyachi, I. Miyamoto, M. Ando, and A. Numata, “Evaluation of surface roughness of ULE substrates machined by Ar+ ion beam,” Microelectron. Eng. 85, 1193–1196 (2008).
[CrossRef]

Pahlovy, S. A.

H. Endo, T. Inaba, S. A. Pahlovy, and I. Miyamoto, “Low energy Xe+ ion beam machining of ULE substrates for EUVL projection optics-Evaluation of high-spatial frequency roughness,” Microelectron. Eng. 87, 982–984 (2010).
[CrossRef]

Peng, X.

Romig, H. W.

L. N. Allen and H. W. Romig, “Demonstration of an ion figuring process,” Proc. SPIE 1333, 22–23 (1990).
[CrossRef]

Rupp, W. J.

R. A. Jones and W. J. Rupp, “Rapid optical fabrication with CCOS,” Proc. SPIE 1333, 34–43 (1990).
[CrossRef]

Schindler, A.

T. Arnold, G. Böhm, R. Fechner, J. Meister, A. Nickel, F. Frost, T. Hänsel, and A. Schindler, “Ultra-precision surface finishing by ion beam and plasma jet techniques—status and outlook,” Nucl. Instrum. Methods Phys. Res., Sect. A 616, 147–156 (2010).
[CrossRef]

T. Haensel, A. Nickel, and A. Schindler, “Ion beam figuring of strongly curved surfaces with a (x,y,z) linear three-axes system,” in Frontiers in Optics 2008/Laser Science XXIV/Plasmonics and Metamaterials/Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2008), paper JWD6.

Schlatmann, R.

R. Schlatmann, J. D. Shindler, and J. Verhoeven, “Evolution of surface morphology during growth and ion erosion of thin films,” Phys. Rev. B 54, 10880–10889 (1996).
[CrossRef]

Shi, F.

Shindler, J. D.

R. Schlatmann, J. D. Shindler, and J. Verhoeven, “Evolution of surface morphology during growth and ion erosion of thin films,” Phys. Rev. B 54, 10880–10889 (1996).
[CrossRef]

Sigmund, P.

P. Sigmund, “Theory of sputtering. I. Sputtering yield of amorphous and polycrystalline targets,” Phys. Rev. 184, 383–416 (1969).
[CrossRef]

Tong, W. M.

W. M. Tong and R. S. Williams, “Kinetics of surface growth: phenomenology, scaling, and mechanisms of smoothing and roughening,” Annu. Rev. Phys. Chem. 45, 401–438 (1994).
[CrossRef]

Umbach, C. C.

C. C. Umbach, R. L. Headrick, and K.-C. Chang, “Spontaneous nanoscale corrugation of ion-eroded SiO2: the role of ion-irradiation-enhanced viscous flow,” Phys. Rev. Lett. 87, 246104 (2001).
[CrossRef]

Verhoeven, J.

R. Schlatmann, J. D. Shindler, and J. Verhoeven, “Evolution of surface morphology during growth and ion erosion of thin films,” Phys. Rev. B 54, 10880–10889 (1996).
[CrossRef]

Vishnyakov, V.

G. Carter and V. Vishnyakov, “Roughening and ripple instabilities on ion-bombarded Si,” Phys. Rev. B 54, 17647–17653 (1996).
[CrossRef]

Wang, J.

Weiser, M.

M. Weiser, “Ion beam figuring for lithography optics,” Nucl. Instrum. Methods Phys. Res., Sect. B 267, 1390–1393 (2009).
[CrossRef]

Williams, R. S.

W. M. Tong and R. S. Williams, “Kinetics of surface growth: phenomenology, scaling, and mechanisms of smoothing and roughening,” Annu. Rev. Phys. Chem. 45, 401–438 (1994).
[CrossRef]

Wu, D.

Xie, X.

Zhou, L.

Annu. Rev. Phys. Chem. (1)

W. M. Tong and R. S. Williams, “Kinetics of surface growth: phenomenology, scaling, and mechanisms of smoothing and roughening,” Annu. Rev. Phys. Chem. 45, 401–438 (1994).
[CrossRef]

Appl. Opt. (4)

Appl. Surf. Sci. (1)

D. Flamm, F. Frost, and D. Hirsch, “Evolution of surface topography of fused by ion beam sputtering,” Appl. Surf. Sci. 179, 95–101 (2001).
[CrossRef]

J. Appl. Phys. (1)

T. M. Mayer, E. Chason, and A. J. Howard, “Roughening instability and ion-induced viscous relaxation of SiO2 surfaces,” J. Appl. Phys. 76, 1633–1643 (1994).
[CrossRef]

J. Phys. (1)

A. Keller, S. Facsko, and W. Moller, “The morphology of amorphous SiO2 surfaces during low energy ion sputtering,” J. Phys. 21, 495305 (2009).
[CrossRef]

J. Vac. Sci. Technol., A (1)

R. M. Bradley and J. M. E. Harper, “Theory of ripple topography induced by ion bombardment,” J. Vac. Sci. Technol., A 6, 2390–2395 (1988).
[CrossRef]

Microelectron. Eng. (2)

Y. Kurashima, S. Miyachi, I. Miyamoto, M. Ando, and A. Numata, “Evaluation of surface roughness of ULE substrates machined by Ar+ ion beam,” Microelectron. Eng. 85, 1193–1196 (2008).
[CrossRef]

H. Endo, T. Inaba, S. A. Pahlovy, and I. Miyamoto, “Low energy Xe+ ion beam machining of ULE substrates for EUVL projection optics-Evaluation of high-spatial frequency roughness,” Microelectron. Eng. 87, 982–984 (2010).
[CrossRef]

Nucl. Instrum. Methods Phys. Res., Sect. A (1)

T. Arnold, G. Böhm, R. Fechner, J. Meister, A. Nickel, F. Frost, T. Hänsel, and A. Schindler, “Ultra-precision surface finishing by ion beam and plasma jet techniques—status and outlook,” Nucl. Instrum. Methods Phys. Res., Sect. A 616, 147–156 (2010).
[CrossRef]

Nucl. Instrum. Methods Phys. Res., Sect. B (3)

M. Weiser, “Ion beam figuring for lithography optics,” Nucl. Instrum. Methods Phys. Res., Sect. B 267, 1390–1393 (2009).
[CrossRef]

M. A. Makeev, R. Cuerno, and A.-L. Barabasi, “Morphology of ion-sputtered surfaces,” Nucl. Instrum. Methods Phys. Res., Sect. B 197, 185–227 (2002).
[CrossRef]

A. Keller, S. Facsko, and W. Moller, “Evolution of ion-induced ripple patterns on SiO2 surfaces,” Nucl. Instrum. Methods Phys. Res., Sect. B 267, 656–659 (2009).
[CrossRef]

Phys. Rev. (1)

P. Sigmund, “Theory of sputtering. I. Sputtering yield of amorphous and polycrystalline targets,” Phys. Rev. 184, 383–416 (1969).
[CrossRef]

Phys. Rev. B (2)

G. Carter and V. Vishnyakov, “Roughening and ripple instabilities on ion-bombarded Si,” Phys. Rev. B 54, 17647–17653 (1996).
[CrossRef]

R. Schlatmann, J. D. Shindler, and J. Verhoeven, “Evolution of surface morphology during growth and ion erosion of thin films,” Phys. Rev. B 54, 10880–10889 (1996).
[CrossRef]

Phys. Rev. Lett. (1)

C. C. Umbach, R. L. Headrick, and K.-C. Chang, “Spontaneous nanoscale corrugation of ion-eroded SiO2: the role of ion-irradiation-enhanced viscous flow,” Phys. Rev. Lett. 87, 246104 (2001).
[CrossRef]

Precis. Eng. (1)

T. W. Drueding, T. G. Bifano, and S. C. Fawcett, “Contouring algorithm for ion figuring,” Precis. Eng. 17, 10–21 (1995).
[CrossRef]

Proc. SPIE (2)

L. N. Allen and H. W. Romig, “Demonstration of an ion figuring process,” Proc. SPIE 1333, 22–23 (1990).
[CrossRef]

R. A. Jones and W. J. Rupp, “Rapid optical fabrication with CCOS,” Proc. SPIE 1333, 34–43 (1990).
[CrossRef]

Other (1)

T. Haensel, A. Nickel, and A. Schindler, “Ion beam figuring of strongly curved surfaces with a (x,y,z) linear three-axes system,” in Frontiers in Optics 2008/Laser Science XXIV/Plasmonics and Metamaterials/Optical Fabrication and Testing, OSA Technical Digest (CD) (Optical Society of America, 2008), paper JWD6.

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Figures (7)

Fig. 1.
Fig. 1.

Experimental results of IBF for high-slope convex spherical surfaces: (a) original surface of sample A, (b) final surface of sample A after the TIF method, (c) original surface of sample B, and (d) final surface of sample B after the FIF method.

Fig. 2.
Fig. 2.

Curve of removed material from the two samples: (a) removed material from sample A along diameter l1 and (b) removed material of sample B along diameter l2.

Fig. 3.
Fig. 3.

Measuring platform for a high-slope convex spherical surface.

Fig. 4.
Fig. 4.

AFM images of fused silica surfaces after the first TIF step: (a) original morphology and (b)–(h) surface topographies at different ion incidence angles (increasing from 0° to 40°). Image size is 2μm×2μm. Blue arrows show the ion bean figuring direction for each image.

Fig. 5.
Fig. 5.

AFM images of fused silica surfaces at different ion incidence angles (0°, 20°, 30° and 40°) after the second TIF step. Image size is 2μm×2μm. Blue arrows show the ion bean figuring direction for each image.

Fig. 6.
Fig. 6.

AFM images of morphology at different fused silica surfaces after FIF. First row: (a) original surface and the fused silica surfaces at different parts (0°, 20°, and 40°) after the first TIF step. Second row: morphology at θ=0°, 20°, 30°, and 40° surface part after the second TIF step.

Fig. 7.
Fig. 7.

PSD functions of two samples during the IBF process.

Equations (8)

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h(r,t)t=C22h(r,t)C22(2h(r,t)),
PSDh(q,t)=PSD(q,t=0)exp(2C(q)t),
h(r,t)t=C22h(r,t)C42(2h(r,t))+η(r,t),
PSDh(q,t)=PSDh(q,t=0)exp(2C(q)t)A1exp(2C(q)t)C(q).
PSDh(q,t)=AC(q).
C2S=FaY(θ)Γ(θ)/n,
C2B=FΩ(E)dcos2θ/n,
C2=C2B+C2S=F[aY(θ)Γ(θ)Ω(E)dcos2θ]/n.

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