Abstract

Ion-beam figuring (IBF) is a precise surface finishing technique used for the production of ultra-precision optical surfaces. In this study, we propose an effective one-dimensional IBF (1D-IBF) method approaching sub-nanometer root mean square (RMS) convergence for flat and spherical mirrors. Our process contains three key aspects. First, to minimize the misalignment of the coordinate systems between the metrology and the IBF hardware, a mirror holder is used to integrate both the sample mirror and the beam removal function (BRF) mirror. In this way, the coordinate relationship can be calculated using the measured BRF center. Second, we propose a novel constrained linear least-squares (CLLS) dwell time calculation algorithm combined with a coarse-to-fine scheme to ensure that the resultant nonnegative dwell time closely and smoothly duplicates the required removal amount. Third, considering the possible errors induced by the translation stage, we propose a dwell time slicing strategy to divide the dwell time into smaller time slices. Experiments using our approaches are performed on flat and spherical mirrors as demonstrations. Measurement results from the nano-accuracy surface profiler (NSP) show that the residual profile errors are reduced to sub-nanometer RMS for both types of mirrors while the surface roughness is not affected by the figuring process, demonstrating the effectiveness of the proposed 1D-IBF method for 1D high-precision optics fabrication.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Edge effect correction using ion beam figuring

Bing Yang, Xuhui Xie, Furen Li, and Lin Zhou
Appl. Opt. 56(32) 8950-8958 (2017)

References

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  1. K. Yamauchi, H. Mimura, S. Matsuyama, H. Yumoto, T. Kimura, Y. Takahashi, K. Tamasaku, and T. Ishikawa, “Focusing mirror for coherent hard x-rays,” in Synchrotron Light Sources and Free-Electron Lasers: Accelerator Physics, Instrumentation and Science Applications, (Springer International Publishing, 2016).
  2. K. Yamauchi, H. Mimura, T. Kimura, H. Yumoto, S. Handa, S. Matsuyama, K. Arima, Y. Sano, K. Yamamura, K. Inagaki, H. Nakamori, J. Kim, K. Tamasaku, Y. Nishino, M. Yabashi, and T. Ishikawa, “Single-nanometer focusing of hard x-rays by kirkpatrick–baez mirrors,” J. Physics: Condens. Matter 23, 394206 (2011).
  3. S. Wilson and J. McNeil, “Neutral ion beam figuring of large optical surfaces,” Proc. SPIE 818, 320–325 (1987).
    [Crossref]
  4. L. N. Allen and H. W. Romig, “Demonstration of an ion-figuring process,” Proc. SPIE 1333, 22–34 (1990).
    [Crossref]
  5. S. R. Wilson, D. W. Reicher, C. Kranenberg, J. R. McNeil, P. L. White, P. M. Martin, and D. E. McCready, “Ion beam milling of fused silica for window fabrication,” Proc. SPIE 1441, 82–86 (1991).
    [Crossref]
  6. C. L. Carnal, C. M. Egert, and K. W. Hylton, “Advanced matrix-based algorithm for ion-beam milling of optical components,” Proc. SPIE 1752, 54–63 (1992).
    [Crossref]
  7. T. W. Drueding, T. G. Bifano, and S. C. Fawcett, “Contouring algorithm for ion figuring,” Precis. Eng. 17, 10–21 (1995).
    [Crossref]
  8. A. Schindler, T. Hänsel, F. Frost, R. Fechner, A. Nickel, H.-J. Thomas, H. Neumann, and D. Hirsch, “Ion beam finishing technology for high precision optics production,” in Optical Fabrication and Testing, (Optical Society of America, 2002), p. OTuB5.
    [Crossref]
  9. I. Preda, A. Vivo, F. Demarcq, S. Berujon, J. Susini, and E. Ziegler, “Ion beam etching of a flat silicon mirror surface: A study of the shape error evolution,” Nucl. Instruments Methods Phys. Res. Sect. A 710, 98–100 (2013).
    [Crossref]
  10. T. Arnold and F. Pietag, “Ion beam figuring machine for ultra-precision silicon spheres correction,” Precis. Eng. 41, 119–125 (2015).
    [Crossref]
  11. M. Idir, L. Huang, N. Bouet, K. Kaznatcheev, M. Vescovi, K. Lauer, R. Conley, K. Rennie, J. Kahn, R. Nethery, and L. Zhou, “A one-dimensional ion beam figuring system for x-ray mirror fabrication,” Rev. Sci. Instrum. 86, 105120 (2015).
    [Crossref] [PubMed]
  12. L. Zhou, M. Idir, N. Bouet, K. Kaznatcheev, L. Huang, M. Vescovi, Y. Dai, and S. Li, “One-dimensional ion-beam figuring for grazing-incidence reflective optics,” J. Synchrotron Radiat. 23, 182–186 (2016).
    [Crossref]
  13. L. Zhou, L. Huang, N. Bouet, K. Kaznatcheev, M. Vescovi, Y. Dai, S. Li, and M. Idir, “New figuring model based on surface slope profile for grazing-incidence reflective optics,” J. Synchrotron Radiat. 23, 1087–1090 (2016).
    [Crossref] [PubMed]
  14. J. F. Wu, Z. W. Lu, H. X. Zhang, and T. S. Wang, “Dwell time algorithm in ion beam figuring,” Appl. Opt. 48, 3930–3937 (2009).
    [Crossref] [PubMed]
  15. M. Demmler, M. Zeuner, F. Allenstein, T. Dunger, M. Nestler, and S. Kiontke, “Ion beam figuring (ibf) for high precision optics,” Proc. SPIE 7591, 75910Y (2010).
    [Crossref]
  16. M. Weiser, “Ion beam figuring for lithography optics,” Nucl. Instruments Methods Phys. Res. Sect. B 267, 1390–1393 (2009).
    [Crossref]
  17. X. Xie and S. Li, “Ion beam figuring technology,” in Handbook of Manufacturing Engineering and Technology, (SpringerLondon, 2015), pp. 1343–1390.
  18. R. Conley, N. Bouet, J. Biancarosa, Q. Shen, L. Boas, J. Feraca, and L. Rosenbaum, “The nsls-ii multilayer laue lens deposition system,” Proc. SPIE 7448, 74480U (2009).
    [Crossref]
  19. S. Li and Y. Dai, Large and Middle-Scale Aperture Aspheric Surfaces: Lapping, Polishing and Measurement (John Wiley & Sons, 2017).
  20. H. Cheng, Independent Variables for Optical Surfacing Systems (Springer, 2016).
  21. L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Model and method to determine dwell time in ion beam figuring,” Nami Jishu yu Jingmi Gongcheng 5, 107–112 (2007).
  22. C. Jiao, S. Li, and X. Xie, “Algorithm for ion beam figuring of low-gradient mirrors,” Appl. Opt. 48, 4090–4096 (2009).
    [Crossref] [PubMed]
  23. H. J. Ferreau, C. Kirches, A. Potschka, H. G. Bock, and M. Diehl, “qpoases: a parametric active-set algorithm for quadratic programming,” Math. Program. Comput. 6, 327–363 (2014).
    [Crossref]
  24. S. Qian and M. Idir, “Innovative nano-accuracy surface profiler for sub-50 nrad rms mirror test,” Proc. SPIE 9687, 96870D (2016).
    [Crossref]

2016 (3)

L. Zhou, M. Idir, N. Bouet, K. Kaznatcheev, L. Huang, M. Vescovi, Y. Dai, and S. Li, “One-dimensional ion-beam figuring for grazing-incidence reflective optics,” J. Synchrotron Radiat. 23, 182–186 (2016).
[Crossref]

L. Zhou, L. Huang, N. Bouet, K. Kaznatcheev, M. Vescovi, Y. Dai, S. Li, and M. Idir, “New figuring model based on surface slope profile for grazing-incidence reflective optics,” J. Synchrotron Radiat. 23, 1087–1090 (2016).
[Crossref] [PubMed]

S. Qian and M. Idir, “Innovative nano-accuracy surface profiler for sub-50 nrad rms mirror test,” Proc. SPIE 9687, 96870D (2016).
[Crossref]

2015 (2)

T. Arnold and F. Pietag, “Ion beam figuring machine for ultra-precision silicon spheres correction,” Precis. Eng. 41, 119–125 (2015).
[Crossref]

M. Idir, L. Huang, N. Bouet, K. Kaznatcheev, M. Vescovi, K. Lauer, R. Conley, K. Rennie, J. Kahn, R. Nethery, and L. Zhou, “A one-dimensional ion beam figuring system for x-ray mirror fabrication,” Rev. Sci. Instrum. 86, 105120 (2015).
[Crossref] [PubMed]

2014 (1)

H. J. Ferreau, C. Kirches, A. Potschka, H. G. Bock, and M. Diehl, “qpoases: a parametric active-set algorithm for quadratic programming,” Math. Program. Comput. 6, 327–363 (2014).
[Crossref]

2013 (1)

I. Preda, A. Vivo, F. Demarcq, S. Berujon, J. Susini, and E. Ziegler, “Ion beam etching of a flat silicon mirror surface: A study of the shape error evolution,” Nucl. Instruments Methods Phys. Res. Sect. A 710, 98–100 (2013).
[Crossref]

2011 (1)

K. Yamauchi, H. Mimura, T. Kimura, H. Yumoto, S. Handa, S. Matsuyama, K. Arima, Y. Sano, K. Yamamura, K. Inagaki, H. Nakamori, J. Kim, K. Tamasaku, Y. Nishino, M. Yabashi, and T. Ishikawa, “Single-nanometer focusing of hard x-rays by kirkpatrick–baez mirrors,” J. Physics: Condens. Matter 23, 394206 (2011).

2010 (1)

M. Demmler, M. Zeuner, F. Allenstein, T. Dunger, M. Nestler, and S. Kiontke, “Ion beam figuring (ibf) for high precision optics,” Proc. SPIE 7591, 75910Y (2010).
[Crossref]

2009 (4)

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

R. Conley, N. Bouet, J. Biancarosa, Q. Shen, L. Boas, J. Feraca, and L. Rosenbaum, “The nsls-ii multilayer laue lens deposition system,” Proc. SPIE 7448, 74480U (2009).
[Crossref]

J. F. Wu, Z. W. Lu, H. X. Zhang, and T. S. Wang, “Dwell time algorithm in ion beam figuring,” Appl. Opt. 48, 3930–3937 (2009).
[Crossref] [PubMed]

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

2007 (1)

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Model and method to determine dwell time in ion beam figuring,” Nami Jishu yu Jingmi Gongcheng 5, 107–112 (2007).

1995 (1)

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

1992 (1)

C. L. Carnal, C. M. Egert, and K. W. Hylton, “Advanced matrix-based algorithm for ion-beam milling of optical components,” Proc. SPIE 1752, 54–63 (1992).
[Crossref]

1991 (1)

S. R. Wilson, D. W. Reicher, C. Kranenberg, J. R. McNeil, P. L. White, P. M. Martin, and D. E. McCready, “Ion beam milling of fused silica for window fabrication,” Proc. SPIE 1441, 82–86 (1991).
[Crossref]

1990 (1)

L. N. Allen and H. W. Romig, “Demonstration of an ion-figuring process,” Proc. SPIE 1333, 22–34 (1990).
[Crossref]

1987 (1)

S. Wilson and J. McNeil, “Neutral ion beam figuring of large optical surfaces,” Proc. SPIE 818, 320–325 (1987).
[Crossref]

Allen, L. N.

L. N. Allen and H. W. Romig, “Demonstration of an ion-figuring process,” Proc. SPIE 1333, 22–34 (1990).
[Crossref]

Allenstein, F.

M. Demmler, M. Zeuner, F. Allenstein, T. Dunger, M. Nestler, and S. Kiontke, “Ion beam figuring (ibf) for high precision optics,” Proc. SPIE 7591, 75910Y (2010).
[Crossref]

Arima, K.

K. Yamauchi, H. Mimura, T. Kimura, H. Yumoto, S. Handa, S. Matsuyama, K. Arima, Y. Sano, K. Yamamura, K. Inagaki, H. Nakamori, J. Kim, K. Tamasaku, Y. Nishino, M. Yabashi, and T. Ishikawa, “Single-nanometer focusing of hard x-rays by kirkpatrick–baez mirrors,” J. Physics: Condens. Matter 23, 394206 (2011).

Arnold, T.

T. Arnold and F. Pietag, “Ion beam figuring machine for ultra-precision silicon spheres correction,” Precis. Eng. 41, 119–125 (2015).
[Crossref]

Berujon, S.

I. Preda, A. Vivo, F. Demarcq, S. Berujon, J. Susini, and E. Ziegler, “Ion beam etching of a flat silicon mirror surface: A study of the shape error evolution,” Nucl. Instruments Methods Phys. Res. Sect. A 710, 98–100 (2013).
[Crossref]

Biancarosa, J.

R. Conley, N. Bouet, J. Biancarosa, Q. Shen, L. Boas, J. Feraca, and L. Rosenbaum, “The nsls-ii multilayer laue lens deposition system,” Proc. SPIE 7448, 74480U (2009).
[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]

Boas, L.

R. Conley, N. Bouet, J. Biancarosa, Q. Shen, L. Boas, J. Feraca, and L. Rosenbaum, “The nsls-ii multilayer laue lens deposition system,” Proc. SPIE 7448, 74480U (2009).
[Crossref]

Bock, H. G.

H. J. Ferreau, C. Kirches, A. Potschka, H. G. Bock, and M. Diehl, “qpoases: a parametric active-set algorithm for quadratic programming,” Math. Program. Comput. 6, 327–363 (2014).
[Crossref]

Bouet, N.

L. Zhou, L. Huang, N. Bouet, K. Kaznatcheev, M. Vescovi, Y. Dai, S. Li, and M. Idir, “New figuring model based on surface slope profile for grazing-incidence reflective optics,” J. Synchrotron Radiat. 23, 1087–1090 (2016).
[Crossref] [PubMed]

L. Zhou, M. Idir, N. Bouet, K. Kaznatcheev, L. Huang, M. Vescovi, Y. Dai, and S. Li, “One-dimensional ion-beam figuring for grazing-incidence reflective optics,” J. Synchrotron Radiat. 23, 182–186 (2016).
[Crossref]

M. Idir, L. Huang, N. Bouet, K. Kaznatcheev, M. Vescovi, K. Lauer, R. Conley, K. Rennie, J. Kahn, R. Nethery, and L. Zhou, “A one-dimensional ion beam figuring system for x-ray mirror fabrication,” Rev. Sci. Instrum. 86, 105120 (2015).
[Crossref] [PubMed]

R. Conley, N. Bouet, J. Biancarosa, Q. Shen, L. Boas, J. Feraca, and L. Rosenbaum, “The nsls-ii multilayer laue lens deposition system,” Proc. SPIE 7448, 74480U (2009).
[Crossref]

Carnal, C. L.

C. L. Carnal, C. M. Egert, and K. W. Hylton, “Advanced matrix-based algorithm for ion-beam milling of optical components,” Proc. SPIE 1752, 54–63 (1992).
[Crossref]

Cheng, H.

H. Cheng, Independent Variables for Optical Surfacing Systems (Springer, 2016).

Conley, R.

M. Idir, L. Huang, N. Bouet, K. Kaznatcheev, M. Vescovi, K. Lauer, R. Conley, K. Rennie, J. Kahn, R. Nethery, and L. Zhou, “A one-dimensional ion beam figuring system for x-ray mirror fabrication,” Rev. Sci. Instrum. 86, 105120 (2015).
[Crossref] [PubMed]

R. Conley, N. Bouet, J. Biancarosa, Q. Shen, L. Boas, J. Feraca, and L. Rosenbaum, “The nsls-ii multilayer laue lens deposition system,” Proc. SPIE 7448, 74480U (2009).
[Crossref]

Dai, Y.

L. Zhou, L. Huang, N. Bouet, K. Kaznatcheev, M. Vescovi, Y. Dai, S. Li, and M. Idir, “New figuring model based on surface slope profile for grazing-incidence reflective optics,” J. Synchrotron Radiat. 23, 1087–1090 (2016).
[Crossref] [PubMed]

L. Zhou, M. Idir, N. Bouet, K. Kaznatcheev, L. Huang, M. Vescovi, Y. Dai, and S. Li, “One-dimensional ion-beam figuring for grazing-incidence reflective optics,” J. Synchrotron Radiat. 23, 182–186 (2016).
[Crossref]

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Model and method to determine dwell time in ion beam figuring,” Nami Jishu yu Jingmi Gongcheng 5, 107–112 (2007).

S. Li and Y. Dai, Large and Middle-Scale Aperture Aspheric Surfaces: Lapping, Polishing and Measurement (John Wiley & Sons, 2017).

Demarcq, F.

I. Preda, A. Vivo, F. Demarcq, S. Berujon, J. Susini, and E. Ziegler, “Ion beam etching of a flat silicon mirror surface: A study of the shape error evolution,” Nucl. Instruments Methods Phys. Res. Sect. A 710, 98–100 (2013).
[Crossref]

Demmler, M.

M. Demmler, M. Zeuner, F. Allenstein, T. Dunger, M. Nestler, and S. Kiontke, “Ion beam figuring (ibf) for high precision optics,” Proc. SPIE 7591, 75910Y (2010).
[Crossref]

Diehl, M.

H. J. Ferreau, C. Kirches, A. Potschka, H. G. Bock, and M. Diehl, “qpoases: a parametric active-set algorithm for quadratic programming,” Math. Program. Comput. 6, 327–363 (2014).
[Crossref]

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]

Dunger, T.

M. Demmler, M. Zeuner, F. Allenstein, T. Dunger, M. Nestler, and S. Kiontke, “Ion beam figuring (ibf) for high precision optics,” Proc. SPIE 7591, 75910Y (2010).
[Crossref]

Egert, C. M.

C. L. Carnal, C. M. Egert, and K. W. Hylton, “Advanced matrix-based algorithm for ion-beam milling of optical components,” Proc. SPIE 1752, 54–63 (1992).
[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.

A. Schindler, T. Hänsel, F. Frost, R. Fechner, A. Nickel, H.-J. Thomas, H. Neumann, and D. Hirsch, “Ion beam finishing technology for high precision optics production,” in Optical Fabrication and Testing, (Optical Society of America, 2002), p. OTuB5.
[Crossref]

Feraca, J.

R. Conley, N. Bouet, J. Biancarosa, Q. Shen, L. Boas, J. Feraca, and L. Rosenbaum, “The nsls-ii multilayer laue lens deposition system,” Proc. SPIE 7448, 74480U (2009).
[Crossref]

Ferreau, H. J.

H. J. Ferreau, C. Kirches, A. Potschka, H. G. Bock, and M. Diehl, “qpoases: a parametric active-set algorithm for quadratic programming,” Math. Program. Comput. 6, 327–363 (2014).
[Crossref]

Frost, F.

A. Schindler, T. Hänsel, F. Frost, R. Fechner, A. Nickel, H.-J. Thomas, H. Neumann, and D. Hirsch, “Ion beam finishing technology for high precision optics production,” in Optical Fabrication and Testing, (Optical Society of America, 2002), p. OTuB5.
[Crossref]

Handa, S.

K. Yamauchi, H. Mimura, T. Kimura, H. Yumoto, S. Handa, S. Matsuyama, K. Arima, Y. Sano, K. Yamamura, K. Inagaki, H. Nakamori, J. Kim, K. Tamasaku, Y. Nishino, M. Yabashi, and T. Ishikawa, “Single-nanometer focusing of hard x-rays by kirkpatrick–baez mirrors,” J. Physics: Condens. Matter 23, 394206 (2011).

Hänsel, T.

A. Schindler, T. Hänsel, F. Frost, R. Fechner, A. Nickel, H.-J. Thomas, H. Neumann, and D. Hirsch, “Ion beam finishing technology for high precision optics production,” in Optical Fabrication and Testing, (Optical Society of America, 2002), p. OTuB5.
[Crossref]

Hirsch, D.

A. Schindler, T. Hänsel, F. Frost, R. Fechner, A. Nickel, H.-J. Thomas, H. Neumann, and D. Hirsch, “Ion beam finishing technology for high precision optics production,” in Optical Fabrication and Testing, (Optical Society of America, 2002), p. OTuB5.
[Crossref]

Huang, L.

L. Zhou, M. Idir, N. Bouet, K. Kaznatcheev, L. Huang, M. Vescovi, Y. Dai, and S. Li, “One-dimensional ion-beam figuring for grazing-incidence reflective optics,” J. Synchrotron Radiat. 23, 182–186 (2016).
[Crossref]

L. Zhou, L. Huang, N. Bouet, K. Kaznatcheev, M. Vescovi, Y. Dai, S. Li, and M. Idir, “New figuring model based on surface slope profile for grazing-incidence reflective optics,” J. Synchrotron Radiat. 23, 1087–1090 (2016).
[Crossref] [PubMed]

M. Idir, L. Huang, N. Bouet, K. Kaznatcheev, M. Vescovi, K. Lauer, R. Conley, K. Rennie, J. Kahn, R. Nethery, and L. Zhou, “A one-dimensional ion beam figuring system for x-ray mirror fabrication,” Rev. Sci. Instrum. 86, 105120 (2015).
[Crossref] [PubMed]

Hylton, K. W.

C. L. Carnal, C. M. Egert, and K. W. Hylton, “Advanced matrix-based algorithm for ion-beam milling of optical components,” Proc. SPIE 1752, 54–63 (1992).
[Crossref]

Idir, M.

L. Zhou, M. Idir, N. Bouet, K. Kaznatcheev, L. Huang, M. Vescovi, Y. Dai, and S. Li, “One-dimensional ion-beam figuring for grazing-incidence reflective optics,” J. Synchrotron Radiat. 23, 182–186 (2016).
[Crossref]

L. Zhou, L. Huang, N. Bouet, K. Kaznatcheev, M. Vescovi, Y. Dai, S. Li, and M. Idir, “New figuring model based on surface slope profile for grazing-incidence reflective optics,” J. Synchrotron Radiat. 23, 1087–1090 (2016).
[Crossref] [PubMed]

S. Qian and M. Idir, “Innovative nano-accuracy surface profiler for sub-50 nrad rms mirror test,” Proc. SPIE 9687, 96870D (2016).
[Crossref]

M. Idir, L. Huang, N. Bouet, K. Kaznatcheev, M. Vescovi, K. Lauer, R. Conley, K. Rennie, J. Kahn, R. Nethery, and L. Zhou, “A one-dimensional ion beam figuring system for x-ray mirror fabrication,” Rev. Sci. Instrum. 86, 105120 (2015).
[Crossref] [PubMed]

Inagaki, K.

K. Yamauchi, H. Mimura, T. Kimura, H. Yumoto, S. Handa, S. Matsuyama, K. Arima, Y. Sano, K. Yamamura, K. Inagaki, H. Nakamori, J. Kim, K. Tamasaku, Y. Nishino, M. Yabashi, and T. Ishikawa, “Single-nanometer focusing of hard x-rays by kirkpatrick–baez mirrors,” J. Physics: Condens. Matter 23, 394206 (2011).

Ishikawa, T.

K. Yamauchi, H. Mimura, T. Kimura, H. Yumoto, S. Handa, S. Matsuyama, K. Arima, Y. Sano, K. Yamamura, K. Inagaki, H. Nakamori, J. Kim, K. Tamasaku, Y. Nishino, M. Yabashi, and T. Ishikawa, “Single-nanometer focusing of hard x-rays by kirkpatrick–baez mirrors,” J. Physics: Condens. Matter 23, 394206 (2011).

K. Yamauchi, H. Mimura, S. Matsuyama, H. Yumoto, T. Kimura, Y. Takahashi, K. Tamasaku, and T. Ishikawa, “Focusing mirror for coherent hard x-rays,” in Synchrotron Light Sources and Free-Electron Lasers: Accelerator Physics, Instrumentation and Science Applications, (Springer International Publishing, 2016).

Jiao, C.

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

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Model and method to determine dwell time in ion beam figuring,” Nami Jishu yu Jingmi Gongcheng 5, 107–112 (2007).

Kahn, J.

M. Idir, L. Huang, N. Bouet, K. Kaznatcheev, M. Vescovi, K. Lauer, R. Conley, K. Rennie, J. Kahn, R. Nethery, and L. Zhou, “A one-dimensional ion beam figuring system for x-ray mirror fabrication,” Rev. Sci. Instrum. 86, 105120 (2015).
[Crossref] [PubMed]

Kaznatcheev, K.

L. Zhou, M. Idir, N. Bouet, K. Kaznatcheev, L. Huang, M. Vescovi, Y. Dai, and S. Li, “One-dimensional ion-beam figuring for grazing-incidence reflective optics,” J. Synchrotron Radiat. 23, 182–186 (2016).
[Crossref]

L. Zhou, L. Huang, N. Bouet, K. Kaznatcheev, M. Vescovi, Y. Dai, S. Li, and M. Idir, “New figuring model based on surface slope profile for grazing-incidence reflective optics,” J. Synchrotron Radiat. 23, 1087–1090 (2016).
[Crossref] [PubMed]

M. Idir, L. Huang, N. Bouet, K. Kaznatcheev, M. Vescovi, K. Lauer, R. Conley, K. Rennie, J. Kahn, R. Nethery, and L. Zhou, “A one-dimensional ion beam figuring system for x-ray mirror fabrication,” Rev. Sci. Instrum. 86, 105120 (2015).
[Crossref] [PubMed]

Kim, J.

K. Yamauchi, H. Mimura, T. Kimura, H. Yumoto, S. Handa, S. Matsuyama, K. Arima, Y. Sano, K. Yamamura, K. Inagaki, H. Nakamori, J. Kim, K. Tamasaku, Y. Nishino, M. Yabashi, and T. Ishikawa, “Single-nanometer focusing of hard x-rays by kirkpatrick–baez mirrors,” J. Physics: Condens. Matter 23, 394206 (2011).

Kimura, T.

K. Yamauchi, H. Mimura, T. Kimura, H. Yumoto, S. Handa, S. Matsuyama, K. Arima, Y. Sano, K. Yamamura, K. Inagaki, H. Nakamori, J. Kim, K. Tamasaku, Y. Nishino, M. Yabashi, and T. Ishikawa, “Single-nanometer focusing of hard x-rays by kirkpatrick–baez mirrors,” J. Physics: Condens. Matter 23, 394206 (2011).

K. Yamauchi, H. Mimura, S. Matsuyama, H. Yumoto, T. Kimura, Y. Takahashi, K. Tamasaku, and T. Ishikawa, “Focusing mirror for coherent hard x-rays,” in Synchrotron Light Sources and Free-Electron Lasers: Accelerator Physics, Instrumentation and Science Applications, (Springer International Publishing, 2016).

Kiontke, S.

M. Demmler, M. Zeuner, F. Allenstein, T. Dunger, M. Nestler, and S. Kiontke, “Ion beam figuring (ibf) for high precision optics,” Proc. SPIE 7591, 75910Y (2010).
[Crossref]

Kirches, C.

H. J. Ferreau, C. Kirches, A. Potschka, H. G. Bock, and M. Diehl, “qpoases: a parametric active-set algorithm for quadratic programming,” Math. Program. Comput. 6, 327–363 (2014).
[Crossref]

Kranenberg, C.

S. R. Wilson, D. W. Reicher, C. Kranenberg, J. R. McNeil, P. L. White, P. M. Martin, and D. E. McCready, “Ion beam milling of fused silica for window fabrication,” Proc. SPIE 1441, 82–86 (1991).
[Crossref]

Lauer, K.

M. Idir, L. Huang, N. Bouet, K. Kaznatcheev, M. Vescovi, K. Lauer, R. Conley, K. Rennie, J. Kahn, R. Nethery, and L. Zhou, “A one-dimensional ion beam figuring system for x-ray mirror fabrication,” Rev. Sci. Instrum. 86, 105120 (2015).
[Crossref] [PubMed]

Li, S.

L. Zhou, M. Idir, N. Bouet, K. Kaznatcheev, L. Huang, M. Vescovi, Y. Dai, and S. Li, “One-dimensional ion-beam figuring for grazing-incidence reflective optics,” J. Synchrotron Radiat. 23, 182–186 (2016).
[Crossref]

L. Zhou, L. Huang, N. Bouet, K. Kaznatcheev, M. Vescovi, Y. Dai, S. Li, and M. Idir, “New figuring model based on surface slope profile for grazing-incidence reflective optics,” J. Synchrotron Radiat. 23, 1087–1090 (2016).
[Crossref] [PubMed]

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

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Model and method to determine dwell time in ion beam figuring,” Nami Jishu yu Jingmi Gongcheng 5, 107–112 (2007).

S. Li and Y. Dai, Large and Middle-Scale Aperture Aspheric Surfaces: Lapping, Polishing and Measurement (John Wiley & Sons, 2017).

X. Xie and S. Li, “Ion beam figuring technology,” in Handbook of Manufacturing Engineering and Technology, (SpringerLondon, 2015), pp. 1343–1390.

Lu, Z. W.

Martin, P. M.

S. R. Wilson, D. W. Reicher, C. Kranenberg, J. R. McNeil, P. L. White, P. M. Martin, and D. E. McCready, “Ion beam milling of fused silica for window fabrication,” Proc. SPIE 1441, 82–86 (1991).
[Crossref]

Matsuyama, S.

K. Yamauchi, H. Mimura, T. Kimura, H. Yumoto, S. Handa, S. Matsuyama, K. Arima, Y. Sano, K. Yamamura, K. Inagaki, H. Nakamori, J. Kim, K. Tamasaku, Y. Nishino, M. Yabashi, and T. Ishikawa, “Single-nanometer focusing of hard x-rays by kirkpatrick–baez mirrors,” J. Physics: Condens. Matter 23, 394206 (2011).

K. Yamauchi, H. Mimura, S. Matsuyama, H. Yumoto, T. Kimura, Y. Takahashi, K. Tamasaku, and T. Ishikawa, “Focusing mirror for coherent hard x-rays,” in Synchrotron Light Sources and Free-Electron Lasers: Accelerator Physics, Instrumentation and Science Applications, (Springer International Publishing, 2016).

McCready, D. E.

S. R. Wilson, D. W. Reicher, C. Kranenberg, J. R. McNeil, P. L. White, P. M. Martin, and D. E. McCready, “Ion beam milling of fused silica for window fabrication,” Proc. SPIE 1441, 82–86 (1991).
[Crossref]

McNeil, J.

S. Wilson and J. McNeil, “Neutral ion beam figuring of large optical surfaces,” Proc. SPIE 818, 320–325 (1987).
[Crossref]

McNeil, J. R.

S. R. Wilson, D. W. Reicher, C. Kranenberg, J. R. McNeil, P. L. White, P. M. Martin, and D. E. McCready, “Ion beam milling of fused silica for window fabrication,” Proc. SPIE 1441, 82–86 (1991).
[Crossref]

Mimura, H.

K. Yamauchi, H. Mimura, T. Kimura, H. Yumoto, S. Handa, S. Matsuyama, K. Arima, Y. Sano, K. Yamamura, K. Inagaki, H. Nakamori, J. Kim, K. Tamasaku, Y. Nishino, M. Yabashi, and T. Ishikawa, “Single-nanometer focusing of hard x-rays by kirkpatrick–baez mirrors,” J. Physics: Condens. Matter 23, 394206 (2011).

K. Yamauchi, H. Mimura, S. Matsuyama, H. Yumoto, T. Kimura, Y. Takahashi, K. Tamasaku, and T. Ishikawa, “Focusing mirror for coherent hard x-rays,” in Synchrotron Light Sources and Free-Electron Lasers: Accelerator Physics, Instrumentation and Science Applications, (Springer International Publishing, 2016).

Nakamori, H.

K. Yamauchi, H. Mimura, T. Kimura, H. Yumoto, S. Handa, S. Matsuyama, K. Arima, Y. Sano, K. Yamamura, K. Inagaki, H. Nakamori, J. Kim, K. Tamasaku, Y. Nishino, M. Yabashi, and T. Ishikawa, “Single-nanometer focusing of hard x-rays by kirkpatrick–baez mirrors,” J. Physics: Condens. Matter 23, 394206 (2011).

Nestler, M.

M. Demmler, M. Zeuner, F. Allenstein, T. Dunger, M. Nestler, and S. Kiontke, “Ion beam figuring (ibf) for high precision optics,” Proc. SPIE 7591, 75910Y (2010).
[Crossref]

Nethery, R.

M. Idir, L. Huang, N. Bouet, K. Kaznatcheev, M. Vescovi, K. Lauer, R. Conley, K. Rennie, J. Kahn, R. Nethery, and L. Zhou, “A one-dimensional ion beam figuring system for x-ray mirror fabrication,” Rev. Sci. Instrum. 86, 105120 (2015).
[Crossref] [PubMed]

Neumann, H.

A. Schindler, T. Hänsel, F. Frost, R. Fechner, A. Nickel, H.-J. Thomas, H. Neumann, and D. Hirsch, “Ion beam finishing technology for high precision optics production,” in Optical Fabrication and Testing, (Optical Society of America, 2002), p. OTuB5.
[Crossref]

Nickel, A.

A. Schindler, T. Hänsel, F. Frost, R. Fechner, A. Nickel, H.-J. Thomas, H. Neumann, and D. Hirsch, “Ion beam finishing technology for high precision optics production,” in Optical Fabrication and Testing, (Optical Society of America, 2002), p. OTuB5.
[Crossref]

Nishino, Y.

K. Yamauchi, H. Mimura, T. Kimura, H. Yumoto, S. Handa, S. Matsuyama, K. Arima, Y. Sano, K. Yamamura, K. Inagaki, H. Nakamori, J. Kim, K. Tamasaku, Y. Nishino, M. Yabashi, and T. Ishikawa, “Single-nanometer focusing of hard x-rays by kirkpatrick–baez mirrors,” J. Physics: Condens. Matter 23, 394206 (2011).

Pietag, F.

T. Arnold and F. Pietag, “Ion beam figuring machine for ultra-precision silicon spheres correction,” Precis. Eng. 41, 119–125 (2015).
[Crossref]

Potschka, A.

H. J. Ferreau, C. Kirches, A. Potschka, H. G. Bock, and M. Diehl, “qpoases: a parametric active-set algorithm for quadratic programming,” Math. Program. Comput. 6, 327–363 (2014).
[Crossref]

Preda, I.

I. Preda, A. Vivo, F. Demarcq, S. Berujon, J. Susini, and E. Ziegler, “Ion beam etching of a flat silicon mirror surface: A study of the shape error evolution,” Nucl. Instruments Methods Phys. Res. Sect. A 710, 98–100 (2013).
[Crossref]

Qian, S.

S. Qian and M. Idir, “Innovative nano-accuracy surface profiler for sub-50 nrad rms mirror test,” Proc. SPIE 9687, 96870D (2016).
[Crossref]

Reicher, D. W.

S. R. Wilson, D. W. Reicher, C. Kranenberg, J. R. McNeil, P. L. White, P. M. Martin, and D. E. McCready, “Ion beam milling of fused silica for window fabrication,” Proc. SPIE 1441, 82–86 (1991).
[Crossref]

Rennie, K.

M. Idir, L. Huang, N. Bouet, K. Kaznatcheev, M. Vescovi, K. Lauer, R. Conley, K. Rennie, J. Kahn, R. Nethery, and L. Zhou, “A one-dimensional ion beam figuring system for x-ray mirror fabrication,” Rev. Sci. Instrum. 86, 105120 (2015).
[Crossref] [PubMed]

Romig, H. W.

L. N. Allen and H. W. Romig, “Demonstration of an ion-figuring process,” Proc. SPIE 1333, 22–34 (1990).
[Crossref]

Rosenbaum, L.

R. Conley, N. Bouet, J. Biancarosa, Q. Shen, L. Boas, J. Feraca, and L. Rosenbaum, “The nsls-ii multilayer laue lens deposition system,” Proc. SPIE 7448, 74480U (2009).
[Crossref]

Sano, Y.

K. Yamauchi, H. Mimura, T. Kimura, H. Yumoto, S. Handa, S. Matsuyama, K. Arima, Y. Sano, K. Yamamura, K. Inagaki, H. Nakamori, J. Kim, K. Tamasaku, Y. Nishino, M. Yabashi, and T. Ishikawa, “Single-nanometer focusing of hard x-rays by kirkpatrick–baez mirrors,” J. Physics: Condens. Matter 23, 394206 (2011).

Schindler, A.

A. Schindler, T. Hänsel, F. Frost, R. Fechner, A. Nickel, H.-J. Thomas, H. Neumann, and D. Hirsch, “Ion beam finishing technology for high precision optics production,” in Optical Fabrication and Testing, (Optical Society of America, 2002), p. OTuB5.
[Crossref]

Shen, Q.

R. Conley, N. Bouet, J. Biancarosa, Q. Shen, L. Boas, J. Feraca, and L. Rosenbaum, “The nsls-ii multilayer laue lens deposition system,” Proc. SPIE 7448, 74480U (2009).
[Crossref]

Susini, J.

I. Preda, A. Vivo, F. Demarcq, S. Berujon, J. Susini, and E. Ziegler, “Ion beam etching of a flat silicon mirror surface: A study of the shape error evolution,” Nucl. Instruments Methods Phys. Res. Sect. A 710, 98–100 (2013).
[Crossref]

Takahashi, Y.

K. Yamauchi, H. Mimura, S. Matsuyama, H. Yumoto, T. Kimura, Y. Takahashi, K. Tamasaku, and T. Ishikawa, “Focusing mirror for coherent hard x-rays,” in Synchrotron Light Sources and Free-Electron Lasers: Accelerator Physics, Instrumentation and Science Applications, (Springer International Publishing, 2016).

Tamasaku, K.

K. Yamauchi, H. Mimura, T. Kimura, H. Yumoto, S. Handa, S. Matsuyama, K. Arima, Y. Sano, K. Yamamura, K. Inagaki, H. Nakamori, J. Kim, K. Tamasaku, Y. Nishino, M. Yabashi, and T. Ishikawa, “Single-nanometer focusing of hard x-rays by kirkpatrick–baez mirrors,” J. Physics: Condens. Matter 23, 394206 (2011).

K. Yamauchi, H. Mimura, S. Matsuyama, H. Yumoto, T. Kimura, Y. Takahashi, K. Tamasaku, and T. Ishikawa, “Focusing mirror for coherent hard x-rays,” in Synchrotron Light Sources and Free-Electron Lasers: Accelerator Physics, Instrumentation and Science Applications, (Springer International Publishing, 2016).

Thomas, H.-J.

A. Schindler, T. Hänsel, F. Frost, R. Fechner, A. Nickel, H.-J. Thomas, H. Neumann, and D. Hirsch, “Ion beam finishing technology for high precision optics production,” in Optical Fabrication and Testing, (Optical Society of America, 2002), p. OTuB5.
[Crossref]

Vescovi, M.

L. Zhou, M. Idir, N. Bouet, K. Kaznatcheev, L. Huang, M. Vescovi, Y. Dai, and S. Li, “One-dimensional ion-beam figuring for grazing-incidence reflective optics,” J. Synchrotron Radiat. 23, 182–186 (2016).
[Crossref]

L. Zhou, L. Huang, N. Bouet, K. Kaznatcheev, M. Vescovi, Y. Dai, S. Li, and M. Idir, “New figuring model based on surface slope profile for grazing-incidence reflective optics,” J. Synchrotron Radiat. 23, 1087–1090 (2016).
[Crossref] [PubMed]

M. Idir, L. Huang, N. Bouet, K. Kaznatcheev, M. Vescovi, K. Lauer, R. Conley, K. Rennie, J. Kahn, R. Nethery, and L. Zhou, “A one-dimensional ion beam figuring system for x-ray mirror fabrication,” Rev. Sci. Instrum. 86, 105120 (2015).
[Crossref] [PubMed]

Vivo, A.

I. Preda, A. Vivo, F. Demarcq, S. Berujon, J. Susini, and E. Ziegler, “Ion beam etching of a flat silicon mirror surface: A study of the shape error evolution,” Nucl. Instruments Methods Phys. Res. Sect. A 710, 98–100 (2013).
[Crossref]

Wang, T. S.

Weiser, M.

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

White, P. L.

S. R. Wilson, D. W. Reicher, C. Kranenberg, J. R. McNeil, P. L. White, P. M. Martin, and D. E. McCready, “Ion beam milling of fused silica for window fabrication,” Proc. SPIE 1441, 82–86 (1991).
[Crossref]

Wilson, S.

S. Wilson and J. McNeil, “Neutral ion beam figuring of large optical surfaces,” Proc. SPIE 818, 320–325 (1987).
[Crossref]

Wilson, S. R.

S. R. Wilson, D. W. Reicher, C. Kranenberg, J. R. McNeil, P. L. White, P. M. Martin, and D. E. McCready, “Ion beam milling of fused silica for window fabrication,” Proc. SPIE 1441, 82–86 (1991).
[Crossref]

Wu, J. F.

Xie, X.

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

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Model and method to determine dwell time in ion beam figuring,” Nami Jishu yu Jingmi Gongcheng 5, 107–112 (2007).

X. Xie and S. Li, “Ion beam figuring technology,” in Handbook of Manufacturing Engineering and Technology, (SpringerLondon, 2015), pp. 1343–1390.

Yabashi, M.

K. Yamauchi, H. Mimura, T. Kimura, H. Yumoto, S. Handa, S. Matsuyama, K. Arima, Y. Sano, K. Yamamura, K. Inagaki, H. Nakamori, J. Kim, K. Tamasaku, Y. Nishino, M. Yabashi, and T. Ishikawa, “Single-nanometer focusing of hard x-rays by kirkpatrick–baez mirrors,” J. Physics: Condens. Matter 23, 394206 (2011).

Yamamura, K.

K. Yamauchi, H. Mimura, T. Kimura, H. Yumoto, S. Handa, S. Matsuyama, K. Arima, Y. Sano, K. Yamamura, K. Inagaki, H. Nakamori, J. Kim, K. Tamasaku, Y. Nishino, M. Yabashi, and T. Ishikawa, “Single-nanometer focusing of hard x-rays by kirkpatrick–baez mirrors,” J. Physics: Condens. Matter 23, 394206 (2011).

Yamauchi, K.

K. Yamauchi, H. Mimura, T. Kimura, H. Yumoto, S. Handa, S. Matsuyama, K. Arima, Y. Sano, K. Yamamura, K. Inagaki, H. Nakamori, J. Kim, K. Tamasaku, Y. Nishino, M. Yabashi, and T. Ishikawa, “Single-nanometer focusing of hard x-rays by kirkpatrick–baez mirrors,” J. Physics: Condens. Matter 23, 394206 (2011).

K. Yamauchi, H. Mimura, S. Matsuyama, H. Yumoto, T. Kimura, Y. Takahashi, K. Tamasaku, and T. Ishikawa, “Focusing mirror for coherent hard x-rays,” in Synchrotron Light Sources and Free-Electron Lasers: Accelerator Physics, Instrumentation and Science Applications, (Springer International Publishing, 2016).

Yumoto, H.

K. Yamauchi, H. Mimura, T. Kimura, H. Yumoto, S. Handa, S. Matsuyama, K. Arima, Y. Sano, K. Yamamura, K. Inagaki, H. Nakamori, J. Kim, K. Tamasaku, Y. Nishino, M. Yabashi, and T. Ishikawa, “Single-nanometer focusing of hard x-rays by kirkpatrick–baez mirrors,” J. Physics: Condens. Matter 23, 394206 (2011).

K. Yamauchi, H. Mimura, S. Matsuyama, H. Yumoto, T. Kimura, Y. Takahashi, K. Tamasaku, and T. Ishikawa, “Focusing mirror for coherent hard x-rays,” in Synchrotron Light Sources and Free-Electron Lasers: Accelerator Physics, Instrumentation and Science Applications, (Springer International Publishing, 2016).

Zeuner, M.

M. Demmler, M. Zeuner, F. Allenstein, T. Dunger, M. Nestler, and S. Kiontke, “Ion beam figuring (ibf) for high precision optics,” Proc. SPIE 7591, 75910Y (2010).
[Crossref]

Zhang, H. X.

Zhou, L.

L. Zhou, L. Huang, N. Bouet, K. Kaznatcheev, M. Vescovi, Y. Dai, S. Li, and M. Idir, “New figuring model based on surface slope profile for grazing-incidence reflective optics,” J. Synchrotron Radiat. 23, 1087–1090 (2016).
[Crossref] [PubMed]

L. Zhou, M. Idir, N. Bouet, K. Kaznatcheev, L. Huang, M. Vescovi, Y. Dai, and S. Li, “One-dimensional ion-beam figuring for grazing-incidence reflective optics,” J. Synchrotron Radiat. 23, 182–186 (2016).
[Crossref]

M. Idir, L. Huang, N. Bouet, K. Kaznatcheev, M. Vescovi, K. Lauer, R. Conley, K. Rennie, J. Kahn, R. Nethery, and L. Zhou, “A one-dimensional ion beam figuring system for x-ray mirror fabrication,” Rev. Sci. Instrum. 86, 105120 (2015).
[Crossref] [PubMed]

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Model and method to determine dwell time in ion beam figuring,” Nami Jishu yu Jingmi Gongcheng 5, 107–112 (2007).

Ziegler, E.

I. Preda, A. Vivo, F. Demarcq, S. Berujon, J. Susini, and E. Ziegler, “Ion beam etching of a flat silicon mirror surface: A study of the shape error evolution,” Nucl. Instruments Methods Phys. Res. Sect. A 710, 98–100 (2013).
[Crossref]

Appl. Opt. (2)

J. Physics: Condens. Matter (1)

K. Yamauchi, H. Mimura, T. Kimura, H. Yumoto, S. Handa, S. Matsuyama, K. Arima, Y. Sano, K. Yamamura, K. Inagaki, H. Nakamori, J. Kim, K. Tamasaku, Y. Nishino, M. Yabashi, and T. Ishikawa, “Single-nanometer focusing of hard x-rays by kirkpatrick–baez mirrors,” J. Physics: Condens. Matter 23, 394206 (2011).

J. Synchrotron Radiat. (2)

L. Zhou, M. Idir, N. Bouet, K. Kaznatcheev, L. Huang, M. Vescovi, Y. Dai, and S. Li, “One-dimensional ion-beam figuring for grazing-incidence reflective optics,” J. Synchrotron Radiat. 23, 182–186 (2016).
[Crossref]

L. Zhou, L. Huang, N. Bouet, K. Kaznatcheev, M. Vescovi, Y. Dai, S. Li, and M. Idir, “New figuring model based on surface slope profile for grazing-incidence reflective optics,” J. Synchrotron Radiat. 23, 1087–1090 (2016).
[Crossref] [PubMed]

Math. Program. Comput. (1)

H. J. Ferreau, C. Kirches, A. Potschka, H. G. Bock, and M. Diehl, “qpoases: a parametric active-set algorithm for quadratic programming,” Math. Program. Comput. 6, 327–363 (2014).
[Crossref]

Nami Jishu yu Jingmi Gongcheng (1)

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Model and method to determine dwell time in ion beam figuring,” Nami Jishu yu Jingmi Gongcheng 5, 107–112 (2007).

Nucl. Instruments Methods Phys. Res. Sect. A (1)

I. Preda, A. Vivo, F. Demarcq, S. Berujon, J. Susini, and E. Ziegler, “Ion beam etching of a flat silicon mirror surface: A study of the shape error evolution,” Nucl. Instruments Methods Phys. Res. Sect. A 710, 98–100 (2013).
[Crossref]

Nucl. Instruments Methods Phys. Res. Sect. B (1)

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

Precis. Eng. (2)

T. Arnold and F. Pietag, “Ion beam figuring machine for ultra-precision silicon spheres correction,” Precis. Eng. 41, 119–125 (2015).
[Crossref]

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

Proc. SPIE (7)

S. Wilson and J. McNeil, “Neutral ion beam figuring of large optical surfaces,” Proc. SPIE 818, 320–325 (1987).
[Crossref]

L. N. Allen and H. W. Romig, “Demonstration of an ion-figuring process,” Proc. SPIE 1333, 22–34 (1990).
[Crossref]

S. R. Wilson, D. W. Reicher, C. Kranenberg, J. R. McNeil, P. L. White, P. M. Martin, and D. E. McCready, “Ion beam milling of fused silica for window fabrication,” Proc. SPIE 1441, 82–86 (1991).
[Crossref]

C. L. Carnal, C. M. Egert, and K. W. Hylton, “Advanced matrix-based algorithm for ion-beam milling of optical components,” Proc. SPIE 1752, 54–63 (1992).
[Crossref]

R. Conley, N. Bouet, J. Biancarosa, Q. Shen, L. Boas, J. Feraca, and L. Rosenbaum, “The nsls-ii multilayer laue lens deposition system,” Proc. SPIE 7448, 74480U (2009).
[Crossref]

M. Demmler, M. Zeuner, F. Allenstein, T. Dunger, M. Nestler, and S. Kiontke, “Ion beam figuring (ibf) for high precision optics,” Proc. SPIE 7591, 75910Y (2010).
[Crossref]

S. Qian and M. Idir, “Innovative nano-accuracy surface profiler for sub-50 nrad rms mirror test,” Proc. SPIE 9687, 96870D (2016).
[Crossref]

Rev. Sci. Instrum. (1)

M. Idir, L. Huang, N. Bouet, K. Kaznatcheev, M. Vescovi, K. Lauer, R. Conley, K. Rennie, J. Kahn, R. Nethery, and L. Zhou, “A one-dimensional ion beam figuring system for x-ray mirror fabrication,” Rev. Sci. Instrum. 86, 105120 (2015).
[Crossref] [PubMed]

Other (5)

A. Schindler, T. Hänsel, F. Frost, R. Fechner, A. Nickel, H.-J. Thomas, H. Neumann, and D. Hirsch, “Ion beam finishing technology for high precision optics production,” in Optical Fabrication and Testing, (Optical Society of America, 2002), p. OTuB5.
[Crossref]

S. Li and Y. Dai, Large and Middle-Scale Aperture Aspheric Surfaces: Lapping, Polishing and Measurement (John Wiley & Sons, 2017).

H. Cheng, Independent Variables for Optical Surfacing Systems (Springer, 2016).

X. Xie and S. Li, “Ion beam figuring technology,” in Handbook of Manufacturing Engineering and Technology, (SpringerLondon, 2015), pp. 1343–1390.

K. Yamauchi, H. Mimura, S. Matsuyama, H. Yumoto, T. Kimura, Y. Takahashi, K. Tamasaku, and T. Ishikawa, “Focusing mirror for coherent hard x-rays,” in Synchrotron Light Sources and Free-Electron Lasers: Accelerator Physics, Instrumentation and Science Applications, (Springer International Publishing, 2016).

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Figures (11)

Fig. 1
Fig. 1 The 1D-IBF hardware used in this study. (a) The multi-layer deposition system at NSLS-II optical metrology and fabrication group. (b) The rectangular grid installed to modify the shape of the ion beam.
Fig. 2
Fig. 2 Schematic illustration of the flow of the 1D-IBF. The BRF is only calculated once and kept invariant for the entire 1D-IBF process. Steps 1 to 5 are performed in a loop.
Fig. 3
Fig. 3 Schematic of a 1D-IBF process along the x axis, where B(x) represents the Gaussian-like BRF and R(x) is the desired removal curve.
Fig. 4
Fig. 4 Schematic of the mirror plate used in the 1D-IBF method.
Fig. 5
Fig. 5 Desired removal curve and dwell time vectors calculated by three different methods. (a) Desired removal curve. (b) Dwell time vector calculated without the inequality constraints. (c) Dwell time vector calculated with inequality constraints using b = 1. (d) Dwell time vector calculated with the coarse-to-fine scheme.
Fig. 6
Fig. 6 BRF learning results for the BRF mirror in the flat-sphere plate.
Fig. 7
Fig. 7 Mechanical Plates used to hold both the BRF mirror and the sample mirror, where A, B, O, and C are mirror edges. The scanning direction is from A to B. (a) Left: the circular flat BRF mirror; right: the circular flat sample mirror. (b) Left: the circular flat BRF mirror; right: the rectangular spherical sample mirror.
Fig. 8
Fig. 8 Results of two iterations of the 1D-IBF process on a flat sample mirror. (a) The slope errors. (b) The RMS and PV values of the slope errors. (c) The height errors. (d) The RMS and PV values of the height errors.
Fig. 9
Fig. 9 Results of two iterations of the 1D-IBF process on a spherical sample mirror. (a) The slope errors. (b) The RMS and PV values of the slope errors. (c) The height errors. (d) The RMS and PV values of the height errors.
Fig. 10
Fig. 10 Radius of curvatures of the spherical sample mirror before and after the 1D-IBF process.
Fig. 11
Fig. 11 PSD curves of the rectangular spherical sample mirror before and after the 1D-IBF process.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

R ( x ) = B ( x ) * T ( x )
R ( x ) = Z m ( x ) Z d ( x ) .
R ( x k ) = i = 0 N t 1 B ( x k ξ i ) T ( ξ i )
( r 0 r 1 r N r 1 ) r = ( b 1 , 1 b 1 , 2 b 1 , N t 1 b 1 , 1 b 2 , 2 b 2 , N t 1 b N r 1 , 1 b N r 1 , 2 b N r 1 , N t 1 ) B ( t 0 t 1 t N t 1 ) t .
Δ = m AO m fp g fp
minimize 1 2 Bt r 2 2 subject to At b t 0
A = ( 1 1 0 1 1 0 1 1 1 1 0 1 1 0 1 1 ) ,
b = ( b 0 , b 1 , , b N IBF 2 , b 0 , , b N IBF 2 )
minimize 1 2 t Ht + q t subject to At b t 0
B ( x ; a , σ , m fp ) = a exp [ ( x m fp ) 4 σ 2 ]

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