Abstract

In a deterministic figuring process, it is critical to guarantee high stability of the removal function as well as the accuracy of the dwell time solution, which directly influence the convergence of the figuring process. Hence, when figuring steep optics, the ion beam is required to keep a perpendicular incidence, and a five-axis figuring machine is typically utilized. In this paper, however, a method for high-precision figuring of high-slope optics is proposed with a linear three-axis machine, allowing for inclined beam incidence. First, the changing rule of the removal function and the normal removal rate with the incidence angle is analyzed according to the removal characteristics of ion beam figuring (IBF). Then, we propose to reduce the influence of varying removal function and projection distortion on the dwell time solution by means of figure error compensation. Consequently, the incident ion beam is allowed to keep parallel to the optical axis. Simulations and experiments are given to verify the removal analysis. Finally, a figuring experiment is conducted on a linear three-axis IBF machine, which proves the validity of the method for high-slope surfaces. It takes two iterations and about 9 min to successfully figure a fused silica sample, whose aperture is 21.3 mm and radius of curvature is 16 mm. The root-mean-square figure error of the convex surface is reduced from 13.13 to 5.86 nm.

© 2010 Optical Society of America

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References

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  1. T. W. Drueding, T. G. Bifano, and S. C. Fawcett, “Contouring algorithm for ion figuring,” Precis. Eng. 17, 10–21 (1995).
    [CrossRef]
  2. L. N. Allen and H. W. Romig, “Demonstration of an ion figuring process,” Proc. SPIE 1333, 22–23 (1990).
    [CrossRef]
  3. L. N. Allen, “Progress in ion figuring large optics,” Proc. SPIE 2428, 237–247 (1995).
    [CrossRef]
  4. L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Machining reachability in ion beam figuring,” Opt. Precis. Eng. 15, 160–166 (2001).
  5. C. Jiao, S. Li, X. Xie, L. Zhou, and W. Duan, “Bayesian principle based dwell time algorithm for ion beam figuring of low gradient mirrors,” J. Mech. Eng. Lab. 45, 253–259 (2009).
    [CrossRef]
  6. T. Haensel, A. Nickel, and A. Schindler, “Ion beam figuring of strongly curved surfaces with a (x,y,z) linear three-axes system,” in Plasmonics and Metamaterials, OSA Technical Digest (CD) (Optical Society of America, 2008), paper JWD6.
  7. R. A. Jones and W. J. Rupp, “Rapid optical fabrication with CCOS,” Proc. SPIE 1333, 34–43 (1990).
    [CrossRef]
  8. A. Schindler, T. Hänsel, F. Frost, R. Fechner, A. Nickel, H. Thomas, H. Neumann, and D. Hirsch, “Ion beam finishing technology for high precision optics production,” in Optical Fabrication and Testing, Vol. 76 of OSA Trends in Optics and Photonics, A.Sawchuk, ed. (2002), paper OTuB5.
  9. P. Sigmund, “A mechanism of surface micro-roughening by ion bombardment,” J. Mater. Sci. Technol. (Sofia) 8, 1545–1553(1973).
  10. 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]
  11. “Particle Interactions with Matter,” http://www.srim.org.
  12. L. Zhou, “Study on theory and technology in ion beam figuring for optical surfaces,” Ph.D. dissertation (National University of Defense Technology, 2008), in Chinese.

2009

C. Jiao, S. Li, X. Xie, L. Zhou, and W. Duan, “Bayesian principle based dwell time algorithm for ion beam figuring of low gradient mirrors,” J. Mech. Eng. Lab. 45, 253–259 (2009).
[CrossRef]

2001

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Machining reachability in ion beam figuring,” Opt. Precis. Eng. 15, 160–166 (2001).

1995

L. N. Allen, “Progress in ion figuring large optics,” Proc. SPIE 2428, 237–247 (1995).
[CrossRef]

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

1990

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

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]

1973

P. Sigmund, “A mechanism of surface micro-roughening by ion bombardment,” J. Mater. Sci. Technol. (Sofia) 8, 1545–1553(1973).

Allen, L. N.

L. N. Allen, “Progress in ion figuring large optics,” Proc. SPIE 2428, 237–247 (1995).
[CrossRef]

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

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]

Dai, Y.

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Machining reachability in ion beam figuring,” Opt. Precis. Eng. 15, 160–166 (2001).

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]

Duan, W.

C. Jiao, S. Li, X. Xie, L. Zhou, and W. Duan, “Bayesian principle based dwell time algorithm for ion beam figuring of low gradient mirrors,” J. Mech. Eng. Lab. 45, 253–259 (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.

A. Schindler, T. Hänsel, F. Frost, R. Fechner, A. Nickel, H. Thomas, H. Neumann, and D. Hirsch, “Ion beam finishing technology for high precision optics production,” in Optical Fabrication and Testing, Vol. 76 of OSA Trends in Optics and Photonics, A.Sawchuk, ed. (2002), paper OTuB5.

Frost, F.

A. Schindler, T. Hänsel, F. Frost, R. Fechner, A. Nickel, H. Thomas, H. Neumann, and D. Hirsch, “Ion beam finishing technology for high precision optics production,” in Optical Fabrication and Testing, Vol. 76 of OSA Trends in Optics and Photonics, A.Sawchuk, ed. (2002), paper OTuB5.

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 Plasmonics and Metamaterials, OSA Technical Digest (CD) (Optical Society of America, 2008), paper JWD6.

Hänsel, T.

A. Schindler, T. Hänsel, F. Frost, R. Fechner, A. Nickel, H. Thomas, H. Neumann, and D. Hirsch, “Ion beam finishing technology for high precision optics production,” in Optical Fabrication and Testing, Vol. 76 of OSA Trends in Optics and Photonics, A.Sawchuk, ed. (2002), paper OTuB5.

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]

Hirsch, D.

A. Schindler, T. Hänsel, F. Frost, R. Fechner, A. Nickel, H. Thomas, H. Neumann, and D. Hirsch, “Ion beam finishing technology for high precision optics production,” in Optical Fabrication and Testing, Vol. 76 of OSA Trends in Optics and Photonics, A.Sawchuk, ed. (2002), paper OTuB5.

Jiao, C.

C. Jiao, S. Li, X. Xie, L. Zhou, and W. Duan, “Bayesian principle based dwell time algorithm for ion beam figuring of low gradient mirrors,” J. Mech. Eng. Lab. 45, 253–259 (2009).
[CrossRef]

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Machining reachability in ion beam figuring,” Opt. Precis. Eng. 15, 160–166 (2001).

Jones, R. A.

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

Li, S.

C. Jiao, S. Li, X. Xie, L. Zhou, and W. Duan, “Bayesian principle based dwell time algorithm for ion beam figuring of low gradient mirrors,” J. Mech. Eng. Lab. 45, 253–259 (2009).
[CrossRef]

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Machining reachability in ion beam figuring,” Opt. Precis. Eng. 15, 160–166 (2001).

Neumann, H.

A. Schindler, T. Hänsel, F. Frost, R. Fechner, A. Nickel, H. Thomas, H. Neumann, and D. Hirsch, “Ion beam finishing technology for high precision optics production,” in Optical Fabrication and Testing, Vol. 76 of OSA Trends in Optics and Photonics, A.Sawchuk, ed. (2002), paper OTuB5.

Nickel, A.

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

A. Schindler, T. Hänsel, F. Frost, R. Fechner, A. Nickel, H. Thomas, H. Neumann, and D. Hirsch, “Ion beam finishing technology for high precision optics production,” in Optical Fabrication and Testing, Vol. 76 of OSA Trends in Optics and Photonics, A.Sawchuk, ed. (2002), paper OTuB5.

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.

A. Schindler, T. Hänsel, F. Frost, R. Fechner, A. Nickel, H. Thomas, H. Neumann, and D. Hirsch, “Ion beam finishing technology for high precision optics production,” in Optical Fabrication and Testing, Vol. 76 of OSA Trends in Optics and Photonics, A.Sawchuk, ed. (2002), paper OTuB5.

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

Sigmund, P.

P. Sigmund, “A mechanism of surface micro-roughening by ion bombardment,” J. Mater. Sci. Technol. (Sofia) 8, 1545–1553(1973).

Thomas, H.

A. Schindler, T. Hänsel, F. Frost, R. Fechner, A. Nickel, H. Thomas, H. Neumann, and D. Hirsch, “Ion beam finishing technology for high precision optics production,” in Optical Fabrication and Testing, Vol. 76 of OSA Trends in Optics and Photonics, A.Sawchuk, ed. (2002), paper OTuB5.

Xie, X.

C. Jiao, S. Li, X. Xie, L. Zhou, and W. Duan, “Bayesian principle based dwell time algorithm for ion beam figuring of low gradient mirrors,” J. Mech. Eng. Lab. 45, 253–259 (2009).
[CrossRef]

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Machining reachability in ion beam figuring,” Opt. Precis. Eng. 15, 160–166 (2001).

Zhou, L.

C. Jiao, S. Li, X. Xie, L. Zhou, and W. Duan, “Bayesian principle based dwell time algorithm for ion beam figuring of low gradient mirrors,” J. Mech. Eng. Lab. 45, 253–259 (2009).
[CrossRef]

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Machining reachability in ion beam figuring,” Opt. Precis. Eng. 15, 160–166 (2001).

L. Zhou, “Study on theory and technology in ion beam figuring for optical surfaces,” Ph.D. dissertation (National University of Defense Technology, 2008), in Chinese.

J. Mater. Sci. Technol. (Sofia)

P. Sigmund, “A mechanism of surface micro-roughening by ion bombardment,” J. Mater. Sci. Technol. (Sofia) 8, 1545–1553(1973).

J. Mech. Eng. Lab.

C. Jiao, S. Li, X. Xie, L. Zhou, and W. Duan, “Bayesian principle based dwell time algorithm for ion beam figuring of low gradient mirrors,” J. Mech. Eng. Lab. 45, 253–259 (2009).
[CrossRef]

J. Vac. Sci. Technol. A

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]

Opt. Precis. Eng.

L. Zhou, Y. Dai, X. Xie, C. Jiao, and S. Li, “Machining reachability in ion beam figuring,” Opt. Precis. Eng. 15, 160–166 (2001).

Precis. Eng.

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

Proc. SPIE

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

L. N. Allen, “Progress in ion figuring large optics,” Proc. SPIE 2428, 237–247 (1995).
[CrossRef]

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

Other

A. Schindler, T. Hänsel, F. Frost, R. Fechner, A. Nickel, H. Thomas, H. Neumann, and D. Hirsch, “Ion beam finishing technology for high precision optics production,” in Optical Fabrication and Testing, Vol. 76 of OSA Trends in Optics and Photonics, A.Sawchuk, ed. (2002), paper OTuB5.

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

“Particle Interactions with Matter,” http://www.srim.org.

L. Zhou, “Study on theory and technology in ion beam figuring for optical surfaces,” Ph.D. dissertation (National University of Defense Technology, 2008), in Chinese.

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Figures (9)

Fig. 1
Fig. 1

Process of figuring a flat surface with a raster scanning mode.

Fig. 2
Fig. 2

IBF of a high-slope surface along the optical axis.

Fig. 3
Fig. 3

Ion beam bombarding the surface at angle θ.

Fig. 4
Fig. 4

Theoretical and experimental curves of the removal rate.

Fig. 5
Fig. 5

Removal result by linearly scanning a spherical surface.

Fig. 6
Fig. 6

Material removed in the linear scanning experiment.

Fig. 7
Fig. 7

Removal function diameter estimated by (a) the 6 σ method and (b) the FWHM.

Fig. 8
Fig. 8

Surface error: (a) original figure error, (b) distribution of normalized peak removal rate, (c) compensated figure error.

Fig. 9
Fig. 9

Figuring results of a high-slope optical surface after (a) the first iteration and (b) the second iteration.

Equations (15)

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

E ( x , y ) = R ( x , y ) * T ( x , y ) = R ( x x , y y ) T ( x , y ) d x d y .
E ( x , y ) = i = 0 j = 0 R ( x x i , y y j ) T ( x i , y j ) Δ x Δ y + ξ ,
K i j = R θ i j R i j ,
R θ i j = R θ ( x x i , y y j ) , R i j = R ( x x i , y y j ) ,
E ( x , y ) = i = 0 j = 0 K i j R ( x x i , y y j ) T ( x j , y j ) Δ x Δ y + ξ .
R ( θ , c 1 , c 2 ) = ( f / n ) Y 0 ( θ ) [ cos θ Γ 1 ( θ ) c 1 Γ 2 ( θ ) c 2 ] ,
Y 0 ( θ ) = p ε n α 2 π σ μ exp ( α 2 2 σ 2 ) B 1 1 / 2 ( θ ) exp ( A 2 ( θ ) 2 B 1 ( θ ) ) ,
Γ 1 ( θ ) = A ( θ ) B 1 ( θ ) sin θ B 2 ( θ ) 2 B 1 ( θ ) ( 1 + A 2 ( θ ) B 1 ( θ ) ) cos θ A ( θ ) C ( θ ) B 1 2 ( θ ) ( 3 + A 2 ( θ ) B 1 ( θ ) ) cos θ , Γ 2 ( θ ) = μ 2 a 2 cos θ ( 1 2 B 2 ( θ ) + A ( θ ) C ( θ ) B 1 ( θ ) ) , A ( θ ) = ( a σ ) 2 sin θ , B 1 ( θ ) = ( a σ ) 2 sin 2 θ + ( a μ ) 2 cos 2 θ , B 2 ( θ ) = ( a σ ) 2 cos θ , C ( θ ) = 1 2 [ ( a μ ) 2 ( a σ ) 2 ] sin θ cos θ ,
{ c 1 = α / r 0 x = α 2 h x 2 ( 0 ) c 2 = α / r 0 y = α 2 h y 2 ( 0 ) ,
R ( θ ) = ( f / n ) Y 0 ( θ ) cos θ .
K i j ( θ ) = R i j ( θ ) R i j .
E ( x , y ) = K ( x , y ) i = 0 j = 0 R ( x x i , y y j ) T ( x i , y j ) Δ x Δ y + ξ .
E ( x , y ) = i = 0 j = 0 R ( x x i , y y j ) T ( x i , y j ) Δ x Δ y + ξ ,
R ( x , y ) = ( 1 / n ) Y 0 ( θ ) cos θ f ( x cos θ , y ) .
R ( x , y ) = K θ R 0 f ( x cos θ , y ) .

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