Abstract

In an effort to optimize the hydrodynamic radial (HyDRa) polishing process for applications where the amount of material that has to be removed implies long polishing times, we have developed a method to determine the optimum correction fraction that has to be made for a given error map, in terms of the level of determinism of the process, the number of iterations, and their associated polishing runs as well as run times.

© 2013 Optical Society of America

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References

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  1. L. N. Allen, R. E. Keim, T. S. Lewis, and J. R. Ullom, “Surface error correction of a Keck 10-m telescope primary mirror segment by ion figuring,” Proc. SPIE 1531, 195–204 (1992).
    [CrossRef]
  2. 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. A 616, 147–156 (2010).
    [CrossRef]
  3. D. D. Walker, D. Brooks, A. King, R. Freeman, R. Morton, G. McCavana, and S. W. Kim, “The precessions tooling for polishing and figuring flat, spherical and aspheric surfaces,” Opt. Express 11, 958–964 (2003).
    [CrossRef]
  4. H. M. Pollicove, E. M. Fess, and J. M. Schoen, “Deterministic manufacturing processes for precision optical surfaces,” Proc. SPIE 5078, 90–96 (2003).
    [CrossRef]
  5. D. W. Kim and J. H. Burge, “Rigid conformal polishing tool using non-linear visco-elastic effect,” Opt. Express 18, 2242–2257 (2010).
    [CrossRef]
  6. E. Ruiz, E. Sohn, L. Salas, and E. Luna, “Hydrodynamic radial flux tool for polishing and grinding optical and semiconductor surfaces,” U.S. patent7,169,012 (30January2007).
  7. E. Sohn, E. Ruiz, L. Salas, E. Luna, and J. Herrera, “HyDRa: polishing with a vortex,” Appl. Opt. 52, 6146–6152 (2013).
    [CrossRef]
  8. E. Ruiz, L. Salas, E. Sohn, E. Luna, J. Herrera, and F. Quiros, “HyDRa: control of parameters for deterministic polishing,” Opt. Express 21, 20334–20345 (2013).
    [CrossRef]

2013 (2)

2010 (2)

D. W. Kim and J. H. Burge, “Rigid conformal polishing tool using non-linear visco-elastic effect,” Opt. Express 18, 2242–2257 (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. A 616, 147–156 (2010).
[CrossRef]

2003 (2)

D. D. Walker, D. Brooks, A. King, R. Freeman, R. Morton, G. McCavana, and S. W. Kim, “The precessions tooling for polishing and figuring flat, spherical and aspheric surfaces,” Opt. Express 11, 958–964 (2003).
[CrossRef]

H. M. Pollicove, E. M. Fess, and J. M. Schoen, “Deterministic manufacturing processes for precision optical surfaces,” Proc. SPIE 5078, 90–96 (2003).
[CrossRef]

1992 (1)

L. N. Allen, R. E. Keim, T. S. Lewis, and J. R. Ullom, “Surface error correction of a Keck 10-m telescope primary mirror segment by ion figuring,” Proc. SPIE 1531, 195–204 (1992).
[CrossRef]

Allen, L. N.

L. N. Allen, R. E. Keim, T. S. Lewis, and J. R. Ullom, “Surface error correction of a Keck 10-m telescope primary mirror segment by ion figuring,” Proc. SPIE 1531, 195–204 (1992).
[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. A 616, 147–156 (2010).
[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. A 616, 147–156 (2010).
[CrossRef]

Brooks, D.

Burge, J. H.

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. A 616, 147–156 (2010).
[CrossRef]

Fess, E. M.

H. M. Pollicove, E. M. Fess, and J. M. Schoen, “Deterministic manufacturing processes for precision optical surfaces,” Proc. SPIE 5078, 90–96 (2003).
[CrossRef]

Freeman, R.

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. A 616, 147–156 (2010).
[CrossRef]

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. A 616, 147–156 (2010).
[CrossRef]

Herrera, J.

Keim, R. E.

L. N. Allen, R. E. Keim, T. S. Lewis, and J. R. Ullom, “Surface error correction of a Keck 10-m telescope primary mirror segment by ion figuring,” Proc. SPIE 1531, 195–204 (1992).
[CrossRef]

Kim, D. W.

Kim, S. W.

King, A.

Lewis, T. S.

L. N. Allen, R. E. Keim, T. S. Lewis, and J. R. Ullom, “Surface error correction of a Keck 10-m telescope primary mirror segment by ion figuring,” Proc. SPIE 1531, 195–204 (1992).
[CrossRef]

Luna, E.

McCavana, G.

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. A 616, 147–156 (2010).
[CrossRef]

Morton, R.

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. A 616, 147–156 (2010).
[CrossRef]

Pollicove, H. M.

H. M. Pollicove, E. M. Fess, and J. M. Schoen, “Deterministic manufacturing processes for precision optical surfaces,” Proc. SPIE 5078, 90–96 (2003).
[CrossRef]

Quiros, F.

Ruiz, E.

Salas, L.

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. A 616, 147–156 (2010).
[CrossRef]

Schoen, J. M.

H. M. Pollicove, E. M. Fess, and J. M. Schoen, “Deterministic manufacturing processes for precision optical surfaces,” Proc. SPIE 5078, 90–96 (2003).
[CrossRef]

Sohn, E.

Ullom, J. R.

L. N. Allen, R. E. Keim, T. S. Lewis, and J. R. Ullom, “Surface error correction of a Keck 10-m telescope primary mirror segment by ion figuring,” Proc. SPIE 1531, 195–204 (1992).
[CrossRef]

Walker, D. D.

Appl. Opt. (1)

Nucl. Instrum. Methods Phys. Res. 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. A 616, 147–156 (2010).
[CrossRef]

Opt. Express (3)

Proc. SPIE (2)

L. N. Allen, R. E. Keim, T. S. Lewis, and J. R. Ullom, “Surface error correction of a Keck 10-m telescope primary mirror segment by ion figuring,” Proc. SPIE 1531, 195–204 (1992).
[CrossRef]

H. M. Pollicove, E. M. Fess, and J. M. Schoen, “Deterministic manufacturing processes for precision optical surfaces,” Proc. SPIE 5078, 90–96 (2003).
[CrossRef]

Other (1)

E. Ruiz, E. Sohn, L. Salas, and E. Luna, “Hydrodynamic radial flux tool for polishing and grinding optical and semiconductor surfaces,” U.S. patent7,169,012 (30January2007).

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Figures (1)

Fig. 1.
Fig. 1.

Total surface error as a function of the number of polishing runs. Diamonds mark the intermediate iterations for surface reevaluation and lines represent eT according to Eq. (4).

Tables (1)

Tables Icon

Table 1. Summarized Polishing and Optimization Data

Equations (11)

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hmin=DV/VmaxS,
r(x,y)=f*e(x,y)+hmin.
r(x,y)dxdy=Vr,
en(x,y)=(1Nf)e(x,y)+k,
e(x,y)21/2=((e(x,y)e)2dxdy)1/2/(dxdy)1/2,
en(x,y)21/2=(1Nf)e(x,y)21/2,
δ(Nr)=NΔ(fe+hmin).
eT2=en2+δ(Nr)2.
Nmin=fe2f2e2+Δ2f2e2+2Δ2fhmine+Δ2hmin2,
e21/2Δ(fe+hmin)f(1f),
f=11+Δ2(e2/e2),

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