Abstract

A straightforward theoretical routine is proposed to design shadowing masks which are used for preparing uniform coatings on flat as well as strongly curved spherical substrates with large diameters in planetary rotation system. By approximating a spherical substrate in planetary rotation to a corresponding flat substrate in simple rotation around the revolution axis, the initial shape of a shadowing mask is determined. The desired uniformity for the spherical substrate is further realized through expanding appropriately the arc length of the initial shadowing mask. Utilizing the shadowing masks designed with the theoretical routine, film uniformities better than 97% are experimentally achieved for large-diameter spherical substrates with ratios of clear aperture to radius of curvature range from approximately −1.0 to 1.3.

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References

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2011 (2)

M. Gross, S. Dligatch, and A. Chtanov, “Optimization of coating uniformity in an ion beam sputtering system using a modified planetary rotation method,” Appl. Opt. 50(9), C316–C320 (2011).
[Crossref] [PubMed]

B. Sassolas, Q. Benoît, R. Flaminio, D. Forest, J. Franc, M. Galimberti, A. Lacoudre, C. Michel, J. L. Montorio, N. Morgado, and L. Pinard, “Thickness uniformity improvement for the twin mirrors used in advanced gravitational wave detectors,” Proc. SPIE 8168, 81681Q, 81681Q-8 (2011).
[Crossref]

2010 (1)

C. C. Jaing, “Designs of masks in thickness uniformity,” Proc. SPIE 7655, 76551Q, 76551Q-8 (2010).
[Crossref]

2009 (1)

2008 (2)

2006 (1)

2005 (1)

2000 (1)

1999 (1)

1996 (1)

H. H. Bauer, M. Heller, and N. Kaiser, “Optical coatings for UV photolithography systems,” Proc. SPIE 2776, 353–365 (1996).
[Crossref]

1973 (1)

1955 (1)

J. A. Dobrowolski and W. Weinstein, “Optical aspherizing by vacuum evaporation,” Nature 175(4458), 646–647 (1955).
[Crossref]

1952 (1)

L. Holland and W. Steckelmacher, “The distribution of thin films condensed on surfaces by the vacuum evaporation method,” Vacuum 2(4), 346–364 (1952).
[Crossref]

Abel-Tibérini, L.

Arkwright, J.

Ashley, E. J.

Bauer, H. H.

H. H. Bauer, M. Heller, and N. Kaiser, “Optical coatings for UV photolithography systems,” Proc. SPIE 2776, 353–365 (1996).
[Crossref]

Bennett, J. M.

Benoît, Q.

B. Sassolas, Q. Benoît, R. Flaminio, D. Forest, J. Franc, M. Galimberti, A. Lacoudre, C. Michel, J. L. Montorio, N. Morgado, and L. Pinard, “Thickness uniformity improvement for the twin mirrors used in advanced gravitational wave detectors,” Proc. SPIE 8168, 81681Q, 81681Q-8 (2011).
[Crossref]

Chtanov, A.

Dligatch, S.

Dobrowolski, J. A.

J. A. Dobrowolski and W. Weinstein, “Optical aspherizing by vacuum evaporation,” Nature 175(4458), 646–647 (1955).
[Crossref]

Flaminio, R.

B. Sassolas, Q. Benoît, R. Flaminio, D. Forest, J. Franc, M. Galimberti, A. Lacoudre, C. Michel, J. L. Montorio, N. Morgado, and L. Pinard, “Thickness uniformity improvement for the twin mirrors used in advanced gravitational wave detectors,” Proc. SPIE 8168, 81681Q, 81681Q-8 (2011).
[Crossref]

B. Sassolas, R. Flaminio, J. Franc, C. Michel, J.-L. Montorio, N. Morgado, and L. Pinard, “Masking technique for coating thickness control on large and strongly curved aspherical optics,” Appl. Opt. 48(19), 3760–3765 (2009).
[Crossref] [PubMed]

Forest, D.

B. Sassolas, Q. Benoît, R. Flaminio, D. Forest, J. Franc, M. Galimberti, A. Lacoudre, C. Michel, J. L. Montorio, N. Morgado, and L. Pinard, “Thickness uniformity improvement for the twin mirrors used in advanced gravitational wave detectors,” Proc. SPIE 8168, 81681Q, 81681Q-8 (2011).
[Crossref]

Franc, J.

B. Sassolas, Q. Benoît, R. Flaminio, D. Forest, J. Franc, M. Galimberti, A. Lacoudre, C. Michel, J. L. Montorio, N. Morgado, and L. Pinard, “Thickness uniformity improvement for the twin mirrors used in advanced gravitational wave detectors,” Proc. SPIE 8168, 81681Q, 81681Q-8 (2011).
[Crossref]

B. Sassolas, R. Flaminio, J. Franc, C. Michel, J.-L. Montorio, N. Morgado, and L. Pinard, “Masking technique for coating thickness control on large and strongly curved aspherical optics,” Appl. Opt. 48(19), 3760–3765 (2009).
[Crossref] [PubMed]

Galimberti, M.

B. Sassolas, Q. Benoît, R. Flaminio, D. Forest, J. Franc, M. Galimberti, A. Lacoudre, C. Michel, J. L. Montorio, N. Morgado, and L. Pinard, “Thickness uniformity improvement for the twin mirrors used in advanced gravitational wave detectors,” Proc. SPIE 8168, 81681Q, 81681Q-8 (2011).
[Crossref]

Gross, M.

Heller, M.

H. H. Bauer, M. Heller, and N. Kaiser, “Optical coatings for UV photolithography systems,” Proc. SPIE 2776, 353–365 (1996).
[Crossref]

Holland, L.

L. Holland and W. Steckelmacher, “The distribution of thin films condensed on surfaces by the vacuum evaporation method,” Vacuum 2(4), 346–364 (1952).
[Crossref]

Jaing, C. C.

C. C. Jaing, “Designs of masks in thickness uniformity,” Proc. SPIE 7655, 76551Q, 76551Q-8 (2010).
[Crossref]

Kaiser, N.

H. H. Bauer, M. Heller, and N. Kaiser, “Optical coatings for UV photolithography systems,” Proc. SPIE 2776, 353–365 (1996).
[Crossref]

Kelkar, P.

P. Kelkar, B. Tirri, R. Wilklow, and D. Peterson, “Deposition and characterization of challenging DUV coatings,” Proc. SPIE 7606, 706708, 706708-8 (2008).
[Crossref]

Lacoudre, A.

B. Sassolas, Q. Benoît, R. Flaminio, D. Forest, J. Franc, M. Galimberti, A. Lacoudre, C. Michel, J. L. Montorio, N. Morgado, and L. Pinard, “Thickness uniformity improvement for the twin mirrors used in advanced gravitational wave detectors,” Proc. SPIE 8168, 81681Q, 81681Q-8 (2011).
[Crossref]

Lemarquis, F.

Lequime, M.

Martínez, A.

Michel, C.

B. Sassolas, Q. Benoît, R. Flaminio, D. Forest, J. Franc, M. Galimberti, A. Lacoudre, C. Michel, J. L. Montorio, N. Morgado, and L. Pinard, “Thickness uniformity improvement for the twin mirrors used in advanced gravitational wave detectors,” Proc. SPIE 8168, 81681Q, 81681Q-8 (2011).
[Crossref]

B. Sassolas, R. Flaminio, J. Franc, C. Michel, J.-L. Montorio, N. Morgado, and L. Pinard, “Masking technique for coating thickness control on large and strongly curved aspherical optics,” Appl. Opt. 48(19), 3760–3765 (2009).
[Crossref] [PubMed]

Montorio, J. L.

B. Sassolas, Q. Benoît, R. Flaminio, D. Forest, J. Franc, M. Galimberti, A. Lacoudre, C. Michel, J. L. Montorio, N. Morgado, and L. Pinard, “Thickness uniformity improvement for the twin mirrors used in advanced gravitational wave detectors,” Proc. SPIE 8168, 81681Q, 81681Q-8 (2011).
[Crossref]

Montorio, J.-L.

Morgado, N.

B. Sassolas, Q. Benoît, R. Flaminio, D. Forest, J. Franc, M. Galimberti, A. Lacoudre, C. Michel, J. L. Montorio, N. Morgado, and L. Pinard, “Thickness uniformity improvement for the twin mirrors used in advanced gravitational wave detectors,” Proc. SPIE 8168, 81681Q, 81681Q-8 (2011).
[Crossref]

B. Sassolas, R. Flaminio, J. Franc, C. Michel, J.-L. Montorio, N. Morgado, and L. Pinard, “Masking technique for coating thickness control on large and strongly curved aspherical optics,” Appl. Opt. 48(19), 3760–3765 (2009).
[Crossref] [PubMed]

Oliver, J. B.

Pereira, N.

Peterson, D.

P. Kelkar, B. Tirri, R. Wilklow, and D. Peterson, “Deposition and characterization of challenging DUV coatings,” Proc. SPIE 7606, 706708, 706708-8 (2008).
[Crossref]

Pinard, L.

B. Sassolas, Q. Benoît, R. Flaminio, D. Forest, J. Franc, M. Galimberti, A. Lacoudre, C. Michel, J. L. Montorio, N. Morgado, and L. Pinard, “Thickness uniformity improvement for the twin mirrors used in advanced gravitational wave detectors,” Proc. SPIE 8168, 81681Q, 81681Q-8 (2011).
[Crossref]

B. Sassolas, R. Flaminio, J. Franc, C. Michel, J.-L. Montorio, N. Morgado, and L. Pinard, “Masking technique for coating thickness control on large and strongly curved aspherical optics,” Appl. Opt. 48(19), 3760–3765 (2009).
[Crossref] [PubMed]

Pompa, O.

Regalado, L. E.

Sassolas, B.

B. Sassolas, Q. Benoît, R. Flaminio, D. Forest, J. Franc, M. Galimberti, A. Lacoudre, C. Michel, J. L. Montorio, N. Morgado, and L. Pinard, “Thickness uniformity improvement for the twin mirrors used in advanced gravitational wave detectors,” Proc. SPIE 8168, 81681Q, 81681Q-8 (2011).
[Crossref]

B. Sassolas, R. Flaminio, J. Franc, C. Michel, J.-L. Montorio, N. Morgado, and L. Pinard, “Masking technique for coating thickness control on large and strongly curved aspherical optics,” Appl. Opt. 48(19), 3760–3765 (2009).
[Crossref] [PubMed]

Steckelmacher, W.

L. Holland and W. Steckelmacher, “The distribution of thin films condensed on surfaces by the vacuum evaporation method,” Vacuum 2(4), 346–364 (1952).
[Crossref]

Talbot, D.

Tirri, B.

P. Kelkar, B. Tirri, R. Wilklow, and D. Peterson, “Deposition and characterization of challenging DUV coatings,” Proc. SPIE 7606, 706708, 706708-8 (2008).
[Crossref]

Underhill, I.

Villa, F.

Weinstein, W.

J. A. Dobrowolski and W. Weinstein, “Optical aspherizing by vacuum evaporation,” Nature 175(4458), 646–647 (1955).
[Crossref]

Wilklow, R.

P. Kelkar, B. Tirri, R. Wilklow, and D. Peterson, “Deposition and characterization of challenging DUV coatings,” Proc. SPIE 7606, 706708, 706708-8 (2008).
[Crossref]

Appl. Opt. (7)

Nature (1)

J. A. Dobrowolski and W. Weinstein, “Optical aspherizing by vacuum evaporation,” Nature 175(4458), 646–647 (1955).
[Crossref]

Opt. Express (1)

Proc. SPIE (4)

C. C. Jaing, “Designs of masks in thickness uniformity,” Proc. SPIE 7655, 76551Q, 76551Q-8 (2010).
[Crossref]

B. Sassolas, Q. Benoît, R. Flaminio, D. Forest, J. Franc, M. Galimberti, A. Lacoudre, C. Michel, J. L. Montorio, N. Morgado, and L. Pinard, “Thickness uniformity improvement for the twin mirrors used in advanced gravitational wave detectors,” Proc. SPIE 8168, 81681Q, 81681Q-8 (2011).
[Crossref]

H. H. Bauer, M. Heller, and N. Kaiser, “Optical coatings for UV photolithography systems,” Proc. SPIE 2776, 353–365 (1996).
[Crossref]

P. Kelkar, B. Tirri, R. Wilklow, and D. Peterson, “Deposition and characterization of challenging DUV coatings,” Proc. SPIE 7606, 706708, 706708-8 (2008).
[Crossref]

Vacuum (1)

L. Holland and W. Steckelmacher, “The distribution of thin films condensed on surfaces by the vacuum evaporation method,” Vacuum 2(4), 346–364 (1952).
[Crossref]

Other (1)

H. A. Macleod, Thin-film Optical Filters (Academic Press, New York, 2001).

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Figures (5)

Fig. 1
Fig. 1

Configuration for coating deposition on a spherical substrate in a planetary rotation system. The evaporation source locates exactly below the revolution orbital.

Fig. 2
Fig. 2

Determination of the factor κ for correcting film thickness uniformity on center and rim positions of a substrate.

Fig. 3
Fig. 3

(a) Photo of one panel of the shadowing mask for a flat substrate with CA = 400mm. (b) Simulated two-dimensional film thickness distribution and (c) experimental radial film thickness profile with the uniformity corrected by the designed shadowing mask.

Fig. 4
Fig. 4

Simulated two-dimensional film thickness distributions on (a) convex substrate with CA = 240mm, RoC = 200mm and (b) concave substrate with CA = 160mm, RoC = −170mm. (c) Thickness uniformity without (red dots) and with (black squares) uniformity correction by shadowing masks for substrates with CA≈200mm and different CA/RoC ratios. Minus sign denotes concave substrates.

Fig. 5
Fig. 5

Transmittances of DUV antireflective coating on a convex spherical lens substrate, measured at four positions indicated in the inset.

Equations (11)

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R=A cosθ cos n ψ | r | 2 ,
| r |= ρ ' 2 +h ' 2 ,
θ=πacos( | r | 2 +Ro C 2 r ' 2 2| r |×RoC ),
ψ=arcsin( ρ' / | r | ),
x(t)=ρcos( ϖ 1 t)+δcos( ϖ 2 t+ϕ),
y(t)=ρsin( ϖ 1 t)+δsin( ϖ 2 t+ϕ),
z(t)= Ro C 2 C A 2 /4 Ro C 2 δ 2 ,
l=d×2π (T T 0 ) T ,
l=κ×d×2π (T T 0 ) T .
Tl× T 2πρ = T 0 1 2 lCA× T 0 2πρCA .
κ= 1 1 T 0 /2T .

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