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.

© 2012 OSA

1. Introduction

Controlling thickness uniformity of optical thin films on large and/or strongly curved substrates is of great importance to fabrication of coated optical components widely used in large-aperture and/or high numerical-aperture (high-NA) optical systems [1, 2]. Many methods have been developed in the past to enhance film thickness uniformity. Among them the most widely adopted is employing simple or planetary rotation stages. Meanwhile, precisely shaped shadowing masks are applied not only to improve the film thickness uniformity but sometimes also to achieve specified thickness profiles [313]. Conventionally, shadowing masks are manufactured via time-consuming trial-and-error approach. Recently, increasing interests have been focused on the application of physical deposition theory to investigate film thickness distribution and theoretical design of shadowing masks. Mask design method on simple rotation stages (SRS) has been well developed benefiting from the simple rotation manner of the substrate holders. For instance, Villa et al. [9] designed shadowing masks used for large area coating on flat, cylindrical, spherical and conical substrates, while Jaing [10] demonstrated the dependence of the shadowing mask shape on the emissive pattern of the evaporation source. Comparatively on planetary rotation stages (PRS) substrates execute not only revolution around the center of the plant but also rotation around the center of the planets. Hence the relationship between the profile of the film thickness and the desired shape of shadowing mask in PRS is not as obvious as in SRS, and it becomes more difficult in developing simple and efficient mask design theory. So far, Bauer et al. [12] realized design of shadowing mask in PRS by changing mask shape with iterative Monte Carlo method. Meanwhile, a purely mathematic method was promoted, which, however, involved complex analysis on trace of the substrates. In this paper we demonstrated a simple and straightforward routine for theoretically designing shadowing masks used to prepare uniform coatings on spherical substrates in a standard PRS. Experimentally good film uniformities have been achieved for spherical substrates with large ratios of clear aperture to radius of curvature.

2. Experiment

The shadowing mask design routine proposed in this paper was checked with optical coatings prepared with a commercially available coating plant from Leybold Optics (SYRUSpro 1110 DUV). In the coating plant, a PRS carrying four substrate holders is implemented in an 1100mm-diameter vacuum chamber. Geometry of the coating plant is schematically illustrated in Fig. 1 . The vertical distance (h) between the evaporation source and the substrate holders is 700mm, and the radius (ρ) of the planet orbital is 300mm. The substrates were placed at the center of the substrate holders. During revolution the holders kept parallel to the source plane. Small-area evaporation sources are located vertically below the planet orbital and shadowing masks are positioned 10mm in the front of (below) the lowest point of the substrate surface. For the determination of the film uniformity on spherical substrates, jigs of the same shape as spherical substrates were prepared with evenly distributed Φ25mm holes along the radical direction for placement of flat substrates with 25mm in diameter. Film thicknesses at corresponding positions on the spherical substrate were represented by the thicknesses of the films deposited on the 25mm-diameter substrates. In our experiment MgF2 was used as coating material and 25mm-diameter silicon plates were used as deposition substrates for film thickness distribution determination. Reflection spectrum of each coated silicon plate was measured with Perkin Elmer Lambda 1050 spectrophotometer. It is revealed that MgF2 film thickness determined via spectroscopic ellipsometry (SE) is approximately linearly proportional to the wavelength value in 400–700 nm range at which the reflectance extrema occur. Accordingly film uniformity on a spherical substrate was obtained from the wavelength shifts or wavelength values corresponding to the reflectance extrema. Deep ultra-violet (DUV) antireflective (AR) coating, centered at 193nm, was prepared by deposition LaF3/MgF2 multilayer on 25mm-diameter DUV-grade fused silica substrates at temperature of 250°C. The design was [MgF2 15.8nm/LaF3 28.12nm/MgF2 36.68nm]. In the experiments, MgF2 was evaporated by electron beam gun while LaF3 was evaporated by molybdenum boat. The run-to-run repeatability of the film thickness uniformity for both materials was above 99.5%. Before transmission measurements with Lambda 1050 spectrophotometer, AR-coated fused silica substrates were treated with ultra-violet radiation for ten minutes for hydrocarbon contamination removal. Ultra-violet radiation at wavelengths of 254nm and 185nm was provided by ten mercury lamps in a commercial UVO cleaner, with 20W power for each lamp.

 

Fig. 1 Configuration for coating deposition on a spherical substrate in a planetary rotation system. The evaporation source locates exactly below the revolution orbital.

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3. Theory

Theory on the film thickness distribution is based on appropriate modeling of the evaporation source as well as an assumption that emitted molecules from the evaporation source behave similarly as illumination [1]. For physical vapor deposition (PVD) by evaporation from small-area source, emissive pattern of the evaporation source is characterized by cosnψ [14, 15], where ψ denotes the angle between the normal to the source surface and the emission direction, n is a real number with its value influenced by the source material and the deposition technique. For configuration shown in Fig. 1, the rate of film deposition onto surface element dS of the substrate is expressed as

R=Acosθcosnψ|r|2,
where r (denoted by r in Fig. 1) represents the vector from the source to element dS, θ is the angle between rand the normal to dS, and A is a constant. For the configuration of the coating plant used in the experiment, θ equals to ψ if substrate surface is flat. For a convex spherical surface with center denoted by O, radius of curvature by RoC and clear aperture by CA, the parameters in Eq. (1) are presented as
|r|=ρ'2+h'2, (2.a)
θ=πacos(|r|2+RoC2r'22|r|×RoC), (2.b)
ψ=arcsin(ρ'/|r|), (2.c)
where r'=ρ2+(h+RoC2CA2/4)2 is the distance between the evaporation source and the center of the spherical surface, ρ' and h' are the horizontal and vertical distances from element dS to the source, respectively. During revolution, the position of the surface element relative to the revolution center (ω) is described as a function of time:
x(t)=ρcos(ϖ1t)+δcos(ϖ2t+ϕ), (3.a)
y(t)=ρsin(ϖ1t)+δsin(ϖ2t+ϕ), (3.b)
z(t)=RoC2CA2/4RoC2δ2, (3.c)
where δ is the horizontal distance from the surface element to the surface center, ϖ1 and ϖ2 are the angular velocities for the planet revolution and rotation, respectively. (δ,ϕ) denotes the horizontal polar coordinates of each surface element with respect to the surface center. z(t), determined by δand the substrate shape, is the vertical distance from the surface element to the revolution plane of the substrate holder. It is independent of time for coating plant used in the experiment. From Eqs. (1) to (3), for specified coating plant configuration with a known source emissive pattern and substrate geometry, deposition rate on the surface element at time t is numerically calculated, and the thickness of the deposited film is obtained by numerical integration of the deposition rate. The corresponding film thickness distribution is obtained by changing the position of the surface element via varying δin 0~CA/2 and ϕin 0~2π. For PVD with ion beam sputtering and other methods on spherical substrates, the film thickness distribution could be obtained similarly by properly modeling the evaporation source and the deposition process.

The last parameter to be determined for calculating the film thickness distribution, the emissive pattern of the coating material, can be obtained by fitting the experimental film thickness profile without shadowing mask for uniformity correction to the corresponding theoretical simulation results. In our coating plant, the emissive patterns of MgF2 and LaF3 materials were both determined to be cos2.0±0.2ψ when the substrate temperature is 250°C.

For flat and other rotationally symmetric substrates in PRS, without shadowing masks the two-dimensional film thickness profiles are rotationally symmetric. As a result the film thickness profile along a line connecting the center of the stage and the center of the rotationally symmetric substrate (Line L in Fig. 1) is insensitive to the substrate rotation, and from the deposition results the motions of the substrates can be equated to simple rotations around the revolution axis. In case of coating on a flat substrate in SRS, the initial shadowing mask for the flat substrate is designed with its shape described by

l=d×2π(TT0)T,
where T0 is the thinnest film thickness and T is the film thickness at distance d away from the revolution axis along Line L. l denotes the arc length of the shadowing mask at the circle with radius d. In our coating plant the thickest film is at the center of the flat surface while the thinnest at the edge. The shadowing mask designed as above leads to a perfect uniformity for optical coating in SRS. However, substrates in PRS are actually in rotation simultaneously. Consequently, this initially designed shadowing mask blocks depositing molecules at positions with either thick or thin films. To obtain the thickness distribution with shadowing mask in place, we simulate the deposition process again with the shadowing mask modeled by an area described by Eq. (4). The shadowing mask can also be divided into several pieces by dividing the arc length l and then evenly distributed in the chamber. In the calculation, if vector r in Fig. 1 crosses any shadowing mask piece during the substrate revolution, the deposition rate equals to zero for the surface element within the time interval of crossing. By expanding the arc length of the initial shadowing mask by a factor κ, a good uniformity can be obtained. That is,
l=κ×d×2π(TT0)T.
For example, with the coating plant configuration shown in Fig. 1, MgF2 film uniformity close to 100% on a flat substrate with diameter 400mm is theoretically obtained when κ2.0. On the other hand, film uniformity correction on a spherical substrate can be realized similarly as on flat substrate. The mask shape is also described by Eq. (5). Simulation results using Matlab software demonstrated that the designed shadowing masks lead to acceptable film uniformities for spherical substrates with various ratios of clear aperture to radius of curvature (CA/RoC).

The value of factor κ is determined as follows. As showed in Fig. 2 , positions A and B are at the rim and center of a substrate surface, with film thickness T0 and T respectively. Coating deposition at position A occurs within area 2πρ×CA, and the average deposition rate at A is approximately T0/2πρCA. Similarly, at position B the deposition occurs at the revolution orbital with the average deposition rate approximatelyT/2πρ. For film uniformity correction of the two positions, a shadowing mask should be designed as denoted by the shadowed area in Fig. 2. The arc length l1l2 of the shadowing mask is determined by Eq. (5). To obtain good film uniformity, with shadowing mask the film thicknesses at positions A and B should be equal, which leads to

Tl×T2πρ=T012lCA×T02πρCA.
The value of factor κ is therefore determined as

 

Fig. 2 Determination of the factor κ for correcting film thickness uniformity on center and rim positions of a substrate.

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κ=11T0/2T.

However, due to the approximations used in the model, the actual shape of the shadowing mask is somewhat different from that presented in Fig. 2. Compared with the optimized value of κ for different substrates, the value given by Eq. (7) is approximately 5% smaller than the desired value, and can be corrected correspondingly.

4. Results and discussion

The proposed routine for designing the shadowing mask was first employed for preparing uniform coating on flat surfaces. Figure 3(a) shows the shape of a shadowing mask designed for a CA = 400mm flat substrate deposited with MgF2 material. For sake of balance and improved uniformity, the shadowing mask was divided into three identical pieces symmetrically positioned in the coating plant. With the help of the designed shadowing mask, experimental film thickness uniformity of approximately 99.6% was achieved, which is in good agreement with the theoretical value of 99.7%. Figures 3(b) and 3(c) present the theoretical two-dimensional film distribution and the corresponding experimental one-dimensional profile, respectively. The excellent agreement between the theoretical and experimental profiles clearly proved the validity of the proposed routine.

 

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.

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The proposed routine was further applied to prepare uniform films on both convex and concave spherical substrates. Figures 4(a) and 4(b) present the theoretical two-dimensional film thickness distributions for a convex spherical with CA = 240mm, RoC = 200mm and a concave spherical surface with CA = 160mm, RoC = −170mm, with film uniformity correction realized by shadowing masks appropriately designed, respectively. It is seen that the shadowing masks lead to film uniformity better than 98% even for strongly curved substrates. Experimentally, film uniformity better than 97% for spherical substrates with CA≈200mm and CA/RoC varying from −0.94 to 1.3 have been achieved, as presented in Fig. 4(c). For example, for a convex spherical substrate with CA = 160mm and RoC = 120mm, by employing the designed shadowing mask, the film uniformity has been improved from approximately 63% to 97%. It is worth mentioning that, shadowing masks designed for a convex substrates also lead to better uniformity for those with the same RoC but smaller CAs. On the other hand, due to the masking effect of the concave substrates themselves, the masks designed for concave substrates cannot be extended to substrates with the same RoC but much smaller CAs. Compared to the iterative Monte Carlo method and the mathematic method promoted by Bauer et al. [12] the routine demonstrated here advanced in simple and fast design process and improved uniformity for spherical substrates.

 

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.

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It must be pointed out that the masking effect relies not only on the shape, but also on the movement manner of the shadowing mask. For any substrate, shadowing mask will not lead to uniform coating after just one or a couple of revolutions. However, movements of the planets are so precisely engineered that the shadowing mask blocks different parts of substrates during each revolution and good uniformity can be realized after sufficient resolutions. The simulated two-dimensional film thickness distributions presented in Figs. 3 and 4 are obtained with 250 revolutions, which correspond to approximately 1500 rotations. On the other hand, un-symmetrical film thickness distributions are found if the substrates experience less than ~10 revolutions in a coating process, which may lead to drastic distortions in the rotationally symmetric Zernike coefficients on surface figure, as revealed by interferometric surface metrology [13].

Shadowing masks designed with the proposed routine were applied to film uniformity control on spherical substrates for high-NA DUV lithography. Figure 5 shows the transmittance uniformity of an anti-reflectively coated lens element. The shape of the fused silica lens element is shown inset in the figure. The diameter of the lens element is 200mm, and the RoCs are 200mm and 370mm, respectively. The transmission spectra were measured for four positions as denoted from center to rim of the substrate. Without uniformity correction, the film thickness uniformities were 72% and 81% for the RoC = 200mm and RoC = 370mm surfaces, respectively. With uniformity correction the thickness uniformity for both surfaces were improved to be better than 99%. The transmittance uniformity of 99.7% at 193nm wavelength was experimentally achieved. The variations of the refractive index and the film thickness, as well as the measurement error on the transmittance were likely responsible for the 0.3% transmittance non-uniformity.

 

Fig. 5 Transmittances of DUV antireflective coating on a convex spherical lens substrate, measured at four positions indicated in the inset.

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5. Conclusion

We have proposed a general routine for theoretically designing the shadowing masks for correcting the thickness uniformity of optical coatings on flat as well as spherical surfaces in a typical PRS. The designed shadowing masks have been applied to control thickness uniformity of coatings on spherical substrates with large CAs and CA/RoC ratios. Film uniformity better than 97% have been experimentally demonstrated when CA/RoC varied from −0.94 to 1.3. The proposed routine has greatly simplified the design and fabrication of the shadowing masks for uniformity correction in PRS. By proper modeling deposition processes, the method could be easily extended to preparing shadowing masks for optical coatings prepared with other deposition methods, such as ion beam sputtering et al., in PRS of other geometries. The routine could also be extended to film uniformity corrections for rotationally symmetrical substrates with other shapes, as well as to film preparations with specified thickness distributions and spectral profiles.

References and links

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

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

3. 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]  

4. J. M. Bennett and E. J. Ashley, “Investigation of film thickness uniformity on substrates located close to the source axis,” Appl. Opt. 12(4), 758–763 (1973). [CrossRef]   [PubMed]  

5. J. Arkwright, I. Underhill, N. Pereira, and M. Gross, “Deterministic control of thin film thickness in physical vapor deposition systems using a multi-aperture mask,” Opt. Express 13(7), 2731–2741 (2005). [CrossRef]   [PubMed]  

6. 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]  

7. 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]  

8. L. Abel-Tibérini, F. Lemarquis, and M. Lequime, “Masking mechanisms applied to thin-film coatings for the manufacturing of linear variable filters for two-dimensional array detectors,” Appl. Opt. 47(30), 5706–5714 (2008). [CrossRef]   [PubMed]  

9. F. Villa, A. Martínez, and L. E. Regalado, “Correction masks for thickness uniformity in large-area thin films,” Appl. Opt. 39(10), 1602–1610 (2000). [CrossRef]   [PubMed]  

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

11. J. B. Oliver and D. Talbot, “Optimization of deposition uniformity for large-aperture National Ignition Facility substrates in a planetary rotation system,” Appl. Opt. 45(13), 3097–3105 (2006). [CrossRef]   [PubMed]  

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

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

14. 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]  

15. F. Villa and O. Pompa, “Emission pattern of real vapor sources in high vacuum: an overview,” Appl. Opt. 38(4), 695–703 (1999). [CrossRef]   [PubMed]  

References

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  1. H. A. Macleod, Thin-film Optical Filters (Academic Press, New York, 2001).
  2. J. A. Dobrowolski and W. Weinstein, “Optical aspherizing by vacuum evaporation,” Nature 175(4458), 646–647 (1955).
    [Crossref]
  3. 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]
  4. J. M. Bennett and E. J. Ashley, “Investigation of film thickness uniformity on substrates located close to the source axis,” Appl. Opt. 12(4), 758–763 (1973).
    [Crossref] [PubMed]
  5. J. Arkwright, I. Underhill, N. Pereira, and M. Gross, “Deterministic control of thin film thickness in physical vapor deposition systems using a multi-aperture mask,” Opt. Express 13(7), 2731–2741 (2005).
    [Crossref] [PubMed]
  6. 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]
  7. 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]
  8. L. Abel-Tibérini, F. Lemarquis, and M. Lequime, “Masking mechanisms applied to thin-film coatings for the manufacturing of linear variable filters for two-dimensional array detectors,” Appl. Opt. 47(30), 5706–5714 (2008).
    [Crossref] [PubMed]
  9. F. Villa, A. Martínez, and L. E. Regalado, “Correction masks for thickness uniformity in large-area thin films,” Appl. Opt. 39(10), 1602–1610 (2000).
    [Crossref] [PubMed]
  10. C. C. Jaing, “Designs of masks in thickness uniformity,” Proc. SPIE 7655, 76551Q, 76551Q-8 (2010).
    [Crossref]
  11. J. B. Oliver and D. Talbot, “Optimization of deposition uniformity for large-aperture National Ignition Facility substrates in a planetary rotation system,” Appl. Opt. 45(13), 3097–3105 (2006).
    [Crossref] [PubMed]
  12. H. H. Bauer, M. Heller, and N. Kaiser, “Optical coatings for UV photolithography systems,” Proc. SPIE 2776, 353–365 (1996).
    [Crossref]
  13. P. Kelkar, B. Tirri, R. Wilklow, and D. Peterson, “Deposition and characterization of challenging DUV coatings,” Proc. SPIE 7606, 706708, 706708-8 (2008).
    [Crossref]
  14. 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]
  15. F. Villa and O. Pompa, “Emission pattern of real vapor sources in high vacuum: an overview,” Appl. Opt. 38(4), 695–703 (1999).
    [Crossref] [PubMed]

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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