Abstract

This paper proposes an innovative method to overcome the low production rate of current linear variable filter (LVF) fabrication. During the fabrication process, a commercial coater is combined with a local mask on a substrate. The proposed analytical thin film thickness model, which is based on the geometry of the commercial coater, is developed to more effectively calculate the profiles of LVFs. Thickness tolerance, LVF zone width, thin film layer structure, transmission spectrum and the effects of variations in critical parameters of the coater are analyzed. Profile measurements demonstrate the efficacy of local mask theory in the prediction of evaporation profiles with a high degree of accuracy.

© 2015 Optical Society of America

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References

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  1. A. Piegari, A. K. Sytchkova, J. Bulir, B. Harnisch, and A. Wuttig, “Thin-film filters for a high resolution miniaturized spectrometer,” Proc. SPIE 7101, 710113 (2008).
    [Crossref]
  2. A. Piegari, J. Bulir, and A. Krasilnikova Sytchkova, “Variable narrow-band transmission filters for spectrometry from space. 2. Fabrication process,” Appl. Opt. 47(13), C151–C156 (2008).
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    [Crossref] [PubMed]
  4. 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]
  5. L. Abel-Tiberini, F. Lemarquis, G. Marchand, L. Roussel, G. Albrand, and M. Lequime, “Manufacturing of linear variable filters with straight iso-thickness lines,” Proc. SPIE 5963, 59630B (2005).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  8. E. Hecht, Optics 4th ed. (Pearson, 2014).
  9. H. Hangus MacLeod, Thin-film Optical Filters 4th ed (Taylor & Francis, 2010).
  10. J.-C. Hsu, “Analysis of the thickness uniformity improved by using wire masks for coating optical bandpass filters,” Appl. Opt. 53(7), 1474–1480 (2014).
    [Crossref] [PubMed]
  11. C. Guo, M. Kong, C. Liu, and B. Li, “Optimization of thickness uniformity of optical coatings on a conical substrate in a planetary rotation system,” Appl. Opt. 52(4), B26–B32 (2013).
    [Crossref] [PubMed]
  12. C. Lee, K. Chuang, and J. Wu, “Thickness distribution of thin films deposited by ion beam deposition,” in Optical Interference Coatings, OSA Technical Digest Series (Optical Society of America, 2001), paper MB4.
  13. J. Pan, F. Zhang, and Y. Yan, “Mask designing of linear variable filters,” in Proceedings of Second International Conference on Thin Film Physics and Applications (1994), pp. 225–228.
    [Crossref]
  14. E. B. Graper, “Distribution and apparent source geometry of electron-beam-heated evaporation sources,” J. Vac. Sci. Technol. 10(1), 100–103 (1973).
    [Crossref]
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    [Crossref] [PubMed]
  16. Tracepro,” http://www.lambdares.com/tracepro .
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2014 (1)

2013 (1)

2012 (2)

2008 (3)

2007 (1)

2006 (1)

2005 (1)

L. Abel-Tiberini, F. Lemarquis, G. Marchand, L. Roussel, G. Albrand, and M. Lequime, “Manufacturing of linear variable filters with straight iso-thickness lines,” Proc. SPIE 5963, 59630B (2005).
[Crossref]

1973 (1)

E. B. Graper, “Distribution and apparent source geometry of electron-beam-heated evaporation sources,” J. Vac. Sci. Technol. 10(1), 100–103 (1973).
[Crossref]

Abel-Tiberini, L.

L. Abel-Tiberini, F. Lemarquis, G. Marchand, L. Roussel, G. Albrand, and M. Lequime, “Manufacturing of linear variable filters with straight iso-thickness lines,” Proc. SPIE 5963, 59630B (2005).
[Crossref]

Abel-Tibérini, L.

Albrand, G.

L. Abel-Tiberini, F. Lemarquis, G. Marchand, L. Roussel, G. Albrand, and M. Lequime, “Manufacturing of linear variable filters with straight iso-thickness lines,” Proc. SPIE 5963, 59630B (2005).
[Crossref]

Bock, W. J.

Bulir, J.

Correia, J. H.

de Graaf, G.

Emadi, A.

Enoksson, P.

Graper, E. B.

E. B. Graper, “Distribution and apparent source geometry of electron-beam-heated evaporation sources,” J. Vac. Sci. Technol. 10(1), 100–103 (1973).
[Crossref]

Guo, C.

Harnisch, B.

A. Piegari, A. K. Sytchkova, J. Bulir, B. Harnisch, and A. Wuttig, “Thin-film filters for a high resolution miniaturized spectrometer,” Proc. SPIE 7101, 710113 (2008).
[Crossref]

Hsu, J.-C.

Kong, M.

Krasilnikova Sytchkova, A.

Lemarquis, F.

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]

L. Abel-Tiberini, F. Lemarquis, G. Marchand, L. Roussel, G. Albrand, and M. Lequime, “Manufacturing of linear variable filters with straight iso-thickness lines,” Proc. SPIE 5963, 59630B (2005).
[Crossref]

Lequime, M.

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]

L. Abel-Tiberini, F. Lemarquis, G. Marchand, L. Roussel, G. Albrand, and M. Lequime, “Manufacturing of linear variable filters with straight iso-thickness lines,” Proc. SPIE 5963, 59630B (2005).
[Crossref]

Li, B.

Liu, C.

Ma, J.

Marchand, G.

L. Abel-Tiberini, F. Lemarquis, G. Marchand, L. Roussel, G. Albrand, and M. Lequime, “Manufacturing of linear variable filters with straight iso-thickness lines,” Proc. SPIE 5963, 59630B (2005).
[Crossref]

Pan, J.

J. Pan, F. Zhang, and Y. Yan, “Mask designing of linear variable filters,” in Proceedings of Second International Conference on Thin Film Physics and Applications (1994), pp. 225–228.
[Crossref]

Piegari, A.

Roussel, L.

L. Abel-Tiberini, F. Lemarquis, G. Marchand, L. Roussel, G. Albrand, and M. Lequime, “Manufacturing of linear variable filters with straight iso-thickness lines,” Proc. SPIE 5963, 59630B (2005).
[Crossref]

Sytchkova, A. K.

A. Piegari, A. K. Sytchkova, J. Bulir, B. Harnisch, and A. Wuttig, “Thin-film filters for a high resolution miniaturized spectrometer,” Proc. SPIE 7101, 710113 (2008).
[Crossref]

Wolffenbuttel, R.

Wolffenbuttel, R. F.

Wu, H.

Wuttig, A.

A. Piegari, A. K. Sytchkova, J. Bulir, B. Harnisch, and A. Wuttig, “Thin-film filters for a high resolution miniaturized spectrometer,” Proc. SPIE 7101, 710113 (2008).
[Crossref]

Yan, Y.

J. Pan, F. Zhang, and Y. Yan, “Mask designing of linear variable filters,” in Proceedings of Second International Conference on Thin Film Physics and Applications (1994), pp. 225–228.
[Crossref]

Zhang, F.

J. Pan, F. Zhang, and Y. Yan, “Mask designing of linear variable filters,” in Proceedings of Second International Conference on Thin Film Physics and Applications (1994), pp. 225–228.
[Crossref]

Appl. Opt. (6)

J. Vac. Sci. Technol. (1)

E. B. Graper, “Distribution and apparent source geometry of electron-beam-heated evaporation sources,” J. Vac. Sci. Technol. 10(1), 100–103 (1973).
[Crossref]

Opt. Express (2)

Proc. SPIE (2)

A. Piegari, A. K. Sytchkova, J. Bulir, B. Harnisch, and A. Wuttig, “Thin-film filters for a high resolution miniaturized spectrometer,” Proc. SPIE 7101, 710113 (2008).
[Crossref]

L. Abel-Tiberini, F. Lemarquis, G. Marchand, L. Roussel, G. Albrand, and M. Lequime, “Manufacturing of linear variable filters with straight iso-thickness lines,” Proc. SPIE 5963, 59630B (2005).
[Crossref]

Other (6)

E. Hecht, Optics 4th ed. (Pearson, 2014).

H. Hangus MacLeod, Thin-film Optical Filters 4th ed (Taylor & Francis, 2010).

Tracepro,” http://www.lambdares.com/tracepro .

F. Reif, Fundamentals of Statistical and Thermal Physics. (McGraw–Hill, 1965).

C. Lee, K. Chuang, and J. Wu, “Thickness distribution of thin films deposited by ion beam deposition,” in Optical Interference Coatings, OSA Technical Digest Series (Optical Society of America, 2001), paper MB4.

J. Pan, F. Zhang, and Y. Yan, “Mask designing of linear variable filters,” in Proceedings of Second International Conference on Thin Film Physics and Applications (1994), pp. 225–228.
[Crossref]

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Figures (11)

Fig. 1
Fig. 1 Schematic diagram of LVF order-sorting filter where the critical wavelength, λC, is defined as the wavelength at which the transmittance is 50% (T = 50%). tU is defined as the upper-bound thickness of the HPF with λC set equal to λm = 1, and tL is the lower-bound thickness with λC set equal to λm = 2.
Fig. 2
Fig. 2 Geometric representation of the evaporation chamber, where the substrate is assumed to be fixed in space, and the source rotates along the vertical axis in the calculation.
Fig. 3
Fig. 3 Schematic of local mask and source. A local mask is positioned next to the substrate with a gap, h, between the two.
Fig. 4
Fig. 4 Ray tracing results for thickness produced with five gap values. The parameters used in the simulation are R = 1100mm, L = 300mm, α = 19° and φ’ = 0°.
Fig. 5
Fig. 5 Thickness profile for (a) h = 1.2mm, (b) h = 1.5mm and (c) h = 1.8mm. Short dashed blue lines represent the upper tolerance and lower tolerance limits.
Fig. 6
Fig. 6 Transmittance T(λ) of positions X1, X2 and X3.
Fig. 7
Fig. 7 Thickness deviations between (a) evaporated film and theoretical model; (b) evaporated film and ray tracing simulation; and (c) ray tracing simulation and theoretical model.
Fig. 8
Fig. 8 Relative thickness versus position X as σ was varied from 0.5 to 2.5. Larger σ produces a thinner film in the unblocked area, which led to abrupt changes in the thickness profiles at X = − 0.50mm and X = 0.45mm.
Fig. 9
Fig. 9 Relative thickness versus position X for three variations in R including ± 1%, ± 5%, and ± 10%. The abrupt points in the thickness curves occurred at X = − 0.50mm in unblocked area and at X = 0.45mm in the blocked area.
Fig. 10
Fig. 10 LVF profiles corresponding to variations in L caused by axial tilt angles (δ) of 1°, 5° and 10°. The results show larger deviations associated with larger axial angles near the abrupt points of X = − 0.50mm and X = 0.45mm.
Fig. 11
Fig. 11 LVF zone widths obtained from the theoretical calculation (WT), the ray tracing simulation (WR), and the evaporated film (WE) vs. mask-to-substrate gap. Coefficients of determination are 0.9998, 0.9890, and 0.9757 for WT, WR, and WE, respectively.

Tables (3)

Tables Icon

Table 1 Definitions of geometric symbols

Tables Icon

Table 2 Thin film layer structures obtained by the Macleod software

Tables Icon

Table 3 Performance of the LVF at positions X1, X2 and X3.

Equations (32)

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mλ=d( sinα+sinβ ),
λ m=1 =2 λ m=2 .
λ C = 1 2 ( λ m=1 + λ m=2 ).
λ m=2 = 2 3   λ C =( 1 1 3 ) λ C ,
λ m=1 = 4 3   λ C =( 1+ 1 3 ) λ C .
λ m=1 t U = λ C t C = λ m=2 t L .
t L = 2 3   t C =( 1 1 3 ) t C =( 133.33% ) t C ,
t U = 4 3   t C =( 1+ 1 3 ) t C =( 1+33.33% ) t C .
t=k 0 φ (cosθ) σ cosθ' r 2 dφ,
t( α )= k 0 2π u mask ( α B α ) (cosθ) σ cosθ' r 2 dφ,
u mask ={  1;α α B , 0;α> α B ,
K=(Rsinαcosφ',Rsinαsinφ',Rcosα),
P=( Lcosφ,Lsinφ,0 ),
n ^ =(sinαcosφ',sinαsinφ',cosα),
z ^  = ( 0,0,1 ),
PK =(Rsinαcosφ'Lcosφ, Rsinαsinφ'Lsinφ,Rcosα),
cosθ= PK z ^ | PK || z ^ | ,
cosθ´= KP n ^ | KP || n ^ | ,
r=| PK |.
t( α )= k 0 2π u mask ( α B α ) (cosθ) σ cosθ' r 2 dφ =k 0 2π u mask ( α B α ) [ Rcosα ( Rsinαcosφ'Lcosφ ) 2 + ( Rsinαsinφ'Lsinφ ) 2 + ( Rcosα ) 2 ] σ ×[ ( LcosφRsinαcosφ' )( Rsinαcosφ' )+( LsinφRsinαsinφ' )( Rsinαsinφ' )+ ( Rcosα ) 2 ( (LcosφRsinαcosφ') 2 + ( LsinφRsinαsinφ' ) 2 + ( Rcosα ) 2 )×R ] ×[   1 ( Rsinαcosφ'Lcosφ ) 2 + ( Rsinαsinφ'Lsinφ ) 2 + ( Rcosα ) 2   ] dφ.
t λ CD = t( X 1 ) 300nm = t( X 2 ) 525nm = t( X 3 ) 750nm .
FWO T i t p,i  × n i λ m=2 ,
t p,i ( X 2 ) 525nm = t p,i ( X 3 ) 750nm t p,i ( X 3 )=(   750 525   ) t p,i ( X 2 ),
ε λ C ( % )( λ C λ CD λ CD )×100%.
T D ET ( % )=( t E t T t T )×100%,
T D ER ( % )=( t E t R t R )×100%,
T D RT ( % )=( t R t T t T )×100%,
u ˜ mask (α)= 1 e ( α α B )/ξ +1 ,
W( μm )=N( pixel )×PS( μm pixel ).
SWPP | λ 2 λ 1 |( nm ) N( pixel ) .
Δ λ FWHM ( nm )=q( pixels )×SWPP( nm pixel ).
Δ λ FWHM ( nm )= q( pixels )×| λ 2 λ 1 |( nm )×PS( μm pixel ) W( μm ) .

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