Abstract

We present an algorithm for the automatic generation of a monitoring spreadsheet that enables the most effective application of the termination level correction algorithm proposed in our previous publication. On a whole the presented monochromatic monitoring strategy entirely eliminates a cumulative effect of thickness errors in optical coating production using direct optical monitoring. The effectiveness of the new monitoring strategy is demonstrated by computational manufacturing experiments in which such error factors as instability of deposition rates, errors in measured transmittance data, shutter delays, and variations of layer refractive indices from their theoretical values are simulated.

© 2007 Optical Society of America

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  1. H. A. Macleod, Thin Film Optical Filters (McGraw-Hill, 1986).
    [CrossRef]
  2. H. Macleod, "Monitoring of optical coatings," Appl. Opt. 20, 82-89 (1981).
    [CrossRef] [PubMed]
  3. R. R. Willey, "Optical thickness monitoring sensitivity improvement using graphical methods," Appl. Opt. 26, 729-737 (1987).
    [CrossRef] [PubMed]
  4. B. T. Sullivan and J. A. Dobrowolski, "Deposition error compensation for optical multilayer coatings. I. Theoretical description," Appl. Opt. 31, 3821-3835 (1992).
    [CrossRef] [PubMed]
  5. A. Zoeller, M. Boos, R. Goetzelmann, H. Hagedorn, and W. Klug, "Substantial progress in optical monitoring by intermittent measurement technique," Proc. SPIE 5963, 105-113 (2005).
  6. A. Zoeller, M. Boos, H. Hagedorn, W. Klug, and C. Schmitt, "High accurate in situ optical thickness monitoring for multilayer coatings," in Proceedings of the 47th Annual SVC Conference (Society of Vacuum Coaters, 2004), pp. 72-78.
  7. P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, "Optical filters: monitoring process allowing the auto-correction of thickness errors," Thin Solid Films 13, 285-290 (1972).
    [CrossRef]
  8. H. A. Macleod, "Turning value monitoring of narrow-band all-dielectric thin film optical filters," Opt. Acta 19, 1-28 (1972).
    [CrossRef]
  9. H. Macleod and D. Richmond, "The effect of errors in the optical monitoring of narrow-band all-dielectric thin film optical filters," Opt. Acta 21, 429-443 (1974).
    [CrossRef]
  10. H. Macleod and E. Pelletier, "Error compensation mechanisms in some thin-film monitoring systems," Opt. Acta 24, 907-930 (1977).
    [CrossRef]
  11. A. V. Tikhonravov and M. K. Trubetskov, "Automated design and sensitivity analysis of wavelength-division multiplexing filters," Appl. Opt. 41, 3176-3182 (2002).
    [CrossRef] [PubMed]
  12. F. Zhao, "Monitoring of periodic multilayers by the level method," Appl. Opt. 24, 3339-3342 (1985).
    [CrossRef] [PubMed]
  13. R. Willey, "Variation of band-edge position with errors in the monitoring of layer termination level for long- and short-wave pass filters," Appl. Opt. 38, 5447-5451 (1999).
    [CrossRef]
  14. A. Tikhonravov, M. Trubetskov, and T. Amotchkina, "Statistical approach to choosing a strategy of monochromatic monitoring of optical coating production," Appl. Opt. 45, 7863-7870 (2006).
    [CrossRef] [PubMed]
  15. C. J. van der Laan, "Optical monitoring of nonquarterwave stacks," Appl. Opt. 25, 753-760 (1986).
    [CrossRef] [PubMed]
  16. C.-C. Lee, K. Wu, C.-C. Kuo, and S.-H. Chen, "Improvement of the optical coating process by cutting layers with sensitive monitoring wavelengths," Opt. Express 13, 4854-4861 (2005).
    [CrossRef] [PubMed]
  17. B. Chun, C. K. Hwangbo, and J. S. Kim, "Optical monitoring of nonquarterwave layers of dielectric multilayer filters using optical admittance," Opt. Express 14, 2473-2480 (2006).
    [CrossRef] [PubMed]
  18. C. Holm, "Optical thin film production with continuous reoptimization of layer thicknesses," Appl. Opt. 18, 1978-1982 (1978).
    [CrossRef]
  19. L. Li and Y. Yen, "Wideband monitoring and measuring system for optical coatings," Appl. Opt. 28, 2890-2894 (1989).
    [CrossRef]
  20. J. A. Dobrowolski and A. Waldorf, "Manufacture of all-dielectric filters with layers of arbitrary thickness and refractive index," J. Opt. Soc. Am. 60, 725 (1970).
  21. A. Tikhonravov and M. Trubetskov, "Eliminating of cumulative effect of thickness errors in monochromatic monitoring of optical coating production: theory," Appl. Opt. 46, 2084-2090 (2007).
    [CrossRef] [PubMed]
  22. A. V. Tikhonravov and M. K. Trubetskov, "Computational manufacturing as a bridge between design and production," Appl. Opt. 44, 6877-6884 (2005).
    [CrossRef] [PubMed]
  23. N. Kaiser and H. K. Pulker, "Some fundamentals of optical thin film growth," in Optical Interference Coatings,N.Kaiser and H.K.Pulker, eds. (Springer-Verlag, 2003), pp. 59-80.
  24. D. Poitras, J. A. Dobrowolski, T. Cassidy, and S. Moisa, "Ion-beam etching for the precise manufacture of optical coatings," Appl. Opt. 42, 4037-4044 (2003).
    [CrossRef] [PubMed]
  25. P. Ma, J. A. Dobrowolski, F. Lin, C. Midwinter, and C. T. McElroy, "Long-wavelength polarizing cutoff filters for the 275-550-nm spectral region," Appl. Opt. 41, 3218-3223 (2002).
    [CrossRef] [PubMed]
  26. C. Clark and H. A. Macleod, "Errors and tolerances in optical coatings," in Proceedings of the 40th Annual SVC Conference (Society of Vacuum Coaters, 1997), pp. 274-279.

2007

2006

2005

2004

A. Zoeller, M. Boos, H. Hagedorn, W. Klug, and C. Schmitt, "High accurate in situ optical thickness monitoring for multilayer coatings," in Proceedings of the 47th Annual SVC Conference (Society of Vacuum Coaters, 2004), pp. 72-78.

2003

N. Kaiser and H. K. Pulker, "Some fundamentals of optical thin film growth," in Optical Interference Coatings,N.Kaiser and H.K.Pulker, eds. (Springer-Verlag, 2003), pp. 59-80.

D. Poitras, J. A. Dobrowolski, T. Cassidy, and S. Moisa, "Ion-beam etching for the precise manufacture of optical coatings," Appl. Opt. 42, 4037-4044 (2003).
[CrossRef] [PubMed]

2002

1999

1997

C. Clark and H. A. Macleod, "Errors and tolerances in optical coatings," in Proceedings of the 40th Annual SVC Conference (Society of Vacuum Coaters, 1997), pp. 274-279.

1992

1989

L. Li and Y. Yen, "Wideband monitoring and measuring system for optical coatings," Appl. Opt. 28, 2890-2894 (1989).
[CrossRef]

1987

1986

1985

1981

1978

1977

H. Macleod and E. Pelletier, "Error compensation mechanisms in some thin-film monitoring systems," Opt. Acta 24, 907-930 (1977).
[CrossRef]

1974

H. Macleod and D. Richmond, "The effect of errors in the optical monitoring of narrow-band all-dielectric thin film optical filters," Opt. Acta 21, 429-443 (1974).
[CrossRef]

1972

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, "Optical filters: monitoring process allowing the auto-correction of thickness errors," Thin Solid Films 13, 285-290 (1972).
[CrossRef]

H. A. Macleod, "Turning value monitoring of narrow-band all-dielectric thin film optical filters," Opt. Acta 19, 1-28 (1972).
[CrossRef]

1970

J. A. Dobrowolski and A. Waldorf, "Manufacture of all-dielectric filters with layers of arbitrary thickness and refractive index," J. Opt. Soc. Am. 60, 725 (1970).

Amotchkina, T.

Boos, M.

A. Zoeller, M. Boos, R. Goetzelmann, H. Hagedorn, and W. Klug, "Substantial progress in optical monitoring by intermittent measurement technique," Proc. SPIE 5963, 105-113 (2005).

A. Zoeller, M. Boos, H. Hagedorn, W. Klug, and C. Schmitt, "High accurate in situ optical thickness monitoring for multilayer coatings," in Proceedings of the 47th Annual SVC Conference (Society of Vacuum Coaters, 2004), pp. 72-78.

Bousquet, P.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, "Optical filters: monitoring process allowing the auto-correction of thickness errors," Thin Solid Films 13, 285-290 (1972).
[CrossRef]

Cassidy, T.

Chen, S.-H.

Chun, B.

Clark, C.

C. Clark and H. A. Macleod, "Errors and tolerances in optical coatings," in Proceedings of the 40th Annual SVC Conference (Society of Vacuum Coaters, 1997), pp. 274-279.

Dobrowolski, J. A.

Fornier, A.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, "Optical filters: monitoring process allowing the auto-correction of thickness errors," Thin Solid Films 13, 285-290 (1972).
[CrossRef]

Goetzelmann, R.

A. Zoeller, M. Boos, R. Goetzelmann, H. Hagedorn, and W. Klug, "Substantial progress in optical monitoring by intermittent measurement technique," Proc. SPIE 5963, 105-113 (2005).

Hagedorn, H.

A. Zoeller, M. Boos, R. Goetzelmann, H. Hagedorn, and W. Klug, "Substantial progress in optical monitoring by intermittent measurement technique," Proc. SPIE 5963, 105-113 (2005).

A. Zoeller, M. Boos, H. Hagedorn, W. Klug, and C. Schmitt, "High accurate in situ optical thickness monitoring for multilayer coatings," in Proceedings of the 47th Annual SVC Conference (Society of Vacuum Coaters, 2004), pp. 72-78.

Holm, C.

Hwangbo, C. K.

Kaiser, N.

N. Kaiser and H. K. Pulker, "Some fundamentals of optical thin film growth," in Optical Interference Coatings,N.Kaiser and H.K.Pulker, eds. (Springer-Verlag, 2003), pp. 59-80.

Kim, J. S.

Klug, W.

A. Zoeller, M. Boos, R. Goetzelmann, H. Hagedorn, and W. Klug, "Substantial progress in optical monitoring by intermittent measurement technique," Proc. SPIE 5963, 105-113 (2005).

A. Zoeller, M. Boos, H. Hagedorn, W. Klug, and C. Schmitt, "High accurate in situ optical thickness monitoring for multilayer coatings," in Proceedings of the 47th Annual SVC Conference (Society of Vacuum Coaters, 2004), pp. 72-78.

Kowalczyk, R.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, "Optical filters: monitoring process allowing the auto-correction of thickness errors," Thin Solid Films 13, 285-290 (1972).
[CrossRef]

Kuo, C.-C.

Lee, C.-C.

Li, L.

L. Li and Y. Yen, "Wideband monitoring and measuring system for optical coatings," Appl. Opt. 28, 2890-2894 (1989).
[CrossRef]

Lin, F.

Ma, P.

Macleod, H.

H. Macleod, "Monitoring of optical coatings," Appl. Opt. 20, 82-89 (1981).
[CrossRef] [PubMed]

H. Macleod and E. Pelletier, "Error compensation mechanisms in some thin-film monitoring systems," Opt. Acta 24, 907-930 (1977).
[CrossRef]

H. Macleod and D. Richmond, "The effect of errors in the optical monitoring of narrow-band all-dielectric thin film optical filters," Opt. Acta 21, 429-443 (1974).
[CrossRef]

Macleod, H. A.

C. Clark and H. A. Macleod, "Errors and tolerances in optical coatings," in Proceedings of the 40th Annual SVC Conference (Society of Vacuum Coaters, 1997), pp. 274-279.

H. A. Macleod, Thin Film Optical Filters (McGraw-Hill, 1986).
[CrossRef]

H. A. Macleod, "Turning value monitoring of narrow-band all-dielectric thin film optical filters," Opt. Acta 19, 1-28 (1972).
[CrossRef]

McElroy, C. T.

Midwinter, C.

Moisa, S.

Pelletier, E.

H. Macleod and E. Pelletier, "Error compensation mechanisms in some thin-film monitoring systems," Opt. Acta 24, 907-930 (1977).
[CrossRef]

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, "Optical filters: monitoring process allowing the auto-correction of thickness errors," Thin Solid Films 13, 285-290 (1972).
[CrossRef]

Poitras, D.

Pulker, H. K.

N. Kaiser and H. K. Pulker, "Some fundamentals of optical thin film growth," in Optical Interference Coatings,N.Kaiser and H.K.Pulker, eds. (Springer-Verlag, 2003), pp. 59-80.

Richmond, D.

H. Macleod and D. Richmond, "The effect of errors in the optical monitoring of narrow-band all-dielectric thin film optical filters," Opt. Acta 21, 429-443 (1974).
[CrossRef]

Roche, P.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, "Optical filters: monitoring process allowing the auto-correction of thickness errors," Thin Solid Films 13, 285-290 (1972).
[CrossRef]

Schmitt, C.

A. Zoeller, M. Boos, H. Hagedorn, W. Klug, and C. Schmitt, "High accurate in situ optical thickness monitoring for multilayer coatings," in Proceedings of the 47th Annual SVC Conference (Society of Vacuum Coaters, 2004), pp. 72-78.

Sullivan, B. T.

Tikhonravov, A.

Tikhonravov, A. V.

Trubetskov, M.

Trubetskov, M. K.

van der Laan, C. J.

Waldorf, A.

J. A. Dobrowolski and A. Waldorf, "Manufacture of all-dielectric filters with layers of arbitrary thickness and refractive index," J. Opt. Soc. Am. 60, 725 (1970).

Willey, R.

Willey, R. R.

Wu, K.

Yen, Y.

L. Li and Y. Yen, "Wideband monitoring and measuring system for optical coatings," Appl. Opt. 28, 2890-2894 (1989).
[CrossRef]

Zhao, F.

Zoeller, A.

A. Zoeller, M. Boos, R. Goetzelmann, H. Hagedorn, and W. Klug, "Substantial progress in optical monitoring by intermittent measurement technique," Proc. SPIE 5963, 105-113 (2005).

A. Zoeller, M. Boos, H. Hagedorn, W. Klug, and C. Schmitt, "High accurate in situ optical thickness monitoring for multilayer coatings," in Proceedings of the 47th Annual SVC Conference (Society of Vacuum Coaters, 2004), pp. 72-78.

Appl. Opt.

H. Macleod, "Monitoring of optical coatings," Appl. Opt. 20, 82-89 (1981).
[CrossRef] [PubMed]

R. R. Willey, "Optical thickness monitoring sensitivity improvement using graphical methods," Appl. Opt. 26, 729-737 (1987).
[CrossRef] [PubMed]

B. T. Sullivan and J. A. Dobrowolski, "Deposition error compensation for optical multilayer coatings. I. Theoretical description," Appl. Opt. 31, 3821-3835 (1992).
[CrossRef] [PubMed]

A. V. Tikhonravov and M. K. Trubetskov, "Automated design and sensitivity analysis of wavelength-division multiplexing filters," Appl. Opt. 41, 3176-3182 (2002).
[CrossRef] [PubMed]

F. Zhao, "Monitoring of periodic multilayers by the level method," Appl. Opt. 24, 3339-3342 (1985).
[CrossRef] [PubMed]

R. Willey, "Variation of band-edge position with errors in the monitoring of layer termination level for long- and short-wave pass filters," Appl. Opt. 38, 5447-5451 (1999).
[CrossRef]

A. Tikhonravov, M. Trubetskov, and T. Amotchkina, "Statistical approach to choosing a strategy of monochromatic monitoring of optical coating production," Appl. Opt. 45, 7863-7870 (2006).
[CrossRef] [PubMed]

C. J. van der Laan, "Optical monitoring of nonquarterwave stacks," Appl. Opt. 25, 753-760 (1986).
[CrossRef] [PubMed]

C. Holm, "Optical thin film production with continuous reoptimization of layer thicknesses," Appl. Opt. 18, 1978-1982 (1978).
[CrossRef]

L. Li and Y. Yen, "Wideband monitoring and measuring system for optical coatings," Appl. Opt. 28, 2890-2894 (1989).
[CrossRef]

A. Tikhonravov and M. Trubetskov, "Eliminating of cumulative effect of thickness errors in monochromatic monitoring of optical coating production: theory," Appl. Opt. 46, 2084-2090 (2007).
[CrossRef] [PubMed]

A. V. Tikhonravov and M. K. Trubetskov, "Computational manufacturing as a bridge between design and production," Appl. Opt. 44, 6877-6884 (2005).
[CrossRef] [PubMed]

D. Poitras, J. A. Dobrowolski, T. Cassidy, and S. Moisa, "Ion-beam etching for the precise manufacture of optical coatings," Appl. Opt. 42, 4037-4044 (2003).
[CrossRef] [PubMed]

P. Ma, J. A. Dobrowolski, F. Lin, C. Midwinter, and C. T. McElroy, "Long-wavelength polarizing cutoff filters for the 275-550-nm spectral region," Appl. Opt. 41, 3218-3223 (2002).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

J. A. Dobrowolski and A. Waldorf, "Manufacture of all-dielectric filters with layers of arbitrary thickness and refractive index," J. Opt. Soc. Am. 60, 725 (1970).

Opt. Acta

H. A. Macleod, "Turning value monitoring of narrow-band all-dielectric thin film optical filters," Opt. Acta 19, 1-28 (1972).
[CrossRef]

H. Macleod and D. Richmond, "The effect of errors in the optical monitoring of narrow-band all-dielectric thin film optical filters," Opt. Acta 21, 429-443 (1974).
[CrossRef]

H. Macleod and E. Pelletier, "Error compensation mechanisms in some thin-film monitoring systems," Opt. Acta 24, 907-930 (1977).
[CrossRef]

Opt. Express

Proc. SPIE

A. Zoeller, M. Boos, R. Goetzelmann, H. Hagedorn, and W. Klug, "Substantial progress in optical monitoring by intermittent measurement technique," Proc. SPIE 5963, 105-113 (2005).

Thin Solid Films

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, "Optical filters: monitoring process allowing the auto-correction of thickness errors," Thin Solid Films 13, 285-290 (1972).
[CrossRef]

Other

H. A. Macleod, Thin Film Optical Filters (McGraw-Hill, 1986).
[CrossRef]

A. Zoeller, M. Boos, H. Hagedorn, W. Klug, and C. Schmitt, "High accurate in situ optical thickness monitoring for multilayer coatings," in Proceedings of the 47th Annual SVC Conference (Society of Vacuum Coaters, 2004), pp. 72-78.

N. Kaiser and H. K. Pulker, "Some fundamentals of optical thin film growth," in Optical Interference Coatings,N.Kaiser and H.K.Pulker, eds. (Springer-Verlag, 2003), pp. 59-80.

C. Clark and H. A. Macleod, "Errors and tolerances in optical coatings," in Proceedings of the 40th Annual SVC Conference (Society of Vacuum Coaters, 1997), pp. 274-279.

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Figures (11)

Fig. 1
Fig. 1

Schematic illustrating the correction of termination levels aimed at eliminating the influence of errors in previously deposited layers: solid curve—theoretical transmittance versus layer optical thickness, dashed curve—actual transmittance versus layer optical thickness; see text for details.

Fig. 2
Fig. 2

Theoretical transmittance of the 38-layer stop band filter (solid curve) and transmittances of the design with 1% relative errors in layer thicknesses (dashed curve).

Fig. 3
Fig. 3

Theoretical monitoring curve for the first three layers of the 38-layer stop band filter (the presented curve corresponds to the first three rows of Table 1).

Fig. 4
Fig. 4

Expected levels of errors in the thicknesses of layers of the 38-layer stop band filter when the level of errors in transmittance monitoring data is 0.05%: light columns, monitoring strategy based on the choice of the most sensitive monitoring wavelength; dark columns, monitoring strategy aimed at minimizing the cumulative effect of thickness errors.

Fig. 5
Fig. 5

Theoretical transmittance of the 38-layer stop band filter (solid curve) and transmittance of the best computationally manufactured filter in the case when passive monitoring strategy MS2 was applied (dashed curve).

Fig. 6
Fig. 6

Errors in the layer physical thicknesses of the best computationally manufactured filter with the spectral transmittance shown in Fig. 5: cumulative effect of thickness errors is clearly observed.

Fig. 7
Fig. 7

Errors in the layer physical thicknesses of one of the computationally manufactured filters when the new active monitoring strategy was applied: typical results.

Fig. 8
Fig. 8

Theoretical transmittance of the 38-layer stop band filter (solid curve) and transmittance of the computationally manufactured filter (dashed curve) in the case of shutter delays with parameters τ 0 = 1   s , σ τ = 0.5   s (see text for details). Errors in the layer thicknesses of this filter are shown in Fig. 9.

Fig. 9
Fig. 9

Errors in the layer physical thicknesses of the computationally manufactured filter with the transmittance shown in Fig. 8: most of the filter layers are overdeposited because of a constant time component τ 0 = 1   s of all shutter delays.

Fig. 10
Fig. 10

Theoretical transmittance of the 38-layer stop band filter (solid curve) and transmittance of one of the computationally manufactured filters (dashed curve) in the case of variations in the refractive indices of high index layers (see text for details). Errors in the layer thicknesses of this filter are shown in Fig. 11.

Fig. 11
Fig. 11

Errors on the layer physical thicknesses of the computationally manufactured filter with the transmittance shown in Fig. 10: errors in the thicknesses of odd layers are partly connected with an attempt to compensate for variations in the refractive indices of high index layers.

Tables (2)

Tables Icon

Table 1 Monitoring Spreadsheet for the 38-Layer Stop Band Filter

Tables Icon

Table 2 Simulated Variations of the Refractive Indices of Several High Index Layers of the Computationally Manufactured Coating with the Transmittance Shown in Fig. 10

Equations (10)

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

h ˜ f i n + h ˜ i n = h f i n + h i n ,
T m o n = T T s 1 R R s ,
T s = 4 n a n s ( n a + n s ) 2 , R s = ( n a n s n a + n s ) 2 ,
R = T s T m o n T s T m o n R s .
M 0 = max { λ j } | T k ( λ j , h ) h | h = 0 ,
M 1 = max { λ j } | T k ( λ j , h ) h | h = h t h .
B ( λ j ) = min { 1 M 0 | T k ( λ j , h ) h | h = 0 , 1 M 1 | T k ( λ j , h ) h | h = h t h } ,
C ( λ j ) = T s Δ T T max ( λ j ) Δ T Θ ( Δ T T s + T max ( λ j ) ) ,
T s T max ( λ j ) < Δ T ,
τ = τ 0 + τ r ,

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