Abstract

We presents what we believe to be a new approach to choosing a sequence of monitoring wavelengths for monochromatic monitoring of optical coating production. The new approach is based on a preproduction estimation of expected levels of errors in thickness of layers of a deposited coating. It is demonstrated that the proposed monitoring strategy reduces the effect of accumulation of thickness errors. An advantage of the new monitoring strategy becomes especially noticeable when the number of monitored layers is equal to several dozens.

© 2006 Optical Society of America

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References

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  1. A. V. Tikhonravov, "Design of optical coatings," in Optical Interference Coatings, N.Kaiser and H.K.Pulker, eds. (Springer-Verlag, 2003), pp. 81-104.
  2. H. A. Macleod, Thin Film Optical Filters (McGraw-Hill, 1986).
    [CrossRef]
  3. H. Macleod, "Monitoring of optical coatings," Appl. Opt. 20, 82-89 (1981).
    [CrossRef] [PubMed]
  4. R. R. Willey, "Optical thickness monitoring sensitivity improvement using graphical methods," Appl. Opt. 26, 729-737 (1987).
    [CrossRef] [PubMed]
  5. 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]
  6. B. Vidal, A. Fornier, and E. Pelletier, "Optical monitoring of nonquarterwave multilayer filters," Appl. Opt. 17, 1038-1047 (1978).
    [CrossRef] [PubMed]
  7. B. Vidal, A. Fornier, and E. Pelletier, "Wideband optical monitoring of nonquarterwave multilayer filters," Appl. Opt. 18, 3851-3856 (1979).
    [PubMed]
  8. B. Vidal and E. Pelletier, "Nonquarterwave multilayer filters: optical monitoring with a minicomputer allowing correction of thickness errors," Appl. Opt. 18, 3857-3862 (1979).
    [PubMed]
  9. B. T. Sullivan and J. A. Dobrowolski, "Deposition error compensation for optical multilayer coatings. II. Experimental results-sputtering system," Appl. Opt. 32, 2351-2360 (1993).
    [CrossRef] [PubMed]
  10. L. Li and Y. Yen, "Wideband monitoring and measuring system for optical coatings," Appl. Opt. 28, 2890-2894 (1989).
    [CrossRef]
  11. B. Sullivan, G. Clarke, T. Akiyama, N. Osborne, M. Ranger, J. A. Dobrowolski, L. Howe, A. Matsumoto, Y. Song, and K. Kikuchi, "High-rate automated deposition system for the manufacture of complex multilayer coatings," Appl. Opt. 39, 157-167 (2000).
    [CrossRef]
  12. A. V. Tikhonravov and M. K. Trubetskov, "On-line characterization and reoptimization of optical coatings," in Proc. SPIE 5250, 406-413 (2004).
    [CrossRef]
  13. A. V. Tikhonravov and M. K. Trubetskov, "Computational manufacturing as a bridge between design and production," Appl. Opt. 44, 6877-6884 (2005).
    [CrossRef] [PubMed]
  14. D. Ristau, T. Gross, and M. Lappschies, "Optical broadband monitoring of conventional and ion process," in Digest of Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE1.
  15. M. Lappschies, B. Goertz, and D. Ristau, "Application of optical broadband monitoring to quasi-rugate filters by ion beam sputtering," in Digest of Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE4.
  16. S. Wilbrandt, R. Leitel, D. Gabler, O. Stenzel, and N. Kaiser, "In situ broadband monitoring and characterization of optical coatings," in Digest of Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE6.
  17. S. Dligatch, "Real time process control and monitoring in multilayer filter deposition," in Digest of Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE5.
  18. A. Zoeller, M. Boos, R. Goetzelmann, H. Hagedorn, and W. Klug, "Substantial progress in optical monitoring by intermittent measurement technique," in Proc. SPIE 5963, 105-113 (2005).
  19. A. Zoeller, M. Boos, H. Hagedorn, W. Klug, and C. Schmitt, "High accurate in situ optical thickness monitoring for multilayer coatings," in Proceedings of 47th Annual SVC Conference (Society of Vacuum Coaters, 2004), pp. 72-78.
  20. 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]
  21. H. A. Macleod, "Turning value monitoring of narrow-band all-dielectric thin film optical filters," Opt. Acta 19, 1-28 (1972).
    [CrossRef]
  22. 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]
  23. H. Macleod and E. Pelletier, "Error compensation mechanisms in some thin-film monitoring systems," Optica Acta 24, 907-930 (1977).
    [CrossRef]
  24. 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]
  25. F. Zhao, "Monitoring of periodic multilayers by the level method," Appl. Opt. 24, 3339-3342 (1985).
    [CrossRef] [PubMed]
  26. 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]
  27. C. J. van der Laan, "Optical monitoring of nonquarterwave stacks," Appl. Opt. 25, 757-760 (1989).
  28. C. Holm, "Optical thin-film production with continuous reoptimization of layer thicknesses," Appl. Opt. 18, 1978-1982 (1978).
    [CrossRef]
  29. C. Grezes-Besset, F. Chazallat, and G. Albrand, "Synthesis and research of the optimum conditions for the optical monitoring of non-quarter-wave multilayers," Appl. Opt. 32, 5612-5618 (1997).
    [CrossRef]
  30. 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]
  31. 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]

2006 (1)

2005 (3)

2004 (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 47th Annual SVC Conference (Society of Vacuum Coaters, 2004), pp. 72-78.

D. Ristau, T. Gross, and M. Lappschies, "Optical broadband monitoring of conventional and ion process," in Digest of Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE1.

M. Lappschies, B. Goertz, and D. Ristau, "Application of optical broadband monitoring to quasi-rugate filters by ion beam sputtering," in Digest of Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE4.

S. Wilbrandt, R. Leitel, D. Gabler, O. Stenzel, and N. Kaiser, "In situ broadband monitoring and characterization of optical coatings," in Digest of Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE6.

S. Dligatch, "Real time process control and monitoring in multilayer filter deposition," in Digest of Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE5.

A. V. Tikhonravov and M. K. Trubetskov, "On-line characterization and reoptimization of optical coatings," in Proc. SPIE 5250, 406-413 (2004).
[CrossRef]

2003 (1)

A. V. Tikhonravov, "Design of optical coatings," in Optical Interference Coatings, N.Kaiser and H.K.Pulker, eds. (Springer-Verlag, 2003), pp. 81-104.

2002 (1)

2000 (1)

1999 (1)

1997 (1)

1993 (1)

1992 (1)

1989 (2)

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

C. J. van der Laan, "Optical monitoring of nonquarterwave stacks," Appl. Opt. 25, 757-760 (1989).

1987 (1)

1986 (1)

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

1985 (1)

1981 (1)

1979 (2)

1978 (2)

1977 (1)

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

1974 (1)

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 (2)

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]

Akiyama, T.

Albrand, G.

Boos, M.

A. Zoeller, M. Boos, R. Goetzelmann, H. Hagedorn, and W. Klug, "Substantial progress in optical monitoring by intermittent measurement technique," in 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 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]

Chazallat, F.

Chen, S.-H.

Chun, B.

Clarke, G.

Dligatch, S.

S. Dligatch, "Real time process control and monitoring in multilayer filter deposition," in Digest of Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE5.

Dobrowolski, J. A.

Fornier, A.

Gabler, D.

S. Wilbrandt, R. Leitel, D. Gabler, O. Stenzel, and N. Kaiser, "In situ broadband monitoring and characterization of optical coatings," in Digest of Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE6.

Goertz, B.

M. Lappschies, B. Goertz, and D. Ristau, "Application of optical broadband monitoring to quasi-rugate filters by ion beam sputtering," in Digest of Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE4.

Goetzelmann, R.

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

Grezes-Besset, C.

Gross, T.

D. Ristau, T. Gross, and M. Lappschies, "Optical broadband monitoring of conventional and ion process," in Digest of Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE1.

Hagedorn, H.

A. Zoeller, M. Boos, R. Goetzelmann, H. Hagedorn, and W. Klug, "Substantial progress in optical monitoring by intermittent measurement technique," in 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 47th Annual SVC Conference (Society of Vacuum Coaters, 2004), pp. 72-78.

Holm, C.

Howe, L.

Hwangbo, C. K.

Kaiser, N.

S. Wilbrandt, R. Leitel, D. Gabler, O. Stenzel, and N. Kaiser, "In situ broadband monitoring and characterization of optical coatings," in Digest of Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE6.

Kikuchi, K.

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," in 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 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.

Lappschies, M.

D. Ristau, T. Gross, and M. Lappschies, "Optical broadband monitoring of conventional and ion process," in Digest of Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE1.

M. Lappschies, B. Goertz, and D. Ristau, "Application of optical broadband monitoring to quasi-rugate filters by ion beam sputtering," in Digest of Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE4.

Lee, C.-C.

Leitel, R.

S. Wilbrandt, R. Leitel, D. Gabler, O. Stenzel, and N. Kaiser, "In situ broadband monitoring and characterization of optical coatings," in Digest of Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE6.

Li, L.

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

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," Optica 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.

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]

Matsumoto, A.

Osborne, N.

Pelletier, E.

Ranger, M.

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]

Ristau, D.

M. Lappschies, B. Goertz, and D. Ristau, "Application of optical broadband monitoring to quasi-rugate filters by ion beam sputtering," in Digest of Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE4.

D. Ristau, T. Gross, and M. Lappschies, "Optical broadband monitoring of conventional and ion process," in Digest of Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE1.

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 47th Annual SVC Conference (Society of Vacuum Coaters, 2004), pp. 72-78.

Song, Y.

Stenzel, O.

S. Wilbrandt, R. Leitel, D. Gabler, O. Stenzel, and N. Kaiser, "In situ broadband monitoring and characterization of optical coatings," in Digest of Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE6.

Sullivan, B.

Sullivan, B. T.

Tikhonravov, A. V.

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

A. V. Tikhonravov and M. K. Trubetskov, "On-line characterization and reoptimization of optical coatings," in Proc. SPIE 5250, 406-413 (2004).
[CrossRef]

A. V. Tikhonravov, "Design of optical coatings," in Optical Interference Coatings, N.Kaiser and H.K.Pulker, eds. (Springer-Verlag, 2003), pp. 81-104.

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]

Trubetskov, M. K.

van der Laan, C. J.

C. J. van der Laan, "Optical monitoring of nonquarterwave stacks," Appl. Opt. 25, 757-760 (1989).

Vidal, B.

Wilbrandt, S.

S. Wilbrandt, R. Leitel, D. Gabler, O. Stenzel, and N. Kaiser, "In situ broadband monitoring and characterization of optical coatings," in Digest of Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE6.

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," in 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 47th Annual SVC Conference (Society of Vacuum Coaters, 2004), pp. 72-78.

Appl. Opt. (16)

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]

B. Vidal, A. Fornier, and E. Pelletier, "Optical monitoring of nonquarterwave multilayer filters," Appl. Opt. 17, 1038-1047 (1978).
[CrossRef] [PubMed]

B. Vidal, A. Fornier, and E. Pelletier, "Wideband optical monitoring of nonquarterwave multilayer filters," Appl. Opt. 18, 3851-3856 (1979).
[PubMed]

B. Vidal and E. Pelletier, "Nonquarterwave multilayer filters: optical monitoring with a minicomputer allowing correction of thickness errors," Appl. Opt. 18, 3857-3862 (1979).
[PubMed]

B. T. Sullivan and J. A. Dobrowolski, "Deposition error compensation for optical multilayer coatings. II. Experimental results-sputtering system," Appl. Opt. 32, 2351-2360 (1993).
[CrossRef] [PubMed]

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

B. Sullivan, G. Clarke, T. Akiyama, N. Osborne, M. Ranger, J. A. Dobrowolski, L. Howe, A. Matsumoto, Y. Song, and K. Kikuchi, "High-rate automated deposition system for the manufacture of complex multilayer coatings," Appl. Opt. 39, 157-167 (2000).
[CrossRef]

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

C. J. van der Laan, "Optical monitoring of nonquarterwave stacks," Appl. Opt. 25, 757-760 (1989).

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

C. Grezes-Besset, F. Chazallat, and G. Albrand, "Synthesis and research of the optimum conditions for the optical monitoring of non-quarter-wave multilayers," Appl. Opt. 32, 5612-5618 (1997).
[CrossRef]

Opt. Acta (2)

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]

Opt. Express (2)

Optica Acta (1)

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

Proc. SPIE (2)

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

A. V. Tikhonravov and M. K. Trubetskov, "On-line characterization and reoptimization of optical coatings," in Proc. SPIE 5250, 406-413 (2004).
[CrossRef]

Thin Solid Films (1)

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 (7)

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

A. V. Tikhonravov, "Design of optical coatings," in Optical Interference Coatings, N.Kaiser and H.K.Pulker, eds. (Springer-Verlag, 2003), pp. 81-104.

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

D. Ristau, T. Gross, and M. Lappschies, "Optical broadband monitoring of conventional and ion process," in Digest of Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE1.

M. Lappschies, B. Goertz, and D. Ristau, "Application of optical broadband monitoring to quasi-rugate filters by ion beam sputtering," in Digest of Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE4.

S. Wilbrandt, R. Leitel, D. Gabler, O. Stenzel, and N. Kaiser, "In situ broadband monitoring and characterization of optical coatings," in Digest of Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE6.

S. Dligatch, "Real time process control and monitoring in multilayer filter deposition," in Digest of Optical Interference Coatings on CD-ROM (Optical Society of America, 2004), paper TuE5.

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Figures (8)

Fig. 1
Fig. 1

Schematic illustrating the relation of the monitoring strategies discussed (gray rectangle) to other monitoring strategies.

Fig. 2
Fig. 2

Theoretical transmittance of the 19-layer ramp coating.

Fig. 3
Fig. 3

Theoretical transmittance of the 42-layer band stop filter.

Fig. 4
Fig. 4

Theoretical transmittance of the 44-layer hot mirror.

Fig. 5
Fig. 5

Sequences of monitoring wavelengths for the ramp coating specified according to Strategy 1 (connected by the gray line) and to Strategy 2 (connected by the black line).

Fig. 6
Fig. 6

Expected levels of errors in the thicknesses of layers of the ramp coating. Light columns, Strategy 1; dark columns, Strategy 2.

Fig. 7
Fig. 7

Expected levels of errors in the thicknesses of layers of the 42-layer band stop filter. Light columns, Strategy 1; dark columns, Strategy 2.

Fig. 8
Fig. 8

Expected levels of errors in the thicknesses of layers of the 44-layer hot mirror. Light columns, Strategy 1; dark columns, Strategy 2.

Tables (1)

Tables Icon

Table 1 Thicknesses of Layers of the Ramp, Band Stop Filter, and Hot Mirror Design

Equations (24)

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

T ( j ) ( d 1 ,   …   ,   d j ; λ ) = T ( j ) ( d 1 t ,   …   ,   d j t ; λ ) + i = 1 j T ( j ) d i δ d i .
d i = d i t + δ d i .
T meas ( 1 ) ( d 1 ; λ 1 ) = T ( 1 ) ( d 1 ; λ 1 ) + δ T meas ( 1 ) .
T meas ( 1 ) ( d 1 ; λ 1 ) = T ( 1 ) ( d 1 t ; λ 1 ) .
T meas ( 1 ) ( d 1 ; λ 1 ) = T ( 1 ) ( d 1 t ; λ 1 ) + T ( 1 ) d 1 δ d 1 + δ T meas ( 1 ) .
T ( 1 ) d 1 δ d 1 + δ T meas ( 1 ) = 0.
δ d 1 = [ 1 / T ( 1 ) d 1 ] δ T meas ( 1 ) .
σ 1 = | 1 / T ( 1 ) d 1 | σ meas .
T meas ( 2 ) ( d 1 , d 2 ; λ 2 ) = T ( 2 ) ( d 1 t , d 2 t ; λ 2 ) + T ( 2 ) d 1 δ d 1 + T ( 2 ) d 2 δ d 2 + δ T meas ( 2 ) .
T meas ( 2 ) ( d 1 , d 2 ; λ 2 ) = T ( 2 ) ( d 1 t , d 2 t ; λ 2 ) .
δ d 2 = [ 1 / T ( 2 ) d 2 ] [ δ T meas ( 2 ) + T ( 2 ) d 1 δ d 1 ] .
α 1 ( 1 ) = 1 / T ( 1 ) d 1 .
δ d 1 = α 1 ( 1 ) ( λ 1 ) δ T meas ( 1 ) ,
δ d 2 = α 1 ( 2 ) ( λ 2 ) δ T meas ( 1 ) + α 2 ( 2 ) ( λ 2 ) δ T meas ( 2 ) ,
α 1 ( 2 ) ( λ ) = [ α 1 ( 1 ) ( λ 1 ) T ( 2 ) d 1 ] / T ( 2 ) d 2 ,
α 2 ( 2 ) ( λ ) = 1 / T ( 2 ) d 2 ,
σ 2 = { i = 1 2 [ α i ( 2 ) ( λ 2 ) ] 2 } 1 / 2 σ meas .
E ( 2 ) ( λ ) = i = 1 2 [ α i ( 2 ) ( λ ) ] 2 .
δ d j = [ 1 / T ( j ) d j ] [ δ T meas ( j ) + T ( j ) d 1 δ d 1 + + T ( j ) d j 1 δ d j 1 ] .
δ d j = α 1 ( j ) ( λ j ) δ T meas ( 1 ) + + α j ( j ) ( λ j ) δ T meas ( j ) ,
α i ( j ) ( λ ) = - [ k = i j 1 α i ( k ) ( λ k ) T ( j ) d k ( λ ) ] / T ( j ) d j ( λ )
α j ( j ) ( λ ) = 1 / T ( j ) d j ( λ ) .
σ j = { i = 1 j [ α i ( j ) ( λ j ) ] 2 } 1 / 2 σ meas .
E ( j ) ( λ ) = i = 1 j [ α i ( j ) ( λ ) ] 2 ,

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