Abstract

A rigorous definition of the error self-compensation effect is provided. An existence of this effect in the case of coating production with broadband optical monitoring of layer thicknesses is investigated for several widely used types of optical coatings.

© 2011 Optical Society of America

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References

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  1. B. Vidal, A. Fornier, and E. Pelletier, “Optical monitoring of nonquarterwave multilayer filters,” Appl. Opt. 17, 1038–1047(1978).
    [Crossref] [PubMed]
  2. B. Vidal, A. Fornier, and E. Pelletier, “Wideband optical monitoring of nonquarterwave multilayer filters,” Appl. Opt. 18, 3851–3856 (1979).
    [Crossref] [PubMed]
  3. B. Vidal and E. Pelletier, “Nonquarterwave multilayer filters: optical monitoring with a minicomputer allowing correction of thickness errors,” Appl. Opt. 18, 3857–3862 (1979).
    [Crossref] [PubMed]
  4. A. V. Tikhonravov, M. K. Trubetskov, M. A. Kokarev, T. V. Amotchkina, A. Duparré, E. Quesnel, D. Ristau, and S. Günster, “Effect of systematic errors in spectral photometric data on the accuracy of determination of optical parameters of dielectric thin films,” Appl. Opt. 41, 2555–2560 (2002).
    [Crossref] [PubMed]
  5. A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, “Investigation of the effect of accumulation of thickness errors in optical coating production using broadband optical monitoring,” Appl. Opt. 45, 7026–7034 (2006).
    [Crossref] [PubMed]
  6. H. A. Macleod, “Monitoring of optical coatings,” Appl. Opt. 20, 82–89 (1981).
    [Crossref] [PubMed]
  7. 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]
  8. A. V. Tikhonravov and M. K. Trubetskov, “Computational manufacturing as a bridge between design and production,” Appl. Opt. 44, 6877–6884 (2005).
    [Crossref] [PubMed]
  9. H. A. Macleod, “Turning value monitoring of narrow-band all dielectric thin film optical filters,” Opt. Acta 19, 1–28 (1972).
    [Crossref]
  10. P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, “Optical filters: monitoring process allowing the autocorrection of thickness errors,” Thin Solid Films 13, 285–290 (1972).
    [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. H. A. Macleod, Thin Film Optical Filters (McGraw-Hill, 1986).
    [Crossref]
  13. A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, “Statistical approach to choosing a strategy of monochromatic monitoring of optical coating production,” Appl. Opt. 45, 7863–7870 (2006).
    [Crossref] [PubMed]
  14. H. Jeffreys, Theory of Probability, 3rd ed. (Clarendon, 1961).

2006 (2)

2005 (1)

2002 (2)

1992 (1)

1981 (1)

1979 (2)

1978 (1)

1972 (2)

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

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, “Optical filters: monitoring process allowing the autocorrection of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[Crossref]

Amotchkina, T. V.

Bousquet, P.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, “Optical filters: monitoring process allowing the autocorrection of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[Crossref]

Dobrowolski, J. A.

Duparré, A.

Fornier, A.

Günster, S.

Jeffreys, H.

H. Jeffreys, Theory of Probability, 3rd ed. (Clarendon, 1961).

Kokarev, M. A.

Kowalczyk, R.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, “Optical filters: monitoring process allowing the autocorrection of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[Crossref]

Macleod, H. A.

H. A. Macleod, “Monitoring of optical coatings,” Appl. Opt. 20, 82–89 (1981).
[Crossref] [PubMed]

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

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

Pelletier, E.

Quesnel, E.

Ristau, D.

Roche, P.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, “Optical filters: monitoring process allowing the autocorrection of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[Crossref]

Sullivan, B. T.

Tikhonravov, A. V.

Trubetskov, M. K.

Vidal, B.

Appl. Opt. (10)

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).
[Crossref] [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).
[Crossref] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, M. A. Kokarev, T. V. Amotchkina, A. Duparré, E. Quesnel, D. Ristau, and S. Günster, “Effect of systematic errors in spectral photometric data on the accuracy of determination of optical parameters of dielectric thin films,” Appl. Opt. 41, 2555–2560 (2002).
[Crossref] [PubMed]

A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, “Investigation of the effect of accumulation of thickness errors in optical coating production using broadband optical monitoring,” Appl. Opt. 45, 7026–7034 (2006).
[Crossref] [PubMed]

H. A. Macleod, “Monitoring of optical coatings,” Appl. Opt. 20, 82–89 (1981).
[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, “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]

A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, “Statistical approach to choosing a strategy of monochromatic monitoring of optical coating production,” Appl. Opt. 45, 7863–7870 (2006).
[Crossref] [PubMed]

Opt. Acta (1)

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

Thin Solid Films (1)

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, and P. Roche, “Optical filters: monitoring process allowing the autocorrection of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[Crossref]

Other (2)

H. Jeffreys, Theory of Probability, 3rd ed. (Clarendon, 1961).

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

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Figures (8)

Fig. 1
Fig. 1

Schematic illustrating the definition of the error self- compensation effect.

Fig. 2
Fig. 2

Comparison of error levels σ i calculated for HM1 based on 50 computational manufacturing experiments (gray bars) with error levels calculated using exact formulas (black bars).

Fig. 3
Fig. 3

Comparison of error levels σ i calculated for HM2 based on 50 computational manufacturing experiments (gray bars) with error levels calculated using exact formulas (black bars).

Fig. 4
Fig. 4

HM1 (top left) and HM2 (bottom left) and respective transmittances (right panes).

Fig. 5
Fig. 5

CM1 (top left) and CM2 (bottom left) and respective transmittances (right panes).

Fig. 6
Fig. 6

BPF1 (top left) and BPF2 (bottom left) and respective transmittances (right panes).

Fig. 7
Fig. 7

NBPF1 (top left) and NBPF2 (bottom left) and respective transmittances (right panes).

Fig. 8
Fig. 8

3LMF1 (top left) and 3LMF2 (bottom left) and respective reflectances (right panes).

Tables (1)

Tables Icon

Table 1 Degrees of Error Self-Compensation Effect for Various Designs

Equations (3)

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F BBM m = { 1 L j = 1 L [ T m ( λ j ) T ( λ j ) ] } 1 / 2 ,
F Random n = { 1 L j = 1 L [ T ^ n ( λ j ) T ( λ j ) ] } 1 / 2 .
S = F Random n F BBM m

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