Abstract

The main theoretical results related to the investigation of the error self-compensation mechanism associated with direct broad band monitoring of optical coating production are presented. The presented results are illustrated using the production of Brewster angle polarizer where this effect is especially strong. Specific properties of the design merit function required for the presence of the error self-compensation effect are discussed and the mechanism of thickness errors correlation by the direct broad band monitoring is described. It is also discussed how one can check whether a strong error self-compensation effect may be expected for a given coating design and specific parameters of the monitoring procedure that will be used for coating production.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Investigation of the error self-compensation effect associated with direct broad band monitoring of coating production

A. V. Tikhonravov, I. V. Kochikov, and A. G. Yagola
Opt. Express 26(19) 24964-24972 (2018)

Comparison of algorithms used for optical characterization of multilayer optical coatings

Tatiana V. Amotchkina, Michael K. Trubetskov, Vladimir Pervak, Sebastian Schlichting, Henrik Ehlers, Detlev Ristau, and Alexander V. Tikhonravov
Appl. Opt. 50(20) 3389-3395 (2011)

Design, production, and reverse engineering of two-octave antireflection coatings

Tatiana V. Amotchkina, Michael K. Trubetskov, Vladimir Pervak, and Alexander V. Tikhonravov
Appl. Opt. 50(35) 6468-6475 (2011)

References

  • View by:
  • |
  • |
  • |

  1. B. Vidal, A. Fornier, and E. Pelletier, “Optical monitoring of nonquarterwave multilayer filters,” Appl. Opt. 17(7), 1038–1047 (1978).
    [PubMed]
  2. B. Vidal, A. Fornier, and E. Pelletier, “Wideband optical monitoring of nonquarterwave multilayer filters,” Appl. Opt. 18(22), 3851–3856 (1979).
    [PubMed]
  3. B. Vidal and E. Pelletier, “Nonquarterwave multilayer filters: optical monitoring with a minicomputer allowing correction of thickness errors,” Appl. Opt. 18(22), 3857–3862 (1979).
    [PubMed]
  4. B. T. Sullivan and J. A. Dobrowolski, “Deposition error compensation for optical multilayer coatings. I. Theoretical description,” Appl. Opt. 31(19), 3821–3835 (1992).
    [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 by broadband optical monitoring,” Appl. Opt. 45(27), 7026–7034 (2006).
    [PubMed]
  6. H. A. Macleod, “Monitoring of optical coatings,” Appl. Opt. 20(1), 82–89 (1981).
    [PubMed]
  7. H. A. Macleod, Thin-Film Optical Filters, 4th ed. (Taylor & Francis, 2010).
  8. 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).
  9. H. A. Macleod, “Turning value monitoring of narrow-band alldielectric thin film optical filters,” Opt. Acta (Lond.) 19, 1–28 (1972).
  10. H. Macleod and E. Pelletier, “Error compensation mechanisms in some thin-film monitoring systems,” Opt. Acta (Lond.) 24, 907–930 (1977).
  11. A. V. Tikhonravov and M. K. Trubetskov, “Automated design and sensitivity analysis of wavelengh-division multiplexing filters,” Appl. Opt. 41(16), 3176–3182 (2002).
    [PubMed]
  12. A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, “Investigation of the error self-compensation effect associated with broadband optical monitoring,” Appl. Opt. 50(9), C111–C116 (2011).
    [PubMed]
  13. V. Zhupanov, I. Kozlov, V. Fedoseev, P. Konotopov, M. Trubetskov, and A. Tikhonravov, “Production of Brewster angle thin film polarizers using a ZrO2/SiO2 pair of materials,” Appl. Opt. 56(4), C30–C34 (2017).
    [PubMed]
  14. A. V. Tikhonravov, I. V. Kochikov, and A. G. Yagola, “Mathematical investigation of the error self-compensation mechanism in optical coating technology,” IPSE (to be published).
  15. A. V. Tikhonravov and M. K. Trubetskov, “Modern design tools and a new paradigm in optical coating design,” Appl. Opt. 51(30), 7319–7332 (2012).
    [PubMed]
  16. G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. (John Hopkins University, 1996).
  17. A. V. Tikhonravov and M. K. Trubetskov, “Computational manufacturing as a bridge between design and production,” Appl. Opt. 44(32), 6877–6884 (2005).
    [PubMed]
  18. A. V. Tikhonravov and M. K. Trubetskov, “Online characterization and re-optimization of optical coatings”, in Advances in Optical Thin Films (SPIE, 2003), pp. 406–413.
  19. T. V. Amotchkina, M. K. Trubetskov, V. Pervak, S. Schlichting, H. Ehlers, D. Ristau, and A. V. Tikhonravov, “Comparison of algorithms used for optical characterization of multilayer optical coatings,” Appl. Opt. 50(20), 3389–3395 (2011).
    [PubMed]
  20. MATLAB version 7.10.0. Natick, MA: The MathWorks Inc. (2010).
  21. Maple 2016. Maplesoft, a division of Waterloo Maple Inc., Waterloo, Ontario.
  22. Wolfram Research, Inc., Mathematica, Version 11.2, Champaign, IL (2017).

2017 (1)

2012 (1)

2011 (2)

2006 (1)

2005 (1)

2002 (1)

1992 (1)

1981 (1)

1979 (2)

1978 (1)

1977 (1)

H. Macleod and E. Pelletier, “Error compensation mechanisms in some thin-film monitoring systems,” Opt. Acta (Lond.) 24, 907–930 (1977).

1972 (2)

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).

H. A. Macleod, “Turning value monitoring of narrow-band alldielectric thin film optical filters,” Opt. Acta (Lond.) 19, 1–28 (1972).

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).

Dobrowolski, J. A.

Ehlers, H.

Fedoseev, V.

Fornier, A.

Kochikov, I. V.

A. V. Tikhonravov, I. V. Kochikov, and A. G. Yagola, “Mathematical investigation of the error self-compensation mechanism in optical coating technology,” IPSE (to be published).

Konotopov, P.

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).

Kozlov, I.

Macleod, H.

H. Macleod and E. Pelletier, “Error compensation mechanisms in some thin-film monitoring systems,” Opt. Acta (Lond.) 24, 907–930 (1977).

Macleod, H. A.

H. A. Macleod, “Monitoring of optical coatings,” Appl. Opt. 20(1), 82–89 (1981).
[PubMed]

H. A. Macleod, “Turning value monitoring of narrow-band alldielectric thin film optical filters,” Opt. Acta (Lond.) 19, 1–28 (1972).

Pelletier, E.

B. Vidal, A. Fornier, and E. Pelletier, “Wideband optical monitoring of nonquarterwave multilayer filters,” Appl. Opt. 18(22), 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(22), 3857–3862 (1979).
[PubMed]

B. Vidal, A. Fornier, and E. Pelletier, “Optical monitoring of nonquarterwave multilayer filters,” Appl. Opt. 17(7), 1038–1047 (1978).
[PubMed]

H. Macleod and E. Pelletier, “Error compensation mechanisms in some thin-film monitoring systems,” Opt. Acta (Lond.) 24, 907–930 (1977).

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).

Pervak, V.

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).

Schlichting, S.

Sullivan, B. T.

Tikhonravov, A.

Tikhonravov, A. V.

Trubetskov, M.

Trubetskov, M. K.

Vidal, B.

Yagola, A. G.

A. V. Tikhonravov, I. V. Kochikov, and A. G. Yagola, “Mathematical investigation of the error self-compensation mechanism in optical coating technology,” IPSE (to be published).

Zhupanov, V.

Appl. Opt. (12)

B. Vidal, A. Fornier, and E. Pelletier, “Optical monitoring of nonquarterwave multilayer filters,” Appl. Opt. 17(7), 1038–1047 (1978).
[PubMed]

B. Vidal, A. Fornier, and E. Pelletier, “Wideband optical monitoring of nonquarterwave multilayer filters,” Appl. Opt. 18(22), 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(22), 3857–3862 (1979).
[PubMed]

B. T. Sullivan and J. A. Dobrowolski, “Deposition error compensation for optical multilayer coatings. I. Theoretical description,” Appl. Opt. 31(19), 3821–3835 (1992).
[PubMed]

A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, “Investigation of the effect of accumulation of thickness errors in optical coating production by broadband optical monitoring,” Appl. Opt. 45(27), 7026–7034 (2006).
[PubMed]

H. A. Macleod, “Monitoring of optical coatings,” Appl. Opt. 20(1), 82–89 (1981).
[PubMed]

A. V. Tikhonravov and M. K. Trubetskov, “Automated design and sensitivity analysis of wavelengh-division multiplexing filters,” Appl. Opt. 41(16), 3176–3182 (2002).
[PubMed]

A. V. Tikhonravov, M. K. Trubetskov, and T. V. Amotchkina, “Investigation of the error self-compensation effect associated with broadband optical monitoring,” Appl. Opt. 50(9), C111–C116 (2011).
[PubMed]

V. Zhupanov, I. Kozlov, V. Fedoseev, P. Konotopov, M. Trubetskov, and A. Tikhonravov, “Production of Brewster angle thin film polarizers using a ZrO2/SiO2 pair of materials,” Appl. Opt. 56(4), C30–C34 (2017).
[PubMed]

A. V. Tikhonravov and M. K. Trubetskov, “Modern design tools and a new paradigm in optical coating design,” Appl. Opt. 51(30), 7319–7332 (2012).
[PubMed]

T. V. Amotchkina, M. K. Trubetskov, V. Pervak, S. Schlichting, H. Ehlers, D. Ristau, and A. V. Tikhonravov, “Comparison of algorithms used for optical characterization of multilayer optical coatings,” Appl. Opt. 50(20), 3389–3395 (2011).
[PubMed]

A. V. Tikhonravov and M. K. Trubetskov, “Computational manufacturing as a bridge between design and production,” Appl. Opt. 44(32), 6877–6884 (2005).
[PubMed]

Opt. Acta (Lond.) (2)

H. A. Macleod, “Turning value monitoring of narrow-band alldielectric thin film optical filters,” Opt. Acta (Lond.) 19, 1–28 (1972).

H. Macleod and E. Pelletier, “Error compensation mechanisms in some thin-film monitoring systems,” Opt. Acta (Lond.) 24, 907–930 (1977).

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).

Other (7)

A. V. Tikhonravov and M. K. Trubetskov, “Online characterization and re-optimization of optical coatings”, in Advances in Optical Thin Films (SPIE, 2003), pp. 406–413.

G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. (John Hopkins University, 1996).

MATLAB version 7.10.0. Natick, MA: The MathWorks Inc. (2010).

Maple 2016. Maplesoft, a division of Waterloo Maple Inc., Waterloo, Ontario.

Wolfram Research, Inc., Mathematica, Version 11.2, Champaign, IL (2017).

A. V. Tikhonravov, I. V. Kochikov, and A. G. Yagola, “Mathematical investigation of the error self-compensation mechanism in optical coating technology,” IPSE (to be published).

H. A. Macleod, Thin-Film Optical Filters, 4th ed. (Taylor & Francis, 2010).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1 Physical thicknesses (a) and theoretical s- and p-transmittances (b) of the 28-layer polarizer design
Fig. 2
Fig. 2 (a) Thickness errors determined for the test polarizer production run, (b) solid curves are s- and p-transmittances corresponding to the design with these errors, dashed curves – transmittances of the design without thickness errors, (c) thickness errors determined for the next polarizer production run, (d) solid curves are s- and p-transmittances corresponding to the design with the second set of errors, dashed curves – transmittances of the design without thickness errors.
Fig. 3
Fig. 3 Examples of s-transmittances (a) and p-transmittances (b) for five designs with uncorrelated thickness errors with the same average error level as in Fig. 2(a).

Tables (2)

Tables Icon

Table 1 Eigenvalues of the matrix A corresponding to the polarizer design from [13].

Tables Icon

Table 2 Angles between the error vectors from Figs. 2(a) and 2(c) and three main eigenvectors of the matrix A.

Equations (14)

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

F= λ { [ T s (λ) ] 2 + [ T p (λ)1 ] 2 } .
δF= 1 2 i,j=1 m 2 F d i d j δ d i δ d j .
A= 2 F d i d j .
δF= i=1 m μ i Q i ,Δ 2 .
T j meas (d)= T j ( d 1 a ,..., d j1 a ,d)+δ T meas
Φ j (d)= min d {λ} [ T j meas (d) T j ( d 1 t ,..., d j t ,d) ] 2
Φ j (d)= {λ} [ i=1 j T j d i δ d i +δ T meas ] 2
Φ j ( d j t +δ d j )= i,k=1 j ( {λ} T j d i T j d k )δ d i δ d k +2 i=1 j ( {λ} T j d i δ T meas )δ d i + {λ} (δ T meas ) 2
Φ j = i,k=1 j ( {λ} T j d i T j d k )δ d i δ d k .
C j = {λ} T j d i T j d k .
δΦ= i=1 j λ i j P i j , D j 2
i=1 j λ i j P i j , D j 2 min
W ij = λ i j { p 1 ij ,..., p j ij ,0,...,0 }
i=1 j W ij Δ 2 min

Metrics