Abstract

We present the effectiveness of global sensitivity analyses of optical coatings manufacturing to assess the robustness of filters by computer experiments. The most critical interactions of layers are determined for a 29 quarter-wave layer bandpass filter and for an antireflection coating with eight non-quarter-wave layers. Two monitoring techniques with the associated production performances are considered, and their influence on the interactions classification is discussed. Global sensitivity analyses by numerical space filling designs give clues to improve filter manufacturing against error effects and to assess the potential robustness of the coatings.

© 2011 Optical Society of America

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References

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  1. R. W. Kennard and L. A. Stone, “Computer aided design of experiment,” Technometrics 11, 137–148 (1969).
    [CrossRef]
  2. M. Sergent, R. Phan-Tan-Luu, and J. Elguero, “Statistical analysis of solvent scales. part 1,” Anales Quimica Int. Ed. 93, 3–6 (1997).
  3. J. S. Park “Optimal Latin-hypercube designs for computer experiments,” J. Statist. Plann. Inference 39, 95–111 (1994).
    [CrossRef]
  4. J. R. Koehler and A. B. Owen, “Computer experiments” in Handbook of Statistics, S.Ghosh and C.R.Rao, eds. (Elsevier, 1996), Vol. 13, pp. 261–308.
    [CrossRef]
  5. A. Saltelli, K. Chan, and E. M. Scott, Sensitivity Analysis(Wiley, 2000).
  6. T. J. Santner, B. J. Williams, and W. I. Notz, The Design and Analysis of Computer Experiments (Springer, 2003).
  7. H. A. Macleod, Thin Film Optical Filters (Hilger, 1986).
    [CrossRef]
  8. P. C. Young, “Data-based mechanistic modelling, generalised sensitivity and dominant mode analysis,” Comput. Phys. Commun. 117, 113–129 (1999).
    [CrossRef]
  9. A. A. Giunta, S. F. Wojtkiewicz, and M. S. Eldred, “Overview of modern design of experiments methods for computational simulations,” in Proceedings of the 41st AIAA Aerospace Sciences Meeting and Exhibit, AIAA-2003-0649 (American Institute of Aeronautics and Astronautics, 2003).
  10. G. G. Wang and S. Shan, “Review of metamodeling techniques in support of engineering design optimization,” J. Mech. Des. 129, 370–380 (2007).
    [CrossRef]
  11. G. E. P. Box, W. G. Hunter, and J. S. Hunter, Statistics for Experimenters (Wiley, 1978).
  12. O. Vasseur, M. Claeys-Bruno, M. Cathelinaud, and M. Sergent, “High dimensional sensitivity analysis of complex optronic systems by experimental designs: applications to the case of the design and the robustness of optical coatings,” Chin. Opt. Lett. 8(1), 21–24 (2010).
    [CrossRef]
  13. H. A. Macleod, “Turning value monitoring of narrow-band all-dielectric thin film optical filters,” Opt. Acta 19, 1–28(1972).
    [CrossRef]
  14. H. A. Macleod and E. Pelletier, “Error compensation mechanisms in some thin-film monitoring systems,” Opt. Acta 24, 907–930 (1977).
    [CrossRef]
  15. M. Born and E. Wolf, Principles of Optics (Pergamon, 1970).
  16. A. N. Baskakov and A. Tikhonravov “Synthesis of two component optical coatings,” Opt. Spectrosc. 56, 915–919 (1984).
  17. 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]
  18. A. Tikhonravov, M. Trubetskov, and T. Amotchkina, “Computational experiments on optical coating production using monochromatic monitoring strategy aimed at eliminating a cumulative effect of thickness errors,” Appl. Opt. 46, 6936–6944 (2007).
    [CrossRef] [PubMed]
  19. B. J. 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]
  20. B. Badoil, F. Lemarchand, M. Cathelinaud, and M. Lequime, “Interest of broadband optical monitoring for thin-film filter manufacturing,” Appl. Opt. 46, 4294–4303(2007).
    [CrossRef] [PubMed]
  21. C. Vassallo, “Reflectivity of multidielectric coatings deposited on the end facet of a weakly guiding dielectric slab waveguide,” J. Opt. Soc. Am. A 5, 1918–1928 (1988).
    [CrossRef]
  22. O. Vasseur, “Reflectivity of dielectric coatings deposited on the end facet of a weakly guiding fiber,” J. Opt. Soc. Am. A 15, 77–83 (1998).
    [CrossRef]
  23. T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486(2007).
    [CrossRef]
  24. V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, G. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15, 257–268 (2009).
    [CrossRef]

2010 (1)

O. Vasseur, M. Claeys-Bruno, M. Cathelinaud, and M. Sergent, “High dimensional sensitivity analysis of complex optronic systems by experimental designs: applications to the case of the design and the robustness of optical coatings,” Chin. Opt. Lett. 8(1), 21–24 (2010).
[CrossRef]

2009 (1)

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, G. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15, 257–268 (2009).
[CrossRef]

2007 (4)

G. G. Wang and S. Shan, “Review of metamodeling techniques in support of engineering design optimization,” J. Mech. Des. 129, 370–380 (2007).
[CrossRef]

A. Tikhonravov, M. Trubetskov, and T. Amotchkina, “Computational experiments on optical coating production using monochromatic monitoring strategy aimed at eliminating a cumulative effect of thickness errors,” Appl. Opt. 46, 6936–6944 (2007).
[CrossRef] [PubMed]

B. Badoil, F. Lemarchand, M. Cathelinaud, and M. Lequime, “Interest of broadband optical monitoring for thin-film filter manufacturing,” Appl. Opt. 46, 4294–4303(2007).
[CrossRef] [PubMed]

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486(2007).
[CrossRef]

2006 (1)

1999 (1)

P. C. Young, “Data-based mechanistic modelling, generalised sensitivity and dominant mode analysis,” Comput. Phys. Commun. 117, 113–129 (1999).
[CrossRef]

1998 (1)

1997 (1)

M. Sergent, R. Phan-Tan-Luu, and J. Elguero, “Statistical analysis of solvent scales. part 1,” Anales Quimica Int. Ed. 93, 3–6 (1997).

1994 (1)

J. S. Park “Optimal Latin-hypercube designs for computer experiments,” J. Statist. Plann. Inference 39, 95–111 (1994).
[CrossRef]

1988 (1)

1984 (1)

A. N. Baskakov and A. Tikhonravov “Synthesis of two component optical coatings,” Opt. Spectrosc. 56, 915–919 (1984).

1977 (1)

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

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]

1969 (1)

R. W. Kennard and L. A. Stone, “Computer aided design of experiment,” Technometrics 11, 137–148 (1969).
[CrossRef]

Amotchkina, T.

Badoil, B.

Baker, J. T.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486(2007).
[CrossRef]

Baskakov, A. N.

A. N. Baskakov and A. Tikhonravov “Synthesis of two component optical coatings,” Opt. Spectrosc. 56, 915–919 (1984).

Benham, V.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486(2007).
[CrossRef]

Bennaï, B.

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, G. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15, 257–268 (2009).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1970).

Bourdon, P.

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, G. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15, 257–268 (2009).
[CrossRef]

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]

Box, G. E. P.

G. E. P. Box, W. G. Hunter, and J. S. Hunter, Statistics for Experimenters (Wiley, 1978).

Canat, G.

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, G. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15, 257–268 (2009).
[CrossRef]

Cathelinaud, M.

O. Vasseur, M. Claeys-Bruno, M. Cathelinaud, and M. Sergent, “High dimensional sensitivity analysis of complex optronic systems by experimental designs: applications to the case of the design and the robustness of optical coatings,” Chin. Opt. Lett. 8(1), 21–24 (2010).
[CrossRef]

B. Badoil, F. Lemarchand, M. Cathelinaud, and M. Lequime, “Interest of broadband optical monitoring for thin-film filter manufacturing,” Appl. Opt. 46, 4294–4303(2007).
[CrossRef] [PubMed]

Chan, K.

A. Saltelli, K. Chan, and E. M. Scott, Sensitivity Analysis(Wiley, 2000).

Chun, B. J.

Claeys-Bruno, M.

O. Vasseur, M. Claeys-Bruno, M. Cathelinaud, and M. Sergent, “High dimensional sensitivity analysis of complex optronic systems by experimental designs: applications to the case of the design and the robustness of optical coatings,” Chin. Opt. Lett. 8(1), 21–24 (2010).
[CrossRef]

Eldred, M. S.

A. A. Giunta, S. F. Wojtkiewicz, and M. S. Eldred, “Overview of modern design of experiments methods for computational simulations,” in Proceedings of the 41st AIAA Aerospace Sciences Meeting and Exhibit, AIAA-2003-0649 (American Institute of Aeronautics and Astronautics, 2003).

Elguero, J.

M. Sergent, R. Phan-Tan-Luu, and J. Elguero, “Statistical analysis of solvent scales. part 1,” Anales Quimica Int. Ed. 93, 3–6 (1997).

Fornier, A.

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]

Giunta, A. A.

A. A. Giunta, S. F. Wojtkiewicz, and M. S. Eldred, “Overview of modern design of experiments methods for computational simulations,” in Proceedings of the 41st AIAA Aerospace Sciences Meeting and Exhibit, AIAA-2003-0649 (American Institute of Aeronautics and Astronautics, 2003).

Goular, G.

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, G. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15, 257–268 (2009).
[CrossRef]

Hunter, J. S.

G. E. P. Box, W. G. Hunter, and J. S. Hunter, Statistics for Experimenters (Wiley, 1978).

Hunter, W. G.

G. E. P. Box, W. G. Hunter, and J. S. Hunter, Statistics for Experimenters (Wiley, 1978).

Hwangbo, C. K.

Jaouën, Y.

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, G. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15, 257–268 (2009).
[CrossRef]

Jolivet, V.

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, G. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15, 257–268 (2009).
[CrossRef]

Kennard, R. W.

R. W. Kennard and L. A. Stone, “Computer aided design of experiment,” Technometrics 11, 137–148 (1969).
[CrossRef]

Kim, J. S.

Koehler, J. R.

J. R. Koehler and A. B. Owen, “Computer experiments” in Handbook of Statistics, S.Ghosh and C.R.Rao, eds. (Elsevier, 1996), Vol. 13, pp. 261–308.
[CrossRef]

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]

Lemarchand, F.

Lequime, M.

Lombard, L.

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, G. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15, 257–268 (2009).
[CrossRef]

Lu, C. A.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486(2007).
[CrossRef]

Macleod, H. A.

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

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 (Hilger, 1986).
[CrossRef]

Moreau, B.

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, G. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15, 257–268 (2009).
[CrossRef]

Notz, W. I.

T. J. Santner, B. J. Williams, and W. I. Notz, The Design and Analysis of Computer Experiments (Springer, 2003).

Owen, A. B.

J. R. Koehler and A. B. Owen, “Computer experiments” in Handbook of Statistics, S.Ghosh and C.R.Rao, eds. (Elsevier, 1996), Vol. 13, pp. 261–308.
[CrossRef]

Park, J. S.

J. S. Park “Optimal Latin-hypercube designs for computer experiments,” J. Statist. Plann. Inference 39, 95–111 (1994).
[CrossRef]

Pelletier, E.

H. A. 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 autocorrection of thickness errors,” Thin Solid Films 13, 285–290 (1972).
[CrossRef]

Phan-Tan-Luu, R.

M. Sergent, R. Phan-Tan-Luu, and J. Elguero, “Statistical analysis of solvent scales. part 1,” Anales Quimica Int. Ed. 93, 3–6 (1997).

Pilkington, D.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486(2007).
[CrossRef]

Pourtal, E.

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, G. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15, 257–268 (2009).
[CrossRef]

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]

Saltelli, A.

A. Saltelli, K. Chan, and E. M. Scott, Sensitivity Analysis(Wiley, 2000).

Sanchez, A. D.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486(2007).
[CrossRef]

Santner, T. J.

T. J. Santner, B. J. Williams, and W. I. Notz, The Design and Analysis of Computer Experiments (Springer, 2003).

Scott, E. M.

A. Saltelli, K. Chan, and E. M. Scott, Sensitivity Analysis(Wiley, 2000).

Sergent, M.

O. Vasseur, M. Claeys-Bruno, M. Cathelinaud, and M. Sergent, “High dimensional sensitivity analysis of complex optronic systems by experimental designs: applications to the case of the design and the robustness of optical coatings,” Chin. Opt. Lett. 8(1), 21–24 (2010).
[CrossRef]

M. Sergent, R. Phan-Tan-Luu, and J. Elguero, “Statistical analysis of solvent scales. part 1,” Anales Quimica Int. Ed. 93, 3–6 (1997).

Shan, S.

G. G. Wang and S. Shan, “Review of metamodeling techniques in support of engineering design optimization,” J. Mech. Des. 129, 370–380 (2007).
[CrossRef]

Shay, T. M.

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486(2007).
[CrossRef]

Stone, L. A.

R. W. Kennard and L. A. Stone, “Computer aided design of experiment,” Technometrics 11, 137–148 (1969).
[CrossRef]

Tikhonravov, A.

Trubetskov, M.

Vassallo, C.

Vasseur, O.

O. Vasseur, M. Claeys-Bruno, M. Cathelinaud, and M. Sergent, “High dimensional sensitivity analysis of complex optronic systems by experimental designs: applications to the case of the design and the robustness of optical coatings,” Chin. Opt. Lett. 8(1), 21–24 (2010).
[CrossRef]

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, G. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15, 257–268 (2009).
[CrossRef]

O. Vasseur, “Reflectivity of dielectric coatings deposited on the end facet of a weakly guiding fiber,” J. Opt. Soc. Am. A 15, 77–83 (1998).
[CrossRef]

Wang, G. G.

G. G. Wang and S. Shan, “Review of metamodeling techniques in support of engineering design optimization,” J. Mech. Des. 129, 370–380 (2007).
[CrossRef]

Williams, B. J.

T. J. Santner, B. J. Williams, and W. I. Notz, The Design and Analysis of Computer Experiments (Springer, 2003).

Wojtkiewicz, S. F.

A. A. Giunta, S. F. Wojtkiewicz, and M. S. Eldred, “Overview of modern design of experiments methods for computational simulations,” in Proceedings of the 41st AIAA Aerospace Sciences Meeting and Exhibit, AIAA-2003-0649 (American Institute of Aeronautics and Astronautics, 2003).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1970).

Young, P. C.

P. C. Young, “Data-based mechanistic modelling, generalised sensitivity and dominant mode analysis,” Comput. Phys. Commun. 117, 113–129 (1999).
[CrossRef]

Anales Quimica Int. Ed. (1)

M. Sergent, R. Phan-Tan-Luu, and J. Elguero, “Statistical analysis of solvent scales. part 1,” Anales Quimica Int. Ed. 93, 3–6 (1997).

Appl. Opt. (2)

Chin. Opt. Lett. (1)

O. Vasseur, M. Claeys-Bruno, M. Cathelinaud, and M. Sergent, “High dimensional sensitivity analysis of complex optronic systems by experimental designs: applications to the case of the design and the robustness of optical coatings,” Chin. Opt. Lett. 8(1), 21–24 (2010).
[CrossRef]

Comput. Phys. Commun. (1)

P. C. Young, “Data-based mechanistic modelling, generalised sensitivity and dominant mode analysis,” Comput. Phys. Commun. 117, 113–129 (1999).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

T. M. Shay, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486(2007).
[CrossRef]

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, G. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15, 257–268 (2009).
[CrossRef]

J. Mech. Des. (1)

G. G. Wang and S. Shan, “Review of metamodeling techniques in support of engineering design optimization,” J. Mech. Des. 129, 370–380 (2007).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Statist. Plann. Inference (1)

J. S. Park “Optimal Latin-hypercube designs for computer experiments,” J. Statist. Plann. Inference 39, 95–111 (1994).
[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. A. Macleod and E. Pelletier, “Error compensation mechanisms in some thin-film monitoring systems,” Opt. Acta 24, 907–930 (1977).
[CrossRef]

Opt. Express (1)

Opt. Spectrosc. (1)

A. N. Baskakov and A. Tikhonravov “Synthesis of two component optical coatings,” Opt. Spectrosc. 56, 915–919 (1984).

Technometrics (1)

R. W. Kennard and L. A. Stone, “Computer aided design of experiment,” Technometrics 11, 137–148 (1969).
[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 (7)

M. Born and E. Wolf, Principles of Optics (Pergamon, 1970).

J. R. Koehler and A. B. Owen, “Computer experiments” in Handbook of Statistics, S.Ghosh and C.R.Rao, eds. (Elsevier, 1996), Vol. 13, pp. 261–308.
[CrossRef]

A. Saltelli, K. Chan, and E. M. Scott, Sensitivity Analysis(Wiley, 2000).

T. J. Santner, B. J. Williams, and W. I. Notz, The Design and Analysis of Computer Experiments (Springer, 2003).

H. A. Macleod, Thin Film Optical Filters (Hilger, 1986).
[CrossRef]

G. E. P. Box, W. G. Hunter, and J. S. Hunter, Statistics for Experimenters (Wiley, 1978).

A. A. Giunta, S. F. Wojtkiewicz, and M. S. Eldred, “Overview of modern design of experiments methods for computational simulations,” in Proceedings of the 41st AIAA Aerospace Sciences Meeting and Exhibit, AIAA-2003-0649 (American Institute of Aeronautics and Astronautics, 2003).

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Figures (4)

Fig. 1
Fig. 1

Transmittance of the perfect bandpass filter and two computer runs (Filters 1 and 2) with errors in the refractive index values (MT-1). The values of δ n i (%) for each layer of Filter 1 are 0.76, 0.29 , 1.21 , 1.92 , 2.09, 0.04, 1.17, 1.91, 1.89, 0.28, 1.04 , 1.98, 2.16 , 1.32 , 1.35 , 1.9, 2, 0.99, 2.24 , 1.57, 1.61, 2.06 , 1.87 , 0.98 , 1.38, 2.43, 1 , 0.29 , and 1.13 . The values of δ n i (%) for each layer of Filter 2 are 0.64, 0.6, 1.29, 1.68 , 1.32 , 0.12, 2.11, 2.09 , 1.09, 1.59 , 2.03, 1.93 , 2.04, 2.29 , 0.43, 0.24, 0.99 , 1.66 , 0.7, 2.13, 0.21 , 1.55, 0.41 , 1.28 , 1.32, 2.19, 1.52, 1, and 2.04.

Fig. 2
Fig. 2

Reflectance of the perfect AR filter and two computer runs (Filters 1 and 2) with errors in the refractive index values (MT-1). The values of δ n i (%) for each layer of Filter 1 are 0.54, 0.22 , 0.28 , 1.06, 0.81, 1.25, 0.67 , and 0.45 . The values of δ n i (%) for each layer of Filter 2 are 0.85, 0.71 , 0.7 , 0.33, 1.23 , 0.22, 0.36 , and 0.69.

Fig. 3
Fig. 3

Transmittance of the perfect bandpass filter and two computer runs (Filters 1 and 2) with errors in refractive index values (MT-2).

Fig. 4
Fig. 4

Reflectance of the perfect AR filter and two computer runs (Filters 1 and 2) with errors in refractive index values (MT-2).

Tables (5)

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Table 1 Nine Major Coefficients of Each Design Show the Most Critical Interactions between Layers for MT-1

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Table 2 Nine Major Coefficients of the Metamodel for MT-1

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Table 3 Most Critical Interactions between Layers for MT-2

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Table 4 Six Most Critical Coefficients for MT-1 and the Relationship between Layers and Spectral Domains

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Table 5 Six Most Critical Coefficients for MT-2 and the Relationship between Layers and Spectral Domains

Equations (3)

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F = i ( T ( λ i ) T p ( λ i ) ) 2  for the bandpass filter,
F = i ( R ( λ i ) R p ( λ i ) ) 2   for the AR coating,
Y = a 0 + i b i X i + i b i , i X i 2 + i < j b i , j X i X j ,

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