Abstract

Several different thin-film design problems were solved by the comprehensive-search, gradual-evolution, minus-filter, flip-flop, and inverse-Fourier-transform, thin-film synthesis methods. In order to compare the relative effectiveness of each method, the results obtained and computation times required by these techniques for primary, intermediate, and final solutions are given.

© 1992 Optical Society of America

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References

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  1. J. A. Dobrowolski, F. C. Ho, A. Belkind, V. A. Koss, “Merit functions for more effective thin film calculations,” Appl. Opt. 28, 2824–2831 (1989).
    [CrossRef] [PubMed]
  2. J. A. Dobrowolski, R. A. Kemp, “Refinement of optical multilayer systems with different optimization procedures,” Appl. Opt. 29, 2876–2893 (1990).
    [CrossRef] [PubMed]
  3. J. A. Dobrowolski, “Computer design of optical coatings,” Thin Solid Films 163, 97–110 (1988).
    [CrossRef]
  4. J. A. Dobrowolski, “Completely automatic synthesis of optical thin film systems,” Appl. Opt. 4, 937–946 (1965).
    [CrossRef]
  5. J. A. Dobrowolski, “Versatile computer program for absorbing optical thin film systems,” Appl. Opt. 20, 74–81 (1981).
    [CrossRef] [PubMed]
  6. J. A. Dobrowolski, “Subtractive method of optical thin-film interference filter design,” Appl. Opt. 12, 1885–1893 (1973).
    [CrossRef] [PubMed]
  7. A. Thelen, “Design of optical minus filters,” J. Opt. Soc. Am. 61, 365–369 (1971).
    [CrossRef]
  8. L. I. Epstein, “Design of optical filters,” J. Opt. Soc. Am. 42, 806–810 (1952).
    [CrossRef]
  9. W. H. Southwell, “Coating design using very thin high- and low-index layers,” Appl. Opt. 24, 457–460 (1985).
    [CrossRef] [PubMed]
  10. J. A. Dobrowolski, “Comparison of the Fourier transform and flip-flop thin-film synthesis methods,” Appl. Opt. 25, 1966–1972 (1986).
    [CrossRef] [PubMed]
  11. J. A. Dobrowolski, D. Lowe, “Optical thin film synthesis program based on the use of Fourier transforms,” Appl. Opt. 17, 3039–3050 (1978).
    [CrossRef] [PubMed]
  12. P. G. Verly, J. A. Dobrowolski, W. J. Wild, R. L. Burton, “Synthesis of high rejection filters with the Fourier transform method,” Appl. Opt. 28, 2864–2875 (1989).
    [CrossRef] [PubMed]
  13. J. A. Dobrowolski, R. A. Kemp, “Flip-flop thin-film design program with enhanced capabilities,” Appl. Opt. 31, 3807–3812 (1992).
    [CrossRef] [PubMed]
  14. J. A. Dobrowolski, S. H. C. Piotrowski, “Refractive index as a variable in the numerical design of optical thin film systems,” Appl. Opt. 21, 1502–1511 (1982).
    [CrossRef] [PubMed]
  15. W. V. Goodell, J. K. Coulter, P. B. Johnson, “Optical constants of Inconel alloy films,” J. Opt. Soc. Am. 63, 185–188 (1973).
    [CrossRef]
  16. L. Edmonds, P. W. Baumeister, M. E. Krisl, N. Boling, “Spectral characteristics of a narrowband rejection filter,” Appl. Opt. 29, 3203–3204 (1990).
    [CrossRef] [PubMed]
  17. T. Skettrup, “Three-layer approximation of dielectric thin film systems,” Appl. Opt. 28, 2860–2863 (1989).
    [CrossRef] [PubMed]

1992 (1)

1990 (2)

1989 (3)

1988 (1)

J. A. Dobrowolski, “Computer design of optical coatings,” Thin Solid Films 163, 97–110 (1988).
[CrossRef]

1986 (1)

1985 (1)

1982 (1)

1981 (1)

1978 (1)

1973 (2)

1971 (1)

1965 (1)

1952 (1)

Baumeister, P. W.

Belkind, A.

Boling, N.

Burton, R. L.

Coulter, J. K.

Dobrowolski, J. A.

J. A. Dobrowolski, R. A. Kemp, “Flip-flop thin-film design program with enhanced capabilities,” Appl. Opt. 31, 3807–3812 (1992).
[CrossRef] [PubMed]

J. A. Dobrowolski, R. A. Kemp, “Refinement of optical multilayer systems with different optimization procedures,” Appl. Opt. 29, 2876–2893 (1990).
[CrossRef] [PubMed]

P. G. Verly, J. A. Dobrowolski, W. J. Wild, R. L. Burton, “Synthesis of high rejection filters with the Fourier transform method,” Appl. Opt. 28, 2864–2875 (1989).
[CrossRef] [PubMed]

J. A. Dobrowolski, F. C. Ho, A. Belkind, V. A. Koss, “Merit functions for more effective thin film calculations,” Appl. Opt. 28, 2824–2831 (1989).
[CrossRef] [PubMed]

J. A. Dobrowolski, “Computer design of optical coatings,” Thin Solid Films 163, 97–110 (1988).
[CrossRef]

J. A. Dobrowolski, “Comparison of the Fourier transform and flip-flop thin-film synthesis methods,” Appl. Opt. 25, 1966–1972 (1986).
[CrossRef] [PubMed]

J. A. Dobrowolski, S. H. C. Piotrowski, “Refractive index as a variable in the numerical design of optical thin film systems,” Appl. Opt. 21, 1502–1511 (1982).
[CrossRef] [PubMed]

J. A. Dobrowolski, “Versatile computer program for absorbing optical thin film systems,” Appl. Opt. 20, 74–81 (1981).
[CrossRef] [PubMed]

J. A. Dobrowolski, D. Lowe, “Optical thin film synthesis program based on the use of Fourier transforms,” Appl. Opt. 17, 3039–3050 (1978).
[CrossRef] [PubMed]

J. A. Dobrowolski, “Subtractive method of optical thin-film interference filter design,” Appl. Opt. 12, 1885–1893 (1973).
[CrossRef] [PubMed]

J. A. Dobrowolski, “Completely automatic synthesis of optical thin film systems,” Appl. Opt. 4, 937–946 (1965).
[CrossRef]

Edmonds, L.

Epstein, L. I.

Goodell, W. V.

Ho, F. C.

Johnson, P. B.

Kemp, R. A.

Koss, V. A.

Krisl, M. E.

Lowe, D.

Piotrowski, S. H. C.

Skettrup, T.

Southwell, W. H.

Thelen, A.

Verly, P. G.

Wild, W. J.

Appl. Opt. (13)

J. A. Dobrowolski, “Completely automatic synthesis of optical thin film systems,” Appl. Opt. 4, 937–946 (1965).
[CrossRef]

J. A. Dobrowolski, “Subtractive method of optical thin-film interference filter design,” Appl. Opt. 12, 1885–1893 (1973).
[CrossRef] [PubMed]

J. A. Dobrowolski, D. Lowe, “Optical thin film synthesis program based on the use of Fourier transforms,” Appl. Opt. 17, 3039–3050 (1978).
[CrossRef] [PubMed]

J. A. Dobrowolski, “Versatile computer program for absorbing optical thin film systems,” Appl. Opt. 20, 74–81 (1981).
[CrossRef] [PubMed]

J. A. Dobrowolski, S. H. C. Piotrowski, “Refractive index as a variable in the numerical design of optical thin film systems,” Appl. Opt. 21, 1502–1511 (1982).
[CrossRef] [PubMed]

W. H. Southwell, “Coating design using very thin high- and low-index layers,” Appl. Opt. 24, 457–460 (1985).
[CrossRef] [PubMed]

J. A. Dobrowolski, “Comparison of the Fourier transform and flip-flop thin-film synthesis methods,” Appl. Opt. 25, 1966–1972 (1986).
[CrossRef] [PubMed]

J. A. Dobrowolski, F. C. Ho, A. Belkind, V. A. Koss, “Merit functions for more effective thin film calculations,” Appl. Opt. 28, 2824–2831 (1989).
[CrossRef] [PubMed]

T. Skettrup, “Three-layer approximation of dielectric thin film systems,” Appl. Opt. 28, 2860–2863 (1989).
[CrossRef] [PubMed]

P. G. Verly, J. A. Dobrowolski, W. J. Wild, R. L. Burton, “Synthesis of high rejection filters with the Fourier transform method,” Appl. Opt. 28, 2864–2875 (1989).
[CrossRef] [PubMed]

J. A. Dobrowolski, R. A. Kemp, “Refinement of optical multilayer systems with different optimization procedures,” Appl. Opt. 29, 2876–2893 (1990).
[CrossRef] [PubMed]

L. Edmonds, P. W. Baumeister, M. E. Krisl, N. Boling, “Spectral characteristics of a narrowband rejection filter,” Appl. Opt. 29, 3203–3204 (1990).
[CrossRef] [PubMed]

J. A. Dobrowolski, R. A. Kemp, “Flip-flop thin-film design program with enhanced capabilities,” Appl. Opt. 31, 3807–3812 (1992).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (3)

Thin Solid Films (1)

J. A. Dobrowolski, “Computer design of optical coatings,” Thin Solid Films 163, 97–110 (1988).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Block diagram of the computer program for the intercomparison of different numerical thin-film synthesis algorithms.

Fig. 2
Fig. 2

Photograph of the NRCC Science Library in Ottawa. The heavy outline represents the target curve for example A.

Fig. 3
Fig. 3

Example A, the NRCC Science Library. For these calculations the overall optical thickness of the layer systems was stipulated to be of the order of 1.0 μm. (The target, primary, intermediate, and final reflectances are represented by boldface, dashed, dotted, and solid curves, respectively.)

Fig. 4
Fig. 4

Example B, filter with 0.0, 0.5, and 1.0 transmission regions. (The target, primary, intermediate, and final transmittances are represented by boldface, dashed, dotted, and solid curves, respectively.)

Fig. 5
Fig. 5

Example C, wide angle black absorber coating.

Fig. 6
Fig. 6

Example A, the NRCC Science Library. The variation with overall thickness of the MF’s calculated with the Fourier-transform method for three different Q functions.

Fig. 7
Fig. 7

Example A, the NRCC Science Library. Rows D2 and E2 represent the results with the flip-flop and Fourier-transform methods that were obtained for an overall thickness of 4.0 μm. (The target, primary, intermediate, and final reflectances are represented by boldface, dashed, dotted, and solid curves, respectively.)

Tables (5)

Tables Icon

Table I Properties of Primary Solutions

Tables Icon

Table II Example A, the NRCC Science Library

Tables Icon

Table III Example B, Filter with 0.0, 0.5, and 1.0 Transmission Regions

Tables Icon

Table IV Example C, Wide Angle Black Absorber Coating

Tables Icon

Table V Properties of Thin-Film Synthesis Methods

Equations (4)

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

d n d x 1 2 n exp ( i k x ) d x = Q ( k ) exp [ i ϕ ( k ) ] = f ( k ) ,
n ( x ) = exp { 2 π 0 Q ( k ) k sin [ i ϕ ( k ) - k x ] d k } ,
n ( x ) = n 0 exp [ 2 p m = - l F ( m p ) ] ,             ( l p x l + 1 p ) .
MF = [ 1 N i = 1 N ( Q i T - Q i P δ Q i ) 2 ] 1 / 2 ,

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