Abstract

This paper reviews the different types of merit functions that have been used in the past in optical thin film calculations. Attention is drawn to the power of merit functions which operate on complicated quantities that require one or more integral expressions for their definition. To prove this point, several thin film problems are solved in which the CIE coordinates, luminous transmittances or reflectances, solar absorptance, and blackbody emittances of a multilayer are specified.

© 1989 Optical Society of America

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  1. Tang Jin-fa, Jiang Bai-chuan, Zheng Quan, “Automatic Design of Optical Thin Films (1)—the Construction of Merit Functions,” J. Zhejiang Univ. 3, 13–18 (1979).
  2. Tang Jin-fa, Zeng Quan, Applied Thin Film Optics (Shanghai Science & Technology, China, 1984), pp. 379–387.
  3. J. A. Dobrowolski, “Versatile Computer Program for Absorbing Optical Thin Film Systems,” Appl. Opt. 20, 74–81 (1981).
    [CrossRef] [PubMed]
  4. J. F. Tang, Q. Zheng, “Automatic Design of Optical Thin-Film Systems—Merit Function and Numerical Optimization Method,” J. Opt. Soc. Am. 72, 1522–1528 (1982).
    [CrossRef]
  5. A. L. Bloom, “Refining and Optimization in Multilayers,” Appl. Opt. 20, 66–73 (1981).
    [CrossRef] [PubMed]
  6. N. Kimura, “Automatic Design of Multilayer Dielectric Films (I),(II),” Jpn. J. Appl. Phys. 31, 739–745 (1962); Jpn. J. Appl. Phys. 32, 199–212 (1963). Technical translations 1085 and 1166 are available from the Canada Institute for Scientific & Technical Information, National Research Council of Canada.
  7. A. V. Tikhonravov, A. Y. Klementeva, “Synthesis of Multilayer Non-Absorbing Coatings by the Method of Steepest Descent,” Vestn. Mosk. Univ. 6, 673–678 (1976).
  8. I. M. Minkov, V. V. Veremei, “Computation of Thin-Layer Coatings with Specified Optical Properties,” Opt. Spectrosc. 37, 571–573 (1974).
  9. A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, “Method for the Calculation of a Multilayer Coating with a Given Reflectivity,” Opt. Spectrosc. 13, 142–146 (1962).
  10. J. A. Dobrowolski, “Completely Automatic Synthesis of Optical Thin Film Systems,” Appl. Opt. 4, 937–946 (1965).
    [CrossRef]
  11. R. T. Maclntyre, “Differential Adjustment of Film Thicknesses,” J. Opt. Soc. Am. 52, 1310 (1962).
  12. H. Zycha, “Refining Algorithm for the Design of Multilayer Filters,” Appl. Opt. 12, 979–983 (1973).
    [CrossRef] [PubMed]
  13. G. Lessman, “Adaptive Self-Optimizing Multilayer Thin Film Design Computer Program,” J. Opt. Soc. Am. 64, 548A (1974).
  14. E. G. Stolov, “Synthesis of Optical Interference Coatings,” Sov. J. Opt. Technol. 43, 352–353 (1976).
  15. A. V. Shatilov, L. P. Tyutikova, “Example of the Calculation of an Interference Filter Using the Method of Successive Synthesis,” Opt. Spectrosc. 14, 227–229 (1963).
  16. J. A. Dobrowolski, “Optical Interference Filters for the Adjustment of Spectral Response and Spectral Power Distribution,” Appl. Opt. 9, 1396–1409 (1970).
    [CrossRef] [PubMed]
  17. E. Pelletier, M. Klapisch, P. Giacomo, “Synthesis of Thin Film Multilayer Systems,” Nouv. Rev. Opt. Appl. 2, 247–254 (1971).
    [CrossRef]
  18. P. Aufmuth, H.-W. Brandt, J. R. Kiehl, “Design and Manufacture of Thin Dielectric Layer Systems for Optical Applications,” Optik (Stuttgart) 50, 329–340 (1978).
  19. Z. Leś, J. Kuroś, “Method for the Synthesis of Semitransparent Wide Band Dielectric Mirrors,” Thin Solid Films 46, 117–126 (1977).
    [CrossRef]
  20. W. J. Wild, H. Buhay, “Thin Film Multilayer Design Optimization Using a Monte Carlo Approach,” Opt. Lett. 11, 745–747 (1986).
    [CrossRef] [PubMed]
  21. H. M. Liddell, “Use of Optimization Techniques in Optical Filter Design,” in Optimization in Action, L. C. W. Dixon, Ed. (Academic, London, 1976).
  22. Y.-F. Zheng, J.-F. Tang, “New Automatic Design Technique for Optical Coatings,” Appl. Opt. 26, 1546–1549 (1987).
    [CrossRef] [PubMed]
  23. G. Wyszecki, W. S. Stiles, Color Science (Wiley, New York, 1967).
  24. H. P. Garg, Treatise on Solar Energy (Wiley, New York, 1982).
  25. R. Siegel, J. R. Howell, “Thermal Radiation Heat Transfer,” NASA Spec. Publ. SP-164 (1968).
  26. E. D. Palik, Ed., Handbook of Optical Constants (Academic, New York, 1985), pp. 303 and 369.
  27. M. E. Whitson, Handbook of the Infrared Optical Properties of Al2O3, C, MgO, and ZrO2, Vol. 1, Report SAMSO-TR75 (U.S. Department of Commerce, Washington, DC, 1975).
  28. W. H. Southwell, “Coating Design Using Very Thin High- and Low-Index Layers,” Appl. Opt. 24, 457–460 (1985).
    [CrossRef] [PubMed]
  29. J. A. Dobrowolski, “Comparison of the Fourier Transform and Flip-Flop Thin-Film Synthesis Methods,” Appl. Opt. 25, 1966–1972 (1986).
    [CrossRef] [PubMed]

1987

1986

1985

1982

1981

1979

Tang Jin-fa, Jiang Bai-chuan, Zheng Quan, “Automatic Design of Optical Thin Films (1)—the Construction of Merit Functions,” J. Zhejiang Univ. 3, 13–18 (1979).

1978

P. Aufmuth, H.-W. Brandt, J. R. Kiehl, “Design and Manufacture of Thin Dielectric Layer Systems for Optical Applications,” Optik (Stuttgart) 50, 329–340 (1978).

1977

Z. Leś, J. Kuroś, “Method for the Synthesis of Semitransparent Wide Band Dielectric Mirrors,” Thin Solid Films 46, 117–126 (1977).
[CrossRef]

1976

E. G. Stolov, “Synthesis of Optical Interference Coatings,” Sov. J. Opt. Technol. 43, 352–353 (1976).

A. V. Tikhonravov, A. Y. Klementeva, “Synthesis of Multilayer Non-Absorbing Coatings by the Method of Steepest Descent,” Vestn. Mosk. Univ. 6, 673–678 (1976).

1974

I. M. Minkov, V. V. Veremei, “Computation of Thin-Layer Coatings with Specified Optical Properties,” Opt. Spectrosc. 37, 571–573 (1974).

G. Lessman, “Adaptive Self-Optimizing Multilayer Thin Film Design Computer Program,” J. Opt. Soc. Am. 64, 548A (1974).

1973

1971

E. Pelletier, M. Klapisch, P. Giacomo, “Synthesis of Thin Film Multilayer Systems,” Nouv. Rev. Opt. Appl. 2, 247–254 (1971).
[CrossRef]

1970

1965

1963

A. V. Shatilov, L. P. Tyutikova, “Example of the Calculation of an Interference Filter Using the Method of Successive Synthesis,” Opt. Spectrosc. 14, 227–229 (1963).

1962

R. T. Maclntyre, “Differential Adjustment of Film Thicknesses,” J. Opt. Soc. Am. 52, 1310 (1962).

A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, “Method for the Calculation of a Multilayer Coating with a Given Reflectivity,” Opt. Spectrosc. 13, 142–146 (1962).

N. Kimura, “Automatic Design of Multilayer Dielectric Films (I),(II),” Jpn. J. Appl. Phys. 31, 739–745 (1962); Jpn. J. Appl. Phys. 32, 199–212 (1963). Technical translations 1085 and 1166 are available from the Canada Institute for Scientific & Technical Information, National Research Council of Canada.

Aufmuth, P.

P. Aufmuth, H.-W. Brandt, J. R. Kiehl, “Design and Manufacture of Thin Dielectric Layer Systems for Optical Applications,” Optik (Stuttgart) 50, 329–340 (1978).

Bai-chuan, Jiang

Tang Jin-fa, Jiang Bai-chuan, Zheng Quan, “Automatic Design of Optical Thin Films (1)—the Construction of Merit Functions,” J. Zhejiang Univ. 3, 13–18 (1979).

Bloom, A. L.

Brandt, H.-W.

P. Aufmuth, H.-W. Brandt, J. R. Kiehl, “Design and Manufacture of Thin Dielectric Layer Systems for Optical Applications,” Optik (Stuttgart) 50, 329–340 (1978).

Buhay, H.

Dobrowolski, J. A.

Ermolaev, A. M.

A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, “Method for the Calculation of a Multilayer Coating with a Given Reflectivity,” Opt. Spectrosc. 13, 142–146 (1962).

Garg, H. P.

H. P. Garg, Treatise on Solar Energy (Wiley, New York, 1982).

Giacomo, P.

E. Pelletier, M. Klapisch, P. Giacomo, “Synthesis of Thin Film Multilayer Systems,” Nouv. Rev. Opt. Appl. 2, 247–254 (1971).
[CrossRef]

Howell, J. R.

R. Siegel, J. R. Howell, “Thermal Radiation Heat Transfer,” NASA Spec. Publ. SP-164 (1968).

Jin-fa, Tang

Tang Jin-fa, Jiang Bai-chuan, Zheng Quan, “Automatic Design of Optical Thin Films (1)—the Construction of Merit Functions,” J. Zhejiang Univ. 3, 13–18 (1979).

Tang Jin-fa, Zeng Quan, Applied Thin Film Optics (Shanghai Science & Technology, China, 1984), pp. 379–387.

Kiehl, J. R.

P. Aufmuth, H.-W. Brandt, J. R. Kiehl, “Design and Manufacture of Thin Dielectric Layer Systems for Optical Applications,” Optik (Stuttgart) 50, 329–340 (1978).

Kimura, N.

N. Kimura, “Automatic Design of Multilayer Dielectric Films (I),(II),” Jpn. J. Appl. Phys. 31, 739–745 (1962); Jpn. J. Appl. Phys. 32, 199–212 (1963). Technical translations 1085 and 1166 are available from the Canada Institute for Scientific & Technical Information, National Research Council of Canada.

Klapisch, M.

E. Pelletier, M. Klapisch, P. Giacomo, “Synthesis of Thin Film Multilayer Systems,” Nouv. Rev. Opt. Appl. 2, 247–254 (1971).
[CrossRef]

Klementeva, A. Y.

A. V. Tikhonravov, A. Y. Klementeva, “Synthesis of Multilayer Non-Absorbing Coatings by the Method of Steepest Descent,” Vestn. Mosk. Univ. 6, 673–678 (1976).

Kuros, J.

Z. Leś, J. Kuroś, “Method for the Synthesis of Semitransparent Wide Band Dielectric Mirrors,” Thin Solid Films 46, 117–126 (1977).
[CrossRef]

Les, Z.

Z. Leś, J. Kuroś, “Method for the Synthesis of Semitransparent Wide Band Dielectric Mirrors,” Thin Solid Films 46, 117–126 (1977).
[CrossRef]

Lessman, G.

G. Lessman, “Adaptive Self-Optimizing Multilayer Thin Film Design Computer Program,” J. Opt. Soc. Am. 64, 548A (1974).

Liddell, H. M.

H. M. Liddell, “Use of Optimization Techniques in Optical Filter Design,” in Optimization in Action, L. C. W. Dixon, Ed. (Academic, London, 1976).

Maclntyre, R. T.

R. T. Maclntyre, “Differential Adjustment of Film Thicknesses,” J. Opt. Soc. Am. 52, 1310 (1962).

Minkov, I. M.

I. M. Minkov, V. V. Veremei, “Computation of Thin-Layer Coatings with Specified Optical Properties,” Opt. Spectrosc. 37, 571–573 (1974).

A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, “Method for the Calculation of a Multilayer Coating with a Given Reflectivity,” Opt. Spectrosc. 13, 142–146 (1962).

Pelletier, E.

E. Pelletier, M. Klapisch, P. Giacomo, “Synthesis of Thin Film Multilayer Systems,” Nouv. Rev. Opt. Appl. 2, 247–254 (1971).
[CrossRef]

Quan, Zeng

Tang Jin-fa, Zeng Quan, Applied Thin Film Optics (Shanghai Science & Technology, China, 1984), pp. 379–387.

Quan, Zheng

Tang Jin-fa, Jiang Bai-chuan, Zheng Quan, “Automatic Design of Optical Thin Films (1)—the Construction of Merit Functions,” J. Zhejiang Univ. 3, 13–18 (1979).

Shatilov, A. V.

A. V. Shatilov, L. P. Tyutikova, “Example of the Calculation of an Interference Filter Using the Method of Successive Synthesis,” Opt. Spectrosc. 14, 227–229 (1963).

Siegel, R.

R. Siegel, J. R. Howell, “Thermal Radiation Heat Transfer,” NASA Spec. Publ. SP-164 (1968).

Southwell, W. H.

Stiles, W. S.

G. Wyszecki, W. S. Stiles, Color Science (Wiley, New York, 1967).

Stolov, E. G.

E. G. Stolov, “Synthesis of Optical Interference Coatings,” Sov. J. Opt. Technol. 43, 352–353 (1976).

Tang, J. F.

Tang, J.-F.

Tikhonravov, A. V.

A. V. Tikhonravov, A. Y. Klementeva, “Synthesis of Multilayer Non-Absorbing Coatings by the Method of Steepest Descent,” Vestn. Mosk. Univ. 6, 673–678 (1976).

Tyutikova, L. P.

A. V. Shatilov, L. P. Tyutikova, “Example of the Calculation of an Interference Filter Using the Method of Successive Synthesis,” Opt. Spectrosc. 14, 227–229 (1963).

Veremei, V. V.

I. M. Minkov, V. V. Veremei, “Computation of Thin-Layer Coatings with Specified Optical Properties,” Opt. Spectrosc. 37, 571–573 (1974).

Vlasov, A. G.

A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, “Method for the Calculation of a Multilayer Coating with a Given Reflectivity,” Opt. Spectrosc. 13, 142–146 (1962).

Whitson, M. E.

M. E. Whitson, Handbook of the Infrared Optical Properties of Al2O3, C, MgO, and ZrO2, Vol. 1, Report SAMSO-TR75 (U.S. Department of Commerce, Washington, DC, 1975).

Wild, W. J.

Wyszecki, G.

G. Wyszecki, W. S. Stiles, Color Science (Wiley, New York, 1967).

Zheng, Q.

Zheng, Y.-F.

Zycha, H.

Appl. Opt.

J. Opt. Soc. Am.

J. F. Tang, Q. Zheng, “Automatic Design of Optical Thin-Film Systems—Merit Function and Numerical Optimization Method,” J. Opt. Soc. Am. 72, 1522–1528 (1982).
[CrossRef]

G. Lessman, “Adaptive Self-Optimizing Multilayer Thin Film Design Computer Program,” J. Opt. Soc. Am. 64, 548A (1974).

R. T. Maclntyre, “Differential Adjustment of Film Thicknesses,” J. Opt. Soc. Am. 52, 1310 (1962).

J. Zhejiang Univ.

Tang Jin-fa, Jiang Bai-chuan, Zheng Quan, “Automatic Design of Optical Thin Films (1)—the Construction of Merit Functions,” J. Zhejiang Univ. 3, 13–18 (1979).

Jpn. J. Appl. Phys.

N. Kimura, “Automatic Design of Multilayer Dielectric Films (I),(II),” Jpn. J. Appl. Phys. 31, 739–745 (1962); Jpn. J. Appl. Phys. 32, 199–212 (1963). Technical translations 1085 and 1166 are available from the Canada Institute for Scientific & Technical Information, National Research Council of Canada.

Nouv. Rev. Opt. Appl.

E. Pelletier, M. Klapisch, P. Giacomo, “Synthesis of Thin Film Multilayer Systems,” Nouv. Rev. Opt. Appl. 2, 247–254 (1971).
[CrossRef]

Opt. Lett.

Opt. Spectrosc.

A. V. Shatilov, L. P. Tyutikova, “Example of the Calculation of an Interference Filter Using the Method of Successive Synthesis,” Opt. Spectrosc. 14, 227–229 (1963).

I. M. Minkov, V. V. Veremei, “Computation of Thin-Layer Coatings with Specified Optical Properties,” Opt. Spectrosc. 37, 571–573 (1974).

A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, “Method for the Calculation of a Multilayer Coating with a Given Reflectivity,” Opt. Spectrosc. 13, 142–146 (1962).

Optik (Stuttgart)

P. Aufmuth, H.-W. Brandt, J. R. Kiehl, “Design and Manufacture of Thin Dielectric Layer Systems for Optical Applications,” Optik (Stuttgart) 50, 329–340 (1978).

Sov. J. Opt. Technol.

E. G. Stolov, “Synthesis of Optical Interference Coatings,” Sov. J. Opt. Technol. 43, 352–353 (1976).

Thin Solid Films

Z. Leś, J. Kuroś, “Method for the Synthesis of Semitransparent Wide Band Dielectric Mirrors,” Thin Solid Films 46, 117–126 (1977).
[CrossRef]

Vestn. Mosk. Univ.

A. V. Tikhonravov, A. Y. Klementeva, “Synthesis of Multilayer Non-Absorbing Coatings by the Method of Steepest Descent,” Vestn. Mosk. Univ. 6, 673–678 (1976).

Other

Tang Jin-fa, Zeng Quan, Applied Thin Film Optics (Shanghai Science & Technology, China, 1984), pp. 379–387.

H. M. Liddell, “Use of Optimization Techniques in Optical Filter Design,” in Optimization in Action, L. C. W. Dixon, Ed. (Academic, London, 1976).

G. Wyszecki, W. S. Stiles, Color Science (Wiley, New York, 1967).

H. P. Garg, Treatise on Solar Energy (Wiley, New York, 1982).

R. Siegel, J. R. Howell, “Thermal Radiation Heat Transfer,” NASA Spec. Publ. SP-164 (1968).

E. D. Palik, Ed., Handbook of Optical Constants (Academic, New York, 1985), pp. 303 and 369.

M. E. Whitson, Handbook of the Infrared Optical Properties of Al2O3, C, MgO, and ZrO2, Vol. 1, Report SAMSO-TR75 (U.S. Department of Commerce, Washington, DC, 1975).

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Figures (5)

Figure 1
Figure 1

Design of purple/pink transmission filters with CIE coordinates x = 0.35 and y = 0.20. Curves A, 1 and 2 represent the calculated spectral transmittance curves of an optimal filter, and of the ten- and eight-layer systems of Table II. The points represent the measured transmittance of an experimentally produced filter.

Fig. 2
Fig. 2

Design of purple/pink reflection filters with CIE coordinates x = 0.35 and y = 0.20. Curves A, 1 and 2 represent the calculated spectral reflectance curves of an optimal filter and of the fifteen- and seven-layer systems of Table II.

Fig. 3
Fig. 3

Design of a filter with CIE coordinates of x = 0.35 and y = 0.20 in transmitted light (a) at normal incidence and (b) in reflected light for 45° incidence. The curves correspond to the fourteen-layer system of Table II.

Fig. 4
Fig. 4

Calculated spectral reflectance (curve 1) of a two-material five-layer antireflection coating on glass designed for visual use. Curve A represents the visibility curve of a light-adapted CIE standard observer.

Fig. 5
Fig. 5

Calculated spectral absorptance and reflectance (curves 1 and 2) of the five-layer selective absorber coating of Table II. Curves A and B represent the normalized solar irradiance at air mass 2 and the emissivity of a blackbody at 600 K.

Tables (2)

Tables Icon

Table I Dispersion of Optical Constants of ZnS and Cryolite Used in Calculations

Tables Icon

Table II Construction Parameters and Performance of Systems

Equations (24)

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M F = [ 1 M i = 1 N W i ( D i ) k ] 1 / k .
D i = Q i T Q i , ( 1 i N ) .
M F = max i [ W i ( D i ) k ] .
D i = | Q i T Q i | δ Q i for | Q i T Q i | δ Q i , = 0 for | Q i T Q i | δ Q i .
M F = λ 1 λ 2 W ( λ ) · D ( λ ) 2 · d λ ,
M F = [ 1 M i = 1 N w i ( D i δ Q i ) k ] 1 / k ,
D i = Q i T ( Q i / c ) ,
c min c c max , max i [ Q i T ] · c max 1 . 0 .
Q i = l = 1 L T i , l .
M F = l = 1 L [ 1 M l i = 1 N l W i , l ( D i , l δ Q i , l ) k ] 1 / k .
M F = Ω 1 [ 1 N i = 1 N ( Q i Q ¯ ) k ] 1 / k + Ω 2 | Q ¯ Q T | .
M F = Ω 1 j = 1 L [ 1 N j i = 1 N j ( Q i , j Q ¯ j ) k ] 1 / k + Ω 2 j = 1 L | Q ¯ j Q j T | .
M F = 1 N 1 i = 1 N 1 W i ( R i ) 2 + 1 N 2 j = 1 N 2 W j / ( R j ) 2 .
M F = { 1 2 N i = 1 N W i [ ( R P , i T R P , i ) 2 + ( R S , i T R S , i ) 2 ] } 1 / 2 .
M F = i = 1 N [ ( R T R ) 2 + ( R T + T T R T ) 2 ] .
M F * = Ω 1 ( M F ) + Ω 2 i = 1 M W i | d ( M F ) d X i | .
M F * = Ω 1 ( M F ) + Ω 2 ( 1 P ) .
I j = λ L , j λ U , j F j ( λ ) · q j ( λ ) · d λ .
Q 1 = I 1 I 1 + I 2 + I 3 ,
Q 2 = I 2 I 1 + I 2 + I 3 .
Q 3 = I 2 / λ L , 2 λ U , 2 F 2 ( λ ) · d λ .
q 1 ( λ ) = 1 . 0 [ T ( λ ) + R ( λ ) ] .
Q 1 = I 1 / λ L , 1 λ U , 1 f 1 ( λ ) · d λ .
q 1 ( λ ) = 1 . 0 R ( λ ) .

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