Abstract

The inverse Fourier transform and flip-flop thin-film synthesis methods are compared and contrasted. Modifications to the flip-flop method are described which make it useful even for the solution of problems that require a large overall film thickness. The two methods were applied to a number of difficult problems. They yielded solutions that were different but of equivalent performance.

© 1986 Optical Society of America

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References

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  1. J. A. Dobrowolski, D. G. Lowe, “Optical Thin Film Synthesis Program Based on the Use of Fourier Transforms,” Appl. Opt. 17, 3039 (1978).
    [CrossRef] [PubMed]
  2. L. Sossi, “A Method for the Synthesis of Multilayer Dielectric Interference Coatings,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 23, 229 (1974).
  3. L. Sossi, “On the Theory of the Synthesis of Multilayer Dielectric Light Filters,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 25, 171 (1976).
  4. 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 (1982).
    [CrossRef] [PubMed]
  5. H. Sankur, W. H. Southwell, “Broadband Gradient-Index Antireflection Coating for ZnSe,” Appl. Opt. 23, 2770 (1984).
    [CrossRef] [PubMed]
  6. W. H. Southwell, “Coating Design Using Very Thin High- and Low-Index Layers,” Appl. Opt. 24, 457 (1985).
    [CrossRef] [PubMed]
  7. L. I. Epstein, “Design of Optical Filters,” J. Opt. Soc. Am. 42, 806 (1952).
    [CrossRef]
  8. Z. N. Elsner, “On the Calculation of Multilayer Interference Coatings with Given Spectral Characteristics,” Opt. Spectrosc. 17, 238 (1964).

1985 (1)

1984 (1)

1982 (1)

1978 (1)

1976 (1)

L. Sossi, “On the Theory of the Synthesis of Multilayer Dielectric Light Filters,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 25, 171 (1976).

1974 (1)

L. Sossi, “A Method for the Synthesis of Multilayer Dielectric Interference Coatings,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 23, 229 (1974).

1964 (1)

Z. N. Elsner, “On the Calculation of Multilayer Interference Coatings with Given Spectral Characteristics,” Opt. Spectrosc. 17, 238 (1964).

1952 (1)

Dobrowolski, J. A.

Elsner, Z. N.

Z. N. Elsner, “On the Calculation of Multilayer Interference Coatings with Given Spectral Characteristics,” Opt. Spectrosc. 17, 238 (1964).

Epstein, L. I.

Lowe, D. G.

Piotrowski, S. H. C.

Sankur, H.

Sossi, L.

L. Sossi, “On the Theory of the Synthesis of Multilayer Dielectric Light Filters,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 25, 171 (1976).

L. Sossi, “A Method for the Synthesis of Multilayer Dielectric Interference Coatings,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 23, 229 (1974).

Southwell, W. H.

Appl. Opt. (4)

Eesti NSV Tead. Akad. Toim. Fuus. Mat. (2)

L. Sossi, “A Method for the Synthesis of Multilayer Dielectric Interference Coatings,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 23, 229 (1974).

L. Sossi, “On the Theory of the Synthesis of Multilayer Dielectric Light Filters,” Eesti NSV Tead. Akad. Toim. Fuus. Mat. 25, 171 (1976).

J. Opt. Soc. Am. (1)

Opt. Spectrosc. (1)

Z. N. Elsner, “On the Calculation of Multilayer Interference Coatings with Given Spectral Characteristics,” Opt. Spectrosc. 17, 238 (1964).

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Figures (11)

Fig. 1
Fig. 1

Filter with a spectral transmittance curve that approximates the silhouette of the Capitol, Washington, designed with the inverse Fourier transform method. Curves B, C, and D correspond to solutions based on an inhomogeneous layer (system B), and to homogeneous multilayers consisting of many (system C) or of only two (system D) refractive indices, respectively.

Fig. 2
Fig. 2

Schematic representation of different starting designs.

Fig. 3
Fig. 3

Schematic representation of different directions of refractive-index change.

Fig. 4
Fig. 4

Flow chart of the NRCC flip-flop program.

Fig. 5
Fig. 5

Best solution for an antireflection coating for extra dense flint.

Fig. 6
Fig. 6

Refractive-index profiles of antireflection coating for extra dense flint obtained with different starting designs and directions of refractive-index change. The broken lines represent the solution prior to the removal of nonessential outermost layers.

Fig. 7
Fig. 7

Three different filters designed with the flip-flop method that have spectral transmittance curves that approximate the silhouette of the Capitol, Washington.

Fig. 8
Fig. 8

y ¯ λ tristimulus filters designed by the inverse Fourier transform (system B) and flip-flop (system CC) methods.

Fig. 9
Fig. 9

Filter with different requirements at different wavelengths designed by the inverse Fourier transform (system B, curve B) and flip-flop methods (system C, curve C).

Fig. 10
Fig. 10

Antireflection coating for extra dense flint. Curves A represent solution aA in Fig. 6; curves B correspond to a solution derived from it; C is the inhomogeneous layer equivalent of solution B.

Fig. 11
Fig. 11

Transmittance of a nine 7λ/4 layer system (B) and of the closest solution obtained by the flip-flop method (C).

Equations (10)

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- d n d x · 1 2 n exp ( i k x ) · d x = Q ( k ) · exp [ i ϕ ( k ) ] = f ( k ) , k = 2 π / λ .
x = 2 0 z n ( u ) · d u ,
Q ( k ) = { ½ [ 1 T ( K ) - T ( k ) ] } 1 / 2 .
n ( x ) = exp { 2 π 0 Q ( k ) k sin [ ϕ ( k ) - k x ] · d k } .
( pre ) i = j = 1 i - 1 ( M j ) ,
( post ) i = j = i + 1 N ( M j ) ,
M i , H = M 1 M 2 M i - 1 H M i + 1 M N - 1 M N = ( pre ) i H ( post ) i ,
M i , L = M 1 M 2 M i - 1 L M i + 1 M N - 1 M N = ( pre ) i L ( post ) i ,
M F = 1 m i = 1 m ( T i T - T i δ T i ) 2 .
0.4 λ 0.45 : R = 0.95 ( reflector ) , 0.5 λ 0.55 : T = 1.00 ( AR coating ) , 0.6 λ 0.65 : T = 0.50 ( beam splitter ) , 0.7 λ 0.75 : T = 1.00 ( AR coating ) .

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