Abstract

A fast automatic synthesis program based on interference minus filters is described. It yields the parameters of a number of individual filters that together match any desired spectral transmittance curve, providing that the spectral range over which the latter is defined is not excessive. It is shown that in practice many of these components can be combined without significantly affecting the performance. When used alone, the program may yield solutions consisting of a large number of layers. It is demonstrated that far fewer layers are needed if intermediate solutions obtained with this program are refined using other automatic synthesis programs. The program is illustrated by a number of rather difficult hypothetical problems.

© 1973 Optical Society of America

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References

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  1. P. W. Baumeister, J. Opt. Soc. Am. 48, 955 (1958).
    [Crossref]
  2. P. W. Baumeister, J. Opt. Soc. Am. 52, 1149 (1962).
    [Crossref]
  3. N. Kimura, Oyo Buturi 31, 739 (1962).
  4. N. Kimura, Oyo Buturi 32, 119 (1963).
  5. R. J. Pegis, D. S. Grey, T. P. Vogl, in Recent Advances in Optimization Techniques, A. Lavi, T. P. Vogl, Eds. (Wiley, New York, 1966), p. 47.
  6. E. Pelletier, M. Klapisch, P. Giacomo, Nouv. Rev. Opt. Appl. 2, 247 (1971).
    [Crossref]
  7. A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, Opt. Spektrosk. 13, 259 (1962); Opt. Spectrosc. 13, 142 (1962).
  8. A. V. Skatilov, L. P. Tyutikova, Opt. Spektrosk. 14, 426 (1963); Opt. Spectrosc. 14, 227 (1963).
  9. E. N. Elsner, Opt. Spektrosk. 17, 446 (1964); Opt. Spectrosc. 17, 238 (1964).
  10. J. A. Dobrowolski, Appl. Opt. 4, 937 (1965).
    [Crossref]
  11. O. S. Heavens, H. M. Liddell, Optica Acta 15, 129 (1968).
  12. J. A. Dobrowolski, G. R. Hanes, C. J. Van der Hoeven, Appl. Opt. 7, 1981 (1968).
    [Crossref] [PubMed]
  13. J. A. Dobrowolski, Appl. Opt. 9, 1396 (1970).
    [Crossref] [PubMed]
  14. S. D. Smith, J. Opt. Soc. Am. 48, 43 (1958).
    [Crossref]
  15. L. Young, Appl. Opt. 6, 297 (1967).
    [Crossref] [PubMed]
  16. A. Thelen, J. Opt. Soc. Am. 61, 365 (1971).
    [Crossref]
  17. L. I. Epstein, J. Opt. Soc. Am. 42, 806 (1952).
    [Crossref]
  18. H. A. Macleod, Thin Film Optical Filters (American Elsevier, New York, 1969).
  19. K. D. Mielenz, J. Res. Natl. Bur. Stand. 63A, 297 (1959).
    [Crossref]

1971 (2)

E. Pelletier, M. Klapisch, P. Giacomo, Nouv. Rev. Opt. Appl. 2, 247 (1971).
[Crossref]

A. Thelen, J. Opt. Soc. Am. 61, 365 (1971).
[Crossref]

1970 (1)

1968 (2)

1967 (1)

1965 (1)

1964 (1)

E. N. Elsner, Opt. Spektrosk. 17, 446 (1964); Opt. Spectrosc. 17, 238 (1964).

1963 (2)

A. V. Skatilov, L. P. Tyutikova, Opt. Spektrosk. 14, 426 (1963); Opt. Spectrosc. 14, 227 (1963).

N. Kimura, Oyo Buturi 32, 119 (1963).

1962 (3)

N. Kimura, Oyo Buturi 31, 739 (1962).

A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, Opt. Spektrosk. 13, 259 (1962); Opt. Spectrosc. 13, 142 (1962).

P. W. Baumeister, J. Opt. Soc. Am. 52, 1149 (1962).
[Crossref]

1959 (1)

K. D. Mielenz, J. Res. Natl. Bur. Stand. 63A, 297 (1959).
[Crossref]

1958 (2)

1952 (1)

Baumeister, P. W.

Dobrowolski, J. A.

Elsner, E. N.

E. N. Elsner, Opt. Spektrosk. 17, 446 (1964); Opt. Spectrosc. 17, 238 (1964).

Epstein, L. I.

Ermolaev, A. M.

A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, Opt. Spektrosk. 13, 259 (1962); Opt. Spectrosc. 13, 142 (1962).

Giacomo, P.

E. Pelletier, M. Klapisch, P. Giacomo, Nouv. Rev. Opt. Appl. 2, 247 (1971).
[Crossref]

Grey, D. S.

R. J. Pegis, D. S. Grey, T. P. Vogl, in Recent Advances in Optimization Techniques, A. Lavi, T. P. Vogl, Eds. (Wiley, New York, 1966), p. 47.

Hanes, G. R.

Heavens, O. S.

O. S. Heavens, H. M. Liddell, Optica Acta 15, 129 (1968).

Kimura, N.

N. Kimura, Oyo Buturi 32, 119 (1963).

N. Kimura, Oyo Buturi 31, 739 (1962).

Klapisch, M.

E. Pelletier, M. Klapisch, P. Giacomo, Nouv. Rev. Opt. Appl. 2, 247 (1971).
[Crossref]

Liddell, H. M.

O. S. Heavens, H. M. Liddell, Optica Acta 15, 129 (1968).

Macleod, H. A.

H. A. Macleod, Thin Film Optical Filters (American Elsevier, New York, 1969).

Mielenz, K. D.

K. D. Mielenz, J. Res. Natl. Bur. Stand. 63A, 297 (1959).
[Crossref]

Minkov, I. M.

A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, Opt. Spektrosk. 13, 259 (1962); Opt. Spectrosc. 13, 142 (1962).

Pegis, R. J.

R. J. Pegis, D. S. Grey, T. P. Vogl, in Recent Advances in Optimization Techniques, A. Lavi, T. P. Vogl, Eds. (Wiley, New York, 1966), p. 47.

Pelletier, E.

E. Pelletier, M. Klapisch, P. Giacomo, Nouv. Rev. Opt. Appl. 2, 247 (1971).
[Crossref]

Skatilov, A. V.

A. V. Skatilov, L. P. Tyutikova, Opt. Spektrosk. 14, 426 (1963); Opt. Spectrosc. 14, 227 (1963).

Smith, S. D.

Thelen, A.

Tyutikova, L. P.

A. V. Skatilov, L. P. Tyutikova, Opt. Spektrosk. 14, 426 (1963); Opt. Spectrosc. 14, 227 (1963).

Van der Hoeven, C. J.

Vlasov, A. G.

A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, Opt. Spektrosk. 13, 259 (1962); Opt. Spectrosc. 13, 142 (1962).

Vogl, T. P.

R. J. Pegis, D. S. Grey, T. P. Vogl, in Recent Advances in Optimization Techniques, A. Lavi, T. P. Vogl, Eds. (Wiley, New York, 1966), p. 47.

Young, L.

Appl. Opt. (4)

J. Opt. Soc. Am. (5)

J. Res. Natl. Bur. Stand. (1)

K. D. Mielenz, J. Res. Natl. Bur. Stand. 63A, 297 (1959).
[Crossref]

Nouv. Rev. Opt. Appl. (1)

E. Pelletier, M. Klapisch, P. Giacomo, Nouv. Rev. Opt. Appl. 2, 247 (1971).
[Crossref]

Opt. Spektrosk. (3)

A. M. Ermolaev, I. M. Minkov, A. G. Vlasov, Opt. Spektrosk. 13, 259 (1962); Opt. Spectrosc. 13, 142 (1962).

A. V. Skatilov, L. P. Tyutikova, Opt. Spektrosk. 14, 426 (1963); Opt. Spectrosc. 14, 227 (1963).

E. N. Elsner, Opt. Spektrosk. 17, 446 (1964); Opt. Spectrosc. 17, 238 (1964).

Optica Acta (1)

O. S. Heavens, H. M. Liddell, Optica Acta 15, 129 (1968).

Oyo Buturi (2)

N. Kimura, Oyo Buturi 31, 739 (1962).

N. Kimura, Oyo Buturi 32, 119 (1963).

Other (2)

R. J. Pegis, D. S. Grey, T. P. Vogl, in Recent Advances in Optimization Techniques, A. Lavi, T. P. Vogl, Eds. (Wiley, New York, 1966), p. 47.

H. A. Macleod, Thin Film Optical Filters (American Elsevier, New York, 1969).

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Figures (9)

Fig. 1
Fig. 1

The chief characteristics of a nonabsorbing minus filter.

Fig. 2
Fig. 2

Principle of filter design with minus filter components.

Fig. 3
Fig. 3

Typical interreflections occurring between the various minus filter components.

Fig. 4
Fig. 4

Flow of calculations in the computer program.

Fig. 5
Fig. 5

Calculated results for a comb filter.

Fig. 6
Fig. 6

Triangular filter with zero transmittance at λ = 0.55 μm.

Fig. 7
Fig. 7

Triangular filter with unit transmittance at λ = 0.55 μm.

Fig. 8
Fig. 8

Filter with a tilted sine shape.

Fig. 9
Fig. 9

Tristimulus y ¯ λ filter.

Tables (2)

Tables Icon

Table I Construction Parameters of Minus Filters Used in Examples

Tables Icon

Table II Optical Thicknesses nt (μm) and Refractive Indexes n of Multilayer Filters Obtained by Refining Starting Designs Comprised of Minus Filters

Equations (16)

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T λ = T λ ( 1 ) · T λ ( 2 ) T λ ( m ) ,
T λ = [ ( T λ ( 1 ) · T λ ( 2 ) ) / ( 1 - R ) ] · [ 1 / ( 1 + F sin 2 θ ) ] ,
R = [ ( 1 - T λ ( 1 ) ) · ( 1 - T λ ( 2 ) ) ] 1 / 2 , F = 4 R / ( 1 - R ) 2 ,
0 = 1 2 ( ϕ 1 + ϕ 2 ) ,
[ ( A / 2 ) C ( A / 2 ) ] [ ( A / 2 ) B ( A / 2 ) ] k [ ( A / 2 ) C ( A / 2 ) ] ,
n A = n S = n M ,
n C x = [ n A ( l + 1 - x ) · N ] 1 / ( l + 1 ) ,             x = 1 , 2 , l .
N = n A · ( cos ( π λ 0 / 2 λ ) cos ( π λ 0 / 2 λ ) - { [ 1 - ( n B / n A ) ] / [ 1 + ( n B / n A ) ] } + { [ 1 - ( n B / n A ) ] / [ 1 + ( n B / n A ) ] } ) 1 / 2 .
[ z / ω ] = 1 - [ T min / 17.676 ] 0.2137 for T min < 0.57 , = 1 - [ T min / 1.508 ] 0.7542 for T min > 0.57.
[ n B / n A ] = [ 1 + sin ( π z / 4 ) ] / [ 1 - sin ( π z / 4 ) ] .
( 1 - T min ) = { [ 1.0 - ( n A / n B ) 2 ( m + 1 ) ] / [ 1.0 + ( n A / n B ) 2 ( m + 1 ) ] } .
k = m - 2 l .
T λ C = T λ ( 1 ) · T λ ( 2 ) ..
T λ R = T λ D / T λ C ,
T = ( 1 / 2 ) ( X + Y ) , λ = ( 0.3 / 2 ) ( X - Y ) + 0.4 ,
Y = - ( 2 / 3 π ) sin ( 3 π X / 2 ) ,

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