Abstract

Many spectral filtering problems require the use of assemblies of layers having thicknesses which bear no obvious relationship to each other. Successful production of these multilayers requires films with thicknesses approximating theoretical values. We show that the optical methods currently used in the production of film assemblies of quarterwave layer thicknesses, which are based on the use of just one single wavelength, are poorly adapted to monitoring the deposition of nonintegral thickness multilayers. In contrast we show that with an optical control system utilizing a broad spectral bandwidth, thickness errors can be reduced. Transmittance measurements with the precision necessary to achieve this improved thickness control are attainable with existing instrumentation. This result is established by a computer simulation of the construction of a specific multilayer and remains valid for other nonquarterwave multilayer filters.

© 1978 Optical Society of America

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References

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  1. J. P. Borgogno, E. Pelletier, Thin Solid Films 34, 357 (1976).J. P. Borgogno, E. Pelletier, submitted to J. Opt. Soc. Am.Nov.1977.
    [CrossRef]
  2. E. Pelletier, P. Giacomo, Nouv. Rev. Opt. Appl. 3, 133 (1972);E. Pelletier, Thèse C.N.R.S.(A.O. 6051), Paris (1970).
    [CrossRef]
  3. F. Abeles, J. Phys. 19, 327 (1958).
  4. P. Giacomo, P. Jacquinot, J. Phys. 13, 59A (1952).
  5. H. A. Macleod, Opt. Acta 19, 1 (1972).
    [CrossRef]
  6. P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, P. Roche, Thin Solid Films 13, 285 (1972).
    [CrossRef]
  7. E. Pelletier, M. Klapisch, P. Giacomo, Nouv. Rev. Opt. Appl. 2, 247 (1971).
    [CrossRef]
  8. E. Pelletier, P. Roche, B. Vidal, Nouv. Rev. Opt. Appl. 7, 353 (1976).
    [CrossRef]
  9. H. A. Macleod, E. Pelletier, Opt. Acta 27, 907 (1977).
    [CrossRef]
  10. A. Fornier, B. Vidal, E. Pelletier, to be published.

1977 (1)

H. A. Macleod, E. Pelletier, Opt. Acta 27, 907 (1977).
[CrossRef]

1976 (2)

E. Pelletier, P. Roche, B. Vidal, Nouv. Rev. Opt. Appl. 7, 353 (1976).
[CrossRef]

J. P. Borgogno, E. Pelletier, Thin Solid Films 34, 357 (1976).J. P. Borgogno, E. Pelletier, submitted to J. Opt. Soc. Am.Nov.1977.
[CrossRef]

1972 (3)

E. Pelletier, P. Giacomo, Nouv. Rev. Opt. Appl. 3, 133 (1972);E. Pelletier, Thèse C.N.R.S.(A.O. 6051), Paris (1970).
[CrossRef]

H. A. Macleod, Opt. Acta 19, 1 (1972).
[CrossRef]

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, P. Roche, Thin Solid Films 13, 285 (1972).
[CrossRef]

1971 (1)

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

1958 (1)

F. Abeles, J. Phys. 19, 327 (1958).

1952 (1)

P. Giacomo, P. Jacquinot, J. Phys. 13, 59A (1952).

Abeles, F.

F. Abeles, J. Phys. 19, 327 (1958).

Borgogno, J. P.

J. P. Borgogno, E. Pelletier, Thin Solid Films 34, 357 (1976).J. P. Borgogno, E. Pelletier, submitted to J. Opt. Soc. Am.Nov.1977.
[CrossRef]

Bousquet, P.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, P. Roche, Thin Solid Films 13, 285 (1972).
[CrossRef]

Fornier, A.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, P. Roche, Thin Solid Films 13, 285 (1972).
[CrossRef]

A. Fornier, B. Vidal, E. Pelletier, to be published.

Giacomo, P.

E. Pelletier, P. Giacomo, Nouv. Rev. Opt. Appl. 3, 133 (1972);E. Pelletier, Thèse C.N.R.S.(A.O. 6051), Paris (1970).
[CrossRef]

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

P. Giacomo, P. Jacquinot, J. Phys. 13, 59A (1952).

Jacquinot, P.

P. Giacomo, P. Jacquinot, J. Phys. 13, 59A (1952).

Klapisch, M.

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

Kowalczyk, R.

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, P. Roche, Thin Solid Films 13, 285 (1972).
[CrossRef]

Macleod, H. A.

H. A. Macleod, E. Pelletier, Opt. Acta 27, 907 (1977).
[CrossRef]

H. A. Macleod, Opt. Acta 19, 1 (1972).
[CrossRef]

Pelletier, E.

H. A. Macleod, E. Pelletier, Opt. Acta 27, 907 (1977).
[CrossRef]

E. Pelletier, P. Roche, B. Vidal, Nouv. Rev. Opt. Appl. 7, 353 (1976).
[CrossRef]

J. P. Borgogno, E. Pelletier, Thin Solid Films 34, 357 (1976).J. P. Borgogno, E. Pelletier, submitted to J. Opt. Soc. Am.Nov.1977.
[CrossRef]

E. Pelletier, P. Giacomo, Nouv. Rev. Opt. Appl. 3, 133 (1972);E. Pelletier, Thèse C.N.R.S.(A.O. 6051), Paris (1970).
[CrossRef]

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, P. Roche, Thin Solid Films 13, 285 (1972).
[CrossRef]

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

A. Fornier, B. Vidal, E. Pelletier, to be published.

Roche, P.

E. Pelletier, P. Roche, B. Vidal, Nouv. Rev. Opt. Appl. 7, 353 (1976).
[CrossRef]

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, P. Roche, Thin Solid Films 13, 285 (1972).
[CrossRef]

Vidal, B.

E. Pelletier, P. Roche, B. Vidal, Nouv. Rev. Opt. Appl. 7, 353 (1976).
[CrossRef]

A. Fornier, B. Vidal, E. Pelletier, to be published.

J. Phys. (2)

F. Abeles, J. Phys. 19, 327 (1958).

P. Giacomo, P. Jacquinot, J. Phys. 13, 59A (1952).

Nouv. Rev. Opt. Appl. (3)

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

E. Pelletier, P. Roche, B. Vidal, Nouv. Rev. Opt. Appl. 7, 353 (1976).
[CrossRef]

E. Pelletier, P. Giacomo, Nouv. Rev. Opt. Appl. 3, 133 (1972);E. Pelletier, Thèse C.N.R.S.(A.O. 6051), Paris (1970).
[CrossRef]

Opt. Acta (2)

H. A. Macleod, E. Pelletier, Opt. Acta 27, 907 (1977).
[CrossRef]

H. A. Macleod, Opt. Acta 19, 1 (1972).
[CrossRef]

Thin Solid Films (2)

P. Bousquet, A. Fornier, R. Kowalczyk, E. Pelletier, P. Roche, Thin Solid Films 13, 285 (1972).
[CrossRef]

J. P. Borgogno, E. Pelletier, Thin Solid Films 34, 357 (1976).J. P. Borgogno, E. Pelletier, submitted to J. Opt. Soc. Am.Nov.1977.
[CrossRef]

Other (1)

A. Fornier, B. Vidal, E. Pelletier, to be published.

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Figures (10)

Fig. 1
Fig. 1

Theoretical performance of a seven-layer beam splitter of design: glass 103.4, 194.9, 89.2, 154.7, 67.7, 80.1, 42.9 (nm) made of ZnS (odd layers) and cryolite (even layers) on glass (n = 1.52). The refractive indices are given in Ref. 8.

Fig. 2
Fig. 2

Diagram illustrating the effect in turning value monitoring of an overshoot on the thickness error in a layer.

Fig. 3
Fig. 3

Simulated production run of the turning value monitoring of the beam splitter of Fig. 1 with a systematic error of α = 0.001 in determining the turning values: — perfect filter; ◊ filter with systematic error.

Fig. 4
Fig. 4

Envelopes showing the transmittance found with successive runs of the beam splitter of Fig. 1 with random errors of 0.005 in determining the turning values. The performance of these simulated filters is summarized in Table II: — perfect filter; — filter with random errors.

Fig. 5
Fig. 5

Envelopes showing the transmittance found with successive runs of the beam splitter of Fig. 1 with random errors of 0.001 in determining the turning values. The performance of these simulated filters is summarized in Table IV: — perfect filter; — filter with random errors.

Fig. 6
Fig. 6

The results of a computer simulation of the seven-layer beam splitter, — perfect filter, △ filter obtained assuming that an absolute transmittance error of 0.015 is made in layer monitoring, each minimum of the monitoring merit function being systematically overshot. ▽ filter obtained assuming that an absolute transmittance error of 0.015 is made in layer monitoring, the deposition of each layer being terminated before the minimum of the merit function.

Fig. 7
Fig. 7

Effect of 0.015 standard deviation transmittance error on the performance of the seven-layer beam splitter using wideband monitoring (400–800 nm): — perfect filter. — Computed filters with transmittance errors. The performance is summarized in Table VII.

Fig. 8
Fig. 8

Effect of 0.010 standard deviation transmittance error on the performance of the seven-layer beam splitter using wideband monitoring (400–800 nm): — perfect filter; — computer filters with transmittance errors. The performance is summarized in Table VIII.

Fig. 9
Fig. 9

Effect of 0.005 standard deviation transmittance error on the performance of the seven-layer beam splitter using wideband monitoring (400–800 nm): — perfect filter; — computed filters with transmittance errors. The performance is summarized in Table IX.

Fig. 10
Fig. 10

Influence of the wideband monitoring process (400–800 nm) on the performance of the seven-layer beam splitter by assuming as in the case of Fig. 8, a random error of transmittance σ(Ti) = 0.010, with an additional systematic overshoot of each minimum of the merit function corresponding to an error of δT = 0.01.

Tables (9)

Tables Icon

Table I Simulation of the Production by Turning Value Monitoring of the Seven-Layer Beam Splitter shown in Fig. 1

Tables Icon

Table II Simulated Production Runs of the Beam Splitter of Fig. 1 Using Turning Value Monitoring with Random Errors of 0.005 In Determing the Turning Values

Tables Icon

Table III Simulated Production Runs of the Beam Splitter of Fig. 1 Using Turning Value Monitoring with Random Errors of 0.003 in Determining the Turning Values

Tables Icon

Table IV Simulated Production Runs of the Beam Splitter of Fig. 1 Using Turning Value Monitoring with Random Errors of 0.001 in Determining the Turning Values

Tables Icon

Table V Simulated Production Runs of the Beam Splitter of Fig. 1 Using Turning Value Monitoring with Random Errors of 0.001 as in Table IV and a Simultaneous Systematic Overshoot of 0.001

Tables Icon

Table VI Error (in nm) In the Thickness of the ith Layer of the Beam Splitter which Occurs when the Transmittance at Termination of Deposition Overshoots the Correct Value of the Spectral Profile over 400–800 nm by δTi)

Tables Icon

Table VII Effect of 0.015 Standard Deviation Transmittance Error on the Performance of the Seven-Layer Beam Splitter Using Wideband Monitoring (400–800 nm)

Tables Icon

Table VIII Effect of 0.010 Standard Deviation Transmittance Error on the Performance of the Seven-Layer Beam Splitter Using Wideband Monitoring (400–800 nm)

Tables Icon

Table IX Effect of 0.005 Standard Deviation Transmittance Error on the Performance of the Seven-Layer Beam Splitter Using Wideband Monitoring (400–800 nm)

Equations (19)

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f i = λ 1 λ 2 | T i ( λ , e i ) T i ( λ , e ) | d λ ,
+ 1.2 , + 6.0 , 0.7 , + 20.6 , 21.4 , + 2.0 , + 21.2 ( nm ) ,
T ¯ = 0.321 Δ T ¯ = 0.049 | Δ T | m = 0.110 ,
1.7 , 7.8 , + 5.1 , 19.6 , + 6.5 , + 8.1 , + 1.5 ( nm ) ,
T ¯ = 0.372 Δ T ¯ = 0.056 | Δ T | m = 0.222 .
T ¯ s
Δ T s ¯
T ¯ s
Δ T s ¯
T ¯ s
Δ T s ¯
T ¯ s
Δ T s ¯
T ¯ s
Δ T ̅
T ¯ s
Δ T ¯
T ¯ s
Δ T ¯

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