Abstract

A white-light interferometric thickness gauge has been developed that provides microinch sensitivity to gauge variations in moving transparent films. The new gauge that is suitable for on-line use can be adapted to monitor continuously the thickness profile of transparent films, the thickness of transparent coatings, and the birefringence of optically anisotropic materials. Its performance is relatively insensitive to variations in chemical composition, film temperature, haze level, and measurement geometry.

© 1972 Optical Society of America

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References

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  1. C. Candler, Modern Interferometers (Hilger & Watts, Glasgow, 1951), p. 223.
  2. J. H. Teeple, A. Strickler, U. S. Patent2,418,647 (1950), assigned to Celanese Corporation.
  3. F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), p. 244.
  4. E. B. Brown, Modern Optics (Reinhold, New York, 1965), p. 77.
  5. F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), p. 262.
  6. J. E. Gibbs, H. A. Gebbie, Infrared Phys. 5, 187 (1965).
    [CrossRef]
  7. L. Mertz, Transformations in Optics (Wiley, New York, 1965), p. 29.

1965 (1)

J. E. Gibbs, H. A. Gebbie, Infrared Phys. 5, 187 (1965).
[CrossRef]

Brown, E. B.

E. B. Brown, Modern Optics (Reinhold, New York, 1965), p. 77.

Candler, C.

C. Candler, Modern Interferometers (Hilger & Watts, Glasgow, 1951), p. 223.

Gebbie, H. A.

J. E. Gibbs, H. A. Gebbie, Infrared Phys. 5, 187 (1965).
[CrossRef]

Gibbs, J. E.

J. E. Gibbs, H. A. Gebbie, Infrared Phys. 5, 187 (1965).
[CrossRef]

Jenkins, F.

F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), p. 244.

F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), p. 262.

Mertz, L.

L. Mertz, Transformations in Optics (Wiley, New York, 1965), p. 29.

Strickler, A.

J. H. Teeple, A. Strickler, U. S. Patent2,418,647 (1950), assigned to Celanese Corporation.

Teeple, J. H.

J. H. Teeple, A. Strickler, U. S. Patent2,418,647 (1950), assigned to Celanese Corporation.

White, H.

F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), p. 262.

F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), p. 244.

Infrared Phys. (1)

J. E. Gibbs, H. A. Gebbie, Infrared Phys. 5, 187 (1965).
[CrossRef]

Other (6)

L. Mertz, Transformations in Optics (Wiley, New York, 1965), p. 29.

C. Candler, Modern Interferometers (Hilger & Watts, Glasgow, 1951), p. 223.

J. H. Teeple, A. Strickler, U. S. Patent2,418,647 (1950), assigned to Celanese Corporation.

F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), p. 244.

E. B. Brown, Modern Optics (Reinhold, New York, 1965), p. 77.

F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), p. 262.

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Figures (14)

Fig. 1
Fig. 1

Two plates set to produce Brewster’s fringes. When the path differences introduced in the two plates are equal, a white-light fringe appears.

Fig. 2
Fig. 2

Michelson interferometer.

Fig. 3
Fig. 3

Interferogram (white-light source).

Fig. 4
Fig. 4

Thickness gauge optics.

Fig. 5
Fig. 5

Interferogram for film gauging.

Fig. 6
Fig. 6

Interferogram for film with transparent coating.

Fig. 7
Fig. 7

Effect of refractive index on coating measurement.

Fig. 8
Fig. 8

Interferometric film gauge modified to correct for variations in film refractive index.

Fig. 9
Fig. 9

Interferogram for birefringent film.

Fig. 10
Fig. 10

Prototype interferometric thickness gauge.

Fig. 11
Fig. 11

Electronics block diagram.

Fig. 12
Fig. 12

Interferometric thickness gauge-proposed installations.

Fig. 13
Fig. 13

Gauge performance on hazy film.

Fig. 14
Fig. 14

Apodization of interferogram: (A) unapodized spectral window; (B) even apodized spectral window.

Equations (13)

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Δ L = 2 n d cos ϕ ,
I = 4 I 0 cos 2 ( δ / 2 ) ,
I ( Δ ) = 4 K 1 K 2 i ( k ) cos 2 ( k Δ / 2 ) d k ,
δ f = 2 k n d cos ϕ .
I ( Δ ) = 4 K 1 K 2 i ( k ) cos 2 ( 2 k n d cos ϕ ) cos 2 ( k Δ / 2 ) d k ,
Δ = ± 2 n d cos ϕ .
α = 2 n d ,
β = 2 n d cos ϕ ,
cos ϕ = β / α .
sin ϕ = sin ϕ / n ,
cos 2 ϕ = 1 - sin 2 ϕ = 1 - [ sin 2 ϕ / ( n ) 2 ] .
n = α sin ϕ / [ ( α 2 - β 2 ) 1 2 ] ,
d = [ ( α 2 - β 2 ) 1 2 ] / 2 sin ϕ ,

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