Abstract

Simple equations are given for determining both refractive index and film thickness from a measurement of interference fringe separation where the question of phase change and the order of the fringes can be disregarded. The equations are quite general, since they apply to fringe maxima or minima for either transmission or reflection and can be used for free-standing films or films on substarates of higher refractive index. Advantages of recording fringes via reflection rather than transmission are discussed. A unique attachment for commercial spectrophotometers for making measurements over a wide range of angles of incidence is described.

© 1971 Optical Society of America

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References

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  1. See, e.g., F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957).
  2. N. J. Harrick, Internal Reflection Spectroscopy (Wiley, Interscience, New York, 1967).
  3. See, e.g., J. D. E. McIntyre, D. E. Aspnes, Surface Sci. 24, 417 (1971).
    [CrossRef]

1971 (1)

See, e.g., J. D. E. McIntyre, D. E. Aspnes, Surface Sci. 24, 417 (1971).
[CrossRef]

Aspnes, D. E.

See, e.g., J. D. E. McIntyre, D. E. Aspnes, Surface Sci. 24, 417 (1971).
[CrossRef]

Harrick, N. J.

N. J. Harrick, Internal Reflection Spectroscopy (Wiley, Interscience, New York, 1967).

Jenkins, F. A.

See, e.g., F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957).

McIntyre, J. D. E.

See, e.g., J. D. E. McIntyre, D. E. Aspnes, Surface Sci. 24, 417 (1971).
[CrossRef]

White, H. E.

See, e.g., F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957).

Surface Sci. (1)

See, e.g., J. D. E. McIntyre, D. E. Aspnes, Surface Sci. 24, 417 (1971).
[CrossRef]

Other (2)

See, e.g., F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957).

N. J. Harrick, Internal Reflection Spectroscopy (Wiley, Interscience, New York, 1967).

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Figures (6)

Fig. 1
Fig. 1

Decomposition of a beam of light into multiple components by reflection at the front and back surface of a thin film.

Fig. 2
Fig. 2

Transmission and reflection from a ½-mil Mylar film at an angle of incidence of 15°. Note that better-defined interference fringes are obtained in reflection and less distortion occurs due to the absorption bands.

Fig. 3
Fig. 3

(a) Optical layout and (b) photograph of attachment (VRA) and accessory (RMA) employed to measure reflection at various angles of incidence. Once this assembly is aligned for one angle of incidence it remains in alignment for all others.

Fig. 4
Fig. 4

Interference fringes recorded via reflection from a ½-mil Mylar film at various angles of incidence.

Fig. 5
Fig. 5

A series of fringe patterns illustrating the appearance of double-fringe patterns at grazing incidence.

Fig. 6
Fig. 6

Use of polarized light to decompose the double-fringe pattern into single-fringe patterns.

Equations (5)

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sin θ = n sin ϕ ,
2 n d cos ϕ = m λ = m / ν ,
2 n d cos ϕ = ( m + ½ ) λ = ( m + ½ ) / ν .
d = Δ m / 2 ( n 2 - sin 2 θ ) 1 2 Δ ν i f ,
n = [ ( sin 2 θ 1 Δ ν 1 2 - sin 2 θ 2 Δ ν 2 2 ) / ( Δ ν 1 2 - Δ ν 2 2 ) ] 1 2 .

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