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A film of gas or liquid has a refractive index which differs from that of the bulk fluid and the surface to which it is attached. This property may be used to determine the thickness of the film remotely provided that its refractive index is known. For a gas, Gladstone and Dale's law gives (m – 1) = Kρ, where m is the refractive index, ρ is the density and K is a constant depending on the constituents. Thus the variation with temperature or pressure is known.

The thickness enters through the phase of the propagating wave, given by mkL, where L is distance travelled and k = 2π/λ is the wave number. The phase of a wave may be measured using Interferometry. If the surface is opaque the interference is observed between waves reflected from the front face of the film and that which is transmitted and reflected from the surface. For normal incidence the difference in phase between the two waves is 2mkt, where t is the thickness. If the film thickness varies a set of interference fringes is observed, the fringe separation being given by the distance over which the phase difference changes by one wavelength of the light. (Newton's rings are an example of this kind of interference). If the surface is transparent the same measurement may be made in transmission, except that in this case a separate reference wave must be employed. Transmission can also be used if the measurement is made along the film. Here the variation in path length, or refractive index, can be obtained as a function of position within the film. This has proved useful, for example, for measuring temperature variation in boundary layers.

Interference fringes are distorted by the presence of other phase objects such as windows or lenses. These effects can be overcome by the use of holography. If a hologram is taken of an object and the reconstructed image is superimposed on the original, then any small changes in the object show up as interference fringes. These are independent of the other phase objects which are constant. In this way undistorted interferometry can be carried out in real time. A similar process is double exposure holography. Here two holograms of the same object are taken on the same plate. On reconstruction interference fringes are seen indicating the differences that have occurred between the two exposures. (See also Holograms and Holographic Interferometry.)

If the film is opaque variations in surface height can be measured by profiling. In this technique fringes are projected onto the surface and their pattern reveals changes in height. Moiré fringes are often employed for this purpose. Provided that the underlying surface is flat the thickness variation is obtained from the height changes.

Further Reading

Sandhu, S. S. and Weinberg, F. J. (1972) J. Phys. E: J. Sci. Inst., 5, 1018-1020.

Williams, D. C. (Ed.) (1993) Optical Methods in Engineering Metrology, Chapman and Hall, London.

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