Abstract

In this work we present the concept of wide band interferometry as opposed to white-light interferometry to introduce a thickness measurement method that gains precision when the bandwidth is reduced to an adequate compromise in order to avoid the distortions arising from the material dispersion. The use of the widest possible band is a well established dogma when the highest resolution is desired in distance measurements with white-light interferometry. We will show that the dogma falls when thickness measurements must be carried out due to material dispersion. In fact the precise knowledge of the frequency dependence of the refractive index is essential for adequate thickness retrieval from the optical experiments. The device we present is also useful to obtain the group refractive index that is necessary to calculate the absolute thickness value. As an example, we show the spreading of a silicone oil on a reference surface in real time.

© 2003 Optical Society of America

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References

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Appl. Opt. (6)

J. Mod. Opt. (1)

P. Sandoz, R. Devillers and A. Plata, �??Unambiguous profilometry by fringe-order identification in whitelight phase-shifting interferometry,�?? J. Mod. Opt. 44, 519-534 (1997)
[CrossRef]

Opt. Lett. (3)

Other (1)

G. P. Agrawal, Nonlinear fiber optics, (Academic Press, 1989), Chap. 3.

Supplementary Material (1)

» Media 1: MOV (2326 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

FFT of a wide band spectrum for a 600µm SF56 sample. Δλ=20nm, λ0=820nm

Fig. 2.
Fig. 2.

FFT of a wide band spectrum for a 600µm SF56 sample. Δλ=600nm, λ0=820nm

Fig. 3.
Fig. 3.

Schematic of the Wide Band thickness measurement device.

Fig. 4.
Fig. 4.

(2.3MB) Movie showing the evolution of the thickness of a silicone oil drop on the surface of a metallic mirror as a function of time. A) Example of the laser diode spectrum modulated. B) Temporal evolution of the oil thickness.

Fig. 5:
Fig. 5:

Lubricant thickness change calculated using the calibration of the spectrometer as a function of the number of fringes times the laser wavelength. The slope of the linear fit has information to compute the first order dispersion of the refractive index.

Equations (6)

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I ( k , Δ l ) = I ref ( k ) + I surf ( k ) + 2 I ref I surf cos ( k Δ l )
I int ( k ) = Exp ( [ k k 0 ] 2 2 Δ k 2 ) Exp ( i k n ( k ) d )
n ( k ) = n 0 + α ( k k 0 ) + β ( k k 0 ) 2 + γ ( k k 0 ) 3 +
I int ( x ) Exp ( [ x d ( n 0 + α k 0 ) ] 2 Δ k 2 2 i + 4 d α Δ k 2 )
x m oil x m air n 0 + α k = n 0 λ d n d λ = n g
s = 1 λ n 0 d n d λ

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