Abstract

We introduce a technique to measure transparent glass slab thickness. It employs a very simple setup combining two interferometers: a forward-going beam scheme and a self-mixing readout of the beam reflected back to the laser source. Interestingly, the difference of the two readouts provides a quantity related to thickness measurement, irrespective of refractive index. We demonstrate this method using samples on a range of thickness from 30 to 1000μm.

© 2010 Optical Society of America

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References

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2008 (2)

2007 (1)

2004 (1)

2003 (1)

2002 (1)

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, J. Opt. A 4, S283 (2002).
[CrossRef]

2000 (1)

1995 (1)

S. Donati, G. Giuliani, and S. Merlo, IEEE J. Quantum Electron. 31, 113 (1995).
[CrossRef]

1992 (1)

W. V. Sorin and D. F. Gray, IEEE Photonics Technol. Lett. 4, 105 (1992).
[CrossRef]

1979 (1)

M. Debenham, G. Dew, and D. E. Putland, Opt. Acta 26, 1487 (1979).
[CrossRef]

Bauer, T.

Beaumont, A.

Bosch, T.

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, J. Opt. A 4, S283 (2002).
[CrossRef]

Burke, J.

Coppola, G.

de Groot, P.

De Nicola, S.

Debenham, M.

M. Debenham, G. Dew, and D. E. Putland, Opt. Acta 26, 1487 (1979).
[CrossRef]

Dew, G.

M. Debenham, G. Dew, and D. E. Putland, Opt. Acta 26, 1487 (1979).
[CrossRef]

Donati, S.

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, J. Opt. A 4, S283 (2002).
[CrossRef]

S. Donati, G. Giuliani, and S. Merlo, IEEE J. Quantum Electron. 31, 113 (1995).
[CrossRef]

S. Donati, Electro-Optical Instrumentation—Sensing and Measuring with Lasers (Prentice Hall, 2004).

Fairman, P. S.

Ferraro, P.

Giuliani, G.

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, J. Opt. A 4, S283 (2002).
[CrossRef]

S. Donati, G. Giuliani, and S. Merlo, IEEE J. Quantum Electron. 31, 113 (1995).
[CrossRef]

Gray, D. F.

W. V. Sorin and D. F. Gray, IEEE Photonics Technol. Lett. 4, 105 (1992).
[CrossRef]

Hart, C.

Heil, J.

Hibino, K.

Kim, M. J.

Kim, S.

Lee, B. H.

Lodice, M.

Merlo, S.

S. Donati, G. Giuliani, and S. Merlo, IEEE J. Quantum Electron. 31, 113 (1995).
[CrossRef]

Na, J.

Norgia, M.

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, J. Opt. A 4, S283 (2002).
[CrossRef]

Oreb, B. F.

Putland, D. E.

M. Debenham, G. Dew, and D. E. Putland, Opt. Acta 26, 1487 (1979).
[CrossRef]

Schmax, S.

Sorin, W. V.

W. V. Sorin and D. F. Gray, IEEE Photonics Technol. Lett. 4, 105 (1992).
[CrossRef]

Sure, T.

Tomlines, P.

Wesner, J.

Wolliams, P.

Appl. Opt. (4)

IEEE J. Quantum Electron. (1)

S. Donati, G. Giuliani, and S. Merlo, IEEE J. Quantum Electron. 31, 113 (1995).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

W. V. Sorin and D. F. Gray, IEEE Photonics Technol. Lett. 4, 105 (1992).
[CrossRef]

J. Opt. A (1)

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, J. Opt. A 4, S283 (2002).
[CrossRef]

Opt. Acta (1)

M. Debenham, G. Dew, and D. E. Putland, Opt. Acta 26, 1487 (1979).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Other (1)

S. Donati, Electro-Optical Instrumentation—Sensing and Measuring with Lasers (Prentice Hall, 2004).

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Figures (3)

Fig. 1
Fig. 1

Experimental setup for thickness measurement with the SMI and self-reference interferometer method. The beam from a laser diode goes across the slab under measurement and reaches PD2; a few percent of power is also reflected by the photodiode entrance window. The back reflected rays trace back the path and reenter the laser cavity, producing a SMI interferometric signal that carries the phase 2 n k L as an amplitude modulation of the power at photodiode PD2. Another signal is provided by photodiode PD2, where we find the superposition (partial, with lateral shift) of transmitted and double-reflected beams in the slab (i.e., a shear interferometer). Upon rotation of the slab by an angle α, the two signals at PD1 and PD2 vary and provide signals to compute n and d.

Fig. 2
Fig. 2

(a) Theoretical SMI phase variation; (b) experimental SMI signal; (c) experimental signal of forward-going interferometer. All results are plotted against rotation angle (degree) for a glass slab thickness of 154 μm .

Fig. 3
Fig. 3

Experimental phase difference Δ φ PD Δ φ SMI for a 154 μm slab and the theoretical line providing the best least-square-fit interpolation.

Tables (1)

Tables Icon

Table 1 Thickness Experimental Results for Some Glass Samples

Equations (5)

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P ( φ ) = P 0 [ 1 + m F ( φ ) ] ,
Δ φ PD = 2 k n d cos θ ,
Δ φ SMI = 2 k d ( n cos θ cos α ) .
Δ φ = Δ φ PD Δ φ SMI = 2 k d cos α ,
Δ ( Δ φ PD ) = 4 π ( d / λ ) Δ n cos θ + 4 π ( Δ d / λ ) n cos θ .

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