Abstract

A method that utilizes the Fresnel diffraction of light from the phase step formed by a transparent wedge is introduced for measuring the refractive indices of transparent solids, liquids, and solutions. It is shown that, as a transparent wedge of small apex angle is illuminated perpendicular to its surface by a monochromatic parallel beam of light, the Fresnel fringes, caused by abrupt change in refractive index at the wedge lateral boundary, are formed on a screen held perpendicular to the beam propagation direction. The visibility of the fringes varies periodically between zero and 1 in the direction normal to the wedge apex. For a known or measured apex angle, the wedge refractive index is obtained by measuring the period length by a CCD. To measure the refractive index of a transparent liquid or solution, the wedge is installed in a transparent rectangle cell containing the sample. Then, the cell is illuminated perpendicularly and the visibility period is measured. By using modest optics, one can measure the refractive index at a relative uncertainty level of 105. There is no limitation on the refractive index range. The method can be applied easily with no mechanical manipulation. The measuring apparatus can be very compact with low mechanical and optical noises.

© 2010 Optical Society of America

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References

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2009 (2)

2008 (1)

2007 (4)

2002 (1)

2000 (1)

1996 (2)

B. Richerzhagen, Appl. Opt. 35, 1650 (1996).
[CrossRef] [PubMed]

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, J. Opt. A 5, 761 (1996).

1993 (1)

1992 (1)

1991 (1)

1984 (1)

1982 (1)

Aalipour, R.

Amiri, M.

Beaumont, A.

Buchanan, M.

Carroll, L.

Daimon, M.

Darudi, A.

de Angelis, M.

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, J. Opt. A 5, 761 (1996).

de Greef, C.

De Nicola, S.

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, J. Opt. A 5, 761 (1996).

Dereniak, E. L.

Ferraro, P.

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, J. Opt. A 5, 761 (1996).

Finizio, A.

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, J. Opt. A 5, 761 (1996).

Finsy, R.

Haghighi, I. M.

Hart, C.

Hassani, K.

Henry, M.

Kafri, O.

Kao, C.-F.

Karny, Z.

Khashan, M. A.

Kuhler, K.

Li, T.

Liu, T.-S.

Lu, S.-H.

Masumura, A.

Moradi, A. R.

Moreels, E.

Nassif, A. Y.

Nemoto, S.

Pan, S.-P.

Pierattini, G.

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, J. Opt. A 5, 761 (1996).

Richerzhagen, B.

Sabatyan, A.

A. Sabatyan and M. T. Tavassoly, Opt. Eng. 46, 128001(2007).
[CrossRef]

Saber, A.

Tan, X.

Tavassoly, M. T.

M. T. Tavassoly, I. M. Haghighi, and K. Hassani, Appl. Opt. 48, 5497 (2009).
[CrossRef]

M. Amiri and M. T. Tavassoly, Opt. Commun. 272, 349(2007).
[CrossRef]

A. Sabatyan and M. T. Tavassoly, Opt. Eng. 46, 128001(2007).
[CrossRef]

Tavassoly, M. Taghi

Tedaldi, M.

Tomlins, P. H.

Woolliams, P.

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Figures (5)

Fig. 1
Fig. 1

(a) Plane wave Σ is incident to a one-dimensional (1D) phase step of height h. (b) A transparent plate of refractive index N immersed in a medium of refractive index N provides a step in transmission.

Fig. 2
Fig. 2

Fresnel diffraction patterns of light diffracted from two 1D phase steps of different heights and the corresponding intensity profiles. As the profiles show, the visibility of the fringes varies with the step height. The step edge is a line parallel to the fringes that passes from point 0 on the profiles.

Fig. 3
Fig. 3

When a transparent wedge of small apex angle is illuminated by a monochromatic parallel beam, the light diffracted from the two sides of the hatched interface produce a diffraction pattern similar to those shown in Fig. 4.

Fig. 4
Fig. 4

Diffraction patterns of the expanded He–Ne laser light diffracted from a BK7 wedge of apex angle α = 0.198 ° , immersed in (a) air, (b) water, (c) acetone, and in ethanol–water solutions of (d) 30% and (e) 80%. The slanted fringes at the center are the traces of the central dark fringe in Fig. 2, whose location and intensity vary periodically by the change of the wedge thickness. The arrows represent the directions of the x and y axes in Fig. 3.

Fig. 5
Fig. 5

Refractive index of the ethanol–water solution versus ethanol concentration obtained experimentally.

Tables (1)

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Table 1 Refractive Indices of Three Different Liquids

Equations (7)

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I n = cos 2 ( ϕ 2 ) + 2 ( C 0 2 + S 0 2 ) sin 2 ( ϕ 2 ) ( C 0 S 0 ) sin ϕ ,
ϕ = 4 π h λ cos θ
ϕ = 2 π λ N h [ n 2 sin 2 θ cos θ ] ,
ϕ = 2 π y λ ( N N ) tan α .
ρ = λ ( N N ) tan α .
N = N + λ ρ tan α .
U ( N ) = λ ρ tan α U ( l ) l ,

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