Abstract

We present a method for dynamically measuring the refractive index distribution in a large range based on the combination of digital holographic interferometry and total internal reflection. A series of holograms, carrying the index information of mixed liquids adhered on a total reflection prism surface, are recorded with CCD during the diffusion process. Phase shift differences of the reflected light are reconstructed exploiting the principle of double-exposure holographic interferometry. According to the relationship between the reflection phase shift difference and the liquid index, two dimensional index distributions can be directly figured out, assuming that the index of air near the prism surface is constant. The proposed method can also be applied to measure the index of solid media and monitor the index variation during some chemical reaction processes.

© 2015 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref]
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2014 (2)

A. Calabuig, M. Matrecano, M. Paturzo, and P. Ferraro, “Common-path configuration in total internal reflection digital holography microscopy,” Opt. Lett. 39(8), 2471–2474 (2014).
[Crossref] [PubMed]

Y. Chu, W. Chang, K. Chen, J. Chen, B. Tsai, and K. Hsu, “Full-field refractive index measurement with simultaneous phase-shift interferometry,” Optik (Stuttg.) 125(13), 3307–3310 (2014).
[Crossref]

2013 (2)

S. Zhang, W. Zhang, P. Geng, and S. Gao, “Fiber Mach-Zehnder interferometer based on concatenated down-and up-tapers for refractive index sensing applications,” Opt. Commun. 288(1), 47–51 (2013).
[Crossref]

Y. Wang, D. N. Wang, C. R. Liao, T. Hu, J. Guo, and H. Wei, “Temperature-insensitive refractive index sensing by use of micro Fabry-Pérot cavity based on simplified hollow-core photonic crystal fiber,” Opt. Lett. 38(3), 269–271 (2013).
[Crossref] [PubMed]

2012 (5)

2010 (1)

2009 (1)

2008 (2)

2007 (1)

2006 (1)

Z. Jian, P. Hsieh, H.-C. Hsieh, H.-W. Chen, and D.-C. Su, “A method for measuring two-dimensional refractive index distribution with the total internal reflection of p-polarized light and the phase-shifting interferometry,” Opt. Commun. 268(1), 23–26 (2006).
[Crossref]

1997 (1)

1985 (1)

D. J. Arndt-Jovin, M. Robert-Nicoud, S. J. Kaufman, and T. M. Jovin, “Fluorescence digital imaging microscopy in cell biology,” Science 230(4723), 247–256 (1985).
[Crossref] [PubMed]

1983 (1)

D. Axelrod, N. L. Thompson, and T. P. Burghardt, “Total internal inflection fluorescent microscopy,” J. Microsc. 129(1), 19–28 (1983).
[Crossref] [PubMed]

1981 (1)

D. Axelrod, “Cell-substrate contacts illuminated by total internal reflection fluorescence,” J. Cell Biol. 89(1), 141–145 (1981).
[Crossref] [PubMed]

Arndt-Jovin, D. J.

D. J. Arndt-Jovin, M. Robert-Nicoud, S. J. Kaufman, and T. M. Jovin, “Fluorescence digital imaging microscopy in cell biology,” Science 230(4723), 247–256 (1985).
[Crossref] [PubMed]

Ash, W. M.

Axelrod, D.

D. Axelrod, N. L. Thompson, and T. P. Burghardt, “Total internal inflection fluorescent microscopy,” J. Microsc. 129(1), 19–28 (1983).
[Crossref] [PubMed]

D. Axelrod, “Cell-substrate contacts illuminated by total internal reflection fluorescence,” J. Cell Biol. 89(1), 141–145 (1981).
[Crossref] [PubMed]

Babovsky, H.

Buehl, J.

Burghardt, T. P.

D. Axelrod, N. L. Thompson, and T. P. Burghardt, “Total internal inflection fluorescent microscopy,” J. Microsc. 129(1), 19–28 (1983).
[Crossref] [PubMed]

Calabuig, A.

Chang, W.

Y. Chu, W. Chang, K. Chen, J. Chen, B. Tsai, and K. Hsu, “Full-field refractive index measurement with simultaneous phase-shift interferometry,” Optik (Stuttg.) 125(13), 3307–3310 (2014).
[Crossref]

Charrière, F.

Chen, H.-W.

Z. Jian, P. Hsieh, H.-C. Hsieh, H.-W. Chen, and D.-C. Su, “A method for measuring two-dimensional refractive index distribution with the total internal reflection of p-polarized light and the phase-shifting interferometry,” Opt. Commun. 268(1), 23–26 (2006).
[Crossref]

Chen, J.

Y. Chu, W. Chang, K. Chen, J. Chen, B. Tsai, and K. Hsu, “Full-field refractive index measurement with simultaneous phase-shift interferometry,” Optik (Stuttg.) 125(13), 3307–3310 (2014).
[Crossref]

Chen, K.

Y. Chu, W. Chang, K. Chen, J. Chen, B. Tsai, and K. Hsu, “Full-field refractive index measurement with simultaneous phase-shift interferometry,” Optik (Stuttg.) 125(13), 3307–3310 (2014).
[Crossref]

Chiu, M. H.

Chu, Y.

Y. Chu, W. Chang, K. Chen, J. Chen, B. Tsai, and K. Hsu, “Full-field refractive index measurement with simultaneous phase-shift interferometry,” Optik (Stuttg.) 125(13), 3307–3310 (2014).
[Crossref]

Colomb, T.

Depeursinge, C.

Di, J.

Eggeling, C.

Ferraro, P.

Gao, S.

S. Zhang, W. Zhang, P. Geng, and S. Gao, “Fiber Mach-Zehnder interferometer based on concatenated down-and up-tapers for refractive index sensing applications,” Opt. Commun. 288(1), 47–51 (2013).
[Crossref]

Geng, P.

S. Zhang, W. Zhang, P. Geng, and S. Gao, “Fiber Mach-Zehnder interferometer based on concatenated down-and up-tapers for refractive index sensing applications,” Opt. Commun. 288(1), 47–51 (2013).
[Crossref]

Grosse, M.

Guo, J.

Guo, Y.

Hell, S. W.

Hsieh, H.-C.

Z. Jian, P. Hsieh, H.-C. Hsieh, H.-W. Chen, and D.-C. Su, “A method for measuring two-dimensional refractive index distribution with the total internal reflection of p-polarized light and the phase-shifting interferometry,” Opt. Commun. 268(1), 23–26 (2006).
[Crossref]

Hsieh, P.

Z. Jian, P. Hsieh, H.-C. Hsieh, H.-W. Chen, and D.-C. Su, “A method for measuring two-dimensional refractive index distribution with the total internal reflection of p-polarized light and the phase-shifting interferometry,” Opt. Commun. 268(1), 23–26 (2006).
[Crossref]

Hsu, K.

Y. Chu, W. Chang, K. Chen, J. Chen, B. Tsai, and K. Hsu, “Full-field refractive index measurement with simultaneous phase-shift interferometry,” Optik (Stuttg.) 125(13), 3307–3310 (2014).
[Crossref]

Hu, T.

Huang, Z.

Jian, Z.

Z. Jian, P. Hsieh, H.-C. Hsieh, H.-W. Chen, and D.-C. Su, “A method for measuring two-dimensional refractive index distribution with the total internal reflection of p-polarized light and the phase-shifting interferometry,” Opt. Commun. 268(1), 23–26 (2006).
[Crossref]

Jiang, B.

Jiang, H.

Jiao, X.

Q. Wang, J. Zhao, X. Jiao, J. Di, and H. Jiang, “Visual and quantitative measurement of the temperature distribution of heat conduction process in glass based on digital holographic interferometry,” J. Appl. Phys. 111(9), 093111 (2012).
[Crossref]

Jovin, T. M.

D. J. Arndt-Jovin, M. Robert-Nicoud, S. J. Kaufman, and T. M. Jovin, “Fluorescence digital imaging microscopy in cell biology,” Science 230(4723), 247–256 (1985).
[Crossref] [PubMed]

Kaufman, S. J.

D. J. Arndt-Jovin, M. Robert-Nicoud, S. J. Kaufman, and T. M. Jovin, “Fluorescence digital imaging microscopy in cell biology,” Science 230(4723), 247–256 (1985).
[Crossref] [PubMed]

Kiessling, A.

Kim, M. K.

Kowarschik, R.

Kühn, J.

Lasser, T.

Lee, J. Y.

Leutenegger, M.

Liao, C. R.

Loock, H. P.

Marquet, P.

Matrecano, M.

Paturzo, M.

Qin, C.

Rappaz, B.

Rauf, A.

Ringemann, C.

Robert-Nicoud, M.

D. J. Arndt-Jovin, M. Robert-Nicoud, S. J. Kaufman, and T. M. Jovin, “Fluorescence digital imaging microscopy in cell biology,” Science 230(4723), 247–256 (1985).
[Crossref] [PubMed]

Su, D. C.

Su, D.-C.

Z. Jian, P. Hsieh, H.-C. Hsieh, H.-W. Chen, and D.-C. Su, “A method for measuring two-dimensional refractive index distribution with the total internal reflection of p-polarized light and the phase-shifting interferometry,” Opt. Commun. 268(1), 23–26 (2006).
[Crossref]

Sun, W.

Thompson, N. L.

D. Axelrod, N. L. Thompson, and T. P. Burghardt, “Total internal inflection fluorescent microscopy,” J. Microsc. 129(1), 19–28 (1983).
[Crossref] [PubMed]

Tian, Z.

Tsai, B.

Y. Chu, W. Chang, K. Chen, J. Chen, B. Tsai, and K. Hsu, “Full-field refractive index measurement with simultaneous phase-shift interferometry,” Optik (Stuttg.) 125(13), 3307–3310 (2014).
[Crossref]

Wang, D. N.

Wang, J.

Wang, L.

Wang, Q.

Wang, Y.

Wei, H.

Yam, S. S.

Yin, D.

Zhang, S.

S. Zhang, W. Zhang, P. Geng, and S. Gao, “Fiber Mach-Zehnder interferometer based on concatenated down-and up-tapers for refractive index sensing applications,” Opt. Commun. 288(1), 47–51 (2013).
[Crossref]

Zhang, W.

S. Zhang, W. Zhang, P. Geng, and S. Gao, “Fiber Mach-Zehnder interferometer based on concatenated down-and up-tapers for refractive index sensing applications,” Opt. Commun. 288(1), 47–51 (2013).
[Crossref]

Zhang, Y.

Zhao, J.

Appl. Opt. (1)

J. Appl. Phys. (1)

Q. Wang, J. Zhao, X. Jiao, J. Di, and H. Jiang, “Visual and quantitative measurement of the temperature distribution of heat conduction process in glass based on digital holographic interferometry,” J. Appl. Phys. 111(9), 093111 (2012).
[Crossref]

J. Cell Biol. (1)

D. Axelrod, “Cell-substrate contacts illuminated by total internal reflection fluorescence,” J. Cell Biol. 89(1), 141–145 (1981).
[Crossref] [PubMed]

J. Microsc. (1)

D. Axelrod, N. L. Thompson, and T. P. Burghardt, “Total internal inflection fluorescent microscopy,” J. Microsc. 129(1), 19–28 (1983).
[Crossref] [PubMed]

Opt. Commun. (2)

S. Zhang, W. Zhang, P. Geng, and S. Gao, “Fiber Mach-Zehnder interferometer based on concatenated down-and up-tapers for refractive index sensing applications,” Opt. Commun. 288(1), 47–51 (2013).
[Crossref]

Z. Jian, P. Hsieh, H.-C. Hsieh, H.-W. Chen, and D.-C. Su, “A method for measuring two-dimensional refractive index distribution with the total internal reflection of p-polarized light and the phase-shifting interferometry,” Opt. Commun. 268(1), 23–26 (2006).
[Crossref]

Opt. Express (6)

Opt. Lett. (5)

Optik (Stuttg.) (1)

Y. Chu, W. Chang, K. Chen, J. Chen, B. Tsai, and K. Hsu, “Full-field refractive index measurement with simultaneous phase-shift interferometry,” Optik (Stuttg.) 125(13), 3307–3310 (2014).
[Crossref]

Science (1)

D. J. Arndt-Jovin, M. Robert-Nicoud, S. J. Kaufman, and T. M. Jovin, “Fluorescence digital imaging microscopy in cell biology,” Science 230(4723), 247–256 (1985).
[Crossref] [PubMed]

Other (1)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge, 2005).

Supplementary Material (3)

NameDescription
» Visualization 1: MOV (5748 KB)      2D phase difference distributions without subtraction of the background noise
» Visualization 2: MOV (5776 KB)      2D phase difference distributions with subtraction of the background noise
» Visualization 3: MOV (5730 KB)      2D index distributions

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Figures (5)

Fig. 1
Fig. 1 (a) TIR phase shift φ s (black) and φ p (red) versus index of the second medium n 2; (b) liquid index n 2 versus TIR phase shift difference Δφ s between two states; (c) measurement deviation of n 2 versus n 2; n 1 = 1.5195, θ 1 = 72.7332°.
Fig. 2
Fig. 2 Experimental setup for recording digital holograms. MO: microscope objective; PH: pinhole; L: lens; HP: half-wave plate; BS1, 2: beam splitters; M1, 2: mirrors.
Fig. 3
Fig. 3 Numerically reconstructed 2D phase difference distributions of homogeneous glycerol-water mixtures with different concentration. (a) 40%; (b) 60%; (c) 75%.
Fig. 4
Fig. 4 Measurement results of the 2D index distributions of mixed liquids. (a) Numerically reconstructed 2D phase difference distributions without subtraction of the background noise (Visualization 1); (b) corresponding 2D phase difference distributions with subtraction of the background noise (Visualization 2); (c) calculated 2D index distributions (Visualization 3). The numbers 1-4 correspond the results at the time of 0s, 3.5s, 9.2s, and 15s, respectively.
Fig. 5
Fig. 5 (a) Liquids index variation of two certain points during the diffusion process; (b) calculated 1D index distributions along with the central vertical lines in Figs. 4(c2)-(c4).

Tables (1)

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Table 1 Measurement results of homogeneous glycerol-water mixtures

Equations (7)

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Δ ϕ o t ( x , y ) = ϕ o t ( x , y ) ϕ o0 ( x , y ) = arg [ O t ( x , y ) / O 0 ( x , y ) ] ,
r s = e x p ( i φ s ) , φ s = 2 arc tan [ n 1 2 sin 2 θ 1 n 2 2 / ( n 1 cos θ 1 ) ] ,
r p = e x p ( i φ p ) , φ p = 2 arc tan [ n 1 n 1 2 sin 2 θ 1 n 2 2 / ( n 2 2 cos θ 1 ) ] .
Δ φ s t ( x , y ) = 2 arc tan n 1 2 sin 2 θ 1 n 2 2 ( x , y ) n 1 cos θ 1 + 2 arc tan n 1 2 sin 2 θ 1 1 n 1 cos θ 1 = Δ ϕ o t ( x , y ) .
n 2 ( x , y ) = n 1 sin 2 θ 1 cos 2 θ 1 tan 2 Γ .
Γ = arc tan [ n 1 2 sin 2 θ 1 1 / ( n 1 cos θ 1 ) ] Δ ϕ o t ( x , y ) / 2 ,
δ n 2 ( x , y ) = | d n 2 ( x , y ) ϕ o t ( x , y ) | δ [ Δ ϕ o t ( x , y ) ] = δ [ Δ ϕ o t ( x , y ) ] n 1 2 cos 2 θ 1 tan Γ sec 2 Γ 2 n 2 ( x , y ) .

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