Abstract

A method for measuring the refractive index (RI) of a small volume of liquid and a capillary wall is presented in this paper. A transparent capillary filled with liquid is used as a cylindrical positive lens; subsequently, the focal length of the lens is derived through the base of paraxial approximation, which is recorded as a function of the RIs of the liquid and capillary wall. With the RI of a capillary wall known, the RI of the liquid can be obtained by measuring the focal length of the lens, which is characterized by a microquantity liquid, spatial resolution, and easy operation. The RI of the capillary wall can be calculated without ruining the capillary if the capillary is filled with a standard liquid (RI is known), the deviation of which is less than 0.003 RIU. The factors affecting accuracy of the measurement, for instance, the depth of a field (DOF) in a reading microscope system and the outer and inner diameters of a capillary are analyzed, while illustrating that the effective DOF plays an essential role in accurate measurement.

© 2013 Optical Society of America

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2012

N. Manohar Reddy, D. Kothandan, S. Chandra Lingam, and A. Ahmad, “A study on refractive index of plasma of blood of patients suffering from tuberculosis,” Int. J. Technol. Eng. 8, 23–25 (2012).

C. Hsu, S. Chen, and Y. Chen, “Measuring the refractive index of transparent materials using high precision circular heterodyne interferometry,” Opt. Lasers Eng. 50, 1689–1693 (2012).
[CrossRef]

H. Arimoto, W. Watanabe, K. Massk, and T. Fukuda, “Measurement of refractive index change induced by dark reaction of photopolymer with digital holographic quantitative phase microscopy,” Opt. Commun. 285, 4911–4917 (2012).
[CrossRef]

D. Kα´čik, P. Tvarožek, I. Martinček, and K. Schuster, “Refractive index measurement based on core-cladding mode interferometry in endlessly single mode fiber,” Optik 123, 1746–1749 (2012).
[CrossRef]

C. Yeh, C. Chow, J. Sung, P. Wu, W. Whang, and F. Tseng, “Measurement of organic chemical refractive indexes using an optical time-domain reflectometer,” Sensors 12, 481–488 (2012).
[CrossRef]

2009

2008

Y. Z. Sun and X. D. Fan, “Analysis of ring resonators for chemical vapor sensor development,” Opt. Express 16, 10256–10268 (2008).

2007

A. Bjeoumikhov, R. Wedell, and S. Bjeoumikhov, “Mono-and polycapillary optics-state of the art and applications,” Opt. Precision Eng. 151932 (2007).

2006

I. M. White, H. Oveys, and X. D. Fan, “Liquid-core optical ring- resonator sensors,” Opt. Lett. 31, 1319–1321 (2006).
[CrossRef]

S. Hua, Y. Luo, and Y. Hong, “Measurement of refractive index of liquid by the equal thickness interference,” Chinese J. Lasers 33, 1542 (2006).

Y. Zhou, G. Jia, G. Zhong, W. Xiang, G. Liu, and C. Liu, “Using precision Fabry-Perot interferometer to measure refractive index of aqueous solution,” Chinese J. Lasers 33, 345 (2006).

2005

M. Friebel and M. Meinke, “Determination of the complex refractive index of highly concentrated hemoglobin solutions using transmittance and reflectance measurements,” J. Biomed. Opt. 10, 064019 (2005).
[CrossRef]

G. N. Jham, R. Velikova, B. N. Damyavova, S. C. Rabelo, J. C. T. Silva, K. A. P. Souza, V. M. M. Valente, and P. R. Cecon, “Preparative silver ion TLC/RP-HPLC determination of coffee triacylglycerol molecular species,” Food Res. Int. 38, 121–126 (2005).
[CrossRef]

2004

S. Singh, “Diffraction method measures refractive indices of liquids,” Phys. Educ. 39, 235 (2004).
[CrossRef]

G. Deng, Z. Cai, Y. Zhang, Y. Xu, S. Wu, and J. Zhou, “Refraction index measurement of transparent material by using diffraction grating and CCD,” Acta Opt. Sin. 24, 99 (2004).

2002

C. T. Culbertson, S. C. Jacobson, and J. M. Ramsey, “Diffusion coefficient measurements in microfluidic devices,” Talanta 56, 365–373 (2002).
[CrossRef]

2000

M. A. Hashan and A. Y. Nassif, “Accurate measurement of the refractive indices of solids and liquids by the double layer interferometer,” Appl. Opt. 39, 5991–5997 (2000).
[CrossRef]

S. A. Alexandrov and I. V. Chernyh, “Interference method for determination of the refractive index and thickness,” Opt. Eng. 39, 2480–2486 (2000).
[CrossRef]

1994

P. Hervé and L. K. J. Vandamme, “General relation between refractive index and energy gap in semiconductors,” Infrared Phys. Technol. 35, 609–615 (1994).
[CrossRef]

1982

D. Couzin, “Depths of field,” SMPE J. 11, 1096–1098 (1982).

Ahmad, A.

N. Manohar Reddy, D. Kothandan, S. Chandra Lingam, and A. Ahmad, “A study on refractive index of plasma of blood of patients suffering from tuberculosis,” Int. J. Technol. Eng. 8, 23–25 (2012).

Alexandrov, S. A.

S. A. Alexandrov and I. V. Chernyh, “Interference method for determination of the refractive index and thickness,” Opt. Eng. 39, 2480–2486 (2000).
[CrossRef]

Arimoto, H.

H. Arimoto, W. Watanabe, K. Massk, and T. Fukuda, “Measurement of refractive index change induced by dark reaction of photopolymer with digital holographic quantitative phase microscopy,” Opt. Commun. 285, 4911–4917 (2012).
[CrossRef]

Bjeoumikhov, A.

A. Bjeoumikhov, R. Wedell, and S. Bjeoumikhov, “Mono-and polycapillary optics-state of the art and applications,” Opt. Precision Eng. 151932 (2007).

Bjeoumikhov, S.

A. Bjeoumikhov, R. Wedell, and S. Bjeoumikhov, “Mono-and polycapillary optics-state of the art and applications,” Opt. Precision Eng. 151932 (2007).

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1997) p. 207.

Cai, Z.

G. Deng, Z. Cai, Y. Zhang, Y. Xu, S. Wu, and J. Zhou, “Refraction index measurement of transparent material by using diffraction grating and CCD,” Acta Opt. Sin. 24, 99 (2004).

Cecon, P. R.

G. N. Jham, R. Velikova, B. N. Damyavova, S. C. Rabelo, J. C. T. Silva, K. A. P. Souza, V. M. M. Valente, and P. R. Cecon, “Preparative silver ion TLC/RP-HPLC determination of coffee triacylglycerol molecular species,” Food Res. Int. 38, 121–126 (2005).
[CrossRef]

Chandra Lingam, S.

N. Manohar Reddy, D. Kothandan, S. Chandra Lingam, and A. Ahmad, “A study on refractive index of plasma of blood of patients suffering from tuberculosis,” Int. J. Technol. Eng. 8, 23–25 (2012).

Chang, S.

S. Chang, “Lasing characteristics of deformed micro cavities,” Ph.D. Thesis (Yale University, 1998).

Chen, S.

C. Hsu, S. Chen, and Y. Chen, “Measuring the refractive index of transparent materials using high precision circular heterodyne interferometry,” Opt. Lasers Eng. 50, 1689–1693 (2012).
[CrossRef]

Chen, Y.

C. Hsu, S. Chen, and Y. Chen, “Measuring the refractive index of transparent materials using high precision circular heterodyne interferometry,” Opt. Lasers Eng. 50, 1689–1693 (2012).
[CrossRef]

Chernyh, I. V.

S. A. Alexandrov and I. V. Chernyh, “Interference method for determination of the refractive index and thickness,” Opt. Eng. 39, 2480–2486 (2000).
[CrossRef]

Chow, C.

C. Yeh, C. Chow, J. Sung, P. Wu, W. Whang, and F. Tseng, “Measurement of organic chemical refractive indexes using an optical time-domain reflectometer,” Sensors 12, 481–488 (2012).
[CrossRef]

Couzin, D.

D. Couzin, “Depths of field,” SMPE J. 11, 1096–1098 (1982).

Culbertson, C. T.

C. T. Culbertson, S. C. Jacobson, and J. M. Ramsey, “Diffusion coefficient measurements in microfluidic devices,” Talanta 56, 365–373 (2002).
[CrossRef]

Cussler, E. L.

E. L. Cussler, Diffusion: Mass Transfer in Fluid Systems, 3rd ed. (Cambridge University, 2007).

Damyavova, B. N.

G. N. Jham, R. Velikova, B. N. Damyavova, S. C. Rabelo, J. C. T. Silva, K. A. P. Souza, V. M. M. Valente, and P. R. Cecon, “Preparative silver ion TLC/RP-HPLC determination of coffee triacylglycerol molecular species,” Food Res. Int. 38, 121–126 (2005).
[CrossRef]

Deng, G.

G. Deng, Z. Cai, Y. Zhang, Y. Xu, S. Wu, and J. Zhou, “Refraction index measurement of transparent material by using diffraction grating and CCD,” Acta Opt. Sin. 24, 99 (2004).

Fan, X. D.

Y. Z. Sun and X. D. Fan, “Analysis of ring resonators for chemical vapor sensor development,” Opt. Express 16, 10256–10268 (2008).

I. M. White, H. Oveys, and X. D. Fan, “Liquid-core optical ring- resonator sensors,” Opt. Lett. 31, 1319–1321 (2006).
[CrossRef]

Friebel, M.

M. Friebel and M. Meinke, “Determination of the complex refractive index of highly concentrated hemoglobin solutions using transmittance and reflectance measurements,” J. Biomed. Opt. 10, 064019 (2005).
[CrossRef]

Fukuda, T.

H. Arimoto, W. Watanabe, K. Massk, and T. Fukuda, “Measurement of refractive index change induced by dark reaction of photopolymer with digital holographic quantitative phase microscopy,” Opt. Commun. 285, 4911–4917 (2012).
[CrossRef]

Ghatak, A.

A. Ghatak, Optics (Tata McGraw-Hill, 2009), Chap. 6.

Gu, Z. T.

Hashan, M. A.

Hervé, P.

P. Hervé and L. K. J. Vandamme, “General relation between refractive index and energy gap in semiconductors,” Infrared Phys. Technol. 35, 609–615 (1994).
[CrossRef]

Hong, Y.

S. Hua, Y. Luo, and Y. Hong, “Measurement of refractive index of liquid by the equal thickness interference,” Chinese J. Lasers 33, 1542 (2006).

Hsu, C.

C. Hsu, S. Chen, and Y. Chen, “Measuring the refractive index of transparent materials using high precision circular heterodyne interferometry,” Opt. Lasers Eng. 50, 1689–1693 (2012).
[CrossRef]

Hua, S.

S. Hua, Y. Luo, and Y. Hong, “Measurement of refractive index of liquid by the equal thickness interference,” Chinese J. Lasers 33, 1542 (2006).

Iizuka, K.

K. Iizuka, Engineering Optics, 3rd ed., Springer Series in Optical Sciences (Springer Science+Business Media, LLC, 2008).

Jacobson, S. C.

C. T. Culbertson, S. C. Jacobson, and J. M. Ramsey, “Diffusion coefficient measurements in microfluidic devices,” Talanta 56, 365–373 (2002).
[CrossRef]

Jham, G. N.

G. N. Jham, R. Velikova, B. N. Damyavova, S. C. Rabelo, J. C. T. Silva, K. A. P. Souza, V. M. M. Valente, and P. R. Cecon, “Preparative silver ion TLC/RP-HPLC determination of coffee triacylglycerol molecular species,” Food Res. Int. 38, 121–126 (2005).
[CrossRef]

Jia, G.

Y. Zhou, G. Jia, G. Zhong, W. Xiang, G. Liu, and C. Liu, “Using precision Fabry-Perot interferometer to measure refractive index of aqueous solution,” Chinese J. Lasers 33, 345 (2006).

Ka´cik, D.

D. Kα´čik, P. Tvarožek, I. Martinček, and K. Schuster, “Refractive index measurement based on core-cladding mode interferometry in endlessly single mode fiber,” Optik 123, 1746–1749 (2012).
[CrossRef]

Kothandan, D.

N. Manohar Reddy, D. Kothandan, S. Chandra Lingam, and A. Ahmad, “A study on refractive index of plasma of blood of patients suffering from tuberculosis,” Int. J. Technol. Eng. 8, 23–25 (2012).

Li, J. Z.

J. Z. Li, Optics Handbook (in Chinese) (Shanxi Science and Technology, 1986).

Liu, C.

Y. Zhou, G. Jia, G. Zhong, W. Xiang, G. Liu, and C. Liu, “Using precision Fabry-Perot interferometer to measure refractive index of aqueous solution,” Chinese J. Lasers 33, 345 (2006).

Liu, G.

Y. Zhou, G. Jia, G. Zhong, W. Xiang, G. Liu, and C. Liu, “Using precision Fabry-Perot interferometer to measure refractive index of aqueous solution,” Chinese J. Lasers 33, 345 (2006).

Luo, Y.

S. Hua, Y. Luo, and Y. Hong, “Measurement of refractive index of liquid by the equal thickness interference,” Chinese J. Lasers 33, 1542 (2006).

Manohar Reddy, N.

N. Manohar Reddy, D. Kothandan, S. Chandra Lingam, and A. Ahmad, “A study on refractive index of plasma of blood of patients suffering from tuberculosis,” Int. J. Technol. Eng. 8, 23–25 (2012).

Martincek, I.

D. Kα´čik, P. Tvarožek, I. Martinček, and K. Schuster, “Refractive index measurement based on core-cladding mode interferometry in endlessly single mode fiber,” Optik 123, 1746–1749 (2012).
[CrossRef]

Massk, K.

H. Arimoto, W. Watanabe, K. Massk, and T. Fukuda, “Measurement of refractive index change induced by dark reaction of photopolymer with digital holographic quantitative phase microscopy,” Opt. Commun. 285, 4911–4917 (2012).
[CrossRef]

Meinke, M.

M. Friebel and M. Meinke, “Determination of the complex refractive index of highly concentrated hemoglobin solutions using transmittance and reflectance measurements,” J. Biomed. Opt. 10, 064019 (2005).
[CrossRef]

Nassif, A. Y.

Oveys, H.

Rabelo, S. C.

G. N. Jham, R. Velikova, B. N. Damyavova, S. C. Rabelo, J. C. T. Silva, K. A. P. Souza, V. M. M. Valente, and P. R. Cecon, “Preparative silver ion TLC/RP-HPLC determination of coffee triacylglycerol molecular species,” Food Res. Int. 38, 121–126 (2005).
[CrossRef]

Ramsey, J. M.

C. T. Culbertson, S. C. Jacobson, and J. M. Ramsey, “Diffusion coefficient measurements in microfluidic devices,” Talanta 56, 365–373 (2002).
[CrossRef]

Schuster, K.

D. Kα´čik, P. Tvarožek, I. Martinček, and K. Schuster, “Refractive index measurement based on core-cladding mode interferometry in endlessly single mode fiber,” Optik 123, 1746–1749 (2012).
[CrossRef]

Seferis, J. C.

J. C. Seferis, Polymer Handbook, I. Brandrup and E. H. Immergut, eds., 3rd ed. (Wiley, 1989), p. VI/451.

Silva, J. C. T.

G. N. Jham, R. Velikova, B. N. Damyavova, S. C. Rabelo, J. C. T. Silva, K. A. P. Souza, V. M. M. Valente, and P. R. Cecon, “Preparative silver ion TLC/RP-HPLC determination of coffee triacylglycerol molecular species,” Food Res. Int. 38, 121–126 (2005).
[CrossRef]

Singh, S.

S. Singh, “Diffraction method measures refractive indices of liquids,” Phys. Educ. 39, 235 (2004).
[CrossRef]

Souza, K. A. P.

G. N. Jham, R. Velikova, B. N. Damyavova, S. C. Rabelo, J. C. T. Silva, K. A. P. Souza, V. M. M. Valente, and P. R. Cecon, “Preparative silver ion TLC/RP-HPLC determination of coffee triacylglycerol molecular species,” Food Res. Int. 38, 121–126 (2005).
[CrossRef]

Sun, Y. Z.

Y. Z. Sun and X. D. Fan, “Analysis of ring resonators for chemical vapor sensor development,” Opt. Express 16, 10256–10268 (2008).

Sung, J.

C. Yeh, C. Chow, J. Sung, P. Wu, W. Whang, and F. Tseng, “Measurement of organic chemical refractive indexes using an optical time-domain reflectometer,” Sensors 12, 481–488 (2012).
[CrossRef]

Tseng, F.

C. Yeh, C. Chow, J. Sung, P. Wu, W. Whang, and F. Tseng, “Measurement of organic chemical refractive indexes using an optical time-domain reflectometer,” Sensors 12, 481–488 (2012).
[CrossRef]

Tvarožek, P.

D. Kα´čik, P. Tvarožek, I. Martinček, and K. Schuster, “Refractive index measurement based on core-cladding mode interferometry in endlessly single mode fiber,” Optik 123, 1746–1749 (2012).
[CrossRef]

Valente, V. M. M.

G. N. Jham, R. Velikova, B. N. Damyavova, S. C. Rabelo, J. C. T. Silva, K. A. P. Souza, V. M. M. Valente, and P. R. Cecon, “Preparative silver ion TLC/RP-HPLC determination of coffee triacylglycerol molecular species,” Food Res. Int. 38, 121–126 (2005).
[CrossRef]

Vandamme, L. K. J.

P. Hervé and L. K. J. Vandamme, “General relation between refractive index and energy gap in semiconductors,” Infrared Phys. Technol. 35, 609–615 (1994).
[CrossRef]

Velikova, R.

G. N. Jham, R. Velikova, B. N. Damyavova, S. C. Rabelo, J. C. T. Silva, K. A. P. Souza, V. M. M. Valente, and P. R. Cecon, “Preparative silver ion TLC/RP-HPLC determination of coffee triacylglycerol molecular species,” Food Res. Int. 38, 121–126 (2005).
[CrossRef]

Wang, Z. Y.

Watanabe, W.

H. Arimoto, W. Watanabe, K. Massk, and T. Fukuda, “Measurement of refractive index change induced by dark reaction of photopolymer with digital holographic quantitative phase microscopy,” Opt. Commun. 285, 4911–4917 (2012).
[CrossRef]

Wedell, R.

A. Bjeoumikhov, R. Wedell, and S. Bjeoumikhov, “Mono-and polycapillary optics-state of the art and applications,” Opt. Precision Eng. 151932 (2007).

Whang, W.

C. Yeh, C. Chow, J. Sung, P. Wu, W. Whang, and F. Tseng, “Measurement of organic chemical refractive indexes using an optical time-domain reflectometer,” Sensors 12, 481–488 (2012).
[CrossRef]

White, I. M.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1997) p. 207.

Wu, P.

C. Yeh, C. Chow, J. Sung, P. Wu, W. Whang, and F. Tseng, “Measurement of organic chemical refractive indexes using an optical time-domain reflectometer,” Sensors 12, 481–488 (2012).
[CrossRef]

Wu, S.

G. Deng, Z. Cai, Y. Zhang, Y. Xu, S. Wu, and J. Zhou, “Refraction index measurement of transparent material by using diffraction grating and CCD,” Acta Opt. Sin. 24, 99 (2004).

Xiang, W.

Y. Zhou, G. Jia, G. Zhong, W. Xiang, G. Liu, and C. Liu, “Using precision Fabry-Perot interferometer to measure refractive index of aqueous solution,” Chinese J. Lasers 33, 345 (2006).

Xu, Y.

G. Deng, Z. Cai, Y. Zhang, Y. Xu, S. Wu, and J. Zhou, “Refraction index measurement of transparent material by using diffraction grating and CCD,” Acta Opt. Sin. 24, 99 (2004).

Yeh, C.

C. Yeh, C. Chow, J. Sung, P. Wu, W. Whang, and F. Tseng, “Measurement of organic chemical refractive indexes using an optical time-domain reflectometer,” Sensors 12, 481–488 (2012).
[CrossRef]

Zhang, Y.

G. Deng, Z. Cai, Y. Zhang, Y. Xu, S. Wu, and J. Zhou, “Refraction index measurement of transparent material by using diffraction grating and CCD,” Acta Opt. Sin. 24, 99 (2004).

Zhong, G.

Y. Zhou, G. Jia, G. Zhong, W. Xiang, G. Liu, and C. Liu, “Using precision Fabry-Perot interferometer to measure refractive index of aqueous solution,” Chinese J. Lasers 33, 345 (2006).

Zhou, J.

G. Deng, Z. Cai, Y. Zhang, Y. Xu, S. Wu, and J. Zhou, “Refraction index measurement of transparent material by using diffraction grating and CCD,” Acta Opt. Sin. 24, 99 (2004).

Zhou, Y.

Y. Zhou, G. Jia, G. Zhong, W. Xiang, G. Liu, and C. Liu, “Using precision Fabry-Perot interferometer to measure refractive index of aqueous solution,” Chinese J. Lasers 33, 345 (2006).

Acta Opt. Sin.

G. Deng, Z. Cai, Y. Zhang, Y. Xu, S. Wu, and J. Zhou, “Refraction index measurement of transparent material by using diffraction grating and CCD,” Acta Opt. Sin. 24, 99 (2004).

Appl. Opt.

Chin. Opt. Lett.

Chinese J. Lasers

S. Hua, Y. Luo, and Y. Hong, “Measurement of refractive index of liquid by the equal thickness interference,” Chinese J. Lasers 33, 1542 (2006).

Y. Zhou, G. Jia, G. Zhong, W. Xiang, G. Liu, and C. Liu, “Using precision Fabry-Perot interferometer to measure refractive index of aqueous solution,” Chinese J. Lasers 33, 345 (2006).

Food Res. Int.

G. N. Jham, R. Velikova, B. N. Damyavova, S. C. Rabelo, J. C. T. Silva, K. A. P. Souza, V. M. M. Valente, and P. R. Cecon, “Preparative silver ion TLC/RP-HPLC determination of coffee triacylglycerol molecular species,” Food Res. Int. 38, 121–126 (2005).
[CrossRef]

Infrared Phys. Technol.

P. Hervé and L. K. J. Vandamme, “General relation between refractive index and energy gap in semiconductors,” Infrared Phys. Technol. 35, 609–615 (1994).
[CrossRef]

Int. J. Technol. Eng.

N. Manohar Reddy, D. Kothandan, S. Chandra Lingam, and A. Ahmad, “A study on refractive index of plasma of blood of patients suffering from tuberculosis,” Int. J. Technol. Eng. 8, 23–25 (2012).

J. Biomed. Opt.

M. Friebel and M. Meinke, “Determination of the complex refractive index of highly concentrated hemoglobin solutions using transmittance and reflectance measurements,” J. Biomed. Opt. 10, 064019 (2005).
[CrossRef]

Opt. Commun.

H. Arimoto, W. Watanabe, K. Massk, and T. Fukuda, “Measurement of refractive index change induced by dark reaction of photopolymer with digital holographic quantitative phase microscopy,” Opt. Commun. 285, 4911–4917 (2012).
[CrossRef]

Opt. Eng.

S. A. Alexandrov and I. V. Chernyh, “Interference method for determination of the refractive index and thickness,” Opt. Eng. 39, 2480–2486 (2000).
[CrossRef]

Opt. Express

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Figures (9)

Fig. 1.
Fig. 1.

Schematic diagram of the cross-section of a capillary: (a) parallel beam passing through the capillary filled with liquid, and a real image is forming on the optical axis; (b) parallel beam passing through the capillary filled with air, and a virtual image is forming on the optical axis.

Fig. 2.
Fig. 2.

Simulation (by ZEMAX software) of parallel beams passing through a capillary filled with different liquids: (a) water (n=1.3331); (b) ethanol (n=1.3612); (c) glycol (n=1.4304); and (d) glycerin (n=1.4650).

Fig. 3.
Fig. 3.

Schematic diagram of the RI measurement setup.

Fig. 4.
Fig. 4.

CMOS images showing focal length of a capillary filled with liquid: (a) focal line and (b) clear-cut edge of a capillary at the position of the capillary axis.

Fig. 5.
Fig. 5.

CMOS images showing the positions of real and virtual images: (a) virtual focal line; (b) real focal line.

Fig. 6.
Fig. 6.

Schematic diagram of the effective numerical aperture [(N.A.)eff] when observing a real image.

Fig. 7.
Fig. 7.

Schematic diagram of the effective numerical aperture [(N.A.)eff] when observing a virtual image.

Fig. 8.
Fig. 8.

RI deviation of liquid (Δn)DOF varied with the RI of liquid (n).

Fig. 9.
Fig. 9.

RI deviation of the capillary wall (Δn0)dev varied with the RI of the capillary wall (n0): Curve A, n=1.3331; Curve B, n=1.3612; Curve C, n=1.4304; Curve D, n=1.6221.

Tables (4)

Tables Icon

Table 1. RI Measurements of Liquid

Tables Icon

Table 2. RI Measurements of Capillary Walls (I)

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Table 3. RI Measurements of Capillary Walls (II)

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Table 4. Effective Numerical Aperture [(N.A.)eff] and Depth of Field [(Δn)DOF] for Microscope Used

Equations (27)

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CBO=BCO=γ.
ABO2=DCO3=α.
OAB=ODC=β.
SAO1=FDO4=θ.
θ=n0β,
α=Rβ/r,
γ=n0Rβ/nr.
d/θ=R/sinDFO,
DFO=θ[πθ(αβ)(π2γ)(αβ)].
d=nn0Rr2nr(n01)+2R(nn0).
d0=n0Rr2(n01)(Rr).
n=2n0Rd2d(Rr)+2n0drn0Rr.
n0=2dn(Rr)2Rd2ndr+nRr.
d1=D1D0,
d2=D2D0.
n0=2n1(Rr)(D1D0)2R(D1D0)2n1r(D1D0)+n1Rr,
n0=2n2(Rr)(D2D0)2R(D2D0)2n2r(D2D0)+n2Rr.
D02(D1+D2)D0+[D1D2n1n2r(D1D2)2(n2n1)]=0.
(Δd)DOF=λ(N.A.)eff2={λd2/h2,ifα<βλ/(N.A.)2,ifαβ.
ΔnΔd=nn0Rrd[2d(Rr)+2n0drn0Rr)].
(Δn)dev=ΔnΔd(Δd)DOF=|nn0Rrd[2d(Rr)+2n0drn0Rr)]|λ(N.A.)eff2.
Δn0Δd=nn0Rrd[2Rd2ndr+nRr)].
(Δn0)dev=Δn0Δd(Δd)DOF=|nn0Rrd[2Rd2ndr+nRr)]|λ(N.A.)eff2.
(Δn)dev=|4n0rd2(n01)[2d(Rr)+2n0drn0Rr]2|·ΔR,
(Δn)dev=|2n0Rd(2d+2n0dn0R)[2d(Rr)+2n0drn0Rr]2|·Δr,
(Δn0)dev=|2dn(2dr+nr22ndr)(2Rd2ndr+nRr)2|·ΔR,
(Δn0)dev=|2dn(2dRnnR22Rd)(2Rd2ndr+nRr)2|·Δr.

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