Abstract

We present a refractometer based on the principle of total internal reflection that can sensitively record, in real time, the refractive index of fluids over a wide range of refractive indices. The device uses a divergent laser beam and a linear diode array, and has no mechanical or optical moving parts, enabling us to achieve the measurement of a refractive index at a sensitivity level of 106. Our refractometer does not rely on interferometry, thus enabling the device to be compact, portable, and inexpensive. To the best of our knowledge, this is the first time a noninterferometric device that performs real-time differential refractometry with a sensitivity of better than 105 has been demonstrated in the literature. We show that our experimental results agree very well with Fresnel theory. We establish a theoretical limit on the sensitivity of this class of refractometers.

© 2006 Optical Society of America

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References

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  1. J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Muller, "The spatial variation of the refractive index in biological cells," Phys. Med. Biol. 41, 369-382 (1996).
    [CrossRef] [PubMed]
  2. F. Bolin, L. Preuss, R. Taylor, and R. Ference, "Refractive index of some mammalian tissues using a fiber optics cladding method," Appl. Opt. 28, 2297-2303 (1989).
    [CrossRef] [PubMed]
  3. J. M. Schmitt and G. Kumar, "Turbulent nature of refractive-index variations in biological tissue," Opt. Lett. 21, 1310-1312 (1996).
    [CrossRef] [PubMed]
  4. J. Lai, Z. Li, C. Wang, and A. He, "Experimental measurement of the refractive index of biological tissues by total internal reflection," Appl. Opt. 44, 1845-1849 (2005).
    [CrossRef] [PubMed]
  5. H. Li and S. Xie, "Measurement method of the refractive index of biotissue by total internal reflection," Appl. Opt. 35, 1793-1795 (1996).
    [CrossRef] [PubMed]
  6. C. Yang, A. Wax, I. Georgakoudi, E. Hanlon, K. Badizadegan, R. R. Dasari, and M. S. Feld, "Interferometric phase-dispersion microscopy," Opt. Lett. 25, 1526-1528 (2000).
    [CrossRef]
  7. T. Kihara and K. Yokomori, "Simultaneous measurement of refractive index and thickness of thin film by polarized reflectances," Appl. Opt. 29, 5069-5073 (1990).
    [CrossRef] [PubMed]
  8. D. J. Bornhop, T. G. Nolan, and N. J. Dovichi, "Subnanoliter laser-based refractive index detector for 0.25-mm I. D. microbore liquid chromatography," J. Chromatogr. 384, 181-187 (1987).
    [CrossRef]
  9. M. L. Eickhoff and J. L. Hall, "Real-time precision refractometry: new approaches," Appl. Opt. 36, 1223-1234 (1997).
    [CrossRef] [PubMed]
  10. R. G. Johnston and W. K. Grace, "Refractive index detector using Zeeman interferometry," Appl. Opt. 29, 4720-4724 (1990).
    [CrossRef] [PubMed]
  11. A. Leung and J. Vandiver, "Automatic refractometer," Opt. Eng. 42, 1128-1131 (2003).
    [CrossRef]
  12. L. M. Bali, R. K. Shukla, P. Srivastava, A. Srivastava, A. Srivastava, and A. Kulshreshtha, "New approach to the measurement of refractive index," Opt. Eng. 44, 058002-058008 (2005), and references therein.
    [CrossRef]
  13. See, for instance, J. Rheims, J. Kosery, and T. Wreidt, "Refractive-index measurements in the near-IR using an Abbe refractometer," Meas. Sci. Technol. 8, 601-605 (1997), and references therein.
  14. K-Patents, Inc., Model PR-03-D, www.kpatents.com, U.S. patent 6,760,098 B2, Harri Salo (July 2004).
  15. Topac, Inc., DUR series, www.topac.com.
  16. See, for example, M. A. Heald and J. B. Marion, Classical Electromagnetic Radiation, 3rd ed. (Saunders College Publishing, 1995).
  17. D. Segelstein, "The complex refractive index of water," M.S. thesis (University of Missouri-Kansas City, 1981).
  18. R. M. Pope and E. S. Fry, "Absorption spectrum (380-700 nm) of pure water. II. Integrating cavity measurements," Appl. Opt. 36, 8710-8723 (1997).
    [CrossRef]
  19. G. H. Meeten and A. N. North, "Refractive index measurement of absorbing and turbid fluids by reflection near the critical angle," Meas. Sci. Technol. 6, 214-221 (1995).
    [CrossRef]
  20. S. Venkatasubbarao, N. Beaudry, Y. Zhao, and R. Chipman, "Evanescent-imaging-ellipsometry-based microarray reader," J. Biomed. Opt. 11, 014028 (2006).
    [CrossRef] [PubMed]

2006 (1)

S. Venkatasubbarao, N. Beaudry, Y. Zhao, and R. Chipman, "Evanescent-imaging-ellipsometry-based microarray reader," J. Biomed. Opt. 11, 014028 (2006).
[CrossRef] [PubMed]

2005 (2)

L. M. Bali, R. K. Shukla, P. Srivastava, A. Srivastava, A. Srivastava, and A. Kulshreshtha, "New approach to the measurement of refractive index," Opt. Eng. 44, 058002-058008 (2005), and references therein.
[CrossRef]

J. Lai, Z. Li, C. Wang, and A. He, "Experimental measurement of the refractive index of biological tissues by total internal reflection," Appl. Opt. 44, 1845-1849 (2005).
[CrossRef] [PubMed]

2003 (1)

A. Leung and J. Vandiver, "Automatic refractometer," Opt. Eng. 42, 1128-1131 (2003).
[CrossRef]

2000 (1)

1997 (2)

1996 (3)

1995 (1)

G. H. Meeten and A. N. North, "Refractive index measurement of absorbing and turbid fluids by reflection near the critical angle," Meas. Sci. Technol. 6, 214-221 (1995).
[CrossRef]

1990 (2)

1989 (1)

1987 (1)

D. J. Bornhop, T. G. Nolan, and N. J. Dovichi, "Subnanoliter laser-based refractive index detector for 0.25-mm I. D. microbore liquid chromatography," J. Chromatogr. 384, 181-187 (1987).
[CrossRef]

Badizadegan, K.

Bali, L. M.

L. M. Bali, R. K. Shukla, P. Srivastava, A. Srivastava, A. Srivastava, and A. Kulshreshtha, "New approach to the measurement of refractive index," Opt. Eng. 44, 058002-058008 (2005), and references therein.
[CrossRef]

Beaudry, N.

S. Venkatasubbarao, N. Beaudry, Y. Zhao, and R. Chipman, "Evanescent-imaging-ellipsometry-based microarray reader," J. Biomed. Opt. 11, 014028 (2006).
[CrossRef] [PubMed]

Beuthan, J.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Muller, "The spatial variation of the refractive index in biological cells," Phys. Med. Biol. 41, 369-382 (1996).
[CrossRef] [PubMed]

Bolin, F.

Bornhop, D. J.

D. J. Bornhop, T. G. Nolan, and N. J. Dovichi, "Subnanoliter laser-based refractive index detector for 0.25-mm I. D. microbore liquid chromatography," J. Chromatogr. 384, 181-187 (1987).
[CrossRef]

Chipman, R.

S. Venkatasubbarao, N. Beaudry, Y. Zhao, and R. Chipman, "Evanescent-imaging-ellipsometry-based microarray reader," J. Biomed. Opt. 11, 014028 (2006).
[CrossRef] [PubMed]

Dasari, R. R.

Dovichi, N. J.

D. J. Bornhop, T. G. Nolan, and N. J. Dovichi, "Subnanoliter laser-based refractive index detector for 0.25-mm I. D. microbore liquid chromatography," J. Chromatogr. 384, 181-187 (1987).
[CrossRef]

Eickhoff, M. L.

Feld, M. S.

Ference, R.

Fry, E. S.

Georgakoudi, I.

Grace, W. K.

Hall, J. L.

Hanlon, E.

He, A.

Helfmann, J.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Muller, "The spatial variation of the refractive index in biological cells," Phys. Med. Biol. 41, 369-382 (1996).
[CrossRef] [PubMed]

Herrig, M.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Muller, "The spatial variation of the refractive index in biological cells," Phys. Med. Biol. 41, 369-382 (1996).
[CrossRef] [PubMed]

Johnston, R. G.

Kihara, T.

Kulshreshtha, A.

L. M. Bali, R. K. Shukla, P. Srivastava, A. Srivastava, A. Srivastava, and A. Kulshreshtha, "New approach to the measurement of refractive index," Opt. Eng. 44, 058002-058008 (2005), and references therein.
[CrossRef]

Kumar, G.

Lai, J.

Leung, A.

A. Leung and J. Vandiver, "Automatic refractometer," Opt. Eng. 42, 1128-1131 (2003).
[CrossRef]

Li, H.

Li, Z.

Meeten, G. H.

G. H. Meeten and A. N. North, "Refractive index measurement of absorbing and turbid fluids by reflection near the critical angle," Meas. Sci. Technol. 6, 214-221 (1995).
[CrossRef]

Minet, O.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Muller, "The spatial variation of the refractive index in biological cells," Phys. Med. Biol. 41, 369-382 (1996).
[CrossRef] [PubMed]

Muller, G.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Muller, "The spatial variation of the refractive index in biological cells," Phys. Med. Biol. 41, 369-382 (1996).
[CrossRef] [PubMed]

Nolan, T. G.

D. J. Bornhop, T. G. Nolan, and N. J. Dovichi, "Subnanoliter laser-based refractive index detector for 0.25-mm I. D. microbore liquid chromatography," J. Chromatogr. 384, 181-187 (1987).
[CrossRef]

North, A. N.

G. H. Meeten and A. N. North, "Refractive index measurement of absorbing and turbid fluids by reflection near the critical angle," Meas. Sci. Technol. 6, 214-221 (1995).
[CrossRef]

Pope, R. M.

Preuss, L.

Schmitt, J. M.

Segelstein, D.

D. Segelstein, "The complex refractive index of water," M.S. thesis (University of Missouri-Kansas City, 1981).

Shukla, R. K.

L. M. Bali, R. K. Shukla, P. Srivastava, A. Srivastava, A. Srivastava, and A. Kulshreshtha, "New approach to the measurement of refractive index," Opt. Eng. 44, 058002-058008 (2005), and references therein.
[CrossRef]

Srivastava, A.

L. M. Bali, R. K. Shukla, P. Srivastava, A. Srivastava, A. Srivastava, and A. Kulshreshtha, "New approach to the measurement of refractive index," Opt. Eng. 44, 058002-058008 (2005), and references therein.
[CrossRef]

L. M. Bali, R. K. Shukla, P. Srivastava, A. Srivastava, A. Srivastava, and A. Kulshreshtha, "New approach to the measurement of refractive index," Opt. Eng. 44, 058002-058008 (2005), and references therein.
[CrossRef]

Srivastava, P.

L. M. Bali, R. K. Shukla, P. Srivastava, A. Srivastava, A. Srivastava, and A. Kulshreshtha, "New approach to the measurement of refractive index," Opt. Eng. 44, 058002-058008 (2005), and references therein.
[CrossRef]

Taylor, R.

Vandiver, J.

A. Leung and J. Vandiver, "Automatic refractometer," Opt. Eng. 42, 1128-1131 (2003).
[CrossRef]

Venkatasubbarao, S.

S. Venkatasubbarao, N. Beaudry, Y. Zhao, and R. Chipman, "Evanescent-imaging-ellipsometry-based microarray reader," J. Biomed. Opt. 11, 014028 (2006).
[CrossRef] [PubMed]

Wang, C.

Wax, A.

Xie, S.

Yang, C.

Yokomori, K.

Zhao, Y.

S. Venkatasubbarao, N. Beaudry, Y. Zhao, and R. Chipman, "Evanescent-imaging-ellipsometry-based microarray reader," J. Biomed. Opt. 11, 014028 (2006).
[CrossRef] [PubMed]

Appl. Opt. (7)

J. Biomed. Opt. (1)

S. Venkatasubbarao, N. Beaudry, Y. Zhao, and R. Chipman, "Evanescent-imaging-ellipsometry-based microarray reader," J. Biomed. Opt. 11, 014028 (2006).
[CrossRef] [PubMed]

J. Chromatogr. (1)

D. J. Bornhop, T. G. Nolan, and N. J. Dovichi, "Subnanoliter laser-based refractive index detector for 0.25-mm I. D. microbore liquid chromatography," J. Chromatogr. 384, 181-187 (1987).
[CrossRef]

Meas. Sci. Technol. (1)

G. H. Meeten and A. N. North, "Refractive index measurement of absorbing and turbid fluids by reflection near the critical angle," Meas. Sci. Technol. 6, 214-221 (1995).
[CrossRef]

Opt. Eng. (2)

A. Leung and J. Vandiver, "Automatic refractometer," Opt. Eng. 42, 1128-1131 (2003).
[CrossRef]

L. M. Bali, R. K. Shukla, P. Srivastava, A. Srivastava, A. Srivastava, and A. Kulshreshtha, "New approach to the measurement of refractive index," Opt. Eng. 44, 058002-058008 (2005), and references therein.
[CrossRef]

Opt. Lett. (2)

Phys. Med. Biol. (1)

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Muller, "The spatial variation of the refractive index in biological cells," Phys. Med. Biol. 41, 369-382 (1996).
[CrossRef] [PubMed]

Other (5)

See, for instance, J. Rheims, J. Kosery, and T. Wreidt, "Refractive-index measurements in the near-IR using an Abbe refractometer," Meas. Sci. Technol. 8, 601-605 (1997), and references therein.

K-Patents, Inc., Model PR-03-D, www.kpatents.com, U.S. patent 6,760,098 B2, Harri Salo (July 2004).

Topac, Inc., DUR series, www.topac.com.

See, for example, M. A. Heald and J. B. Marion, Classical Electromagnetic Radiation, 3rd ed. (Saunders College Publishing, 1995).

D. Segelstein, "The complex refractive index of water," M.S. thesis (University of Missouri-Kansas City, 1981).

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Figures (7)

Fig. 1
Fig. 1

Principle of TIR-based refractometry. (a) A sample, whose refractive index n sample is to be determined, is placed on the top of the glass prism (refractive index n prism ). (b) Representative plot of I r / I i versus θ i , based on Fresnel theory [Eq. (2)]. The regions of TIR and refraction (non-TIR) are indicated. The critical angle θ c corresponds to the sharp TIR–non-TIR transition. The encircled region is where a small change in θ i leads to a large change in I r / I i . Note that θ i increases to the left in this figure.

Fig. 2
Fig. 2

Schematic of the refractometer. The dashed arrow inside the sample is the refracted ray corresponding to the case of θ i < θ c , which leads to a darkened portion in the beam spot falling on the pixel array. TIR occurs for angles of θ i > θ c . See the text for an explanation of the symbols in the figure.

Fig. 3
Fig. 3

Calculating the least intensity change discernible by a pixel. The dark edge demarcating the TIR and non-TIR regions moves to a different location within the pixel N c when the sample's refractive index n sample changes slightly. Assuming the dark edge to be initially located at the center of N c , the change in illuminated area is ≈ α Δ a , where α is the pixel diameter and Δ a is the spatial shift of the dark edge.

Fig. 4
Fig. 4

(a) Reflected intensity distribution across the diode array for a diverging Gaussian laser beam incident on the prism–sample interface for four different samples: (1) A, “sample” is air. TIR occurs for all incident angles. (2) S1, sample is a 50 % DMSO–water solution. (3) S2, sample is a 30 % DMSO–water solution. (4) W, sample is distilled water. (b) I r / I i curves, corrected for optical noise due to stray laser light scattering as described in the text, for W and samples S1 and S2. The solid curves are theoretical curves obtained from the Fresnel Eq. (2) after device calibration has been performed as described in Section 4.

Fig. 5
Fig. 5

(a) Magnified view of the I r / I i curves in the TIR–non-TIR transition region for three different DMSO–water solutions F1–F3 of close-lying concentrations 19.012 % , 18.0775 % , and 17.2689 % , respectively. The axis of calibration is the horizontal dotted line drawn in the noise-free region near, but not at, the TIR–non-TIR transition point (see Section 4 for further explanation). The reference curve is F1, with all other refractive indices being measured relative to the Abbe value of 1.3615 for F1. The solid lines are merely drawn to aid the eye. (b) Vertically expanded view of the I r / I i curves for F1, F2, F3, and distilled water (W) in the vicinity of the axis of calibration which forms the x axis in this figure. Note the break in the x axis to accommodate water in the figure.

Fig. 6
Fig. 6

Twenty-four different DMSO–water samples were systematically prepared so that a wide range of differences in the refractive index may be measured and displayed. All the lines are parallel to each other. Note the “band” formed by the 12 samples with close-lying values of the refractive index. These samples are not distinguished by the Abbe refractometer, but are clearly resolved by our device (see Fig. 7).

Fig. 7
Fig. 7

Eight samples with the closest-lying refractive indices from the curves shown in Fig. 6. The refractive index for an unknown sample is always read from the point of intersection of the I r / I i curve for the sample with the calibration axis which is the x axis here. Our device clearly resolves the two pairs of lines A and B, and C and D, for which the differences in the refractive index are 4 × 10 6 and 3 × 10 6 , respectively.

Tables (1)

Tables Icon

Table 1 Refractive Indices for Samples F2 and F3 and Water was Measured by Our Abbe Refractometer and Our Calibrated Device a

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

θ c = sin 1 ( n sample / n prism )
I r I i = tan 2 ( θ i θ r ) tan 2 ( θ i + θ r ) ,
θ i = β + δ 1 + tan 1 [ a i ( b + n prism ( c + d ) cos   ϕ r cos   ϕ + δ 2 ) 1 ] ,
a i = N α 2 ( N 0 N i N 0 ) ,
Δ i = ( I α Δ a ) R .
Δ θ c Δ i I α R ( b + n prism ( c + d ) cos   ϕ r cos   ϕ ) 1 ,
Δ n sample n prism 2 n sample 2 Δ θ c .

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