Abstract

We describe an immersion liquid and data analysis method for the simultaneous determination of the refractive index and concentration of pigments by measurement of light transmission of suspensions. A new innovation is that, in the event that two different pigments are simultaneously present in a suspension, it is possible to detect the refractive index of an unknown pigment with the aid of half-width of transmittance and, furthermore, to obtain the concentration of the unknown pigment.

© 2010 Optical Society of America

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References

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  1. J. Räty, K.-E. Peiponen, and T. Asakura, UV-Visible Reflection Spectroscopy of Liquids (Springer, 2004).
  2. S.-H. Lee, Y. Roichman, G.-R. Yi, S.-H. Kim, S.-M. Yang, A. Blaaderen, P. Oostrum, and D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Opt. Express 15, 18275–18282 (2007).
    [CrossRef] [PubMed]
  3. X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610nm,” Phys. Med. Biol. 48, 4165–4172 (2003).
    [CrossRef]
  4. J. G. Webster, The Measurement, Instrumentation and Sensor Handbook (CRC, 1999).
  5. S.-C. Su, “A rapid and accurate procedure for the determination of refractive indices of regulated asbestos minerals,” Am. Mineral. 88, 1979–1982 (2003).
  6. M. Jonasz, G. Fournier, and D. Stramski, “Photometric immersion refractometry: a method for determining the refractive index of marine microbial particles from beam attenuation,” Appl. Opt. 36, 4214–4220 (1997).
    [CrossRef] [PubMed]
  7. A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation using infra red laser beams,” Nature 330, 769–771 (1987).
    [CrossRef] [PubMed]
  8. L. Bremer, R. Tuinier, and S. Jahromi, “High refractive index nanocomposite fluids for immersion lithography,” Langmuir 25, 2390–2401 (2009).
    [CrossRef] [PubMed]
  9. A. V. Papaev, G. V. Simonenko, V. V. Tuchin, and T. P. Denisova, Opt. Spectrosc. 101, 46–53 (2006).
    [CrossRef]
  10. J. M. S. Saarela, S. M. Heikkinen, T. E. J. Fabritius, A. T. Haapala, and R. A. Myllylä, “Refractive index matching improves optical object detection in paper,” Meas. Sci. Technol. 19, 055710–055717 (2008).
    [CrossRef]
  11. I. Niskanen, J. Räty, and K.-E. Peiponen, “Measurement of refractive index of transparent particles by incorporating a multifunction spectrophotometer and immersion liquid method,” Appl. Opt. 46, 5404–5407 (2007).
    [CrossRef] [PubMed]
  12. I. Niskanen, J. Räty, and K.-E. Peiponen, “Estimation of effective refractive index of birefringent particles using a combination of immersion liquid method and light scattering,” Appl. Spectrosc. 62, 399–401 (2008).
    [CrossRef] [PubMed]
  13. I. Niskanen, J. Räty, and K.-E. Peiponen, “A method for detection of the refractive index of irregular shapes solid pigments in light absorbing liquid matrix,” Talanta 81, 1322–1324(2010).
    [CrossRef] [PubMed]
  14. E. E. El-Hinnawi, Methods in Chemical and Mineral Microscopy (Elsevier, 1966).
  15. K. Lattaud, S. Vilminot, C. Hirlimann, H. Parant, J. Schoelkopf, and P. Gane, “Index of refraction enhancement of calcite particles coated with zinc carbonate,” Solid State Sci. 8, 1222–1228 (2006).
    [CrossRef]
  16. K. Koivunen, I. Niskanen, K.-E. Peiponen, and H. Paulapuro, “Novel nanostructured PCC fillers,” J. Mater. Sci. 44, 477–482 (2009).
    [CrossRef]
  17. P. G. Weidler and F. Friedrich, “Determination of the refractive index of particles in the clay and sub-micrometer size range,” Am. Mineral. 92, 1130–1132 (2007).
    [CrossRef]
  18. I. Niskanen, J. Räty, and K.-E. Peiponen, “Assessment of refractive index of pigments by Gaussian fitting of light backscattering data in context of the liquid immersion method,” Appl. Spectrosc. 64, 558–561 (2010).
    [CrossRef] [PubMed]
  19. E. D. Palik, Handbook of Optical Constants of Solids III(Academic, 1998).
  20. L. Neimo, Papermaking Chemistry (Gummerus, 1999).

2010 (2)

I. Niskanen, J. Räty, and K.-E. Peiponen, “A method for detection of the refractive index of irregular shapes solid pigments in light absorbing liquid matrix,” Talanta 81, 1322–1324(2010).
[CrossRef] [PubMed]

I. Niskanen, J. Räty, and K.-E. Peiponen, “Assessment of refractive index of pigments by Gaussian fitting of light backscattering data in context of the liquid immersion method,” Appl. Spectrosc. 64, 558–561 (2010).
[CrossRef] [PubMed]

2009 (2)

K. Koivunen, I. Niskanen, K.-E. Peiponen, and H. Paulapuro, “Novel nanostructured PCC fillers,” J. Mater. Sci. 44, 477–482 (2009).
[CrossRef]

L. Bremer, R. Tuinier, and S. Jahromi, “High refractive index nanocomposite fluids for immersion lithography,” Langmuir 25, 2390–2401 (2009).
[CrossRef] [PubMed]

2008 (2)

J. M. S. Saarela, S. M. Heikkinen, T. E. J. Fabritius, A. T. Haapala, and R. A. Myllylä, “Refractive index matching improves optical object detection in paper,” Meas. Sci. Technol. 19, 055710–055717 (2008).
[CrossRef]

I. Niskanen, J. Räty, and K.-E. Peiponen, “Estimation of effective refractive index of birefringent particles using a combination of immersion liquid method and light scattering,” Appl. Spectrosc. 62, 399–401 (2008).
[CrossRef] [PubMed]

2007 (3)

2006 (2)

A. V. Papaev, G. V. Simonenko, V. V. Tuchin, and T. P. Denisova, Opt. Spectrosc. 101, 46–53 (2006).
[CrossRef]

K. Lattaud, S. Vilminot, C. Hirlimann, H. Parant, J. Schoelkopf, and P. Gane, “Index of refraction enhancement of calcite particles coated with zinc carbonate,” Solid State Sci. 8, 1222–1228 (2006).
[CrossRef]

2003 (2)

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610nm,” Phys. Med. Biol. 48, 4165–4172 (2003).
[CrossRef]

S.-C. Su, “A rapid and accurate procedure for the determination of refractive indices of regulated asbestos minerals,” Am. Mineral. 88, 1979–1982 (2003).

1997 (1)

1987 (1)

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation using infra red laser beams,” Nature 330, 769–771 (1987).
[CrossRef] [PubMed]

Asakura, T.

J. Räty, K.-E. Peiponen, and T. Asakura, UV-Visible Reflection Spectroscopy of Liquids (Springer, 2004).

Ashkin, A.

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation using infra red laser beams,” Nature 330, 769–771 (1987).
[CrossRef] [PubMed]

Blaaderen, A.

Bremer, L.

L. Bremer, R. Tuinier, and S. Jahromi, “High refractive index nanocomposite fluids for immersion lithography,” Langmuir 25, 2390–2401 (2009).
[CrossRef] [PubMed]

Brock, R. S.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610nm,” Phys. Med. Biol. 48, 4165–4172 (2003).
[CrossRef]

Denisova, T. P.

A. V. Papaev, G. V. Simonenko, V. V. Tuchin, and T. P. Denisova, Opt. Spectrosc. 101, 46–53 (2006).
[CrossRef]

Dziedzic, J. M.

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation using infra red laser beams,” Nature 330, 769–771 (1987).
[CrossRef] [PubMed]

El-Hinnawi, E. E.

E. E. El-Hinnawi, Methods in Chemical and Mineral Microscopy (Elsevier, 1966).

Fabritius, T. E. J.

J. M. S. Saarela, S. M. Heikkinen, T. E. J. Fabritius, A. T. Haapala, and R. A. Myllylä, “Refractive index matching improves optical object detection in paper,” Meas. Sci. Technol. 19, 055710–055717 (2008).
[CrossRef]

Fournier, G.

Friedrich, F.

P. G. Weidler and F. Friedrich, “Determination of the refractive index of particles in the clay and sub-micrometer size range,” Am. Mineral. 92, 1130–1132 (2007).
[CrossRef]

Gane, P.

K. Lattaud, S. Vilminot, C. Hirlimann, H. Parant, J. Schoelkopf, and P. Gane, “Index of refraction enhancement of calcite particles coated with zinc carbonate,” Solid State Sci. 8, 1222–1228 (2006).
[CrossRef]

Grier, D. G.

Haapala, A. T.

J. M. S. Saarela, S. M. Heikkinen, T. E. J. Fabritius, A. T. Haapala, and R. A. Myllylä, “Refractive index matching improves optical object detection in paper,” Meas. Sci. Technol. 19, 055710–055717 (2008).
[CrossRef]

Heikkinen, S. M.

J. M. S. Saarela, S. M. Heikkinen, T. E. J. Fabritius, A. T. Haapala, and R. A. Myllylä, “Refractive index matching improves optical object detection in paper,” Meas. Sci. Technol. 19, 055710–055717 (2008).
[CrossRef]

Hirlimann, C.

K. Lattaud, S. Vilminot, C. Hirlimann, H. Parant, J. Schoelkopf, and P. Gane, “Index of refraction enhancement of calcite particles coated with zinc carbonate,” Solid State Sci. 8, 1222–1228 (2006).
[CrossRef]

Hu, X.-H.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610nm,” Phys. Med. Biol. 48, 4165–4172 (2003).
[CrossRef]

Jacobs, K. M.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610nm,” Phys. Med. Biol. 48, 4165–4172 (2003).
[CrossRef]

Jahromi, S.

L. Bremer, R. Tuinier, and S. Jahromi, “High refractive index nanocomposite fluids for immersion lithography,” Langmuir 25, 2390–2401 (2009).
[CrossRef] [PubMed]

Jonasz, M.

Kim, S.-H.

Koivunen, K.

K. Koivunen, I. Niskanen, K.-E. Peiponen, and H. Paulapuro, “Novel nanostructured PCC fillers,” J. Mater. Sci. 44, 477–482 (2009).
[CrossRef]

Lattaud, K.

K. Lattaud, S. Vilminot, C. Hirlimann, H. Parant, J. Schoelkopf, and P. Gane, “Index of refraction enhancement of calcite particles coated with zinc carbonate,” Solid State Sci. 8, 1222–1228 (2006).
[CrossRef]

Lee, S.-H.

Lu, J. Q.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610nm,” Phys. Med. Biol. 48, 4165–4172 (2003).
[CrossRef]

Ma, X.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610nm,” Phys. Med. Biol. 48, 4165–4172 (2003).
[CrossRef]

Myllylä, R. A.

J. M. S. Saarela, S. M. Heikkinen, T. E. J. Fabritius, A. T. Haapala, and R. A. Myllylä, “Refractive index matching improves optical object detection in paper,” Meas. Sci. Technol. 19, 055710–055717 (2008).
[CrossRef]

Neimo, L.

L. Neimo, Papermaking Chemistry (Gummerus, 1999).

Niskanen, I.

Oostrum, P.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids III(Academic, 1998).

Papaev, A. V.

A. V. Papaev, G. V. Simonenko, V. V. Tuchin, and T. P. Denisova, Opt. Spectrosc. 101, 46–53 (2006).
[CrossRef]

Parant, H.

K. Lattaud, S. Vilminot, C. Hirlimann, H. Parant, J. Schoelkopf, and P. Gane, “Index of refraction enhancement of calcite particles coated with zinc carbonate,” Solid State Sci. 8, 1222–1228 (2006).
[CrossRef]

Paulapuro, H.

K. Koivunen, I. Niskanen, K.-E. Peiponen, and H. Paulapuro, “Novel nanostructured PCC fillers,” J. Mater. Sci. 44, 477–482 (2009).
[CrossRef]

Peiponen, K.-E.

Räty, J.

Roichman, Y.

Saarela, J. M. S.

J. M. S. Saarela, S. M. Heikkinen, T. E. J. Fabritius, A. T. Haapala, and R. A. Myllylä, “Refractive index matching improves optical object detection in paper,” Meas. Sci. Technol. 19, 055710–055717 (2008).
[CrossRef]

Schoelkopf, J.

K. Lattaud, S. Vilminot, C. Hirlimann, H. Parant, J. Schoelkopf, and P. Gane, “Index of refraction enhancement of calcite particles coated with zinc carbonate,” Solid State Sci. 8, 1222–1228 (2006).
[CrossRef]

Simonenko, G. V.

A. V. Papaev, G. V. Simonenko, V. V. Tuchin, and T. P. Denisova, Opt. Spectrosc. 101, 46–53 (2006).
[CrossRef]

Stramski, D.

Su, S.-C.

S.-C. Su, “A rapid and accurate procedure for the determination of refractive indices of regulated asbestos minerals,” Am. Mineral. 88, 1979–1982 (2003).

Tuchin, V. V.

A. V. Papaev, G. V. Simonenko, V. V. Tuchin, and T. P. Denisova, Opt. Spectrosc. 101, 46–53 (2006).
[CrossRef]

Tuinier, R.

L. Bremer, R. Tuinier, and S. Jahromi, “High refractive index nanocomposite fluids for immersion lithography,” Langmuir 25, 2390–2401 (2009).
[CrossRef] [PubMed]

Vilminot, S.

K. Lattaud, S. Vilminot, C. Hirlimann, H. Parant, J. Schoelkopf, and P. Gane, “Index of refraction enhancement of calcite particles coated with zinc carbonate,” Solid State Sci. 8, 1222–1228 (2006).
[CrossRef]

Webster, J. G.

J. G. Webster, The Measurement, Instrumentation and Sensor Handbook (CRC, 1999).

Weidler, P. G.

P. G. Weidler and F. Friedrich, “Determination of the refractive index of particles in the clay and sub-micrometer size range,” Am. Mineral. 92, 1130–1132 (2007).
[CrossRef]

Yamane, T.

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation using infra red laser beams,” Nature 330, 769–771 (1987).
[CrossRef] [PubMed]

Yang, P.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610nm,” Phys. Med. Biol. 48, 4165–4172 (2003).
[CrossRef]

Yang, S.-M.

Yi, G.-R.

Am. Mineral. (2)

S.-C. Su, “A rapid and accurate procedure for the determination of refractive indices of regulated asbestos minerals,” Am. Mineral. 88, 1979–1982 (2003).

P. G. Weidler and F. Friedrich, “Determination of the refractive index of particles in the clay and sub-micrometer size range,” Am. Mineral. 92, 1130–1132 (2007).
[CrossRef]

Appl. Opt. (2)

Appl. Spectrosc. (2)

J. Mater. Sci. (1)

K. Koivunen, I. Niskanen, K.-E. Peiponen, and H. Paulapuro, “Novel nanostructured PCC fillers,” J. Mater. Sci. 44, 477–482 (2009).
[CrossRef]

Langmuir (1)

L. Bremer, R. Tuinier, and S. Jahromi, “High refractive index nanocomposite fluids for immersion lithography,” Langmuir 25, 2390–2401 (2009).
[CrossRef] [PubMed]

Meas. Sci. Technol. (1)

J. M. S. Saarela, S. M. Heikkinen, T. E. J. Fabritius, A. T. Haapala, and R. A. Myllylä, “Refractive index matching improves optical object detection in paper,” Meas. Sci. Technol. 19, 055710–055717 (2008).
[CrossRef]

Nature (1)

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation using infra red laser beams,” Nature 330, 769–771 (1987).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Spectrosc. (1)

A. V. Papaev, G. V. Simonenko, V. V. Tuchin, and T. P. Denisova, Opt. Spectrosc. 101, 46–53 (2006).
[CrossRef]

Phys. Med. Biol. (1)

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610nm,” Phys. Med. Biol. 48, 4165–4172 (2003).
[CrossRef]

Solid State Sci. (1)

K. Lattaud, S. Vilminot, C. Hirlimann, H. Parant, J. Schoelkopf, and P. Gane, “Index of refraction enhancement of calcite particles coated with zinc carbonate,” Solid State Sci. 8, 1222–1228 (2006).
[CrossRef]

Talanta (1)

I. Niskanen, J. Räty, and K.-E. Peiponen, “A method for detection of the refractive index of irregular shapes solid pigments in light absorbing liquid matrix,” Talanta 81, 1322–1324(2010).
[CrossRef] [PubMed]

Other (5)

E. E. El-Hinnawi, Methods in Chemical and Mineral Microscopy (Elsevier, 1966).

E. D. Palik, Handbook of Optical Constants of Solids III(Academic, 1998).

L. Neimo, Papermaking Chemistry (Gummerus, 1999).

J. G. Webster, The Measurement, Instrumentation and Sensor Handbook (CRC, 1999).

J. Räty, K.-E. Peiponen, and T. Asakura, UV-Visible Reflection Spectroscopy of Liquids (Springer, 2004).

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of the multifunction spectrophotometer: (a) transmission and (b) reflection measurement configuration. D, detector; P, polarizer. Polarization state and the angle of light incidence can be automatically chosen. The wavelength of the light can be scanned in the UV–visible range. The prism used for measurement is a Dove prism. The rectangle with dotted interior denotes the volume of the suspension in contact with the face of the prism, and the double-ended arrow indicates that the volume of the measurement compartment can be manually adjusted.

Fig. 2
Fig. 2

(a) Transmission data of Ca F 2 as a function of the refractive index difference of an immersion liquid at 589 nm (the solid line is a Gaussian line used for fitting the experimental data) and (b) Ca F 2 concentration as a function of half-width refractive index. The solid line in (b) is for linear data fitting.

Fig. 3
Fig. 3

(a) Transmission data of Ca F 2 / Al 2 Si O 5 mixture as a function of the refractive index of an immersion liquid at 589 nm (b) Ca F 2 concentration as a function of effective refractive index of a Ca F 2 / Al 2 Si O 5 mixture, and (c) Ca F 2 concentration as a function of half-width refractive index of a Ca F 2 / Al 2 Si O 5 mixture. Solid lines present Gaussian fitting of the data.

Equations (4)

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

n 21 = V 1 n 2 + V 2 n 2 V 1 + V 1 .
R s = r s r s * = ( cos θ i N r 2 sin 2 θ i cos θ i + N r 2 sin 2 θ i ) ( cos θ i N r 2 sin 2 θ i cos θ i + N r 2 sin 2 θ i ) * ,
S ( N r ) = i = 1 M ( R m ( θ i ) R s ( θ i , N r ) ) 2 ,
T = b + A exp [ ( n 21 n pigment ) 2 / ( 2 σ ) 2 ] ,

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