Abstract

Scattering is a useful tool for the determination of particle size in solution. In particular, spectroscopic analysis of backscattering renders the possibility of a simplified experimental setup and direct data processing using Mie theory. We show that a simple technique based on near-infrared (NIR) backscattering spectroscopy together with the development of the corresponding algorithm based on Fourier transform (FT) and Mie theory are a powerful tool for sizing microparticles in the range from 8 to 60  μm diameter. There are three wavelength intervals in the NIR, within which different diameter ranges were analyzed. In each one, the FT yields a coarse diameter value with an uncertainty dependent on the wavelength range. A more accurate value is obtained by further applying cross correlation between experimental and theoretical spectra. This latter step reduces the uncertainty in diameter determination between 30% and 40%, depending on wavelength interval and particle diameter. These results extend previous information on visible backscattering spectroscopy applied to sizing microparticles in the range between 1 and 24  μm diameter. This technique could be the basis for the construction of a portable and practical instrument.

© 2007 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2006 (1)

F. Videla, D. Schinca, and L. B. Scaffardi, "Sizing particles by backscattering spectroscopy and Fourier análisis," Opt. Eng. 45, 048001 (2006).
[CrossRef]

2004 (1)

2003 (2)

H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, "Noninvasive sizing of subcellular organelles with light scattering spectroscopy," IEEE J. Sel. Top. Quantum Electron. 9, 267-276 (2003).
[CrossRef]

F. A. Videla, D. C. Schinca, and J. O. Tocho, "Alternative method for concentration retrieval in differential optical absorption spectroscopy for atmospheric-gas pollutant measurements," Appl. Opt. 42, 3653-3661 (2003).
[CrossRef] [PubMed]

1997 (1)

1996 (2)

S. Min and A. Gomez, "High-resolution size measurements of single spherical particles with a fast Fourier transform of the angular scattering intensity," Appl. Opt. 35, 4919-4926 (1996).
[CrossRef] [PubMed]

L. B. Scaffardi, J. O. Tocho, L. L. Yebrin, and C. S. Cantera, "Sizing particles used in the leather industry by light scattering," Opt. Eng. 35, 52-56 (1996).
[CrossRef]

1993 (1)

1979 (1)

D. Perner and U. Platt, "Detection of nitrous acid in the atmosphere by differential optical absorption," Geophys. Res. Lett. 6, 917-920 (1979).
[CrossRef]

1908 (1)

G. Mie, "Beitrage zur Optik trüber Medien speziell kolloidaler Metallösungen," Ann. Phys. 25, 317-445 (1908).

Bigio, I.

Bigio, I. J.

H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, "Noninvasive sizing of subcellular organelles with light scattering spectroscopy," IEEE J. Sel. Top. Quantum Electron. 9, 267-276 (2003).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Boyer, J.

Cantera, C. S.

L. B. Scaffardi, J. O. Tocho, L. L. Yebrin, and C. S. Cantera, "Sizing particles used in the leather industry by light scattering," Opt. Eng. 35, 52-56 (1996).
[CrossRef]

Chernyshev, A.

Chu, B.

B. Chu, Laser Light Scattering: Basic Principles and Practice (Academic, 1991).

Cipolloni, P. B.

H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, "Noninvasive sizing of subcellular organelles with light scattering spectroscopy," IEEE J. Sel. Top. Quantum Electron. 9, 267-276 (2003).
[CrossRef]

Edner, H.

Fang, H.

H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, "Noninvasive sizing of subcellular organelles with light scattering spectroscopy," IEEE J. Sel. Top. Quantum Electron. 9, 267-276 (2003).
[CrossRef]

Freedman, S. D.

H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, "Noninvasive sizing of subcellular organelles with light scattering spectroscopy," IEEE J. Sel. Top. Quantum Electron. 9, 267-276 (2003).
[CrossRef]

Fuselier, T.

Gomez, A.

Gouesbet, G.

G. Gouesbet and G. Gréhan, eds., Optical Particle Sizing (Plenum, 1988).

Gréhan, G.

G. Gouesbet and G. Gréhan, eds., Optical Particle Sizing (Plenum, 1988).

Hanlon, E. B.

H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, "Noninvasive sizing of subcellular organelles with light scattering spectroscopy," IEEE J. Sel. Top. Quantum Electron. 9, 267-276 (2003).
[CrossRef]

Hoekstra, A.

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Itzkan, I.

H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, "Noninvasive sizing of subcellular organelles with light scattering spectroscopy," IEEE J. Sel. Top. Quantum Electron. 9, 267-276 (2003).
[CrossRef]

Johnson, T.

Kimerer, L. M.

H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, "Noninvasive sizing of subcellular organelles with light scattering spectroscopy," IEEE J. Sel. Top. Quantum Electron. 9, 267-276 (2003).
[CrossRef]

Laven, P.

P. Laven, MiePlot, 2005, http://www.philiplaven.com/mieplot.htm.

Maltsev, V.

Mie, G.

G. Mie, "Beitrage zur Optik trüber Medien speziell kolloidaler Metallösungen," Ann. Phys. 25, 317-445 (1908).

Min, S.

Mourant, J.

Ollero, M.

H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, "Noninvasive sizing of subcellular organelles with light scattering spectroscopy," IEEE J. Sel. Top. Quantum Electron. 9, 267-276 (2003).
[CrossRef]

Perelman, L. T.

H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, "Noninvasive sizing of subcellular organelles with light scattering spectroscopy," IEEE J. Sel. Top. Quantum Electron. 9, 267-276 (2003).
[CrossRef]

Perner, D.

D. Perner and U. Platt, "Detection of nitrous acid in the atmosphere by differential optical absorption," Geophys. Res. Lett. 6, 917-920 (1979).
[CrossRef]

Platt, U.

D. Perner and U. Platt, "Detection of nitrous acid in the atmosphere by differential optical absorption," Geophys. Res. Lett. 6, 917-920 (1979).
[CrossRef]

Ragnarson, P.

Scaffardi, L. B.

F. Videla, D. Schinca, and L. B. Scaffardi, "Sizing particles by backscattering spectroscopy and Fourier análisis," Opt. Eng. 45, 048001 (2006).
[CrossRef]

L. B. Scaffardi, J. O. Tocho, L. L. Yebrin, and C. S. Cantera, "Sizing particles used in the leather industry by light scattering," Opt. Eng. 35, 52-56 (1996).
[CrossRef]

Schinca, D.

F. Videla, D. Schinca, and L. B. Scaffardi, "Sizing particles by backscattering spectroscopy and Fourier análisis," Opt. Eng. 45, 048001 (2006).
[CrossRef]

Schinca, D. C.

Semyanov, K.

Spannare, S.

Svanberg, S.

Tarasov, P.

Tocho, J. O.

Videla, F.

F. Videla, D. Schinca, and L. B. Scaffardi, "Sizing particles by backscattering spectroscopy and Fourier análisis," Opt. Eng. 45, 048001 (2006).
[CrossRef]

Videla, F. A.

Vitkin, E.

H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, "Noninvasive sizing of subcellular organelles with light scattering spectroscopy," IEEE J. Sel. Top. Quantum Electron. 9, 267-276 (2003).
[CrossRef]

Yebrin, L. L.

L. B. Scaffardi, J. O. Tocho, L. L. Yebrin, and C. S. Cantera, "Sizing particles used in the leather industry by light scattering," Opt. Eng. 35, 52-56 (1996).
[CrossRef]

Zaman, M. M.

H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, "Noninvasive sizing of subcellular organelles with light scattering spectroscopy," IEEE J. Sel. Top. Quantum Electron. 9, 267-276 (2003).
[CrossRef]

Zharinov, A.

Appl. Opt. (5)

Geophys. Res. Lett. (1)

D. Perner and U. Platt, "Detection of nitrous acid in the atmosphere by differential optical absorption," Geophys. Res. Lett. 6, 917-920 (1979).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

H. Fang, M. Ollero, E. Vitkin, L. M. Kimerer, P. B. Cipolloni, M. M. Zaman, S. D. Freedman, I. J. Bigio, I. Itzkan, E. B. Hanlon, and L. T. Perelman, "Noninvasive sizing of subcellular organelles with light scattering spectroscopy," IEEE J. Sel. Top. Quantum Electron. 9, 267-276 (2003).
[CrossRef]

Opt. Eng. (2)

L. B. Scaffardi, J. O. Tocho, L. L. Yebrin, and C. S. Cantera, "Sizing particles used in the leather industry by light scattering," Opt. Eng. 35, 52-56 (1996).
[CrossRef]

F. Videla, D. Schinca, and L. B. Scaffardi, "Sizing particles by backscattering spectroscopy and Fourier análisis," Opt. Eng. 45, 048001 (2006).
[CrossRef]

Other (5)

G. Gouesbet and G. Gréhan, eds., Optical Particle Sizing (Plenum, 1988).

B. Chu, Laser Light Scattering: Basic Principles and Practice (Academic, 1991).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

G. Mie, "Beitrage zur Optik trüber Medien speziell kolloidaler Metallösungen," Ann. Phys. 25, 317-445 (1908).

P. Laven, MiePlot, 2005, http://www.philiplaven.com/mieplot.htm.

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Figures (14)

Fig. 1
Fig. 1

Experimental raw backscatter spectra for monomodal samples of 5, 8, 10, and 20   μm latex particle diameters suspended in water.

Fig. 2
Fig. 2

Experimental setup.

Fig. 3
Fig. 3

(a) Experimental baseline-corrected backscattering spectra for monomodal samples of 8, 10, and 20   μm latex particle diameters suspended in water. (b) FT of the spectra of (a).

Fig. 4
Fig. 4

(a) Experimental backscattering spectrum for a multimodal sample consisting of a mixture of latex particles of 8, 10, and 20   μm diameters suspended in water. (b) FT of the spectra of (a).

Fig. 5
Fig. 5

Relation between the particle diameter and the FT peak position for five diameter values corresponding to spectra in the 750 8 5 0   nm range. Open circles correspond to theoretical calculations. Filled stars correspond to experimental values for the same diameters. The linear fit is on theoretical values.

Fig. 6
Fig. 6

Cross-correlation results between the mixture spectrum of Fig. 4(a) and calculated monomodal spectra for several diameters at approximately (a) 8 μm, (b) 10   μm , and (c) 20   μm . The span of the horizontal axis corresponds to the uncertainty given by the FWHM of the FT curve.

Fig. 7
Fig. 7

Calculated backscattering coefficients for different spherical particles as a function of wavelength.

Fig. 8
Fig. 8

Calculated backscattering intensity for (a) 20, 25, and 30   μm particle diameters between 1060 and 1100   nm and (b) 40, 50, and 60   μm particle diameters between 1110 and 1150   nm .

Fig. 9
Fig. 9

FT of spectra of (a) Fig. 8(a) and (b) Fig. 8(b).

Fig. 10
Fig. 10

Particle diameter versus FT peak position for (a) 20, 25, and 30   μm particle diameters (circles with error bars) and linear regression (line) for the 1060 1 1 0 0   nm range and (b) 40, 50, and 60   μm particle diameters (circles with error bars) and linear regression (line) for the 1110 1 1 5 0   nm range. The error bars represent the uncertainty given by the FWHM of the FT curve.

Fig. 11
Fig. 11

Experimental backscattering spectrum. The data were processed according to the guidelines described in the text.

Fig. 12
Fig. 12

Stacked FT of the experimental spectra of Fig. 11.

Fig. 13
Fig. 13

Comparison of the particle diameter versus the FT peak position relation for calculated 20 6 0   μm particle diameters (circles with error bars) and experimental 20, 30, and 50   μm particle diameters.

Fig. 14
Fig. 14

Correlation values for backscattering spectrum corresponding to a 20   μm nominal diameter. The span of the horizontal axis corresponds to the uncertainty interval derived from the FWHM of the FT curve.

Tables (1)

Tables Icon

Table 1 Spectral Intervals and Particle Diameters Analyzed with Backscattering Spectroscopy Using FT and Cross Correlation a

Equations (3)

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C ( φ ) = λ low λ high I exp ( λ , d FT ) I MIE ( λ , d FT + φ ) d λ ,
n w ( λ ) = 1.324 + 3046 / λ 2 for   water ,
n p ( λ ) = 1.59 + 15 × 10 3 ( 1 / λ 2 1 / 589.32 2 ) for   polystyrene   particles .

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