Abstract

A Fourier transform was applied to size an individual spherical particle from an angular light-scattering pattern. The position of the peak in the amplitude spectrum has a strong correlation with the particle size. A linear equation retrieved from regression analysis of theoretically simulated patterns provides a relation between the particle size and the location of the amplitude spectrum’s peak. The equation can be successfully applied to characterize particles of size parameters that range from 8 to 180 (corresponding to particle sizes that range from 1.2 to 27.2 μm at a wavelength of 0.633 μm). The precision of particle sizing depends on the refractive index and reaches a value of 60 nm within refractive-index region from 1.35 to 1.70. We have analyzed four samples of polystyrene microspheres with mean diameters of 1.9, 2.6, 3.0, and 4.2 μm and a sample of isovolumetrically sphered erythrocytes with a scanning flow cytometer to compare the accuracy of our new method with that of others.

© 2004 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2000 (3)

H.-H. Qiu, W. Jia, C. T. Hsu, M. Sommerfeld, “High accuracy optical particle sizing in phase-Doppler anemometry,” Meas. Sci. Technol. 11, 142–151 (2000).
[CrossRef]

V. P. Maltsev, “Scanning flow cytometry for individual particle analysis,” Rev. Sci. Instrum. 71, 243–255 (2000).
[CrossRef]

C. Godefroy, M. Adjouadi, “Particle sizing in a flow environment using light scattering patterns,” Part. Part. Syst. Charact. 17, 47–55 (2000).
[CrossRef]

1998 (1)

J. T. Soini, A. V. Chernyshev, P. E. Hanninen, E. Soini, V. P. Maltsev, “A new design of the flow cuvette and optical set-up for the scanning flow cytometer,” Cytometry 31, 78–84 (1998).
[CrossRef] [PubMed]

1997 (1)

1996 (1)

1995 (1)

I. K. Ludlow, J. Everitt, “Application of Gegenbauer analysis to light scattering from spheres,” Phys. Rev. E 5, 2516–2526 (1995).
[CrossRef]

1994 (1)

V. P. Maltsev, “Estimation of morphological characteristics of single particles from light scattering data in flow cytometry,” Russ. Chem. Bull. 43, 1115–1124 (1994).
[CrossRef]

1985 (2)

1983 (1)

Y. R. Kim, L. Ornstein, “Isovolumetric sphering of erythrocytes for more accurate and precise cell volume measurement by flow cytometry,” Cytometry 3, 419–427 (1983).
[CrossRef] [PubMed]

1980 (1)

1979 (1)

I. K. Ludlow, P. H. Kaye, “A scanning diffractometer for the rapid analysis of microparticles and biological cells,” J. Colloid Interface Sci. 69, 571–589 (1979).
[CrossRef]

Adjouadi, M.

C. Godefroy, M. Adjouadi, “Particle sizing in a flow environment using light scattering patterns,” Part. Part. Syst. Charact. 17, 47–55 (2000).
[CrossRef]

Bartholdi, M.

Bohren, C. F.

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

Chernyshev, A. V.

J. T. Soini, A. V. Chernyshev, P. E. Hanninen, E. Soini, V. P. Maltsev, “A new design of the flow cuvette and optical set-up for the scanning flow cytometer,” Cytometry 31, 78–84 (1998).
[CrossRef] [PubMed]

Epstein, E. A.

Everitt, J.

I. K. Ludlow, J. Everitt, “Application of Gegenbauer analysis to light scattering from spheres,” Phys. Rev. E 5, 2516–2526 (1995).
[CrossRef]

Godefroy, C.

C. Godefroy, M. Adjouadi, “Particle sizing in a flow environment using light scattering patterns,” Part. Part. Syst. Charact. 17, 47–55 (2000).
[CrossRef]

Gomez, A.

Grinbaum, A.

Hanninen, P. E.

J. T. Soini, A. V. Chernyshev, P. E. Hanninen, E. Soini, V. P. Maltsev, “A new design of the flow cuvette and optical set-up for the scanning flow cytometer,” Cytometry 31, 78–84 (1998).
[CrossRef] [PubMed]

Hiebert, R. D.

Hsu, C. T.

H.-H. Qiu, W. Jia, C. T. Hsu, M. Sommerfeld, “High accuracy optical particle sizing in phase-Doppler anemometry,” Meas. Sci. Technol. 11, 142–151 (2000).
[CrossRef]

Huffman, D. R.

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

Jia, W.

H.-H. Qiu, W. Jia, C. T. Hsu, M. Sommerfeld, “High accuracy optical particle sizing in phase-Doppler anemometry,” Meas. Sci. Technol. 11, 142–151 (2000).
[CrossRef]

Kaye, P. H.

I. K. Ludlow, P. H. Kaye, “A scanning diffractometer for the rapid analysis of microparticles and biological cells,” J. Colloid Interface Sci. 69, 571–589 (1979).
[CrossRef]

Kerker, M.

Kim, Y. R.

Y. R. Kim, L. Ornstein, “Isovolumetric sphering of erythrocytes for more accurate and precise cell volume measurement by flow cytometry,” Cytometry 3, 419–427 (1983).
[CrossRef] [PubMed]

Lopatin, V. N.

Ludlow, I. K.

I. K. Ludlow, J. Everitt, “Application of Gegenbauer analysis to light scattering from spheres,” Phys. Rev. E 5, 2516–2526 (1995).
[CrossRef]

I. K. Ludlow, P. H. Kaye, “A scanning diffractometer for the rapid analysis of microparticles and biological cells,” J. Colloid Interface Sci. 69, 571–589 (1979).
[CrossRef]

Maltsev, V. P.

V. P. Maltsev, “Scanning flow cytometry for individual particle analysis,” Rev. Sci. Instrum. 71, 243–255 (2000).
[CrossRef]

J. T. Soini, A. V. Chernyshev, P. E. Hanninen, E. Soini, V. P. Maltsev, “A new design of the flow cuvette and optical set-up for the scanning flow cytometer,” Cytometry 31, 78–84 (1998).
[CrossRef] [PubMed]

V. P. Maltsev, V. N. Lopatin, “A parametric solution of the inverse light-scattering problem for individual spherical particles,” Appl. Opt. 36, 6102–6108 (1997).
[CrossRef] [PubMed]

V. P. Maltsev, “Estimation of morphological characteristics of single particles from light scattering data in flow cytometry,” Russ. Chem. Bull. 43, 1115–1124 (1994).
[CrossRef]

Metz, M. H.

Min, S.

Ornstein, L.

Y. R. Kim, L. Ornstein, “Isovolumetric sphering of erythrocytes for more accurate and precise cell volume measurement by flow cytometry,” Cytometry 3, 419–427 (1983).
[CrossRef] [PubMed]

Qiu, H.-H.

H.-H. Qiu, W. Jia, C. T. Hsu, M. Sommerfeld, “High accuracy optical particle sizing in phase-Doppler anemometry,” Meas. Sci. Technol. 11, 142–151 (2000).
[CrossRef]

Quist, G. M.

Salzman, G. C.

Soini, E.

J. T. Soini, A. V. Chernyshev, P. E. Hanninen, E. Soini, V. P. Maltsev, “A new design of the flow cuvette and optical set-up for the scanning flow cytometer,” Cytometry 31, 78–84 (1998).
[CrossRef] [PubMed]

Soini, J. T.

J. T. Soini, A. V. Chernyshev, P. E. Hanninen, E. Soini, V. P. Maltsev, “A new design of the flow cuvette and optical set-up for the scanning flow cytometer,” Cytometry 31, 78–84 (1998).
[CrossRef] [PubMed]

Sommerfeld, M.

H.-H. Qiu, W. Jia, C. T. Hsu, M. Sommerfeld, “High accuracy optical particle sizing in phase-Doppler anemometry,” Meas. Sci. Technol. 11, 142–151 (2000).
[CrossRef]

Tycko, D. H.

Wyatt, P. J.

Appl. Opt. (4)

Cytometry (2)

J. T. Soini, A. V. Chernyshev, P. E. Hanninen, E. Soini, V. P. Maltsev, “A new design of the flow cuvette and optical set-up for the scanning flow cytometer,” Cytometry 31, 78–84 (1998).
[CrossRef] [PubMed]

Y. R. Kim, L. Ornstein, “Isovolumetric sphering of erythrocytes for more accurate and precise cell volume measurement by flow cytometry,” Cytometry 3, 419–427 (1983).
[CrossRef] [PubMed]

J. Colloid Interface Sci. (1)

I. K. Ludlow, P. H. Kaye, “A scanning diffractometer for the rapid analysis of microparticles and biological cells,” J. Colloid Interface Sci. 69, 571–589 (1979).
[CrossRef]

J. Opt. Soc. Am. A (1)

Meas. Sci. Technol. (1)

H.-H. Qiu, W. Jia, C. T. Hsu, M. Sommerfeld, “High accuracy optical particle sizing in phase-Doppler anemometry,” Meas. Sci. Technol. 11, 142–151 (2000).
[CrossRef]

Part. Part. Syst. Charact. (1)

C. Godefroy, M. Adjouadi, “Particle sizing in a flow environment using light scattering patterns,” Part. Part. Syst. Charact. 17, 47–55 (2000).
[CrossRef]

Phys. Rev. E (1)

I. K. Ludlow, J. Everitt, “Application of Gegenbauer analysis to light scattering from spheres,” Phys. Rev. E 5, 2516–2526 (1995).
[CrossRef]

Rev. Sci. Instrum. (1)

V. P. Maltsev, “Scanning flow cytometry for individual particle analysis,” Rev. Sci. Instrum. 71, 243–255 (2000).
[CrossRef]

Russ. Chem. Bull. (1)

V. P. Maltsev, “Estimation of morphological characteristics of single particles from light scattering data in flow cytometry,” Russ. Chem. Bull. 43, 1115–1124 (1994).
[CrossRef]

Other (2)

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

M. R. Melamed, T. Lindmo, M. L. Mendelsohn, eds., Flow Cytometry and Sorting (Wiley-Liss, New York, 1990).

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Figures (6)

Fig. 1
Fig. 1

(a) Light-scattering pattern with (b) spectrum of an individual spherical particle. Dashed curve, modifying function F(θ). (c) Light-scattering pattern modified by multiplication by function F(θ), (d) spectrum.

Fig. 2
Fig. 2

Size parameters of particles with refractive indices n = 1.39, n = 1.49, n = 1.59, and n = 1.70 as a function of peak frequency index P f .

Fig. 3
Fig. 3

(a) Scatterplot of the peak amplitude as a function of size and phase-shift parameters. (b) Maximal errors in calculation of size parameter from Eq. (2) (lighter curve) and from Eq. (3) (darker curve).

Fig. 4
Fig. 4

Calculated dependency of coefficient k on relative refractive index (squares) and approximating equations for fitting them.

Fig. 5
Fig. 5

(a) Typical experimental indicatrix of a polystyrene bead measured with a SFC and modified indicatrix. (b) Spectral decomposition.

Fig. 6
Fig. 6

Distribution of the sizes of polystyrene latex microspheres and sphered erythrocytes obtained in two ways: (a) based on Eq. (2) and (b) based on the FLSI method.

Tables (1)

Tables Icon

Table 1 Comparison of Equations for the Spectral Decomposition and FLSI Methods of Particle Sizing

Equations (5)

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Fθ=sin2π θ-θlθh-θl,
α=kPF,
α=k1+k1/AFPF+k2,
k=1739.1-2981.0 m+1427.1 m2,
k=105.0+73.5 m,

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