Abstract

The application in light scattering of the Mueller matrix ratio 〈S 34〉/〈S 11〉 for determining average particle size is extended to a large size parameter range for spherical or randomly oriented rod-shaped particles such as micro-organisms. It is shown that combining the graph of this ratio with a Coulter counter measurement of particle volume gives results in agreement with microscopic measurements. Thus this combination provides a method to measure particle diameter and width simultaneously in real time for elongated particles such as bacteria, which are measured in vivo with this method. An approximate empirical formula is developed to estimate the motion of the extrema in the graph of the oscillating matrix ratio as size changes occur. This formula is also shown to be consistent with wavelength changes.

© 2004 Optical Society of America

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References

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  1. W. P. Van de Merwe, Z. Z. Li, B. V. Bronk, J. Czege, “Polarized light scattering for rapid observation of bacterial size changes,” Biophys. J. 73, 500–506 (1997).
    [Crossref] [PubMed]
  2. W. P. Van De Merwe, D. R. Huffman, B. V. Bronk, “Reproducibility and sensitivity of polarized light scattering for identifying bacterial suspensions,” Appl. Opt. 28, 5052–5057 (1989).
    [Crossref] [PubMed]
  3. B. V. Bronk, W. P. Van De Merwe, M. Stanley, “An in-vivo measure of average bacterial cell size from a polarized light scattering function,” Cytometry 13, 155–162 (1992).
    [Crossref]
  4. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  5. L. A. Matheson, J. L. Saunderson, “Optical and electrical properties of polystyrene,” in Styrene, Its Polymers, Copolymers and Derivatives, R. H. Boundy, R. F. Boyer, eds., American Chemical Society Monograph Series (Hafner Publishing, New York, 1952), pp. 517–573.
  6. B. V. Bronk, S. D. Druger, J. Czege, W. P. Van de Merwe, “Measuring diameters of rod-shaped bacteria in vivo with polarized light scattering,” Biophys. J. 69, 1170–1177 (1995).
    [Crossref] [PubMed]
  7. B. V. Bronk, W. P. Van De Merwe, Z. Z. Li, J. Czege, “In vitro method for detecting toxicants by changes in pattern of polarized light scattering,” in Advances in Animal Alternatives for Safety and Efficacy Testing, H. Salem, S. A. Katz, eds. (CRC Press, Boca Raton, Fla., 1997), pp. 427–432.
  8. B. V. Bronk, Z. Z. Li, J. Czégé, “Polarized light scattering as a rapid and sensitive assay for metal toxicity to bacteria,” J. Appl. Toxicol. 21, 107–113 (2001).
    [Crossref] [PubMed]
  9. B. Bronk, M. Milham, Z. Li, J. Czege, “Polarized light scattering to provide size distributions for microorganisms,” in Proceedings of the First Joint Conference on Point Detection, D. McQuestion, ed. (Science and Technology Corp., Hampton, Va., 2000).
  10. C. L. Woldringh, N. B. Grover, R. F. Rosenberger, A. Zaritsky, “Dimensional rearrangement of rod-shaped bacteria following nutritional shift-up,” J. Theor. Biol. 86, 441–454 (1980).
    [Crossref] [PubMed]
  11. B. V. Bronk, W. P. Van de Merwe, D. R. Huffman, “Polarized light scattering as a means for detecting subtle changes in microbial populations,” in Modern Techniques for Rapid Microbiological Analysis, W. H. Nelson, ed. (VCH, New York, 1991), pp. 171–197.

2001 (1)

B. V. Bronk, Z. Z. Li, J. Czégé, “Polarized light scattering as a rapid and sensitive assay for metal toxicity to bacteria,” J. Appl. Toxicol. 21, 107–113 (2001).
[Crossref] [PubMed]

1997 (1)

W. P. Van de Merwe, Z. Z. Li, B. V. Bronk, J. Czege, “Polarized light scattering for rapid observation of bacterial size changes,” Biophys. J. 73, 500–506 (1997).
[Crossref] [PubMed]

1995 (1)

B. V. Bronk, S. D. Druger, J. Czege, W. P. Van de Merwe, “Measuring diameters of rod-shaped bacteria in vivo with polarized light scattering,” Biophys. J. 69, 1170–1177 (1995).
[Crossref] [PubMed]

1992 (1)

B. V. Bronk, W. P. Van De Merwe, M. Stanley, “An in-vivo measure of average bacterial cell size from a polarized light scattering function,” Cytometry 13, 155–162 (1992).
[Crossref]

1989 (1)

1980 (1)

C. L. Woldringh, N. B. Grover, R. F. Rosenberger, A. Zaritsky, “Dimensional rearrangement of rod-shaped bacteria following nutritional shift-up,” J. Theor. Biol. 86, 441–454 (1980).
[Crossref] [PubMed]

Bohren, C. F.

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

Bronk, B.

B. Bronk, M. Milham, Z. Li, J. Czege, “Polarized light scattering to provide size distributions for microorganisms,” in Proceedings of the First Joint Conference on Point Detection, D. McQuestion, ed. (Science and Technology Corp., Hampton, Va., 2000).

Bronk, B. V.

B. V. Bronk, Z. Z. Li, J. Czégé, “Polarized light scattering as a rapid and sensitive assay for metal toxicity to bacteria,” J. Appl. Toxicol. 21, 107–113 (2001).
[Crossref] [PubMed]

W. P. Van de Merwe, Z. Z. Li, B. V. Bronk, J. Czege, “Polarized light scattering for rapid observation of bacterial size changes,” Biophys. J. 73, 500–506 (1997).
[Crossref] [PubMed]

B. V. Bronk, S. D. Druger, J. Czege, W. P. Van de Merwe, “Measuring diameters of rod-shaped bacteria in vivo with polarized light scattering,” Biophys. J. 69, 1170–1177 (1995).
[Crossref] [PubMed]

B. V. Bronk, W. P. Van De Merwe, M. Stanley, “An in-vivo measure of average bacterial cell size from a polarized light scattering function,” Cytometry 13, 155–162 (1992).
[Crossref]

W. P. Van De Merwe, D. R. Huffman, B. V. Bronk, “Reproducibility and sensitivity of polarized light scattering for identifying bacterial suspensions,” Appl. Opt. 28, 5052–5057 (1989).
[Crossref] [PubMed]

B. V. Bronk, W. P. Van De Merwe, Z. Z. Li, J. Czege, “In vitro method for detecting toxicants by changes in pattern of polarized light scattering,” in Advances in Animal Alternatives for Safety and Efficacy Testing, H. Salem, S. A. Katz, eds. (CRC Press, Boca Raton, Fla., 1997), pp. 427–432.

B. V. Bronk, W. P. Van de Merwe, D. R. Huffman, “Polarized light scattering as a means for detecting subtle changes in microbial populations,” in Modern Techniques for Rapid Microbiological Analysis, W. H. Nelson, ed. (VCH, New York, 1991), pp. 171–197.

Czege, J.

W. P. Van de Merwe, Z. Z. Li, B. V. Bronk, J. Czege, “Polarized light scattering for rapid observation of bacterial size changes,” Biophys. J. 73, 500–506 (1997).
[Crossref] [PubMed]

B. V. Bronk, S. D. Druger, J. Czege, W. P. Van de Merwe, “Measuring diameters of rod-shaped bacteria in vivo with polarized light scattering,” Biophys. J. 69, 1170–1177 (1995).
[Crossref] [PubMed]

B. V. Bronk, W. P. Van De Merwe, Z. Z. Li, J. Czege, “In vitro method for detecting toxicants by changes in pattern of polarized light scattering,” in Advances in Animal Alternatives for Safety and Efficacy Testing, H. Salem, S. A. Katz, eds. (CRC Press, Boca Raton, Fla., 1997), pp. 427–432.

B. Bronk, M. Milham, Z. Li, J. Czege, “Polarized light scattering to provide size distributions for microorganisms,” in Proceedings of the First Joint Conference on Point Detection, D. McQuestion, ed. (Science and Technology Corp., Hampton, Va., 2000).

Czégé, J.

B. V. Bronk, Z. Z. Li, J. Czégé, “Polarized light scattering as a rapid and sensitive assay for metal toxicity to bacteria,” J. Appl. Toxicol. 21, 107–113 (2001).
[Crossref] [PubMed]

Druger, S. D.

B. V. Bronk, S. D. Druger, J. Czege, W. P. Van de Merwe, “Measuring diameters of rod-shaped bacteria in vivo with polarized light scattering,” Biophys. J. 69, 1170–1177 (1995).
[Crossref] [PubMed]

Grover, N. B.

C. L. Woldringh, N. B. Grover, R. F. Rosenberger, A. Zaritsky, “Dimensional rearrangement of rod-shaped bacteria following nutritional shift-up,” J. Theor. Biol. 86, 441–454 (1980).
[Crossref] [PubMed]

Huffman, D. R.

W. P. Van De Merwe, D. R. Huffman, B. V. Bronk, “Reproducibility and sensitivity of polarized light scattering for identifying bacterial suspensions,” Appl. Opt. 28, 5052–5057 (1989).
[Crossref] [PubMed]

B. V. Bronk, W. P. Van de Merwe, D. R. Huffman, “Polarized light scattering as a means for detecting subtle changes in microbial populations,” in Modern Techniques for Rapid Microbiological Analysis, W. H. Nelson, ed. (VCH, New York, 1991), pp. 171–197.

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

Li, Z.

B. Bronk, M. Milham, Z. Li, J. Czege, “Polarized light scattering to provide size distributions for microorganisms,” in Proceedings of the First Joint Conference on Point Detection, D. McQuestion, ed. (Science and Technology Corp., Hampton, Va., 2000).

Li, Z. Z.

B. V. Bronk, Z. Z. Li, J. Czégé, “Polarized light scattering as a rapid and sensitive assay for metal toxicity to bacteria,” J. Appl. Toxicol. 21, 107–113 (2001).
[Crossref] [PubMed]

W. P. Van de Merwe, Z. Z. Li, B. V. Bronk, J. Czege, “Polarized light scattering for rapid observation of bacterial size changes,” Biophys. J. 73, 500–506 (1997).
[Crossref] [PubMed]

B. V. Bronk, W. P. Van De Merwe, Z. Z. Li, J. Czege, “In vitro method for detecting toxicants by changes in pattern of polarized light scattering,” in Advances in Animal Alternatives for Safety and Efficacy Testing, H. Salem, S. A. Katz, eds. (CRC Press, Boca Raton, Fla., 1997), pp. 427–432.

Matheson, L. A.

L. A. Matheson, J. L. Saunderson, “Optical and electrical properties of polystyrene,” in Styrene, Its Polymers, Copolymers and Derivatives, R. H. Boundy, R. F. Boyer, eds., American Chemical Society Monograph Series (Hafner Publishing, New York, 1952), pp. 517–573.

Milham, M.

B. Bronk, M. Milham, Z. Li, J. Czege, “Polarized light scattering to provide size distributions for microorganisms,” in Proceedings of the First Joint Conference on Point Detection, D. McQuestion, ed. (Science and Technology Corp., Hampton, Va., 2000).

Rosenberger, R. F.

C. L. Woldringh, N. B. Grover, R. F. Rosenberger, A. Zaritsky, “Dimensional rearrangement of rod-shaped bacteria following nutritional shift-up,” J. Theor. Biol. 86, 441–454 (1980).
[Crossref] [PubMed]

Saunderson, J. L.

L. A. Matheson, J. L. Saunderson, “Optical and electrical properties of polystyrene,” in Styrene, Its Polymers, Copolymers and Derivatives, R. H. Boundy, R. F. Boyer, eds., American Chemical Society Monograph Series (Hafner Publishing, New York, 1952), pp. 517–573.

Stanley, M.

B. V. Bronk, W. P. Van De Merwe, M. Stanley, “An in-vivo measure of average bacterial cell size from a polarized light scattering function,” Cytometry 13, 155–162 (1992).
[Crossref]

Van de Merwe, W. P.

W. P. Van de Merwe, Z. Z. Li, B. V. Bronk, J. Czege, “Polarized light scattering for rapid observation of bacterial size changes,” Biophys. J. 73, 500–506 (1997).
[Crossref] [PubMed]

B. V. Bronk, S. D. Druger, J. Czege, W. P. Van de Merwe, “Measuring diameters of rod-shaped bacteria in vivo with polarized light scattering,” Biophys. J. 69, 1170–1177 (1995).
[Crossref] [PubMed]

B. V. Bronk, W. P. Van De Merwe, M. Stanley, “An in-vivo measure of average bacterial cell size from a polarized light scattering function,” Cytometry 13, 155–162 (1992).
[Crossref]

W. P. Van De Merwe, D. R. Huffman, B. V. Bronk, “Reproducibility and sensitivity of polarized light scattering for identifying bacterial suspensions,” Appl. Opt. 28, 5052–5057 (1989).
[Crossref] [PubMed]

B. V. Bronk, W. P. Van de Merwe, D. R. Huffman, “Polarized light scattering as a means for detecting subtle changes in microbial populations,” in Modern Techniques for Rapid Microbiological Analysis, W. H. Nelson, ed. (VCH, New York, 1991), pp. 171–197.

B. V. Bronk, W. P. Van De Merwe, Z. Z. Li, J. Czege, “In vitro method for detecting toxicants by changes in pattern of polarized light scattering,” in Advances in Animal Alternatives for Safety and Efficacy Testing, H. Salem, S. A. Katz, eds. (CRC Press, Boca Raton, Fla., 1997), pp. 427–432.

Woldringh, C. L.

C. L. Woldringh, N. B. Grover, R. F. Rosenberger, A. Zaritsky, “Dimensional rearrangement of rod-shaped bacteria following nutritional shift-up,” J. Theor. Biol. 86, 441–454 (1980).
[Crossref] [PubMed]

Zaritsky, A.

C. L. Woldringh, N. B. Grover, R. F. Rosenberger, A. Zaritsky, “Dimensional rearrangement of rod-shaped bacteria following nutritional shift-up,” J. Theor. Biol. 86, 441–454 (1980).
[Crossref] [PubMed]

Appl. Opt. (1)

Biophys. J. (2)

W. P. Van de Merwe, Z. Z. Li, B. V. Bronk, J. Czege, “Polarized light scattering for rapid observation of bacterial size changes,” Biophys. J. 73, 500–506 (1997).
[Crossref] [PubMed]

B. V. Bronk, S. D. Druger, J. Czege, W. P. Van de Merwe, “Measuring diameters of rod-shaped bacteria in vivo with polarized light scattering,” Biophys. J. 69, 1170–1177 (1995).
[Crossref] [PubMed]

Cytometry (1)

B. V. Bronk, W. P. Van De Merwe, M. Stanley, “An in-vivo measure of average bacterial cell size from a polarized light scattering function,” Cytometry 13, 155–162 (1992).
[Crossref]

J. Appl. Toxicol. (1)

B. V. Bronk, Z. Z. Li, J. Czégé, “Polarized light scattering as a rapid and sensitive assay for metal toxicity to bacteria,” J. Appl. Toxicol. 21, 107–113 (2001).
[Crossref] [PubMed]

J. Theor. Biol. (1)

C. L. Woldringh, N. B. Grover, R. F. Rosenberger, A. Zaritsky, “Dimensional rearrangement of rod-shaped bacteria following nutritional shift-up,” J. Theor. Biol. 86, 441–454 (1980).
[Crossref] [PubMed]

Other (5)

B. V. Bronk, W. P. Van de Merwe, D. R. Huffman, “Polarized light scattering as a means for detecting subtle changes in microbial populations,” in Modern Techniques for Rapid Microbiological Analysis, W. H. Nelson, ed. (VCH, New York, 1991), pp. 171–197.

B. Bronk, M. Milham, Z. Li, J. Czege, “Polarized light scattering to provide size distributions for microorganisms,” in Proceedings of the First Joint Conference on Point Detection, D. McQuestion, ed. (Science and Technology Corp., Hampton, Va., 2000).

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

L. A. Matheson, J. L. Saunderson, “Optical and electrical properties of polystyrene,” in Styrene, Its Polymers, Copolymers and Derivatives, R. H. Boundy, R. F. Boyer, eds., American Chemical Society Monograph Series (Hafner Publishing, New York, 1952), pp. 517–573.

B. V. Bronk, W. P. Van De Merwe, Z. Z. Li, J. Czege, “In vitro method for detecting toxicants by changes in pattern of polarized light scattering,” in Advances in Animal Alternatives for Safety and Efficacy Testing, H. Salem, S. A. Katz, eds. (CRC Press, Boca Raton, Fla., 1997), pp. 427–432.

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Figures (10)

Fig. 1
Fig. 1

Experimental results (solid line) showing 〈S 34〉/〈S 11〉 as a function of scattering angle for polystyrene spheres (Sigma) of 0.80-μm average diameter and refractive index of 1.585 + 0.0001i (from Matheson and Saunderson)5 with a diode laser at ∼668 nm. The calculation (dotted curve) was made by use of the exact Mie solution (e.g., Bohren and Huffman)4 with the same parameters, but assuming a Gaussian distribution of spherical diameters with a coefficient of variation of 4%.

Fig. 2
Fig. 2

Volume distribution obtained with Coulter counter measurements of nominal (Duke) 1.335 ± 0.022-μm-diameter polystyrene spheres. The fit is calibrated to this nominal volume. The standard deviation of the fitted curve (Gaussian) is ∼19%, which is substantially larger than that obtained from the nominal value given by the manufacturer. Part of this is likely due to Coulter counter electronic noise as well as error from the use of a large orfice.

Fig. 3
Fig. 3

Microscopic image of Escherichia coli in log phase used to measure length and diameter. The rectangular bar is 5.00 μm.

Fig. 4
Fig. 4

S 34〉/〈S 11〉 for E. coli K12 bacteria taken after overnight growth. Scattering was with 633-nm laser light.

Fig. 5
Fig. 5

Angle of 〈S 34〉/〈S 11〉 extrema as a function of polystyrene sphere diameter. Points are from experimental graphs as in Fig. 4. Curves are a power-law fit. The lowest curve relates to the first observed maximum (i.e., smallest scattering angle). The second lowest relates to the first minimum and so on. Measured extrema, for a particular sphere size, fall on a vertical line.

Fig. 6
Fig. 6

Wavelength study. Angle of maxima of 〈S 34〉/〈S 11〉 versus wave number for polystyrene spheres of 1.0-μm average diameter.

Fig. 7
Fig. 7

S 34〉/〈S 11〉 versus scattering angle for 1.0-μm polystyrene spheres immersed in three different media. Filled circles with solid curve, water, refractive index of n = 1.33; open circles, ethylene glycol, refractive index of n = 1.43; open diamonds, glycerin, refractive index of n = 1.47.

Fig. 8
Fig. 8

Volume distribution of growing E. coli k12 bacteria obtained with (a) the Coulter counter and (b) phase contrast microscopic measurements. Fitted curves are log normal in (a) and (b), the horizontal axis is in cubic micrometers. (See first Gr; LB in Table 2.)

Fig. 9
Fig. 9

Angle of 〈S 34〉/〈S 11〉 experimental extrema as a function of rod diameter for bacteria plotted with (a) the experimental extrema of polystyrene spheres (size corrected for change in wavelength) and (b) a Mie calculation for distribution of bacterial spheres with approximately the same refractive index as the bacteria (1.37 + 0.0001i), diameters as indicated, and a coefficient of variation (i.e., standard deviation/average) of 10% for 10% diameters. In (a) the solid curves represent a power-law fit to the rod diameter of bacteria, the dashed curves represent a power-law fit to the spheres, and the power is in the 1.0 to 1.2 range. In (b) the solid curves represent a power-law fit to experimental angles and rod diameter of bacteria, and the dashed curves represent a fit to calculated angles and input diameters for an idealized case of bacterial spheres.

Fig. 10
Fig. 10

Diameter of E. coli H266 obtained from 〈S 34〉/〈S 11〉 values and Fig. 9(a) as a function of time after a nutritional upshift experiment compared with the results obtained by microscopic measurement. Solid curve, current experimental result from scattering; dashed curve, measurements taken with a microscope as reported in Ref. 10.

Tables (2)

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Table 1 Comparison of Measured and Calculated Extrema Anglesa

Tables Icon

Table 2 Comparison of Microscopic and Coulter Counter Determined Volumes

Equations (3)

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V=π/6D3,
V=π/4D2L-D+π/6D3.
A=CX-y,

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