Abstract

In article I of this series, calculations and graphs of the depolarization ratio, D(Θ,λ)=1<S22>/<S11>, for light scattered from an ensemble of single-aerosolized Bacillus spores using the discrete dipole approximation (DDA) (sometimes also called the coupled dipole approximation) were presented. The Sij in these papers denote the appropriate Mueller matrix elements. We compare graphs for different size parameters for both D(Θ,λ) and the ratio R34(Θ,λ)=<S34>/<S11>. The ratio R34(Θ,λ) was shown previously to be sensitive to diameters of rod-shaped and spherical bacteria suspended in liquids. The present paper isolates the effect of length changes and shows that R34(Θ,λ) is not very sensitive to these changes, but D(Θ,λ) is sensitive to length changes when the aspect ratio becomes small enough. In the present article, we extend our analysis to vegetative bacteria which, because of their high percentage of water, generally have a substantially lower index of refraction than spores. The parameters used for the calculations were chosen to simulate values previously measured for log-phase Escherichia coli. Each individual E. coli bacterium appears microscopically approximately like a right-circular cylinder, capped smoothly at each end by a hemisphere of the same diameter. With the present model we focus particular attention on determining the effect, if any, of length changes on the graphs of D(Θ,λ) and R34(Θ,λ). We study what happens to these two functions when the diameters of the bacteria remain constant and their basic shape remains that of a capped cylinder, but with total length changed by reducing the length of the cylindrical part of each cell. This approach also allows a test of the model, since the limiting case as the length of the cylindrical part approaches zero is exactly a sphere, which is known to give a value identically equal to zero for D(Θ,λ) but not for R34(Θ,λ).

© 2009 Optical Society of America

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References

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    [CrossRef] [PubMed]
  3. S. D. Druger, J. Czege, Z. Z. Li, and B. V. Bronk, “Calculations of light scattering measurements predicting sensitivity of depolarization to shape changes of spores and bacteria,” Tech. Rep. ECBC-TR-607 (Edgewood Chemical Biological Center, 2008).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  13. E. Arakawa, P. S. Tuminello, B. N. Khare, and M. E. Milham, “Optical properties of ovalbumin in 0.130-2.50 μm spectral region,” Biopolymers 62, 122-128 (2001).
    [CrossRef] [PubMed]
  14. E. T. Arakawa, P. S. Tuminello, B. N. Khare, and M. E. Milham, “Optical properties of Erwinia herbicola bacteria at 0.190-2.50 micron,” Biopolymers 72, 391-398(2003).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]

2009 (1)

2006 (3)

2004 (1)

2003 (1)

E. T. Arakawa, P. S. Tuminello, B. N. Khare, and M. E. Milham, “Optical properties of Erwinia herbicola bacteria at 0.190-2.50 micron,” Biopolymers 72, 391-398(2003).
[CrossRef] [PubMed]

2001 (1)

E. Arakawa, P. S. Tuminello, B. N. Khare, and M. E. Milham, “Optical properties of ovalbumin in 0.130-2.50 μm spectral region,” Biopolymers 62, 122-128 (2001).
[CrossRef] [PubMed]

1999 (1)

1995 (1)

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

1994 (1)

1992 (1)

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

1973 (2)

G. M. Hale and M. R. Querry, “Optical constants of water in the 200 nm to 200 micrometer wavelength region,” Appl. Opt. 12, 555-563 (1973).
[CrossRef] [PubMed]

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705-714 (1973).
[CrossRef]

Arakawa, E.

E. Arakawa, P. S. Tuminello, B. N. Khare, and M. E. Milham, “Optical properties of ovalbumin in 0.130-2.50 μm spectral region,” Biopolymers 62, 122-128 (2001).
[CrossRef] [PubMed]

Arakawa, E. T.

E. T. Arakawa, P. S. Tuminello, B. N. Khare, and M. E. Milham, “Optical properties of Erwinia herbicola bacteria at 0.190-2.50 micron,” Biopolymers 72, 391-398(2003).
[CrossRef] [PubMed]

Bohren, C. F.

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

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983), 383, pp. 65-67.

Bronk, B. V.

S. D. Druger, J. Czege, Z. Z. Li, and B. V. Bronk, “Light scattering calculations exploring sensitivity of depolarization to shape changes for: I. Single spores in air,” Appl. Opt. 48, 716-724 (2009). Note: the values used for the indices of refraction for Bacillus cereus spores were mistakenly attributed by one of us (BVB) to M. Querry and M. Milham. The experimental data were actually due to P. S. Tuminello, M. E. Milham, B. N. Khare, and E. T. Arakawa.
[CrossRef] [PubMed]

W. P. Van De Merwe, J. Czege, M. E. Milham, and B. V. Bronk, “Rapid optically based measurements of diameter and length for spherical or rod-shaped bacteria in vivo,” Appl. Opt. 43, 5295-5302 (2004).
[CrossRef] [PubMed]

S. D. Druger and B. V. Bronk, “Internal and scattered electric fields in the discrete dipole approximation,” J. Opt. Soc. Am. B 16, 2239-2246 (1999).
[CrossRef]

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

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

S. D. Druger, J. Czege, Z. Z. Li, and B. V. Bronk, “Calculations of light scattering measurements predicting sensitivity of depolarization to shape changes of spores and bacteria,” Tech. Rep. ECBC-TR-607 (Edgewood Chemical Biological Center, 2008).

Czege, J.

Czégé, J.

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

Draine, B. T.

Druger, S. D.

Flatau, P. J.

Hale, G. M.

Hoekstra, A. G.

Huffman, D. R.

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

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983), 383, pp. 65-67.

Kattawar, G. W.

Khare, B. N.

E. T. Arakawa, P. S. Tuminello, B. N. Khare, and M. E. Milham, “Optical properties of Erwinia herbicola bacteria at 0.190-2.50 micron,” Biopolymers 72, 391-398(2003).
[CrossRef] [PubMed]

E. Arakawa, P. S. Tuminello, B. N. Khare, and M. E. Milham, “Optical properties of ovalbumin in 0.130-2.50 μm spectral region,” Biopolymers 62, 122-128 (2001).
[CrossRef] [PubMed]

Li, C.

Li, Z. Z.

Maltsev, V. P.

Milham, M. E.

W. P. Van De Merwe, J. Czege, M. E. Milham, and B. V. Bronk, “Rapid optically based measurements of diameter and length for spherical or rod-shaped bacteria in vivo,” Appl. Opt. 43, 5295-5302 (2004).
[CrossRef] [PubMed]

E. T. Arakawa, P. S. Tuminello, B. N. Khare, and M. E. Milham, “Optical properties of Erwinia herbicola bacteria at 0.190-2.50 micron,” Biopolymers 72, 391-398(2003).
[CrossRef] [PubMed]

E. Arakawa, P. S. Tuminello, B. N. Khare, and M. E. Milham, “Optical properties of ovalbumin in 0.130-2.50 μm spectral region,” Biopolymers 62, 122-128 (2001).
[CrossRef] [PubMed]

Pennypacker, C. R.

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705-714 (1973).
[CrossRef]

Purcell, E. M.

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705-714 (1973).
[CrossRef]

Querry, M. R.

Stanley, M.

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

Tuminello, P. S.

E. T. Arakawa, P. S. Tuminello, B. N. Khare, and M. E. Milham, “Optical properties of Erwinia herbicola bacteria at 0.190-2.50 micron,” Biopolymers 72, 391-398(2003).
[CrossRef] [PubMed]

E. Arakawa, P. S. Tuminello, B. N. Khare, and M. E. Milham, “Optical properties of ovalbumin in 0.130-2.50 μm spectral region,” Biopolymers 62, 122-128 (2001).
[CrossRef] [PubMed]

Van De Merwe, W. P.

W. P. Van De Merwe, J. Czege, M. E. Milham, and B. V. Bronk, “Rapid optically based measurements of diameter and length for spherical or rod-shaped bacteria in vivo,” Appl. Opt. 43, 5295-5302 (2004).
[CrossRef] [PubMed]

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

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

Yang, P.

You, Y.

Yurkin, M. A.

Appl. Opt. (4)

Astrophys. J. (1)

E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705-714 (1973).
[CrossRef]

Biophys. J. (1)

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

Biopolymers (2)

E. Arakawa, P. S. Tuminello, B. N. Khare, and M. E. Milham, “Optical properties of ovalbumin in 0.130-2.50 μm spectral region,” Biopolymers 62, 122-128 (2001).
[CrossRef] [PubMed]

E. T. Arakawa, P. S. Tuminello, B. N. Khare, and M. E. Milham, “Optical properties of Erwinia herbicola bacteria at 0.190-2.50 micron,” Biopolymers 72, 391-398(2003).
[CrossRef] [PubMed]

Cytometry (1)

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

J. Opt. Soc. Am. A (3)

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

Other (3)

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

S. D. Druger, J. Czege, Z. Z. Li, and B. V. Bronk, “Calculations of light scattering measurements predicting sensitivity of depolarization to shape changes of spores and bacteria,” Tech. Rep. ECBC-TR-607 (Edgewood Chemical Biological Center, 2008).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983), 383, pp. 65-67.

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Figures (11)

Fig. 1
Fig. 1

Length distribution for log-phase E. coli B/r.

Fig. 2
Fig. 2

Graphs of the depolarization ratio versus angle for scattering wavelength 1.328 μm for a “dipole sphere” of diameter 1.2 μm , refractive index 1.373, at orientation angles ϕ = 57 ° , θ = 17 ° modeled with either 1021 dipoles or 8025 dipoles as indicated. The values of the parameter Y in Eq. (1) are 0.628 for 1021 dipoles and 0.314 for 8025. The values of D ( Θ , λ ) calculated for orientation angles Θ = ϕ = 0 coincide with the horizontal axis on the scale of this graph because of the symmetrical dipole placement. For the other orientation, D ( Θ , λ ) approaches zero as predicted for increasing dipole number.

Fig. 3
Fig. 3

Results on a (a) linear scale and (b) logarithmic scale for D ( Θ , λ ) averaged over orientations for both the capped cylinder with a shape close to spherical ( L = 1.5 μm ; d = 1.2 μm ) and for the pseudosphere for n = 1.373 with λ = 1.328 μm in both cases. The calculations used 8829 dipoles for the sphere and 10,719 dipoles for the capped cylinder, giving a Y value in Eq. (1) of about 0.3 in both cases. The values for the sphere are close to the correct value of zero showing that Eq. (1) is adequate on the scale of the linear graph. For a short capped cylinder, the calculated values of D become small but nonzero as they should in approaching the limiting zero value.

Fig. 4
Fig. 4

Graph of the ratio R 34 ( Θ , λ ) versus Θ for a sphere of di ameter 1.2 μm and n = 1.373 and λ = 1.328 μm , from calculations using the DDA model with 8025 dipoles at two different orientations. Either orientation of the pseudosphere of dipoles is seen to produce a result close to the graph resulting from the exact Mie solution.

Fig. 5
Fig. 5

D ( Θ , λ ) versus Θ for models A, B, C, and D from Table 1 with fixed diameter = 0.8 μm and averages over the length distribution for each set as well as an orientation average, with λ = 1.266 μm . Average lengths for each distribution are indicated in the figure.

Fig. 6
Fig. 6

D ( Θ , λ ) versus Θ is shown for vegetative cells having individual lengths from sets A and B with fixed diameter of 0.8 μm for (a)  n = 1.37 (vegetative bacteria) and (b)  n = 1.505 (spores). The averaging was over orientation only. The length for each calculation is shown in the figure. The scattering wavelength for both figures is 1.266 μm .

Fig. 7
Fig. 7

(a)  R 34 ( Θ , λ ) for n = 1.37 and λ = 1.266 μm averaged over orientation and length for the four model sets of Table 1 with fixed diameter of 0.8 μm . The average length for each set is indicated in the graph. (b) Graphs are shown for same function and parameters used for the single lengths indicated (with orientation averaging only).

Fig. 8
Fig. 8

Orientation averaged (a)  D ( Θ , λ ) and (b)  R 34 ( Θ , λ ) , both calculated for n = 1.374 with λ = 1.266 μm for a single fixed length, L = 5.5 μm and varying diameters. The radius, R, of the cylinder is indicated for each calculation.

Fig. 9
Fig. 9

Depolarization ratio, orientation averaged for capped cylinders of diameter 0.65 μm for several single short lengths as shown using n = 1.374 and λ = 1.266 μm .

Fig. 10
Fig. 10

Uncorrelated averages of D ( Θ , λ ) over all lengths and diameters for length sets A (short) are denoted by a dashed line and length set D (long) are denoted by a solid line with weightings as indicated in Table 3. The averages were also over orientations. The index and wavelength were n = 1.374 and λ = 1.266 μm . The same diameter distribution is assumed for both length sets.

Fig. 11
Fig. 11

Uncorrelated averages over all lengths and diameters for R 34 ( Θ , λ ) with weightings as indicated in Table 3. Averages are over orientations also. The short bacteria are set A denoted by the dashed line. The long bacteria are set D denoted by the solid line. The same diameter distribution is assumed for both sets.

Tables (3)

Tables Icon

Table 1 Length Distribution for Log-Phase E. coli B/r Grown in a Minimal Medium [5, 6, 7] and Similar Length Distributions Used in Modeling

Tables Icon

Table 2 Diameter Distribution for Log-Phase E. coli B/r Grown in a Minimal Medium [5, 6] and Similar One for Models Used in Present Paper

Tables Icon

Table 3 Weightings for Uncorrelated Averages over the Lengths of Model Sets A and D, Table 1, Together with the Model Diameters of Table 2 a

Equations (2)

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Y = n k a < 1 2
V = π r 2 ( L 2 r / 3 ) ,

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