Abstract

Calculations of the depolarization ratio, D(Θ,λ)=1S22/S11, for light scattered from an ensemble or cloud of single aerosolized spores in air were studied using the discrete dipole approximation (DDA), sometimes also called the coupled-dipole approximation. Here Sij is the appropriate Mueller matrix element for scattering angle Θ and wavelength λ. The effect of modest shape changes on D(Θ,λ) was determined. The shapes compared were prolate ellipsoids versus right circular cylinders joined smoothly to end caps consisting of hemispheres of the same diameter as the cylinder. Using the same models, the graphs of S34/S11 versus angle were compared with those for D(Θ,λ). The latter shows sensitivity to length in some cases we examined, while S34/S11 does not. Size parameters and optical constants suggested by measurements of Bacillus cereus endospores were used. An ensemble of spores was modeled with prolate spheroids. The results of this model were compared with results of a model using the same size and optical parameters, but for capped cylinders. The two models produced distinguishably different results for the same parameters. In calculations for all the graphs shown, averaging over random orientations was performed. Averaging over size distributions similar to those from experimental measurements was performed where indicated. The results show that measurements of D(Θ,λ) could be quite useful in characterizing the shape of particles in an unknown aerosol and for distinguishing between two likely shapes, but not to reconstruct the shapes from the graphs alone without additional information.

© 2009 Optical Society of America

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2006 (2)

2004 (2)

1999 (1)

1998 (1)

M. I. Mischenko and K. Sassen, “Depolarization of lidar returns by small ice crystals: an application to contrails,” Geophys. Res. Lett. 25, 309-312 (1998).
[CrossRef]

1995 (1)

B. V. Bronk, S. D. Druger, J. Czege, and 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]

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 (1)

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

Bohren, C. F.

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

Bronk, B. V.

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. Czege, and 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, 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. Czege and B. V. Bronk, “Process and apparatus for measurements of Mueller matrix parameters of polarized light scattering,” International Patent application PCT/US2006/03846, filing date 10 March 2006. U.S. patent applied for.

S. 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,” ECBC-TR-607 (Edgewood Chemical Biological Center, Aberdeen Proving Ground, April 2008).

Czege, J.

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. Czege, and 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]

J. Czege and B. V. Bronk, “Process and apparatus for measurements of Mueller matrix parameters of polarized light scattering,” International Patent application PCT/US2006/03846, filing date 10 March 2006. U.S. patent applied for.

S. 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,” ECBC-TR-607 (Edgewood Chemical Biological Center, Aberdeen Proving Ground, April 2008).

Donovan, D. P.

Draine, B. T.

Druger, S.

S. 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,” ECBC-TR-607 (Edgewood Chemical Biological Center, Aberdeen Proving Ground, April 2008).

Druger, S. D.

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. Czege, and 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]

Flatau, P. J.

Hoekstra, A. G.

Huffman, D. R.

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

Kattawar, G. W.

Li, C.

Li, Z. Z.

S. 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,” ECBC-TR-607 (Edgewood Chemical Biological Center, Aberdeen Proving Ground, April 2008).

Macke, A.

Maltsev, V. P.

Milham, M. E.

Mischenko, M. I.

M. I. Mischenko and K. Sassen, “Depolarization of lidar returns by small ice crystals: an application to contrails,” Geophys. Res. Lett. 25, 309-312 (1998).
[CrossRef]

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]

Quante, M.

Querry, M. R.

M. R. Querry and M. E. Milham, Dectection Science Consulting, 13803 Manor Glen Road, Baldwin, Md. 21012 (personal communication, 2006).

Sassen, K.

M. I. Mischenko and K. Sassen, “Depolarization of lidar returns by small ice crystals: an application to contrails,” Geophys. Res. Lett. 25, 309-312 (1998).
[CrossRef]

Schlimme, I.

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]

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. Czege, and 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, 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. (3)

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. Czege, and 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, 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]

Geophys. Res. Lett. (1)

M. I. Mischenko and K. Sassen, “Depolarization of lidar returns by small ice crystals: an application to contrails,” Geophys. Res. Lett. 25, 309-312 (1998).
[CrossRef]

J. Opt. Soc. Am. A (2)

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

Other (4)

S. 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,” ECBC-TR-607 (Edgewood Chemical Biological Center, Aberdeen Proving Ground, April 2008).

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

M. R. Querry and M. E. Milham, Dectection Science Consulting, 13803 Manor Glen Road, Baldwin, Md. 21012 (personal communication, 2006).

J. Czege and B. V. Bronk, “Process and apparatus for measurements of Mueller matrix parameters of polarized light scattering,” International Patent application PCT/US2006/03846, filing date 10 March 2006. U.S. patent applied for.

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Figures (10)

Fig. 1
Fig. 1

(a) Transmission electron micrograph of Bacillus cereus spores with a 2 μm polystyrene sphere on bottom left used to calibrate exact magnification. Only frames with such a sphere were used, so that the calibration was accurate. (b) A few of these spores better isolated and enlarged to show shape. The translucent material around the spores is from the exosporium, which is peculiar to spores of only a few species of Bacilli.

Fig. 2
Fig. 2

(a) Lognormal fit to length and (b) diameter distribution from TEM measurements for Bacillus cereus spores.

Fig. 3
Fig. 3

Depolarization ratio for a capped cylinder of length 1.5 μm and radius 0.35 μm averaged over orientation only, with a scattering wavelength of 1.551 μm and n = 1.503 + 0.000402 i . The two graphs are not distinguishable on this scale, which shows an adequacy of orientation averaging over a 9 × 15 grid.

Fig. 4
Fig. 4

Mueller matrix element (a)  S 11 and (b)  S 22 for an ensemble of spores averaged only over orientations for the single size spore with a length of 0.975 μm , and a diameter or minor axis of 0.54 μm . The scattering wavelength is 800 nm . Results for both models are shown.

Fig. 5
Fig. 5

Graphs scaled linearly for Mueller matrix elements S 11 and S 22 for the capped cylinder model only, for an ensemble of spores averaged only over orientations for the single size spore with a length of 0.975 μm , and diameters of either (a)  0.54 μm or (b)  0.75 μm . The scattering wavelength is 800 nm . Corresponding graphs of D ( Θ , λ ) are shown in Figs. 6, 8.

Fig. 6
Fig. 6

(a) Depolarization ratio for an ensemble of spores of single size with a length of 0.975 μm and a diameter or minor axis of 0.54 μm averaged only over orientation. The scattering wavelength is 800 nm . (b)  S 34 / S 11 for spores with the same parameters averaged over orientation.

Fig. 7
Fig. 7

(a)  D ( Θ , λ ) for a model spore of length 1.5375 μm and a diameter or minor axis of 0.75 μm . (b)  S 34 / S 11 . Both graphs are averaged over spore orientation. The scattering wavelength is 800 nm .

Fig. 8
Fig. 8

(a)  D ( Θ , λ ) for spore models of length 0.975 μm and width 0.75 μm . (b)  S 34 / S 11 for this case. Both graphs are for averages over spore orientation. The scattering wavelength is 800 nm .

Fig. 9
Fig. 9

Graphs are shown for scattering wavelength 800 nm for (a)  D ( Θ , λ ) and (b)  S 34 / S 11 . Weighted correlated averages were taken over a sporelike size distribution as in the model distribution given in Table 1. The orientation average was over a 9 × 15 grid.

Fig. 10
Fig. 10

Graphs for backscattering ( Θ = 180 ° ) depolarization ratio versus wavelength for the two particle shape models of single spores, both models averaged for size and orientation with the correlated experimental B. cereus spore parameters of Table 1. From the left, the wavelengths are 266, 355, 410, 750, 1551, and 3389 nm . The backscatter results for both models overlap at 410 nm , and also at 3389 nm .

Tables (2)

Tables Icon

Table 1 Diameter and Length Distributions

Tables Icon

Table 2 Index of Refraction of B. cereus Spores at Representative Wavelengths

Equations (9)

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S i j = I β I S i j I ,
( E s E s ) = e i k ( r z ) i k r ( S 2 S 3 S 4 S 1 ) ( E i E i ) .
( I s Q s U s V s ) = 1 k 2 r 2 ( S 11 S 12 S 13 S 14 S 21 S 22 S 23 S 24 S 31 S 32 S 33 S 34 S 41 S 42 S 43 S 44 ) ( I i Q i U i V i ) .
D ( Θ , λ ) = 1 S 22 S 11 ,
S 11 = 1 2 ( | S 1 | 2 + | S 2 | 2 + | S 3 | 2 + | S 4 | 2 ) ,
S 22 = 1 2 ( | S 1 | 2 + | S 2 | 2 | S 3 | 2 | S 4 | 2 ) .
α = 3 4 M π n 2 1 n 2 + 2 ,
Y = n k s < 1 2
( x / a ) 2 + ( y / a ) 2 + ( z / b ) 2 1 ,

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