In article I of this series, calculations and graphs of the depolarization ratio, $D(\mathrm{\Theta },\lambda )=1-<S_{22}>/<S_{11}>$ , 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 $D(\mathrm{\Theta },\lambda )$ and the ratio $R_{34}(\mathrm{\Theta },\lambda )=<S_{34}>/<S_{11}>$ . The ratio $R_{34}(\mathrm{\Theta },\lambda )$ 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 $R_{34}(\mathrm{\Theta },\lambda )$ is not very sensitive to these changes, but $D(\mathrm{\Theta },\lambda )$ 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 $D(\mathrm{\Theta },\lambda )$ and $R_{34}(\mathrm{\Theta },\lambda )$ . 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 $D(\mathrm{\Theta },\lambda )$ but not for $R_{34}(\mathrm{\Theta },\lambda )$ .

© 2009 Optical Society of America

1. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
2. 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]
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).
4. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983), 383, pp. 65-67.
5. 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]
6. 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]
7. 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]
8. Y. You, G. W. Kattawar, C. Li, and P. Yang, “Internal dipole radiation as a tool for particle identification,” Appl. Opt. 45, 9115-9124 (2006). [CrossRef] [PubMed]
9. B. T. Draine and P. J. Flatau, “Discrete dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491-1499(1994). [CrossRef]
10. M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “ I. Theoretical effects,” J. Opt. Soc. Am. A 23, 2578-2591 (2006). [CrossRef]
11. M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “Convergence of the discrete dipole approximation. II. An extrapolation technique to increase the accuracy,” J. Opt. Soc. Am. A 23, 2592-2601 (2006). [CrossRef]
12. 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]
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]
15. E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705-714 (1973). [CrossRef]
16. 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]

Appl. Opt.

• 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]
• Y. You, G. W. Kattawar, C. Li, and P. Yang, “Internal dipole radiation as a tool for particle identification,” Appl. Opt. 45, 9115-9124 (2006). [CrossRef] [PubMed]
• 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]

Astrophys. J.

• 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.

• 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

• 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

• 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

• B. T. Draine and P. J. Flatau, “Discrete dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491-1499(1994). [CrossRef]
• M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “ I. Theoretical effects,” J. Opt. Soc. Am. A 23, 2578-2591 (2006). [CrossRef]
• M. A. Yurkin, V. P. Maltsev, and A. G. Hoekstra, “Convergence of the discrete dipole approximation. II. An extrapolation technique to increase the accuracy,” J. Opt. Soc. Am. A 23, 2592-2601 (2006). [CrossRef]

J. Opt. Soc. Am. B

• 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]

Other

• 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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