Light scattering calculations exploring sensitivity of depolarization ratio to shape changes. II. Single rod-shaped vegetative bacteria in air.

In article I of this series, calculations and graphs of the depolarization ratio, D(Theta,lambda)=1-/, 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(Theta,lambda) and the ratio R34(Theta,lambda)=/. The ratio R34(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 R34(Theta,lambda) is not very sensitive to these changes, but D(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(Theta,lambda) and R34(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(Theta,lambda) but not for R34(Theta,lambda).

Light scattering calculations exploring sensitivity of depolarization ratio to shape changes. I. Single spores in air.

Calculations of the depolarization ratio, D(Theta, lambda) = 1 - (S22)/(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 S(ij) is the appropriate Mueller matrix element for scattering angle Theta and wavelength lambda. The effect of modest shape changes on D(Theta, lambda) 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(Theta, lambda). 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(Theta, lambda) 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.