Accuracy of RGD approximation for computing light scattering properties of diffusing and motile bacteria

The quasi-elastic light scattering has become an established technique for a rapid and quantitative characterization of an average motility pattern of motile bacteria in suspensions. Essentially all interpretations of the measured light scattering intensities and spectra so far are based on the Rayleigh-Gans-Debye (RGD) approximation. Since the range of sizes of bacteria of interest is generally larger than the wavelength of light used in the measurement, one is not certain of the justification for the use of the RGD approximation. In this paper we formulate a method by which both the scattering intensity and the quasi-elastic light scattering spectra can be calculated from a rigorous scattering theory. For a specific application we study the case of bacteria Escherichia coli (about 1 microm in size) by using numerical solutions of the scattering field amplitudes from a prolate spheroid, which is known to simulate optical properties of the bacteria well. We have computed (1) polarized scattered light intensity vs scattering angle for a randomly oriented bacteria population; (2) polarized scattered field correlation functions for both a freely diffusing bacterium and for a bacterium undergoing a straight line motion in random directions and with a Maxwellian speed distribution; and (3) the corresponding depolarized scattered intensity and field correlation functions. In each case sensitivity of the result to variations of the index of refraction and size of the bacterium is investigated. The conclusion is that within a reasonable range of parameters applicable to E. coli, the accuracy of the RGD is good to within 10% at all angles for the properties (1) and (2), and the depolarized contributions in (3) are generally very small.