Rayleigh-Gans-Debye Approximation Research Articles

Conservative dichroism in the rayleigh—gans—debye approximation

An integral expression is given for the imaginary part −Δ n″ of the complex birefringence in the Rayleigh-Gans-Debye approximation. It is evaluated for the case of strongly aligned, isotropic, oblate, and prolate spheroidal particles in order to illustrate the dependence of Δ n″ on particle shape and size. In contrast to the Rayleigh approximation, where Δ n″ increases proportionally with the volume of the scattering particle, the RGD approximation shows that Δ n″ passes through a maximum then becomes zero at large particle sizes. The interpretation of linea dichroism measurements is discussed.

The birefringence of colloidal dispersions in the Rayleigh and anomalous diffraction approximations

A modification is proposed of the anomalous diffraction optical theory for particles sensitive to the polarization state of the incident light. It is shown how the birefringence of colloidal dispersions may be obtained from this modified theory. It is also shown that an intrinsically anisotropic sphere of arbitrary size and an anisotropic Rayleigh scatterer both possess the same type of forward scattering matrix although they have very different magnitudes of their effective polarizability anisotropy. An intrinsically anisotropic nonspherical particle in the anomalous diffraction approximation does not possess the same angular dependence of its forward scattering matrix as a Rayleigh scatterer. As in the Rayleigh—Debye—Gans approximation, there is no optical anisotropy of the particle due to its nonspherical shape in the anomalous diffraction approximation.

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.

Anisotropy of the optical polarizability in the Rayleigh—Debye—Gans approximation

Anisotropy of the optical polarizability in the Rayleigh—Debye—Gans approximation

Infrared electrooptic scattering from bacterial suspensions

Electrically induced changes in the intensity of scattered visible electromagnetic radiation, from polydisperse aqueous suspensions of rod-like bacteria, can not lead to exact information on the electrical parameters of the bacteria because the suspensions do not satisfy the Rayleigh—Gans—Debye approximation limiting conditions. However, study of scattering changes at infrared wavelengths permits detailed information on the electrical dipole moments to be obtained. Measurements have been made on suspensions of Escherichia coli and Thiobacillus ferrooxidans chosen as model systems. Both bacteria are characterized by a net induced dipole moment directed along, and a net permanent dipole moment directed across the major particle axis. By comparing data in the infrared and visible spectral regions for transient scattering changes for E. coli suspensions it appears that, as long as the preparation is sufficiently polydisperse, particle sizes can be evaluated in suitable cases using either region of the spectrum.