| Popis: |
Bacteria can be said to be small particles in terms of their volume and can be modelled as near-index particles when the average refractive index of their body is close to that of the medium in which they are suspended. This is the case with water based environments whereas the bacterial scatterer is said to be a 'soft particle' and within the Rayleigh-Debye experimental bounds of applicability. However, discrepancies in the past have illustrated insufficiency of geometric assumptions, such as spherical symmetry and simplistic internal structures, as well as the assumption of 'transparency' of the particle. The aim of this work is to generalize the Rayleigh-Debye approximation in order to apply them to a wider class of not necessarily soft scatterers, hence departing from |m --- 1| < 1 to |m --- 1| < 1. We start by establishing a connection between the assumption on the functional expression of the internal field of small particles and that of the function of refractive index, to a generalisation for arbitrary number of layers within a particle of spherical symmetry. Based on the modification of the Rayleigh-Debye approximation (mRDG) with Bessel functions we proceed to formulate an extended version of the arbitrary layers particle for ellipsoidal forms. An application of this n-layer generalised mRDG to the bacterial domain optical properties via simulation, re-establishes the limits of the Rayleigh-Debye approximation as a result of the internal field modification. Finally, we consider the problem of populations of cells modelled as multilayered geometrical structure, consistent with assumptions from bacteriology concerning size distributions and their relationship to statistical frequency functions. The latter problem is examined both when the independent scattering condition is satisfied and when it is violated, leading to increased probability of multiple scattering. Examination of ensembles of inhomogeneous particles was possible due to our generalised approximation which is essentially acting on any infinitesimal volume, within the boundaries of the said layered structured particles, and is the main result of this work. The mathematical treatment presented within this thesis acts as an extension of the known near-index techniques in the theory of scattering for unlimited number of layers and internal distributions of refractive index. |
