Scattering Lorenz-Mie

Figure 7-41 Far-field Lorenz-Mie scattered light intensity distribution, characterizing the primary, monochromatic rainbow (van Beeck and Riethmuller 1996 a)).

Scattering by a Uniform Dielectric Sphere (Lorenz-Mie Scattering)... 

The angular distribution for Lorenz-Mie scattering by a uniform dielectric sphere is illustrated in Fig.4.1 where the incident radiation of wavelength X = 488 nm is scattered by a uniform dielectric sphere of radius a and refractive index, m = 1.5 relative to the external medium. Curves are drawn for various values of the sphere s size parameter (a = Zira/x). 

The coherent inelastic scattering and Lorenz-Mie scattering are compared in Figs. 4.15-17 for three values of the size parameter a. Results are given for the incident radiation polarized both parallel and perpendicular to the scattering plane. There... 

Fig.4.15. Coherent inelastic scattering Ij and the corresponding Lorenz-Mie scattering are plotted vs scattering angle a = 1 and mi = 1.5...

Several theories have been developed to explain the rainbow phenomena, including the Lorenz-Mie theory, Airy s theory, the complex angular momentum theory that provides an approximation to the Lorenz-Mie theory, and the theory based on Huy gen s principle. Among these theories, only the Lorenz-Mie theory provides an exact solution for the scattering of electromagnetic waves by a spherical particle. The implementation of the rainbow thermometry for droplet temperature measurement necessitates two functional relationships. One relates the rainbow angle to the droplet refractive index and size, and the other describes the dependence of the refractive index on temperature of the liquid of interest. The former can be calculated on the basis of the Lorenz-Mie theory, whereas the latter may be either found in reference handbooks/literature or calibrated in laboratory. 

The angular scattering approach is the principal aim of this work. The properties of the Lorenz-Mie intensity coefficients are treated in some detail in order to illustrate their utilization for the determination of particle size distribution, refractive index and number concentration. In a related paper the internal structure of polymer latex spheres is considered (8 ). ... 

Early instruments employed low (forward) angle laser light scattering (LALLS) but these have been replaced by multi-angle instruments. MALLS instruments use Lorenz-Mie (often referred to as Mie) theory or Fraunhofer diffraction theory. 

If the agglomeration is not considered, calculation of required radiative properties of soot particles will be straightforward. Since the size of an individual soot sphere is much smaller than the wavelength of radiation, the Rayleigh limit (for small x = kD/X) to the Lorenz-Mie theory can be used. Then, the soot absorption and scattering efficiency factors are given as... 

Laser Induced Fluorescence (LIF) and Scattering Methods (Lorenz-Mie, Rayleigh, Raman)... 

Long, M.B., Multi-Dimensional Imaging in Combusting Flows by Lorenz-Mie, Rayleigh and Raman Scattering, Instrumentation for Flows with Combustion (Taylor, A.M.P.K., ed.), Academic Press, 468-508 (1993). 

The general elastically scattered field of the sphere is calculated by the Lorenz-Mie theory and is denoted ra)-... 

The turbidity of a highly dilute latex sample will provide information about the number and/or size of the polymer particles. If the system is sufficiently dilute to preclude multiple scattering, the turbidity at various wavelengths may be related to the concentration and size of the polymer panicles by Lorenz-Mie theory (see Section 12.3.2). This has been done by Heller and co-workers [31,32]. Since the method involves only sample dilution followed by turbidity analysis by a UV-visible spectrophotometer, it is a natural choice for continuous, online use. 

The complexity of the problem is illustrated in Figure 12.6, which shows a three-dimensional plot of the scattering envelope. Exact solutions to the Lorenz-Mie equations have, thus far, been limited to spheres and oriented ellipsoids. There are, however, well-known limiting cases, namely, Rayleigh scattering, Mie scattering and diffraction scattering. 

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