Lorenz—Mie theory

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. 

We are grateful to Mr. R. N. Rowell for assistance in the preparation of magnetic tape records of the Lorenz-Mie theory computations which were carried out at the University of Massachusetts Computer Center. The tape records were used under the direction of M. L. Prueitt with his program PICTURE at the University of California Los Alamos Scientific Laboratory to generate the computer-drawn perspective graphs. The work was supported in part by grants from the National Science Foundation. 

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... 

Fly Ash Particles. When coal particles burn in a combustion system, the ash present in coal coalesces into small micron- and submicron-sized particles and are carried throughout the system [240]. It has been shown that the shape of the fly ash particles in combustion chambers is primarily spherical. This suggests that, if the complex index of refraction of fly ash particles is known, the Lorenz-Mie theory can be used to determine the required radiative properties. 

Figure 7-36 Computed phase/diameter relations for conventional and planar PDA in a dual-mode PDA (Tropea et al. 1996), (GLMT generalized Lorenz-Mie theory, GO. geometrical optics, SPDA standard PDA, PPDA planar PDA)...

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. 

Pottier et al. (2005) predicted the radiation characteristics of C. reinhardtii using the Lorenz-Mie theory assuming that (i) the cells were homogeneous and spherical, (ii) the refractive index was constant over the PAR and equal to 1.55, and (iii) the absorption index was given by... 

Lorenz—Mie theory predicts the absorption Cabs,x and scattering cross-... 

Fig. 7 compares the experimentally measured (A and C) absorption Cahs,x and (B and D) scattering Csca,x cross-sections between 400 and 700 nm of monodisperse latex spheres 2.02 and 4.5 pm diameter with Lorenz—Mie theory predictions using the complex index of refraction of latex reported by Ma et al. (2003). Flere also, the good agreement between theoretical and experimental results successfully validated the experimental setup and the data analysis. Similar vaHdation has been performed with the same polydisperse polystyrene latex microspheres and randomly oriented and infinitely long glass fibers considered for validating the scattering phase function measurements, as illustrated in Fig. 6 (Berberoglu and Pilon, 2007).

Figure 7 Experimental measurement and Lorenz-Mie theory predictions of the average absorption Cabs,i and scattering Csca,i cross-sections between 400 and 700 nm of monodisperse polystyrene latex microspheres with diameters d equal to (A and B) 2.02 pm and (C and D) 4.5 pm, respectively (Kandilian, 2014).

The model of inelastic scattering described in this chapter is based upon the assumption that the active molecule can be represented by a classical oscillating electric dipole whose strength is determined by the strength of the local field at the exciting frequency given by the Lorenz-Mie theory. These assumptions should be reasonable for many molecules embedded in weakly absorbing particles. Recent experiments on fluorescence confirm the qualitative features predicted by the model. 

Figure 4-49 Ray traces indicating the three significant modes of scattaing—reflection and first- and second-order refraction—for a water droplet (top) light scattering of a Gaussian beam from a water droplet, simulated using the Fouiia- Lorenz-Mie theory (bottom courtesy of C. Tropea and N. Damaschke, Technische Universitat Darmstadt,...

---