Measurement of aerosol size distribution function using Mie scattering—Mathematical considerations

Information content of scattering measurements and characterization of spheroids

“…Obviously, R i defined this way provides a quantitative indicator of the overall dependence of the ith kernel function at the i 's selected. Furthermore, this definition is consistent with our previous work (Ma, 2007) and can be tailored flexibly to fit different applications. When the range of narrows (i.e., when min approaches max ), Eq.…”

“…Mathematically, such redundancy occurs when the kernel functions, S i 's, are not mutually independent. Therefore, such experimental redundancy can be avoided by analyzing the inter-dependency of the kernel functions involved (Ma, 2007).…”

“…In the case where the shapes of the spheroidal scatters are monodispersed and known a priori (i.e., is fixed and known), as assumed so far, the approach described in Ma (2007) for spherical scatterers can be adopted with minor modification for the analysis of spheroidal scatterers. More specifically, the difference between a kernel function, S i , and its approximation by linear combination of the other kernel functions, can be quantified by the minimum value of the following expression (with respect to w 1 , w 2 , ... , and w N , the weights used in the linear combination):…”

“…In a previous paper (Ma, 2007), a method was developed to analyze the information content of Mie scattering measurements when applied to the determination of SDF of spherical particles. This method involves the analysis of the dependency among the kernel functions (i.e., the Mie extinction/scattering coefficients) and has been demonstrated to minimize the number of measurements and reveal the optimal wavelengths and angles to perform the scattering measurements.…”

Measurement and Evaluation of Elastic Light Scattering from a Single Levitated Irregular Particle

“…The Lorenz-Mie theory was a classical method to calculate the scattering properties of a single homogeneous particle. It was not only used to calculate scattering and absorption cross-sections but also the angular scattering for diameter of spherical particle, refractive index, and wavelength of incident light (De Leeuw and Lamberts, 1987;Ma, 2007;Li et al, 2012;Dlugach and Mishchenko, 2014;Han et al, 2014;Greengard et al, 2015;Briard et al, 2016). The phase function was dependent on the refractive index, the incident wavelength, and the particle size.…”