Effect of Particle Shape Irregularities on the Angular Profiles of Scattering Matrix Elements (2002)

We discuss a methodology to determine the scattering characteristics of irregular-shaped particles. We concentrate on particles with sharp edges and broken corners in order to simulate actual ceramic and metallic particles. A volume-integral formulation (encoded in AGGLOME) is used to determine the angular profiles of their scattering matrix elements. A compendium of results is given in a series of figures. These numerical results show that if the scattering matrix elements of such irregular shaped particles are measured in carefully conducted experiments at specified angular regions, their shapes and sizes can be inferred. INTRODUCTION Characterization of size and structure of small particles is required in many fields, including process control and monitoring, biological and pharmaceutical research, atmospheric remote sensing, environmental pollution detection, as well as combustion systems. During the last decade, using the elliptically polarized light scattering concept, we have investigated spherical and cylindrical particles, as well as agglomerates. This approach is based on the measurement of the scattering matrix elements of single scatterers and is known to be the most comprehensive particle characterization methodology. There are several accounts available in the literature that focus on calculation of the irregular shaped particle properties. A detailed review of past models was given in a book compiled by Mischenko et al. and was recently the focus of a conference dedicated to light scattering techniques. Unfortunately, the data available for the scattering matrix elements of irregular shaped particles are quite limited. In this paper, we extend the available data base to irregularly shaped particles. Below, we discuss the ________________________ †Ph. D. Candidate, Radiative Transfer Laboratory ‡Professor, Radiative Transfer Laboratory, menguc@engr.uky.edu effects of shape, size, degree of irregularity, the complex index of refraction, and wavelength on the scattering matrix elements of cubical, rectangularpiped, and pyramidal particles. These structures are quite common in practice, as the lattice structure of metallic compounds favor formation of these shapes. In addition, imperfections in a given process, as well as natural grinding and collision between the particles, yield broken structures. It is imperative to understand the effect of shape and imperfections on the scattering signals from these particles in order to characterize these particles via light scattering techniques. ANALYSIS AND FORMULATION The analysis we present here is based on the measurement of the polarization of the scattered light by a cloud of particles. If we know how a given particle changes the polarization of incident light, then we can use that information as its “fingerprints” and estimate the shape variations. To do this, we need to understand the relationship between the change in polarization of the incident and scattered waves. The polarization state of a beam can be described as a column vector of the four Stokes parameters. Here, for clarity, we omit the multiplicative factor k/2ωμ, and use the brackets to indicate the time-averages: These four parameters can be obtained by using a set of four filters in front of the incident beam. If the first filter is isotropic, it allows all the energy to go through. The other three are polarizing filters: the second one is a linear polarizer oriented horizontally, the third is a linear polarizer oriented at 45 degrees from horizontal in the clockwise direction, and the fourth is a circular polarizer. By measuring the irradiance that passes * // * // * // * // * * // // * * // // E E E E i V E E E E U E E E E Q E E E E I