SESSION 8

PARTICLES RADIATION

Chairman: A.V. Nenarokomov

SCATTERING MATRIX ELEMENTS OF AGGLOMERATES: EXPERIMENTAL DATA AND THEORETICAL PREDICTIONS

S. Manickavasgam, C.A. Klusek, and M.P. Mengüç
Department of Mechanical Engineering, University of Kentucky
Lexington, KY 40506-0108, U.S.A.

ABSTRACT. Understanding the structure of small particles, such as soot agglomerates, cotton fibers, as well as small micro-organisms such as phytoplankton is crucial to the development of effective remote sensing and control algorithms. One of the most effective ways of determining the details of these structures is the use of optical diagnostics. The angular distribution of light scattered by these particles is quite sensitive to their sizes; however, it gives little clue about their structure. Light, however, has two additional properties, its polarization and its wavelength, which can be used to recover more information about the structure of the particles.

In a series of recent articles, we have outlined the theoretical approaches to determining the scattering matrix elements for different types of particles, including fractal-like soot agglomerates, cylindrical fibers, radially inhomogeneous spheres, and irregularly shaped phytoplankton [1-5]. Although these studies showed the feasibility of the approach, it is important to devise an effective experimental system which allows us to measure these elements accurately.

In this paper we present a series of results from our experiments conducted to determine the elements of the scattering (Mueller) matrix for different types of particles. As the light source, a Nd:YAG laser, operating at a wavelength of 532 nm, is used, although the experimental system is designed to cover the wavelength spectrum from 400 nm to 1900 nm. The light incident on the test cell is modulated using a polarizer and a quarter wave plate. The scattered light, after passing through another quarter wave plate and another polarizer, is collected at angular range of 30° to 150°. By changing the alignment of the polarizers and the quarter wave plates, the polarization state of both the incident and the detected light can be altered. This change allows us to identify the structure of the particles.

Figure 1 illustrates the angular variations of the matrix elements S₁₁, S₁₂, S₃₃, and S₄₄ for fractal- like soot agglomerates of different sizes. The fractal dimension D_f of the agglomerates is assumed to be 1.8, and the prefactor K_f is taken to be 8.0 or 10.0. The "sets" indicated on the figures correspond to different size distributions. The experimental data, which were obtained at three different heights in a diffusion flame, are also shown. These results show agreement between the experiments and the predictions. It is obvious that if a robust inversion algorithm is developed, we can accurately recover the fractal structure and the size distribution of the particles. If experiments are carried out over a broad wavelength range, the spectal variation of the complex index of refraction can also be recovered.

This paper will focus on the use of a new optical alignment to recover the S₃₄ element, which is the most sensitive of the matrix elements to agglomerate morphology. We will present extensive theoretical data to outline this sensitivity and discuss a new algorithm to recover the required parameters of the agglomerates.

REFERENCES

1. Govindan, R., Manickavasagam, S., and Mengüç, M. P., "Measuring the Mueller matrix elements of soot agglomerates," in Radiative Transfer I, Proceedings of the First International Symposium on Radiative Transfer, Ed. M.P. Mengüç, Begell House, pp. 280-295, 1996.
2. Manickavasagam, S., and Mengüç, M.P., "Scattering matrix elements of fractal-like soot agglomerates," Applied Optics, Vol. 36, No.6, pp. 113-1357, 1997.
3. Manickavasagam, S., and Mengüç, M.P., "Scattering matrix elements of coated infinite cylinders," submitted to Applied Optics, 1997.
4. Bhanti, D., Manickavasagam, S., and Mengüç, M.P., "Identification of non-homogeneous spherical particles from their scattering matrix elements," Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 56, No.4, pp. 591-608, 1996.
5. Mengüç, M.P., and Manickavasagam, S., "Characterization of size and structure of agglomerates and inhomogeneous particles via polarized light," International Journal of Engineering Sciences, 1997 (in press).

Figure 1. Comparison of normalized, measured angular profiles of S_ij with numerical results. D_f = 1.8; K_f = 8.0 and 10.0

MONTE CARLO SIMULATION OF LIGHT SCATTERING BY INHOMOGENEOUS SPHERES

Gerhard Göbel*, Andreas Lippek*, Thomas Wriedt**, and Klaus Bauckhage*
* Department of Chemical Engineering, University of Bremen
** Stiftung Institut für Werkstofftechnik (IWT), Bremen

Our work addresses the light scattering properties of large inhomogeneous droplets. Such particles occur during the spray drying of milk or coffee. These are processes of high relevance in food technology. The quality of the dried food powder is strongly influenced by the parameters of the spraying process (droplet size and velocity distributions). Therefore a non-intrusive on-line characterization of these systems is highly appreciated. The application of standard optical particle sizing techniques to such spray drying processes is somewhat difficult due to the fact that the particles in question are inhomogeneous. Milk (for production of milk powder) for example consists of lipid globules suspended in water. Coffee (for production of instant coffee powder) is an aqueous solution of solid coffee grains. The inhomogenities scatter and/or absorb light, which is refracted to the inside of the so called host particle. Thus the light scattering properties of the host are disturbed with respect to the homogeneous case. Diameter distributions measured e.g. with a phase Doppler anemometer are broadened with respect to the real size distribution.

Highly sophisticated approaches to the scattering of nonspherical and inhomogeneous particles have been developed in the recent past. There have been approaches to the light scattering problem of a sphere with one or more arbitrarily located inhomogenities inside a sphere. The later work well for the case of a single particle within a large host. For a larger number of scatterers inside the host numerical difficulties arise. At present none of these theories is capable of predicting the light scattering properties of the particles in question here. The number of participating particles within the large host droplet is too high for the problem to be treated as a multiple scattering. Instead it seems appropriate to regard the scattering of light by such inhomogeneous particles as a process of radiative transfer inside a participating (scattering and/or absorbing) medium with boundaries according to the shape of the scatterer.

As analytical solutions of the equation of radiative transfer are not available for boundaries required in our problem, We employ a Monte Carlo approach and follow single photons on their path through the chosen setup. The photon tracing is performed in a three dimensional geometry. Though we restrict ourselves to spherical host shape within this presentation, elliptical particle shapes in arbitrary orientation can be considered in general. The photon start position and orientation can be chosen to yield either a plane wave or a Gaussian beam profile and arbitrary initial states of polarization. Fresnel-formulas are employed at the tangential surface at the point, where the photon hits the host's boundary in order to decide for the photon to be reflected or refracted. Therefore the host size parameter has to be chosen large enough to allow the laws of geometrical optics to be applied.

We use Mie's theory to describe the scattering of the suspended inhomogeneities. From their size d_inh, index of refraction n + i k relative to the host material, and their number concentration c, the mean free photon path is evaluated. By means of a random process the photon path lengths between succeeding scattering processes are chosen to yield on the average. The well known Henyey Greenstein phase function is used to describe the angular scattering by the inhomogenities, i.e. the change of the photon propagation direction, though the value for the asymmetry parameter g of the single scattering process is taken from Mie calculations. The final data evaluation is performed with respect to scattering angle, state of polarization, and scattering order. Scattering orders higher than third order refraction are rare and therefore not treated separately. Diffraction is not considered.

Other than in many Monte-Carlo simulations of radiative transfer processes we have to correctly trace the phase of the individual photons in order to yield the undisturbed scattering properties - according to the underlying geometrical optics approach - within the limit of vanishing concentration of inhomogenities. This is one of two limiting cases to our simulation. The second limiting case is given by Schoenberg's solution for the scattering pattern of a large sphere with a diffusely reflecting (Lambert) surface. A sphere composed of a participating medium of huge optical depth will be equivalent to a sphere, whose surface follows Lambert's law. In addition, the undisturbed reflectance of the host particle surface is observable. For both limiting cases excellent agreement with our Monte Carlo results can be found. For any scattering situation in between no exact solution is available at present to check our results.

We will present Monte Carlo results for various scattering situations. The course of the scattering pattern is observed while the scattering properties of the host material are changed. The limiting cases (pure geometrical optics and Schoenberg) can be obtained, as well as a gradual transition between them, while the concentration of scatterers is increased. These effects are most obvious in angular areas, where long photon paths inside the host contribute dominantly. Thus the influence of size and concentration of inhomogeneities on the scattering behavior of a large droplet are predictable, together with possible drawbacks on various optical particle sizing techniques.

CALCULATION OF INFRARED AND MICROWAVE RADIATIVE PROPERTIES OF METAL COATED MICROFIBERS