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Light scattering by flakes
Department of Astronomy, University of Florida, Gainesville, FL 32611,USA.
This work examines how thin flakes in for example a cometary atmosphere can be recognized by the way they scatter light. The investigation includes both theoretical modeling and microwave analogue measurements of light scattered by flakes with a size of the order of a few wavelengths and larger. The theoretical modeling adds the transmitted field found using Babinet's principle and Fresnel's equations, to an existing model for dielectric edges within the framework of geometrical theory of diffraction. This gives an approximate solution to the scattering by thin 2-dimensional dielectric flakes. The laboratory measurements simulate light scattering by 0.25 |im thick randomly orientated circular silicate flakes of 8 |im diameter.
The modeling of light scattering by flakes is motivated by the desire to recognize flake-like particles in a cometary atmosphere through their light scattering properties. The dynamics of Geminid meteoroids during atmospheric flight and of the Geminid meteor stream in space indicate that flakes may have been produced during cometary activity on asteroid 3200 Phaethon [1,2]. Further, laboratory simulation of sublimating particle/ice mixtures representing "dirty" ice surfaces on atmosphereless Solar System bodies has shown that thin flakes may indeed form .
The geometric optics approximation is applicable when the dimensions of the particle are much larger than the wavelength. The T-matrix method has been used for scattering by flakes up to 15 wavelengths in extent , In this work, we model the light scattering by flakes within the premises of geometric theory of diffraction (GTD), in order to obtain a computationally fast yet accurate method for the scattering by thin flakes in the size range of a few wavelengths and larger.
Parallel to the theoretical modeling we have done an experimental investigation, in which we take advantage of the unique microwave scattering facility at the University of Florida , Here, based on the principle of electromagnetic similitude, micron sized particles in the visual region are scaled to centimeter sized particles in the microwave region, which allow precise control of the particle and its orientation. The broadband capability of this facility allows us to measure the scattering in the wavelength interval 2.7-4 mm, which we use to simulate the 0.44-0.65 urn visual range. This enables us to obtain spectral properties such as color and polarimetric color experimentally in addition to intensity and polarization.
To illustrate the importance of diffraction when modeling the scattering by a flake, the scattering by a perfectly conducting thin flake with parallel edges was calculated using the
GTD solution in . Figure 1 shows the intensity (given in units of the scattering matrix following the notation in ) and polarization of the scattering by an infinitely long 5.5 X wide flake averaged over rotation is shown and compared with microwave test measurements. The experimentally obtained intensity (but not the polarization) has been shifted to best fit the intensity calculation since the laboratory scattering measurements necessarily are for a flake of finite length. Scattering averaged over rotation here means the average'of the scattered light as the flake is rotated about its long dimension, which is kept perpendicular to the scattering plane. In this case there is no transmitted radiation and the comparison with the microwave data is very good. Note that using geometric optics only, or geometric optics with scalar Fraunhofer diffraction to model the scattering would fail in this case since these approximations yield no polarization.
To extend the modeling to the light scattering by a 2-dimensional dielectric thin flake, we first apply an approximate solution for scattering by impedance wedges  to treat the two parallel edges of the flake. However, as the transmitted radiation is not taken into account, this yields only the externally diffracted field. Using Babinet's principle and Fresnel's equations we find a solution also for the transmitted field. By adding the external and transmitted diffracted field vectors we arrive at an approximate model for the total scattering by a 2-dimensional thin dielectric flake. The result from this approach to describe the light scattered by a 6.3 X wide dielectric (complex refractive index m = 2.5 + i0.02) thin flake averaged over rotation, is shown in Figure 2. An overall good agreement with test measurements is found in intensity and the main structure in the polarization is also reproduced.
! ' '! 1 1 ' 1
— calculation + measurement
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