ABSTRACT
We present experimentally determined scattering matrix elements of birefringent rutile particles in water as a function of the scattering angle for a wavelength of 633 nm (in air). These elements are compared with the results of T-matrix calculations for prolate spheroids. For the diagonal matrix elements the results of the T-matrix calculations are in good agreement with those of the measurements. A good fit for the whole matrix, including the off-diagonal elements, is obtained when we compensate for the birefringence of the rutile particles by performing the computations for spheroids with a slightly larger length/width ratio than measured.
ABSTRACT
We derive theoretically and validate numerically general relationships for the elements of the backscattering matrix and for the linear, delta(L), and circular, delta(C), backscattering depolarization ratios for nonspherical particles in random orientation. For the practically important case of randomly oriented particles with a plane of symmetry or particles and their mirror particles occurring in equal numbers and in random orientation, delta(C) = 2delta(L)/(1 - delta(L)). Extensive T-matrix computations for randomly oriented spheroids demonstrate that, although both delta(L) and delta(C) are indicators of particle nonsphericity, they cannot be considered a universal measure of the departure of particle shape from that of a sphere and have no simple dependence on particle size and refractive index.
ABSTRACT
We consider two topics pertaining to light scattering by circular cylinders. (A) Scattering properties of cylinders with increasing aspect ratio are studied. It is shown that the solution for finite cylinders does not converge to the solution for infinitely long cylinders if the aspect ratio increases. This is due to differences in the treatment of diffraction for finite and infinite cylinders. (B) Finite cylinders have sharp edges, so their scattering properties differ from those of spheroids having the same aspect ratio. To illustrate these differences we present scattering matrix elements of cylinders and spheroids for a large set of aspect ratios. To handle the large amount of data, the scattering matrix elements as functions of aspect ratio and scattering angle are presented in so-called three-dimensional figures.
ABSTRACT
Changes in the radiance and state of polarization of a beam of radiation can often be described by means of a pure Mueller matrix. Such a 4 × 4 matrix transforms Stokes parameters and can be expressed in terms of the elements of a 2 × 2 Jones matrix. Relations between the two types of matrix are discussed. Explicit expressions are given for changes of a pure Mueller matrix that are caused by certain elementary changes of its Jones matrix, such as when its transpose, complex conjugate, or Hermitian conjugate are taken. It is shown that every pure Mueller matrix has a simple and elegant structure, which is embodied by interrelations that involve either only squares of the elements or only products of different elements. All possible interrelations for the elements of a general pure Mueller matrix are derived from this simple structure.
ABSTRACT
An experimental setup for measuring scattering matrices of various kinds of small particles is described. By using polarization modulation eight scattering-matrix elements, six of which are independent (or four in the case of spheres), can be obtained from four separate measurements. Test results for water droplets are presented as well as preliminary results for irregularly shaped quartz (SiO(2)) particles with an effective radius of approximately 15 microm. Four inequalities yielding conditions for combinations of scattering-matrix elements were used for checking all the results presented.
