We use cookies to offer you a better experience, personalize content, tailor advertising, provide social media features, and better understand the use of our services. To learn more or modify/prevent the use of cookies, see our Cookie Policy and Privacy Policy. We show that the standard, single-expansion extended boundary condition method provides convergent scattering results for osculating dielectric spheres and discuss the implications of this result. ... Aydin and Seliga (1984) Barber and Barber and Bates and Wong (1974) Bringi and Seliga (1977a) Bringi and Seliga (1980) Doicu and Wriedt (1997c) Hizal (1980) Lakhtakia and Iskander (1983a) Lapalme and Patitsas (1993a) Li et al. (2001) Mishchenko and Videen (1999) Mishchenko and Lacis (2003) Prodi et al. (1999) Schuh and Wriedt (2003) Ström and Zheng (1987) Sturniolo et al. (1995) Videen et al. (1996) Warner and Hizal (1976) Waterman (1965) Waterman (1971) Waterman (1973) Waterman (1979) Waterman (1980) Wriedt and Doicu (1997) Yeh et al. (1982a 368 ... The T-matrix method is one of the most powerful and widely used theoretical techniques for the computation of electromagnetic scattering by single and composite particles, discrete random media, and particles in the vicinity of an interface separating two half-spaces with different refractive indices. This paper presents a comprehensive database of T-matrix publications since the inception of the technique in 1965 through early 2004. ... The T-matrix (or EBCM) method [1] has in recent years been used to compute light-scattering (LS) properties on bispherical clusters [2,3]. A proposed approach-merging two spheres together as a single scatterer-has proved infeasible due to convergence problems [4]. ... The T-matrix is used to calculate the extinction cross section of bispherical particle systems in random orientation for a monospherical size parameter x=0.01. Differences between bispherical and monospherical (Mie) results are shown for a range of values of the refractive index. It is found that the size of the T-matrix that needs to be calculated can be large, thus preventing simple dipole approximations from being used. Once the T-matrix is computed, however, only a small number of terms is needed to obtain cross section values. Fractal-like aggregates are commonly modeled as assemblies of spheres positioned in point contact only. The necking phenomenon is usually neglected. Such approach has some advantages, e.g. faster light scattering simulation programs can be used, however it may results in many additional errors and inaccuracies. In our study we try to approximate them and select the most suitable connection model. In our work we focus on the impact of the necking phenomenon on the optical properties of two and five monodisperse soot particles. The results show that small connections can be neglected. Different connection types (the cylindrical, the linear and the quadratic connector) can be used interchangeably, therefore, we recommend the most basic one (i.e. the cylindrical connector). Additionally, when particles are not positioned in point contact (they tend to overlap) this phenomenon should not be omitted due to its impact on the resulting scattering cross sections. The introduction of the Sh-matrices in the T-matrix method allows the shape-dependent parameters to be separated from size- and refractive-index-dependent parameters. In many case this allows analytic solutions of the corresponding surface integrals to be obtained. In this manuscript we derive and analyze the analytical solution for merging spheres at different degrees of merging. The Sh- (shape) matrix contains the morphology-dependent parameters that can be incorporated with the size- and refractive-index-dependent parameters to form the T-matrix using analytical operations. In some instances, the integrals that describe the Sh-matrix are simplified sufficiently that they may be solved analytically. In this manuscript we use the Sh-matrix formalism to present an analytical solution for the light scattering from two merging prolate and oblate spheroids. Such a solution has relevance in environmental monitoring of spores, whose morphology is approximately spheroidal and often form end-on chains. We use the Sh-matrix formalism that contains the shape-dependent parameters of the T-matrix to derive an analytic solution for the light scattering from two merging spheres at different degrees of merging. The integral expressions for the Sh-matrix elements are simpler than those of the T-matrix elements and, for two merging spheres, these integrals can be solved analytically. Our calculations show that when the spheres merge, the primary fringes that are circular for non-merging spheres become distorted. Secondary fringes due to the interference of the waves emanating from the two spheres begin to appear when the spheres are merged approximately 50%. Published by Elsevier B.V.

The derivation of the Sh-matrices using the T-matrix method allows the shape-dependent parameters to be separated from size- and refractive-index-dependent parameters. This separation also allows for the surface integrals to be solved and for analytic solutions to the light scattering from some irregular morphologies to be found. In this manuscript we derive solutions for capsule-shaped and bi-sphere particles. We analyze the two-dimensional patterns resulting from these two different simulants of Bacillus subtilis spores. The large differences between the patterns suggest that simple approximations to complicated particles may not be adequate. The nature of the scattering of light is thought to be well understood when the medium is made up of independent scatterers that are much larger than the wavelength of that light. This is not the case when the size of the scattering objects is similar to or smaller than the wavelength or the scatterers are not independent. In an attempt to examine the applicability of independent particle scattering models, to planetary regoliths, a dataset of experimental results were compared with theoretical predictions. Videen G, Ngo D, Hart MB. Opt Commun 1996;125:275}87. Mishchenko MI, Travis LD. JQSRT 1998;60:309}24. Mi Mishchenko Dw Mackowski Mishchenko MI, Mackowski DW. Opt Lett 1994;19:1604}6. Cvm Van Der Mee Jw Hovenier van der Mee CVM, Hovenier JW. Astron Astrophys 1990;228:559}68. Mugnai A, Wiscombe WJ. Appl Opt 1986;25:1235}44. Lewin L. IEEE Trans Microwave Theory Tech 1970;18:1041}7. General relations for the elements of scattering matrices of spherical and non-spherical particles are discussed.These relations can be used for theoretical purposes, but also for testing scattering matrices that have been obtained numerically or experimentally. Investigation of the scattering properties of hydrometeors, especially those of nonspherical hydrometeors, has become increasingly important in connection with the estimation of depolarization due to hydrometeors in terrestrial and earth-space microwave communication systems. Scattering from nonspherical hydrometeors is also important in remote sensing of precipitation parameters. This paper first reviews various analytical-numerical approaches for the calculation of single-scattering properties of nonspherical hydrometeors. Approaches for the analysis of the practical problems, such as depolarization phenomena and rain scatter interference, are outlined in order to see how the single-scattering calculations are related to these problems. The present knowledge of incoherent scattering effects on rain attenuation, cross polarization, and channel transfer characteristics at the microwave and millimeter wave region is also reviewed. M.I. Mishchenko, G. Videen / Journal of Quantitative Spectroscopy & Radiative Transfer 63 (1999) 231}236 235 Upon defining vector spherical partial waves {Ψn} as a basis, a matrix equation is derived describing scattering for general incidence on objects of arbitrary shape. With no losses present, the scattering matrix is then obtained in the symmetric, unitary form S=-Q̂′*Q̂*, where (perfect conductor) Q̂ is the Schmidt orthogonalization of Qnn′=(k/π)∫dσ·[(∇×ReΨn)×Ψn′], integration extending over the object surface. For quadric (separable) surfaces, Q itself becomes symmetric, effecting considerable simplification. A secular equation is given for constructing eigenfunctions of general objects. Finally, numerical results are presented and compared with experimental measurements. The fields from a system composed of two conducting, osculating spheres are derived using an extension of Mie theory. The boundary conditions are satisfied on both surfaces by expanding the fields in terms of vector spherical harmonics and translating them between the coordinate systems of the two spheres. We give explicit expressions for the far-field and the cross-sections. Order-of-scatter methods diverge when finding the scattered field coefficients, so the coefficients must be found directly. Splittings are discovered in the solutions of the scattered field, and we find very good agreement between the average of the solutions with experimental microwave backscatter measurements.

Employing a conserved‐flux concept, the T‐matrix equations describing boundary‐value problems of potential theory and electromagnetic scattering are obtained without recourse to the Huygens principle or physically fictitious fields. For scattering by dielectric objects, tangential electric and magnetic fields on the surface are both represented in a single expansion, cutting the computation in half. In the low‐frequency limit the dynamical equations are shown to reduce to the static case, and numerical computations then indicate that in comparison with other approaches, the present method can achieve as much as an order of magnitude reduction in the number of equations and unknowns needed for a given accuracy. New exact relations are found between the electrostatic and magnetostatic problems, and analytical results are also obtained from the equations, with and without truncation. The equivalence of applying the Extended Boundary Condition and the continuity conditions of the tangential field components at sharp boundaries for deriving methods to solve electromagnetic scattering problems is demonstrated in spherical coordinates. We show that both conditions provide the same transition matrix to determine the unknown expansion coefficients of the scattered field in terms of vector spherical wave functions. In this way, a generalization of the Separation of Variables Method to non-spherical scattering problems is achieved which allows a unified mathematical description of different numerical techniques. We describe how the T-matrix approach can be used to compute analytically the Stokes scattering matrix for randomly oriented bispheres with touching or separated components. Computations for randomly oriented bispheres with touching components are compared with those for volume-equivalent randomly oriented prolate spheroids with an aspect ratio of 2 and for a single volume-equivalent sphere. We show that cooperative (multiple-scattering) effects can make bispheres more efficient depolarizers than spheroids in the back-scattering direction. Scitation is the online home of leading journals and conference proceedings from AIP Publishing and AIP Member Societies In this paper, we study the behavior of the scattering efficiency Qsca, the absorption efficiency Qabs, the single-scattering albedo ω, the asymmetry factor g, and the backscattered fraction for isotropically incident radiation β¯ for randomly oriented rotationally symmetric nonspherical particles of radii r = r0[1 + εTn(cosθs)], where Tn is a Chebyshev polynomial of order n. By taking n = 2, 3, 4, 6, 8, and 20, and ε = -0.2 to 0.2 in steps of 0.05, twenty-three different shapes have been considered for these Chebyshev particles. The scattering calculations have been carried out using the Extended Boundary Conditions Method for individual particles with refractive index m˜ = 1.5-0.02i in the equal-volume-sphere size parameter range 1 ≤ x ≤ 25. Unshapeaveraged and shape-averaged nonspherical single-scattering quantities have then been compared to corresponding size-averaged (over Δx = 0.1x) spherical results. It is shown that nonsphericity always increases Qabs for size parameters larger than ~10, while it decreases g—and correspondingly increases β¯—in the size range 8 ≤ x ≤ 15. Qsca seems to be on the average somewhat larger for nonspherical particles, while ω tends to be smaller. Concavity almost always enhances the spherical-nonspherical differences. Methods based on the Rayleigh hypothesis (e.g. the point-matching method) for numerically solving wave-diffraction problems are shown to be equivalent to the exact extended-boundary-condition method. It is concluded that the Rayleigh hypothesis is exact, although, in general, it is necessary to interpret it in the generalised function sense. The usefulness of point matching when the expansion representing the field diverges in the matching region is discussed in relation to previous work. It is shown that the presence of a metal boundary does not necessarily imply divergence of series representations at the boundary position. The Rayleigh hypothesis, which bears on this, and the extended-boundary-condition method are equivalent only in a restricted sense; the latter is hypersensitive to minute deviations of the field on the reduced boundary and is therefore unsuited to point matching for some shapes. A numerical example is examined in which the use of a divergent series gives little evidence of error from use in the divergent region. Attention is drawn to recent work in which the use of a sutliciently smooth spectral expansion is shown to be able to convert a series of divergent terms into a usable convergent series, permitting valid numerical computations with otherwise divergent representations.