The comparison between the Mie theory and the Rayleigh approximation to calculate the EM scattering by partially charged sand
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Scattering described today as “Rayleigh scattering" represents something that is far short of what Rayleigh actually contributed to the topic in both optics and acoustics. This limited view seems to lie in a few papers in which he truncates series solutions for practical computations, thus leading to scattering of the form (ka)4 for ka≪ 1, where k is the wavenumber and a is the radius of the sphere and for selected limitations on index of refraction. These approximations led optical scientists to equating “Rayleigh scattering" to little more than “the blue sky.” In 1908, Gustav Mie developed a theory for plane-wave scattering from a sphere to which the names “Mie theory” and “Mie scattering” have been indelibly attached to many applications in optics. It is virtually unknown, especially in optics, that Rayleigh actually developed the full theory of plane-wave scattering from a sphere in 1878 (primarily Section 334, Vol. 2, The Theory of Sound, Macmillan), including original contributions in the concurrently developing mathematics of Bessel functions. The motivation of this presentation is to establish a means of treating weak scattering from bubbles based on their contribution as a distribution of spheres by combining Rayleigh and Mie.
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Scattering phase function is a very important physical parameter in lidar detection of multiple scattering returns.In this paper,scattering phase function of one particle radius is calculated by recursive formula of Mie theory.The result of forward and backward scattering peaks increase when the radius of particle has added according to the theory of scattering.At the same time,scattering phase function of non-one particle radius is calculated by recursive formula of Mie theory,which can use for research on multiple scattering of aerosols such as atmosphere,fog,clouds and so on.
Phase function
Particle (ecology)
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The four nonzero light-scattering matrix element curves for spheres near the Rayleigh and Rayleigh–Gans limit are calculated using Mie theory and compared as the respective limits are approached by a large, high-refractive-index Mie sphere.
Matrix (chemical analysis)
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Extinction (optical mineralogy)
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An alternative to using the traditional scattering angle θ to describe light scattering from a uniform dielectric sphere is the dimensionless parameter qR, where R is the radius of the sphere, q = 2k sin(θ/2), and k is the wavenumber of the incident light. Simple patterns appear in the scattered intensity if qR is used in place of θ. These patterns are characterized by the envelopes approximating the scattered intensity distributions and are quantified by the phase-shift parameter ρ = 2kR | m − 1 |, where m is the real refractive index of the sphere. Here we find new patterns in these envelopes when the scattered intensity is normalized to the Rayleigh differential cross section. Mie scattering is found to be similar to Rayleigh scattering when ρ < 1 and follows simple patterns for ρ > 1, which evolve predictably as a function of ρ. These patterns allow us to present a unifying picture of the evolution of Mie scattering for changes in kR and m.
Dimensionless quantity
Forward scatter
Wavenumber
Intensity
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Numerical accounts for plane polarization electromagnetic wave scattering have been made for spherical particles with consideration of their absorption ability with use of Mie theory in single scattering approximation. Accurate analytical calculations of scattering indicatrix have been carried out for three cases: weak, strong, and mean particle absorption. New condition of using Rayleigh approximation has been found for mean and strong absorption particles that simplifies the interpretation of experimental data. The influence of media resonance properties on the scattering light has been analysed with use of Lorentz bioscillation model. The light scattering from MgO particles has been performed with help of the theory mentioned about.
Discrete dipole approximation
Hyperboloid model
Biological small-angle scattering
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A multiple scattering method is described for calculating extinction, absorption and scattering cross-sections for dielectric particles of arbitrary shape, whose dimensions are comparable to the wavelength of the incident radiation. Numerical application to spheres agrees well with the Mie theory. An extension for a collection of arbitrarily shaped particles with application to zodiacal light is also given.
Zodiacal light
Extinction (optical mineralogy)
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Scattering described today as "Rayleigh Scattering" represents something that is far short of what Rayleigh actually contributed to the topic in both optics and acoustics. This limited view seems to lie in a few papers in which he truncates series solutions for practical computations, thus leading to scattering of the form , where k is the wavenumber and a is the radius of the sphere and for selected limitations on index of refraction. These approximations led optical scientists to equating "Rayleigh scattering" to little more than "the blue sky." In 1908 Gustav Mie developed a theory for plane-wave scattering from a sphere to which the names "Mie theory" and "Mie scattering" have been indelibly attached to many applications in optics. It is virtually unknown, especially in optics, that Rayleigh actually developed the full theory of plane-wave scattering from a sphere in 1878 (primarily section 334, 2. The Theory of Sound, Macmillan), including original contributions in the concurrently developing mathematics of Bessel functions. The motivation of this presentation is to establish a means of treating weak scattering from bubbles based on their contribution as a distribution of spheres by combining Rayleigh and Mie.
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