Modeling Fluctuations in Scattered Waves

Jakeman, E.; Ridley, Kevin D.

doi:10.1201/9781420012163

Cited by 61 publications

(52 citation statements)

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“…Light polarization and coherence [1][2][3][4][5][6][7] have become the focus of numerous works, and were accompanied by the emergence of unified theories [8,9]. Additional complexity was brought by the introduction of random media, hence mixing spatial and temporal disorders [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Spatial depolarization of light from the bulks: electromagnetic prediction

Zerrad¹,

Tortel²,

Soriano³

et al. 2015

Opt. Express

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Section: Introductionmentioning

confidence: 99%

Spatial depolarization of light from the bulks: electromagnetic prediction

Zerrad¹,

Tortel²,

Soriano³

et al. 2015

Opt. Express

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“…This sought to capture the effects of significant large-scale correlated structure within the scatterer that vitiate any appeal to the central limit theorem as a justification for a more conventional Gaussian statistical model. Since then the model has grown to maturity, and the K -distribution, whose probability density function (PDF) is expressed in terms of a modified Bessel function of the second kind (Abramowitz & Stegun 1965), and is analytically tractable, adaptable and robust, has found widespread application (Jakeman & Ridley 2006;Ward et al 2006). Capturing the two-point or correlation properties of the scattered radiation has always been more problematic and invariably based on simplified models (Tough & Ward 2002) which, in the main, exploit the representation of the intensity of the scattered radiation as a Rayleigh process (generated by scattering by the small scale structure on the surface) with a 'local power' that itself varies as a gamma process and so models the modulation of the local scattering by large scale structures (Ward 1981;Ward et al 2006).…”

Section: Introductionmentioning

confidence: 99%

Coupled dynamics of populations supported by discrete sites and their continuum limit

Field

Tough²

2010

Proc. R. Soc. A.

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The illumination of single population behaviour subject to the processes of birth, death and immigration has provided a basis for the discussion of the non-Gaussian statistical and temporal correlation properties of scattered radiation. As a first step towards the modelling of its spatial correlations, we consider the populations supported by an infinite chain of discrete sites, each subject to birth, death and immigration and coupled by migration between adjacent sites. To provide some motivation, and illustrate the techniques we will use, the migration process for a single particle on an infinite chain of sites is introduced and its diffusion dynamics derived. A certain continuum limit is identified and its properties studied via asymptotic analysis. This forms the basis of the multi-particle model of a coupled population subject to single site birth, death and immigration processes, in addition to inter-site migration. A discrete rate equation is formulated and its generating function dynamics derived. This facilitates derivation of the equations of motion for the first-and second-order cumulants, thus generalizing the earlier results of Bailey through the incorporation of immigration at each site. We present a novel matrix formalism operating in the time domain that enables solution of these equations yielding the mean occupancy and inter-site variances in the closed form. The results for the first two moments at a single time are used to derive expressions for the asymptotic time-delayed correlation functions, which relates to Glauber's analysis of an Ising model. The paper concludes with an analysis of the continuum limit of the birth-death-immigration-migration process in terms of a path integral formalism. The continuum rate equation and evolution equation for the generating function are developed, from which the evolution equation of the mean occupancy is derived, in this limit. Its solution is provided in closed form.

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“…The echo amplitude of the prolate spheroid is then a function of the random variable #. Fundamental probability theory can be used to derive the PDF for the scattering amplitude of a randomly oriented object, when the probability distribution of # is already known [3]. A similar approach has been used in the past to derive the echo PDF of a patch of scatterers with arbitrary echo distributions in the beam [7,8].…”

Section: Aperture B(8)mentioning

confidence: 99%

“…The correlation between the parameters of the theoretical distribution and the physical characteristics of clutter is then inferred statistically, rather than being derived from first principles. The majority of previous studies on modeling radar and sonar clutter utilize a similar approach [1][2][3][4]. A statistical model for the echo amplitude of clutter must account for several factors that will affect the shape of the distribution and the degree to which it is non-Rayleigh [5].…”

Section: Introductionmentioning

confidence: 99%

Non-Rayleigh scattering by a randomly oriented elongated scatterer

Bhatia¹

2012

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The echo statistics of a randomly rough, randomly oriented prolate spheroid that is randomly located in a beampattern are investigated from physics-based principles both analytically and by Monte Carlo methods. This is a direct-path geometry in which reflections from neighboring boundaries are not a factor. The center of the prolate spheroid is assumed to be confined to the plane containing the MRA (maximum response axis). Additionally, the rotation of the prolate spheroid is assumed to always be in this plane. The statistics and, in particular, the tails of the probability density function (PDF) and probability of false alarm (PFA) are shown to be strongly non-Rayleigh and a strong function of shape of scatterer. The tails are shown to increase above that associated with a Rayleigh distribution with increasing degree of elongation (aspect ratio) of the scatterer and when roughness effects are introduced. And, as also shown in previous studies, the effects associated with the scatterer being randomly located in the beam contribute to the non-Rayleigh nature of the echo. The analytically obtained results are compared to Monte Carlo simulations for verification.

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Modeling Fluctuations in Scattered Waves

Cited by 61 publications

References 0 publications

Spatial depolarization of light from the bulks: electromagnetic prediction

Spatial depolarization of light from the bulks: electromagnetic prediction

Coupled dynamics of populations supported by discrete sites and their continuum limit

Non-Rayleigh scattering by a randomly oriented elongated scatterer

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