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It has been seen recently that when probing a nanoscale object to determine, for example, size or position via light scattering, significant advantage in measurement precision can be gained from exploiting phase singularities in a…
A classical way for exploring the scattering behavior of a small sphere is to approximate Mie coefficients with a Taylor series expansion. This ansatz delivered a plethora of insightful results, mostly for small spheres supporting localized…
We develop a theory for waveform-diverse moving-target synthetic-aperture radar, in the case in which a single moving antenna is used for both transmitting and receiving. We assume that the targets (scattering objects) are moving linearly,…
No surface is perfectly planar at all scales. The notion of flatness of a surface therefore depends on the size of the probe used to observe it. As a consequence rough interfaces are abundant in nature. Here the old, but still active field…
To study how geometrical shape affect the light scattering properties for an ensemble of randomly orientated particles, the single scattering matrices including complete polarization information are calculated statistically for a group of…
The methods of determining the fractal dimension and irregularity scale in simulated galaxy catalogs and the application of these methods to the data of the 2dF and 6dF catalogs are analyzed. Correlation methods are shown to be correctly…
Measurements of a well-characterised standard sample can verify the performance of an instrument. Typically, small-angle neutron scattering instruments are used to investigate a wide range of samples and may often be used in a number of…
This paper outlines a method of obtaining the relation between the singly scattered signal and the Fourier-spectrum of medium dielectric permititvity fluctuations, with due regard for the fact that the scattering volume is determined by…
Using classical electrodynamics we determine the angular dependence of the light intensities radiated in second and third harmonic generation by spherical metal clusters. Forward and backward scattering is analyzed in detail. Also resonance…
Snow is a highly complex medium composed of ice crystals of various shapes and sizes. Knowledge of its intrinsic optical properties such as the scattering and absorption coefficient is tantamount to radiative transfer models in climate…
The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using…
In this paper we consider the generalized Radon transform $\mathcal R$ in the plane. Let $f$ be a piecewise smooth function, which has a jump across a smooth curve $\mathcal S$. We obtain a formula, which accurately describes view aliasing…
In automotive radar applications, multiple radars are used in all vehicles for improving the imaging quality. However this causes radar-to-radar interference from neighbouring vehicles, thus reducing the imaging quality. One metric to…
Remote sensing hyperspectral and more generally spectral instruments are common tools to decipher surface features in Earth and Planetary science. While linear mixture is the most common approximation for compounds detection (mineral,…
Grazing-angle scattering (GAS) is a type of Bragg scattering of waves in slanted non-uniform periodic gratings, when the diffracted order satisfying the Bragg condition propagates at a grazing angle with respect to the boundaries of a…
This paper presents a new method to model X-ray scattering on random rough surfaces. It combines the approaches we presented in two previous papers -- \zs\cite{zhao03} \& \pz\cite{zhao15}. An actual rough surface is (incompletely) described…
The generalized spherical Radon transform associates the mean values over spherical tori to a function $f$ defined on $\mathbb{S}^3 \subset \mathbb{H}$, where the elements of $\mathbb{S}^3$ are considered as quaternions representing…
Scattering and absorption of X-rays by interstellar dust is calculated for a model consisting of carbonaceous grains and amorphous silicate grains. The calculations employ realistic dielectric functions with structure near X-ray absorption…
We present analytic expressions for the scattering of light by an extended atomic cloud. We obtain the solution for the mean-field excitation of different atomic spherical distributions driven by an uniform laser, including the initial…
We show that the errors due to atmospheric refraction are present in the magnitudes determined with the Difference Images Analysis method. In case of single, unblended stars the size of the effect agrees with the theoretical prediction. But…