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Aiming at the problem of poor tracking performance of traditional filtering algorithms for maneuvering extended targets, an improved interactive multimodel second-order extended Kalman filter (IMM-SOEKF) algorithm is proposed in this article. First, the Markov transfer probability matrix is updated using the probabilities within the neighboring time points between each model to improve the switching speed of the models in the algorithm and the matching accuracy. In addition, according to the state parameters and shape information of the target, the second-order extended Kalman filter (SOEKF) is used for tracking the estimation of the target. By incorporating the measurement covariance equation from the filtering algorithm into the likelihood function calculation, new likelihood probability and model weight assignments are obtained using the maximum likelihood function method to improve the tracking accuracy for extended targets and the robustness of the algorithm. Finally, simulation and data processing results show that the algorithm has higher tracking accuracy compared with other state-of-the-art algorithms.

Debye series expansion (DSE) is developed for electromagnetic (light) scattering by a charged sphere. By comparing our results with Mie theory (for a charged sphere) and with DSE (for a neutral sphere), we verify our theory numerically. DSE is employed for calculation of far-field intensity, and absorption and extinction efficiencies of charged spherical particles illuminated by a plane wave. The influences of various parameters (including surface charge, refractive index, size parameters, Debye mode, etc.) are studied. The rainbow produced by charged particles is analyzed. These results are of great significance in many fields including particle sizing, optical tweezers, etc.

•The stability of Rh2B and RhB2 under high pressures were studied.•The elastic anisotropy of Rh2B and RhB2 was studied in detail.•The pressure effects on properties were studied.

The effects of the individual scattering process on the formations of both the particle hologram and its corresponding reconstructed three-dimensional particle image are investigated using the Debye series. A particle hologram model using the Debye series decomposes the object wave into different scattering modes and thus permits evaluating the effects of the individual scattering process [diffraction, reflection, transmission, refractions with (p−1) internal reflections] on the particle holography quantitatively. In the Gabor inline holography of a transparent droplet, the transmission light causes small discrepancies between the hologram fringes of an opaque particle (diffraction) and a transparent particle near the zero point of the Bessel-like modulation function, eventually giving rise to the glory spot in the center of the reconstructed dark particle image. For off-axis holography, this paper reveals the effects of reflection, particularly total reflection by bubbles, transmission, and refractions with (p−1) internal reflections of the scattered light on the formation and the reconstructed glory spot images of typical forward and backward off-axis holography.

Carbon nitrides are excellent candidates for extreme hardness materials. In this work, a new I4̅3m phase of C3N2has been uncovered by replacing part of the nitrogen atoms in the cagelike diamondoid nitrogen N10with carbon atoms. This phase is mechanically and dynamically stable up to at least 50 GPa. The elastic anisotropy of I4̅3m-C3N2is investigated by comparing with previously proposed α-C3N2. The tensile directional dependence of Young’s modulus obeys the following trend: E[111]>E[110]>E[100]. Electronic structure calculations reveal that I4̅3m-C3N2is hole conducting. Hardness calculation shows that the I4̅3m-C3N2is superhard with a hardness of 72.9 GPa.

On the basis of generalized Lorenz-Mie theory, the Debye series expansion (DSE) for radiation pressure forces (RPF) exerted on a multilayered sphere induced by focused beams is introduced. The DSE can isolate the contribution of each scattering process to RPF, and give a physical explanation of RPF. Typically, the RPF induced by a Gaussian beam is studied. The DSE is employed to the simulation of RPF corresponding to different scattering processes (diffraction, reflection, refraction, etc.) in detail, and gives the physical mechanism of RPF. The effects of various parameters, such as scattering mode p, beam position, and radius of core for coated spheres, to RPF is researched.

By means of geometrical optics we present an approximation method for acceleration of the computation of the scattering intensity distribution within a forward angular range (0-60°) for gradient-index spheres illuminated by a plane wave. The incident angle of reflected light is determined by the scattering angle, thus improving the approximation accuracy. The scattering angle and the optical path length are numerically integrated by a general-purpose integrator. With some special index models, the scattering angle and the optical path length can be expressed by a unique function and the calculation is faster. This method is proved effective for transparent particles with size parameters greater than 50. It fails to give good approximation results at scattering angles whose refractive rays are in the backward direction. For different index models, the geometrical-optics approximation is effective only for forward angles, typically those less than 60° or when the refractive-index difference of a particle is less than a certain value.

The Debye series has been a key tool for the understanding of light scattering features, and it is also a convenient method for understanding and improving the design of optical instruments aimed at optical particle sizing. Gouesbet has derived the Debye series formulation for generalized Lorenz-Mie theory (GLMT). However, the scattering object is a homogeneous sphere, and no numerical result is provided. The Debye series formula for plane-wave scattering by multilayered spheres has been derived before. We have devoted our work to the Debye series of Gaussian beam scattering by multilayered spheres. The integral localized approximation is employed in the calculation of beam-shape coefficients (BSCs) and allows the study of the scattering characteristics of particles illuminated by the strongly focused beams. The formula and code are verified by the comparison with the results produced by GLMT and also by the comparison with the result for the case of plane-wave incidence. The formula is also employed in the simulation of the first rainbow by illuminating the particle with one or several narrow beams.

We derive the formula of the Debye-series decomposition for normally incident plane-wave scattering by an infinite multilayered cylinder. A comparison of the scattering diagrams calculated by the Debye series and Mie theory for a graded-index polymer optical fiber is given and the agreement is found to be satisfied. This approach permits us to simulate the rainbow intensity distribution of any single order and the interference of several orders, which is of good use to the study of the scattering characteristics of an inhomogeneous cylinder and to the measurement of the refractive index profile of an inhomogeneous cylinder.

We have derived the formula for the Debye-series decomposition for light scattering by a multilayered sphere. This formulism permits the mechanism of light scattering to be studied. An efficient algorithm is introduced that permits stable calculation for a large sphere with many layers. The formation of triple first-order rainbows by a three-layered sphere and single-order rainbows and the interference of different-order rainbows by a sphere with a gradient refractive index, are then studied by use of the Debye model and Mie calculation. The possibility of taking only one single mode or several modes for each layer is shown to be useful in the study of the scattering characteristics of a multilayered sphere and in the measurement of the sizes and refractive indices of particles.

The selection of the type of the structured beam is great importance in the study of optical and first-order rainbow scattering by a particle. The Airy light-sheet is a specific type of limited-diffracting beam (in 2D), which has been used in investigations related to radiation forces and torque. Equally important and of practical significance is the study of the electromagnetic/optical resonance and first-order rainbow scattering by a dielectric sphere. The purpose of this paper is to calculate the electromagnetic resonance scattering, energy efficiencies and far-field scattered intensity of a lossless homogeneous dielectric spherical particle of arbitrary size, illuminated by a linearly-polarized non-diffracting electromagnetic Airy light-sheet. A rigorous parametric study is undertaken here to investigate the effect of varying the light-sheet parameters γ, kw0, and its polarization state as well as the size parameter kaof the lossless dielectric sphere on the scattering efficiencies and intensity. The analysis is extended to examine the first-order rainbow scattering phenomenon in the context of Airy light-sheets with different polarizations. Numerical results show that kw0, γ, kaand the state of polarization affect the amplitude and scattering directivity patterns of the efficiencies and intensity. Rainbow scattering arises along the polar scattering angle θ=143°, and is minimally influenced by the different values of the parameters kw0, γ, polarization, and ka. The results are of some practical significance in optical resonance scattering and related applications in optical tweezers, super-resolution imaging, particle characterization, and the measurement of temperature, velocity and size of a liquid jet to name a few applications.

The photonic nanojet (PNJ) produced by a vector Bessel beam irradiating a dielectric spheroidal particle is investigated using the Discrete Dipole Approximation. The influence of the beam center, beam order, beam polarization type, and half cone angle of the vector Bessel beam on the characteristics of PNJ is analyzed. Several characteristics of PNJ including maximum intensity, the focal length, the effective length, and full width at half maximum are considered. The results show that the characteristics of the PNJ can be controlled by changing the four parameters of the Bessel beam. We think it will help to enhance the application of Bessel beams in generating PNJ and provide new properties to generate PNJ.