Kirchhoff Approximation Method Research Articles

A Hybrid Finite Element Method – Kirchhoff Approximation Method for Modeling Acoustic Scattering from an Underwater Vehicle Model with Alberich Coatings with Periodic Internal Cavities

Anechoic tiles can significantly reduce the echo intensity of underwater vehicles, thereby increasing the difficulty of detecting such vehicles. However, the computational efficiency of conventional methods such as the finite element method (FEM) and the boundary element method (BEM) has its limitations. A fast hybrid method for modeling acoustic scattering from underwater vehicles with anechoic tiles with periodic internal cavities, is developed by combining the Kirchhoff approximation (KA) and FEM. The accuracy and rapidity of the KA method were validated by FEM. According to the actual situation, the reflection coefficients of rubber materials with two different structures under rigid backing are simulated by FEM. Using the KA method, the acoustic scattering characteristics of the underwater vehicle with anechoic tiles are obtained by inputting the reflection coefficients and the target’s geometric grid. Experiments on the monostatic target strength (TS) in the frequency range of 1 to 20 kHz and time domain echo characteristics of acoustic scattering on a benchmark scale model with anechoic tiles are conducted. The research results indicate that the TS values and echo characteristic curves of the KA solutions closely approximate the experimental results, which verifies the accuracy of the KA method in calculating the TS and echo characteristics of underwater vehicles with anechoic tiles.

Analyzing Vortex Light Beam Scattering Characteristics from a Random Rough Surface

The propagation and scattering of vortex light beams in complex media have significant implications in the fields of laser imaging, optical manipulation, and communication. This paper investigates the scattering characteristics of vortex light beams from a random rough surface. Firstly, a two-dimensional Gaussian rough surface is generated using the Monte Carlo method combined with the linear filtering method. Subsequently, the vortex beams are decomposed into the superposition of infinite plane waves, and the scattering of each plane wave from the rough surface is calculated using the Kirchhoff Approximation method. Numerical results of the angle distribution and spatial distribution of OAM scattering Laser Radar Cross Section (LRCS) are presented, varying with different surface roughness parameters for a rough aluminum surface and the beam’s parameters. The results demonstrate that the scattering of vortex beams is influenced by the beam’s parameters, such as Orbital Angular Momentum (OAM) mode number and elevation angle, which may bring new insights into vortex wave-matter interactions and their applications in high resolution imaging.

Research and modeling of the bistatic acoustic scattering characteristics of novel multi-faceted conning tower

The overall acoustic echo of a submarine is greatly dependent on the conning tower. For enhancing the acoustic stealth performance of a submarine, it is necessary to research an innovative design scheme of the conning tower to reduce its bistatic target strength (TS). The aim of this work is to reduce the bistatic TS of a conning tower by varying its geometry and streamlining. The accuracy in modeling the acoustic scattering of a conning tower using the Kirchhoff approximation (KA) was validated, compared with finite element analysis. Several angular conning tower geometries were designed to analyze the effect of streamlining and the number of lateral facets on TS using the KA method. In consideration of the actual situation, the acoustic effect of backing medium was analyzed by comparing water-filled elastic hulls with rigid hulls. From the observed TS calculation results, it is shown that the non-streamlined four lateral-facet conning tower geometries are optimal for acoustic stealth performance during the range of receiving angles from -30 degrees to 30 degrees. Furthermore, elastic hulls and rigid hulls provide similar spatial distribution regularities in bistatic configuration with the rigidity affecting the magnitude of the TS.

Inverse Synthetic Aperture LiDAR Imaging of Rough Targets under Small Rotation Angles

Inverse synthetic aperture LiDAR (ISAL) breaks through the limitations of the diffraction limit and achieves ultra-long-distance radar imaging with centimeter-level resolution. However, because ISAL obtains a high resolution, it is accompanied by a high sampling rate and a large data volume, and the processing process is complicated, which is not conducive to fast real-time imaging of ISAL targets. At the same time, considering that actual non-cooperative targets cannot obtain full-angle ISAL images during movement, in this paper, the Kirchhoff approximation method based on two-dimensional Fourier transform is used to calculate the scattering echo of the rough surface of the target, and then, the rough surface scattering echo of the target coordinate system is obtained through coordinate transformation. After vector superposition, the scattered echo and ISAL image of the rough target are finally obtained, and then the influence of the rotation angle on the ISAL imaging of the rough plate and the rough target is discussed. It is found that a small rotation angle range can also achieve clear ISAL imaging of rough targets, and the influence of different roughness on the ISAL imaging results of different rough targets under a small rotation angle is analyzed. When the roughness is decreased, the target scattering mainly comes from coherent scattering, and the target edge becomes sharper. As the roughness increases, the image energy distribution becomes more uniform. Theoretical and simulation experiments verify the feasibility of ISAL imaging of rough targets under small rotation angles.

Modeling of bistatic scattering from an underwater non-penetrable target using a Kirchhoff approximation method

A numerical triangulation and transformation into the time domain of a Kirchhoff approximation (KA) method is proposed for the modeling of bistatic scattering from an underwater non-penetrable target. The time domain solution in this approximation can be split up into two parts: the solution of reflected field, contributing around the specular direction, and the solution of shadow radiation, contributing around the forward direction. An average solution in the time domain satisfying the reciprocity principle is presented. The solution is expressed in terms of non-singular functions. The proposed method is validated against a normal mode method for bistatic scattering from a rigid sphere. Moreover, the reflected and shadow highlights on the surface of the sphere are shown to verify the integration surface of the reflected field and shadow radiation. It is also tested against a finite element method and an experiment involving a scaled Benchmark Target Strength Simulation Submarine model. The time-angle bistatic spectra for the model are evaluated by the direct and transformed average solutions of KA, and the former accelerates its speed of calculation. The results are good, and show that this method can be used to predict the bistatic scattered field of a non-penetrable target.

Modeling Bistatic Coherent Scattering From Multilayered Rough Surface Using Its Effective Dielectric Constant at P- and L-Bands

This paper proposes a closed-form asymptotic solution for the bistatic coherent scattering of a multilayered rough surface structure based upon its effective dielectric constant (EDC) in specular direction. The EDC is modeled by establishing an equivalence of the coherent scattering between the multilayered rough surface structure and a half-space homogeneous medium. The scattering solution is then solved using the scalar Kirchhoff approximation (SKA) method. This new method is referred to as the SKA-EDC method, and it is applied to analyze the sensitivity of the EDC and coherent reflectivity to bare soils with realistic parameters at P- and L- bands. The result indicates that EDC can give different responses to the soil moisture variations with respect to the coherent reflectivity, enabling the potentials of root-zone soil moisture retrieval. At incidence angle smaller than 35°, EDC gives the same value for both polarizations, and the coherent reflectivity can show a significant response to soil at depths < 15-50 cm at 0.80 GHz and <5-15 cm at 1.57 GHz, depending on soil moisture. The simulation also demonstrates that subsurface roughness has a trivial effect on the EDC and coherent reflectivity for three-rough-surfaces separated by continuously dielectric profiles. Subsurface can thus be assumed to be flat for reducing uncertainty in soil moisture inversion algorithms when the subsurface roughness is unknown.

An advanced two-scale model of EM backscattering from rough surfaces

Based on the random and composite rough surface theory, an advanced two-scale model (ATSM) is proposed to calculate the electromagnetic scattering from the rough surface. The large-scale rough surface part is calculated by Kirchhoff Approximation Method (KAM). Compared with the previous two-scale method, the small-scale roughness is calculated by the Advanced Integral Equation Method (AIEM), which can improve the calculation accuracy and applicability range in terms of the roughness and frequency. By calculating the rough surface backscattering, it can be proved that the proposed two-scale method agrees well with the KAM results for near-vertical incidence and is identical to the AIEM results for large-angle incidence. It should be noted that the proposed method can make up for the drawback that KA decays too fast for swept incidence. The proposed ATSM is also compared with the Shooting and Bouncing Ray (SBR) method and the Poggio-MillerChang-Harrington-Wu-Tsai (PMCHWT) method to verify the accuracy.

Deep learning for light scattering computation: Reconstructing light scattering fields from 1-D randomly rough surfaces as an example

As targets can often be treated as randomly rough surfaces in optical bands, light scattered from them carries rich information, therefore, light scattering analysis has been used in various applications such as remote sensing and target identification. Compared to experimental light scattering detection, numerical light scattering computation is still an essential tool to understand the functions of randomly rough surface features on scattered light in the theoretical level. However, classical numerical methods rely on statistical process consisting of massive randomly rough surface generation, scattered light calculation and ensemble average computation to obtain stable results of light scattering fields, therefore they suffer from heavy computation load and low processing efficiency. To solve such problem, deep neural networks are designed here to directly obtain the stable light scattering fields but completely avoid the statistical process; and an example of reconstructing light scattering fields from 1-D randomly rough surfaces is reported. Compared to the classical Kirchhoff approximation method in high accuracy but low efficiency, the proposed deep learning method not only provides accurate light scattering results, but also remarkably accelerates the processing speed, thus opens a new way for numerical light scattering computation in broader scopes.

Macroscopic Dielectric Constant Model for Layered Media With Rough Surfaces

A macroscopic dielectric constant (MDC) model is proposed to describe the impact of a dielectric layered medium with two-layer rough surfaces (TLRSs) on 2-D electromagnetic scattering. The MDC model is based on the Kirchhoff approximation (KA) method to find an equivalence between the total fields on a TLRS and on a single-layer rough surface (SLRS). With this model, evaluating the scattering over a TLRS can be reduced to a simple SLRS scattering problem. The KA method is used in conjunction with the MDC model to calculate the bistatic scattering coefficients at different surface roughness conditions. The results are in good consistency with the values obtained using the method of moments. Extensive numerical results confirm that the MDC varies along the profile of the top surface as the surface roughness increases, and the variations in the surface roughness and medium depth can significantly affect the fluctuation and mean value of MDC.

Computational Simulation and Modeling of Freak Waves Based on Longuet-Higgins Model and Its Electromagnetic Scattering Calculation

In order to solve the weak nonlinear problem in the simulation of strong nonlinear freak waves, an improved phase modulation method is proposed based on the Longuet-Higgins model and the comparative experiments of wave spectrum in this paper. Experiments show that this method can simulate the freak waves at fixed time and fixed space coordinates. In addition, by comparing the target wave spectrum and the freak wave measured in Tokai of Japan from the perspective of B-F instability and spectral peakedness, it is proved that the waveform of the simulated freak waves can not only maintain the spectral structure of the target ocean wave spectrum, but also accord with the statistical characteristics of the wave sequences. Then, based on the Kirchhoff approximation method and the modified Two-Scale Method, the electromagnetic scattering model of the simulated freak waves is established, and the normalized radar cross section (NRCS) of the freak waves and their background sea surfaces is analyzed. The calculation results show that the NRCS of the freak waves is usually smaller than their large-scale background sea surfaces. It can be concluded that when the neighborhood NRCS difference is less than or equal to −12 dB, we can determine where the freak waves are.

HF Sky wave hop-propagation on earth’s surfaces in different conditions

HF Radio waves can be reflected by the ionosphere and the earth’s surface and propagate long distance from the transmitter to the receiver with several hops, which is also called sky wave propagation. Path loss of sky wave propagation varies with different conditions of ionosphere and types of the earth’s surfaces. In order to get a deeper insight into the multi-hop sky wave propagation, we establish a model to investigate calculate the propagation losses under certain circumstances. We separate the path loss into three parts, namely the free space propagation loss (FSPL), the ionosphere propagation loss (IPL) and the sea surface reflection loss (SSRL). The FSPL and the IPL are calculated by using the propagation loss equations from ITU (International Telecommunication Union) standard. The SSRL is estimated by Pierson-Moscowitz (PM) sea wave spectrum and Kirchhoff approximation (KA) method. The model results agree well with the existing observations that the strength of the reflection off the turbulent ocean attenuates more than that of the clam ocean.

A fast algorithm to compute shadow areas for Kirchhoff approximation-based underwater acoustic scattering simulation

Kirchhoff approximation method is a fast underwater acoustic scattering numerical method which adaptive to engineering application. Shadow areas calculation is one of the most important factors for computational efficiency. In this paper, several existing shadow domain calculation methods for underwater acoustic numerical simulation based on Kirchhoff approximation are introduced. On this basis, a fast sheltering method based on the linked-list search algorithm is proposed. Linked-list search algorithm uses element geometric center to express the element space position and projects the geometric center on incident wave plane along the incident sound ray. And linked-list relationship of elements is established by dividing background mesh cell on the screen. The algorithm achieves fast calculation by using linked-list relationship and optimizing the calculation path. Linked-list search algorithm and all-pair search algorithm are compared and analyzed by an example of numerical simulation. The computational efficiency of the fast shadow domain algorithm is verified by comparing the results of the two algorithms. And the suggestions for further improving the computational efficiency of the algorithm are proposed.

Determination of roughness and correlation length of dielectric surfaces in nano/micro scales using Kirchhoff Approximation method

In this paper determination of surface roughness and correlation length for dielectrics were extensively investigated by applying Kirchhoff Approximation method for second order. The technique is based on two dimensional analysis of scattered light intensity from a dielectric rough surface. The result show that the scattered intensities from a dielectric rough surface for the second order approximation are almost the same as for the first order. The results also show that by using Kirchhoff Approximation method, both surface roughness and correlation length simultaneously can be determined, if the scattered light intensity for two different incident angles is known. The investigations also show that the accuracy for evaluating the ratio of scattered light intensity to incident light intensity can influence the results.

Full angular Stokes vectors of light scattering from two-dimensional randomly rough surfaces by Kirchhoff approximation method

Light scattering from rough surfaces remains an important area of interest as it has great potential in a wide variety of fields such as polarized imaging and target identification. Compared to existing simulative methods, the Kirchhoff approximation method offers a much higher calculation efficiency and easy polarization setting that is especially fit for polarized scattering research. In this paper, by studying full angular Stokes vectors via the Kirchhoff approximation from two-dimensional (2D) randomly rough surfaces with various materials, the difference between Stokes vectors of metals and dielectrics is discovered. Moreover, we have successfully explained the distinction between metals and dielectrics by the phase difference between the incident and scattered waves using theoretical analysis. We believe the research could provide an easy and robust criterion for distinguishing metals and dielectrics in various fields such as laser radar and remote sensing.

Hybrid method of scattering from a dielectric target above a rough surface: TM case

A hybrid method, combining analytic Kirchhoff approximation (KA) and numerical method of moment (MoM), is developed to solve the 2D scattering problem of a dielectric target with arbitrary cross section above a moderate perfect electric conductor (PEC) rough surface under TM-polarized tapered wave incidence. Consider the target as the MoM region and the rough surface as the KA region, the induced current on the rough surface is obtained through the KA method, which depends on the incident tapered wave and the field illuminating by current distribution on the target, leaving only unknowns on the target region. In order to reduce the computational costs further, the rough surface is truncated to speed up computation of the scattering contribution from the rough surface to the target. Compared with the conventional MoM, the hybrid method is very efficient to solve the composite scattering problem of target above rough surface, especially for long underlying rough surface. Simulation results validate the effectiveness and accuracy of the hybrid method.

Numerical validation of the generalized Harvey–Shack surface scatter theory

The generalized Harvey–Shack (GHS) surface scatter theory is numerically compared to the classical small perturbation method, the Kirchhoff approximation method, and the rigorous method of moments for one-dimensional ideally conducting surfaces whose surface power spectral density function is Gaussian or exhibits an inverse power law (fractal) behavior. In spite of its simple analytic form, our numerical comparison shows that the new GHS theory is valid (with reasonable accuracy) over a broader range of surface parameter space than either of the two classical surface scatter theories.

Time-Domain Physical Optics Method for the Analysis of Wide-Band EM Scattering from Two-Dimensional Conducting Rough Surface

Time-domain physical optics (TDPO) method is extended to investigate electromagnetic (EM) scattering from two-dimensional (2D) perfectly electrically conducting (PEC) rough surface in both time domain and frequency domain. The scheme requires relatively small amounts of computer memory and CPU time, and has advantage over the Kirchhoff Approximation (KA) method in obtaining transient response of rough surface by a program run. The 2D Gaussian randomly rough surface is generated by Monte Carlo method and then is partitioned into small triangle facets through the meshing preprocess. The accuracy of TDPO is validated by comparing the numerical results with those obtained by the KA method in both backward and specular directions. The transient response and its frequency distribution of radar cross section (RCS) from rough surface is shown, respectively. The scattering results from rough surface with different size in the specular direction are given. The influence of the root mean square height (σ) and correlation length (l) on electromagnetic scattering from PEC rough surface is discussed in detail. Finally, the comparisons of backscattering results at different incident angles are presented and analyzed.

A hybrid reconstruction algorithm for fluorescence tomography using Kirchhoff approximation and finite element method

Fluorescence molecular tomography is a promising imaging modality and has developed fast in the past years. However, challenges remain in its reconstruction, especially for the reconstruction accuracy and computational efficiency. Generally, an analytical method is computationally efficient while a numerical method has advantages in the reconstruction accuracy for arbitrary geometries. To achieve high reconstruction accuracy at low computational cost, a hybrid method that combines an analytical method based on Kirchhoff approximation (KA) and a numerical method based on finite element method (FEM) is proposed. This method is tested with numerical simulations and phantom experiments. Results of numerical simulations indicate that with the hybrid method, the reconstruction accuracy is improved while the computational time decreases by 40-70% compared with the standalone KA method and FEM. Phantom experiments validate its feasibility for practical applications.

Investigation on scattering from a plasma-coated target over a rough sea surface using a multi-hybrid method

An iterative strategy combining the Kirchhoff approximation (KA) with the hybrid finite element–boundary integral (FE-BI) method is presented to consider electromagnetic scattering from a coated target above a rough sea surface. The multi-hybrid method considers the multiple-scattering interactions between target and underlying surface based on equivalent principle and currents updating scheme. The hybrid FE-BI-KA method, which is an improved and generalized version of a previous KA–Method of Moments (MoM) technique, can deal with an inhomogeneous target. Numerical results are given to evaluate the validity of the multi-hybrid technique, and then the hybrid method is employed to investigate electromagnetic scattering from a plasma-coated airfoil above a rough sea surface, including the effects of several key parameters on stealth performance, such as plasma angular frequency and electron collision frequency.

Multi-hybrid method for investigation of EM scattering from inhomogeneous object above a dielectric rough surface

An iterative strategy combining Kirchhoff approximation^(KA) with the hybrid finite element-boundary integral (FE-BI) method is presented in this paper to study the interactions between the inhomogeneous object and the underlying rough surface. KA is applied to study scattering from underlying rough surfaces, whereas FE-BI deals with scattering from the above target. Both two methods use updated excitation sources. Huygens equivalence principle and an iterative strategy are employed to consider the multi-scattering effects. This hybrid FE-BI-KA scheme is an improved and generalized version of previous hybrid Kirchhoff approximation-method of moments (KA-MoM). This newly presented hybrid method has the following advantages: (1) the feasibility of modeling multi-scale scattering problems (large scale underlying surface and small scale target); (2) low memory requirement as in hybrid KA-MoM; (3) the ability to deal with scattering from inhomogeneous (including coated or layered) scatterers above rough surfaces. The numerical results are given to evaluate the accuracy of the multi-hybrid technique; the computing time and memory requirements consumed in specific numerical simulation of FE-BI-KA are compared with those of MoM. The convergence performance is analyzed by studying the iteration number variation caused by related parameters. Then bistatic scattering from inhomogeneous object of different configurations above dielectric Gaussian rough surface is calculated and the influences of dielectric compositions and surface roughness on the scattering pattern are discussed.