A Monte Carlo study of the rough-sea-surface influence on the radarscattering from two-dimensional ships

The generalized forward-backward (GFB) method was introduced in Pino et al. (1999) for computing the electromagnetic scattering from two-dimensional targets on a rough surface. The GFB method is used in this article to generate numerical data for a Monte Carlo simulation of the horizontally polarized radar cross section (RCS) of two-dimensional ship-like targets on random rough sea surfaces. The RCS is computed as a function of the incidence angle and wind speed for a large number of surface realizations. It is found that the mean RCS of a given target on a rough surface is generally lower than or equal to the RCS of the same target on a flat surface, while the maximum RCS is usually greater than or equal to the flat-surface case. It is also observed that the variations in the RCS introduced by the rough surface become less significant as the elevation angle approaches grazing     

Monte Carlo simulation of electromagnetic scattering fromtwo-dimensional random rough surfaces

The fast multipole method fast Fourier transform (FMM-FFT) method is developed to compute the scattering of an electromagnetic wave from a two-dimensional (2-D) rough surface. The resulting algorithm computes a matrix-vector multiply in O(N log N) operations. This algorithm is shown to be more efficient than another O(N log N) algorithm, the multilevel fast multipole algorithm (MLFMA), for surfaces of small height. For surfaces with larger roughness, the MLFMA is found to be more efficient. Using the MLFMA, Monte Carlo simulations are carried out to compute the statistical properties of the electromagnetic scattering from 2-D random rough surfaces using a workstation. For the rougher surface, backscattering enhancement is clearly observable as a pronounced peak in the backscattering direction of the computed bistatic scattering coefficient. For the smoother surface, the Monte Carlo results compare well with the results of the approximate Kirchhoff theory     

The generalized forward-backward method for analyzing thescattering from targets on ocean-like rough surfaces

In Holliday et al. (1995, 1996), the iterative forward-backward (FB) method has been proposed to solve the magnetic field integral equation (MFIE) for smooth one-dimensional (1-D) rough surfaces. This method has proved to be very efficient, converging in a very small number of iterations. Nevertheless, this solution becomes unstable when some obstacle, like a ship or a large breaking wave, is included in the original problem. In this paper, we propose a new method: the generalized forward-backward (GFB) method to solve such kinds of complex problems. The approach is formulated for the electric field integral equation (EFIE), which is solved using a hybrid combination of the conventional FB method and the method of moments (MoM), the latter of which is only applied over a small region around the obstacle. The GFB method is shown to provide accurate results while maintaining the efficiency and fast convergence of the conventional FB method. Some numerical results demonstrate the efficiency and accuracy of the new method even for low-grazing angle scattering problems     

Forward-backward method with spectral acceleration for scattering from Layered rough surfaces

A fast method of moments is presented to calculate electromagnetic wave scattering from layered one-dimensional rough surfaces. The formulation is provided for M stratified homogeneous regions, separated by M-1 rough surfaces, and solved using point matching and pulse basis functions. Compared to the single surface case, the solution of scattering from M-1 surfaces requires significantly more memory and computational time. To facilitate the solution, the forward-backward method with spectral acceleration is applied. As an example, a dielectric layer on a perfect electric conductor surface is studied. The numerical results are compared with the analytical solution for layered flat surfaces to partly validate the formulation. The accuracy, efficiency, and convergence of the method are then studied for various rough surfaces and layer permittivities.     

Numerical convergence in periodic method of moments analysis of frequency-selective surfaces based on wire elements

We present a subdomain formulation of the periodic method of moments (PMM) with thin-wire kernel for analyzing frequency-selective surfaces (FSSs) with rectilinear wire-type elements. Analysis of the convergence of the impedance matrix for a FSS with aligned unidirectional elements indicates the effect of individual oscillatory and decaying components. For the individual impedance elements of this FSS, we prove and demonstrate the universality of their envelopes as a function of shell size in the spectral domain. For N wire segments, the PMM converges according to O(N/sup 4/). The dependence on the order of polynomial basis functions shows a geometric progression. The theory is also applied to a single-layer FSS having asymmetrically split segmented rings.     

New method for the efficient summation of double infinite series arising from the spectral domain analysis of frequency selective surfaces

When the method of moments (MoM) in the spectral domain is applied to the analysis of frequency selective surfaces, the entries of the MoM matrix are slowly convergent double infinite series. In this paper, a two-step acceleration technique is developed which makes it possible the fast and accurate computation of these double series in the particular case where subsectional rooftops are used as basis functions. The technique is based on a combination of the use of Kummer's transformation, the use of Poisson's transformation, and the determination of judicious Chebyshev polynomial interpolations of some of the spectral discrete functions involved in the infinite series. The results obtained show that when all the double series of the MoM matrix are to be computed with an accuracy of three significant figures, the new acceleration technique turns out to be about one thousand times faster than brute-force computation, and a few times faster than the acceleration technique based on fast Fourier transform.     

快速多极子在任意截面均匀介质柱散射中的应用

采用快速多极子法（FMM）加速后的矩量法（MoM）求解由电磁场等效原理导出的关于均匀介质柱表面等铲电磁流的积分方程,进而计算其电磁散射特性,FMM的引入使计算时间和内存开销都从O(N^2）降到O（N^3/2）,且并不增加多少复杂度。最后给出了一些介质柱体RCS的算例。     

Microwave emission of rough ocean surfaces with full spatialspectrum based on the multilevel expansion method

Microwave emission of ocean surfaces with full spatial spectrum is studied in this paper. For ocean surfaces with full spectrum, the rms height of roughness can be many wavelengths, and the surface size must be chosen to be larger than the longest scale wave in the spectrum. Due to computer resources, it is not straightforward to conduct numerical simulations of emission from rough surfaces with large rms height and size since a large number of unknowns will be involved. In this paper, the multilevel expansion of the sparse matrix canonical grid (SMCG) method, which is available for surfaces with large rms heights, is used to study the emission of one-dimensional (1-D) ocean surfaces. The computational complexity and the memory requirement are still on the order of O(N log (N)) and O (N), respectively, as in the SMCG method. Ocean surfaces with size 1024 wavelengths (21.9 m at 14 GHz) and spatial spectrum bandwidth between 0.858 rads/m (corresponding to the longest scale of 341.3 wavelengths) and 4691.5 rads/m (corresponding to the shortest scale of 1/16 wavelengths), which is rather wide to be regarded as a full spectrum, are studied. The maximum of the electromagnetic wavenumber-surface rms height product is up to 25.18. The surface is modeled as a lossy dielectric surface with large relative permittivity rather than as a perfectly conducting surface, which is often adopted as an approximation in the active remote sensing of ocean surfaces. A relatively high sampling density is used to ensure accuracy. The effects of the low and high portions of the spectrum on the emissivity are studied numerically. Monte Carlo simulation for ocean surfaces is also performed by exploiting the efficiency of the multilevel expansion method and the use of parallel computing techniques. The convergence of the results with respect to the sampling density is also illustrated     

Implementation of a forward-backward procedure for the fast analysis of electromagnetic radiation/scattering from two-dimensional large phased arrays

Forward-backward method (FBM) was successfully developed for the analysis of electromagnetic radiation/scattering from one-dimensional (1-D) phased array in an efficiency appealing fashion. The FBM applications to treat 2-D array problems are developed in this paper. Acceleration algorithm, performing better than the novel spectrum acceleration algorithm used for 1-D FBM computation, is also developed for this 2-D FBM so the unique advantages of high efficiency and O(N/sub tot/) computational complexity as in the 1-D problems can be retained where N/sub tot/ is the total number of array element. Numerical examples are presented to demonstrate its validity.     

VOIR: a volumetric image reconstruction algorithm based on Fouriertechniques for inversion of the 3-D Radon transform

A novel volumetric image reconstruction algorithm known as VOIR is presented for inversion of the 3-D Radon transform or its radial derivative. The algorithm is a direct implementation of the projection slice theorem for plane integrals. It generalizes one of the most successful methods in 2-D Fourier image reconstruction involving concentric-square rasters to 3-D; in VOIR, the spectral data, which is calculated by fast Fourier techniques, lie on concentric cubes and are interpolated by a bilinear method on the sides of these concentric cubes. The algorithm has great computational advantages over filtered-backprojection algorithms; for images of side dimension N, the numerical complexity of VOIR is O(N(3) log N) instead of O(N (4)) for backprojection techniques. An evaluation of the image processing performance is reported by comparison of reconstructed images from simulated cone-beam scans of a contrast and resolution test object. The image processing performance is also characterized by an analysis of the edge response from the reconstructed images.     

Time domain adaptive integral method for surface integral equations

An efficient marching-on-in-time (MOT) scheme is presented for solving electric, magnetic, and combined field integral equations pertinent to the analysis of transient electromagnetic scattering from perfectly conducting surfaces residing in an unbounded homogenous medium. The proposed scheme is the extension of the frequency-domain adaptive integral/pre-corrected fast-Fourier transform (FFT) method to the time domain. Fields on the scatterer that are produced by space-time sources residing on its surface are computed: 1) by locally projecting, for each time step, all sources onto a uniform auxiliary grid that encases the scatterer; 2) by computing everywhere on this grid the transient fields produced by the resulting auxiliary sources via global, multilevel/blocked, space-time FFTs; 3) by locally interpolating these fields back onto the scatterer surface. As this procedure is inaccurate when source and observer points reside close to each other; and 4) near fields are computed classically, albeit (pre-)corrected, for errors introduced through the use of global FFTs. The proposed scheme has a computational complexity and memory requirement of O(N/sub t/N/sub s/log/sup 2/N/sub s/) and O(N/sub s//sup 3/2/) when applied to quasiplanar structures, and of O(N/sub t/N/sub s//sup 3/2/log/sup 2/N/sub s/) and O(N/sub s//sup 2/) when used to analyze scattering from general surfaces. Here, N/sub s/ and N/sub t/ denote the number of spatial and temporal degrees of freedom of the surface current density. These computational cost and memory requirements are contrasted to those of classical MOT solvers, which scale as O(N/sub t/N/sub s//sup 2/) and O(N/sub s//sup 2/), respectively. A parallel implementation of the scheme on a distributed-memory computer cluster that uses the message-passing interface is described. Simulation results demonstrate the accuracy, efficiency, and the parallel performance of the implementation.     

Conjugate gradient acceleration of maximum-likelihood imagerestoration

A maximum-likelihood iterative deconvolution algorithm is accelerated using a conjugate gradient technique with a minimum mean square error criterion. Significant acceleration over previous techniques is achieved with little additional computation. Restorations with and without noise are presented which indicate the number of iterations required reduces from O(N) to O(√N)     

Fast and accurate algorithm for electromagnetic scattering from 1-D dielectric ocean surfaces

A fast and accurate multigrid (MG) algorithm is presented for the direct method-of-moments (MoM) numerical simulation of radar scattering from large-scale one-dimensional (1-D) dielectric randomly rough surfaces. The proposed MG algorithm combines the desirable features of the generalized conjugate residual preconditioned iterative procedure and a parallel implementation of the spectral acceleration scheme proposed by Chou and Johnson. In addition, the paper proposes effective preconditioning schemes designed to further enhance the numerical efficiency of the proposed algorithm. The accelerated MG algorithm was benchmarked against the exact MG solution for both transverse electric and transverse magnetic polarizations. The efficiency of the proposed algorithm facilitates scattering calculations from electrically large surfaces. Hence, the algorithm was used to assess the performance of an approximate physical-optics scattering model used for ocean forward scattering simulations at the Johns Hopkins University Applied Physics Laboratory (JHU/APL). The validations are performed at X-band and W-band frequencies.     

A hierarchical FFT algorithm (HIL-FFT) for the fast analysis of transient electromagnetic scattering phenomena

A fast algorithm for accelerating the time-marching solution of time-domain integral equations pertinent to the analysis of free-space electromagnetic scattering from perfectly conducting, platelike and uniformly meshed structures is presented. The matrix-vector multiplications required by the time-marching scheme are accelerated by use of the fast Fourier transform (FFT). This acceleration is achieved in a multilevel fashion by hierarchically grouping sparse interactions to extract denser pieces that are efficiently evaluated by the FFT. The total computational cost and storage requirements of this algorithm scale as O(N/sub t/N/sub s/log/sup 2/ N/sub s/) and O(N/sup 1.5/), respectively, as opposed to O(N/sub t/N/sub s//sup 2/) and O(N/sub s//sup 2/) for classical time-marching methods (N/sub s/ and N/sub t/ denote the total number of spatial unknowns and time steps, respectively). Simulation results demonstrate the accuracy and efficiency of the algorithm.     

Monte Carlo simulations of wave scattering from lossy dielectricrandom rough surfaces using the physics-based two-grid method and thecanonical-grid method

In using the method of moments to solve scattering by lossy dielectric surfaces, usually a single dense grid (SDG) with 30 points per wavelength is required for accurate results. A single coarse grid (SCG) of ten points per wavelength does not give accurate results. However, the central processing unit (CPU) and memory requirements of SDG are much larger than that of SCG. In a physics-based two-grid method (PBTG) two grids are used: a dense grid and a coarse grid. The method is based on the two observations: (1) Green's function of the lossy dielectric is attenuative and (2) the free-space Green's function is slowly varying on the dense grid. In this paper, the PBTG method is combined with the banded-matrix iterative approach/canonical grid method to solve rough surface scattering problem for both TE and TM cases and also for near grazing incidence. We studied cases of dielectric permittivities as high as (25+i)ϵ₀ and incidence angle up to 85°. Salient features of the numerical results are: (1) an SCG has poorer accuracy for TM case than TE case; (2) PBTG-banded-matrix iterative approach/canonical grid BMIA/CAG method speeds up CPU and preserves the accuracy; it has an accuracy comparable to single dense grid and yet has CPU comparable to single coarse grid; (3) PBTG-BMIA/CAG gives accurate results for emissivity calculations and also for low grazing backscattering problems (LGBA); and (4) the computational complexity and the memory requirements of the present algorithm are O(N log(N)) and O(N), respectively, where N is the number of surface unknowns on the coarse grid     

Efficient Analysis of Aperture Antennas on Generally Shaped Convex Multilayered Surfaces Using a Hybrid SD-UTD Method

A novel hybrid method is described for analyzing convex multilayered conformal array antennas. The hybrid method is based on the spectral domain approach in combination with the ray-based uniform theory of diffraction (UTD) method. The analysis is divided in two parts. First, the spectral domain approach is accelerated by using an asymptotic extraction technique where the extracted term of the Green's function is calculated using UTD. It is shown that this new approach results in significant acceleration of the existing spectral domain algorithm without losing accuracy. The modified spectral domain method is then used in the second part where generally shaped convex multilayered surfaces are analyzed by using sets of canonically shaped surfaces (spheres and/or circular cylinders). Their radii are obtained using the UTD formulation, which contains important information such as distance and curvature of the generally shaped surface along each geodesic. The results obtained using the new algorithm are compared to the available results (calculated and measured) for different conformal antennas, showing very good agreement.      

Photochemical gas lasers and hybrid (solid/gas) blue-green femtosecond systems

The review summarizes milestones and major breakthrough results obtained in the course of the development of a photochemical method applied to optical excitation of gas lasers on electronic molecular transitions by radiation from such unconventional pump sources as high-temperature electrical discharges and strong shock waves in gas. It also describes principles and techniques applied in hybrid (solid/gas) high-intensity laser systems emitting in the blue-green spectral region, and discusses wavelength scaling of laser-matter interaction by the example of laser wake-field acceleration (LWFA), high-order harmonic generation (HHG) and “water window” soft X-ray lasers. One of the most significant results of the photochemical method development consists in emerging broad bandwidth lasers (XeF(C-A), Xe₂Cl, and Kr₂F) operating in the blue-green spectral range, which have potential for amplification of ultra-short (down to 10 fs) optical pulses towards the Petawatt peak power level. The main goal of this review is to argue that the active media of these lasers may provide a basis for the development of fs systems generating super-intense ultrashort laser pulses in the visible spectral range. Some specific hybrid schemes, comprising solid state front-ends and photodissociation XeF(C-A) power boosting amplifiers, are described. They are now under development at the Lasers Plasmas and Photonic Processes (LP3) Laboratory (Marseille, France), the P.N. Lebedev Physical Institute (Moscow, Russia) and the Institute of High-Current Electronics (Tomsk, Russia) with the aim of conducting proof-of-principle experiments. Some consequences of the visible-wavelength laser field interaction with matter are also surveyed to demonstrate advantages of short driver wavelength in the considered examples. One of the most important consequences is the possibility of coherent soft X-ray generation within the “water window” spectral range with the use of short wavelength driver pulses to pump a recombination laser.     

Thin-stratified medium fast-multipole algorithm for solvingmicrostrip structures

An accurate and efficient technique called the thin-stratified medium fast-multipole algorithm (TSM-FMA) is presented for solving integral equations pertinent to electromagnetic analysis of microstrip structures, which consists of the full-wave analysis method and the application of the multilevel fast multipole algorithm (MLFMA) to thin stratified structures. In this approach, a new form of the electric-field spatial-domain Green's function is developed in a symmetrical form which simplifies the discretization of the integral equation using the method of moments (MoM). The patch may be of arbitrary shape since their equivalent electric currents are modeled with subdomain triangular patch basis functions. TSM-FMA is introduced to speed up the matrix-vector multiplication which constitutes the major computational cost in the application of the conjugate gradient (CG) method. TSM-FMA reduces the central processing unit (CPU) time per iteration to O(N log N) for sparse structures and to O(N) for dense structures, from O(N³) for the Gaussian elimination method and O(N²) per iteration for the CG method. The memory requirement for TSM-FMA also scales as O(N log N) for sparse structures and as O(N) for dense structures. Therefore, this approach is suitable for solving large-scale problems on a small computer     

利用HITEMP2010 的Malkmus 窄谱带模型参数库构建研究

为精确求解发动机高温燃气红外辐射特性,需要调用描述气体辐射传输特性的谱带参数如光谱吸收系数或光谱透过率,而谱带参数随气体温度、波数变化而变化。首先采用逐线计算方法,比较分析了气体分子谱线参数HITRAN2008和其高温扩展版本HITEMP2010的适用范围;其次,针对逐线计算复杂且效率低的问题,提出了一种基于Malkmus统计窄谱带模型的谱带参数库构建方法并开发了计算程序,在此基础上,分别计算了CO2、H2O的均匀路径单组分光谱特性、非均匀路径单组分光谱特性,还计算了CO2、H2O、N2组合的非均匀路径多组分光谱特性。研究表明:计算结果和试验数据吻合较好,说明所提出的基于HITEMP2010的Malkmus统计窄谱带模型适用于高温燃气辐射传输特性计算。     

A multilevel matrix decomposition algorithm for analyzingscattering from large structures

A multilevel algorithm is presented for analyzing scattering from electrically large surfaces. The algorithm accelerates the iterative solution of integral equations that arise in computational electromagnetics. The algorithm permits a fast matrix-vector multiplication by decomposing the traditional method of moment matrix into a large number of blocks, with each describing the interaction between distant scatterers. The multiplication of each block by a trial solution vector is executed using a multilevel scheme that resembles a fast Fourier transform (FFT) and that only relies on well-known algebraic techniques. The computational complexity and the memory requirements of the proposed algorithm are O(N log² N)