Spherical Wave Decomposition Research Articles

An Effective Method for Antenna Radiation Pattern Reconstruction Based on Phaseless Measurement in a Reverberation Chamber

It has been shown that the angular correlation of the antenna can be obtained by rotating it in a reverberation chamber (RC) and the radiation pattern of the antenna under test (AUT) can be reconstructed from the measured correlation coefficients using spherical wave decomposition. However, the correlation coefficient needs to be obtained by measuring the complex-valued S-parameters in an RC, which is no longer applicable to active antenna tests where the phase information is unavailable. To solve this problem, we propose an antenna radiation pattern reconstruction method based on phaseless measurement in an RC. In this method, the power correlation coefficient of AUT is calculated using the signal amplitude received by the antenna at different angles. According to the relationship between complex correlation coefficient and power correlation coefficient of the AUT, the nonlinear least squares method is used to reverse the spherical wave coefficients and reconstruct the antenna radiation pattern. Simulations and measurements are carried out in RC and anechoic chamber, which demonstrated the feasibility and applicability of the proposed method.

An Accurate Millimeter-Wave Imaging Algorithm for Close-Range Monostatic System.

An efficient and more accurate millimeter-wave imaging algorithm, applied to a close-range monostatic personnel screening system, with consideration of dual path propagation loss, is presented in this paper. The algorithm is developed in accordance with a more rigorous physical model for the monostatic system. The physical model treats incident waves and scattered waves as spherical waves with a more rigorous amplitude term as per electromagnetic theory. As a result, the proposed method can achieve a better focusing effect for multiple targets in different range planes. Since the mathematical methods in classical algorithms, such as spherical wave decomposition and Weyl identity, cannot handle the corresponding mathematical model, the proposed algorithm is derived through the method of stationary phase (MSP). The algorithm has been validated by numerical simulations and laboratory experiments. Good performance in terms of computational efficiency and accuracy has been observed. The synthetic reconstruction results show that the proposed algorithm has significant advantages compared with the classical algorithms, and the reconstruction by using full-wave data generated by FEKO further verifies the validity of the proposed algorithm. Finally, the proposed algorithm performs as expected over real data acquired by our laboratory prototype.

Efficient Millimeter-Wave Imaging Algorithm for Layered Dielectrics Based on MIMO-SAR With Nonuniform Transmitting Array

In this letter, an efficient near-field millimeter-wave (MMW) imaging algorithm is presented for layered dielectrics based on multiple-input–multiple-output synthetic aperture radar (MIMO-SAR) with nonuniform transmitting array. First, the model of target echo under MIMO-SAR configuration is built by dyadic Green's function, and the precise spectral echo expression is obtained through fast Fourier transform (FFT) and spherical-wave decomposition. Then, the image reconstruction of sparse MIMO-SAR is divided into separate single-input–multiple-output (SIMO)-SAR imaging problems, and the target's subimage corresponding to different SIMO-SAR setup can be quickly solved by employing inverse FFT, multistep phase compensation and wavenumber integration. Finally, the fully focused MIMO-SAR reconstructed image will be obtained by coherently accumulating all the SIMO-SAR results. Simulation analysis and experimental results validate the effectiveness the proposed algorithm.

An Efficient MMW 3-D Imaging Algorithm for Near-Field MIMO-SAR With Nonuniform Transmitting Array

In this letter, an efficient millimeter-wave (MMW) frequency-domain imaging algorithm is presented for 3-D object reconstruction of the near-field multiple-input–multiple-output synthetic aperture radar (MIMO-SAR) with nonuniform transmitting array. For each single-input–multiple-output (SIMO) case of the MIMO-SAR setup, the precise spectral echo expression is derived by spherical-wave decomposition and fast Fourier transform (FFT) operations. To obtain the linear phase in range direction, the multiorder approximation theory is employed to expand the coupling phases, and thus the target subimage can be reconstructed by utilizing phase compensation, central wavenumber approximation, and inverse FFT. Finally, the fully focused 3-D image for MIMO setup will be realized through accumulating all the SIMO subimages. Compared with the existing representative algorithms, our method avoids complicated interpolation and achieves high-quality fast imaging with only matrix multiplication and a small amount of iteration operations. The experimental results validate the effectiveness of the proposed algorithm.

An Efficient mmW Frequency-Domain Imaging Algorithm for Near-Field Scanning 1-D SIMO/MIMO Array

In recent years, millimeter-wave (mmW) 3D imaging technology for scanning 1D single-input multiple-output (SIMO) or multiple-input multiple-output (MIMO) array has been extensively studied due to its unique advantages in near-field applications. However, current imaging algorithms for this kind of scheme are not satisfactory, either of low quality since irrational approximations are introduced, or too slow as the back projection method is employed. In this paper, an efficient frequency-domain imaging algorithm is developed to fetch up these shortages. The precise spectral expression of the echo signal within SIMO data is derived through spherical-wave decomposition and fast Fourier transform (FFT) operations. By properly approximating the nonlinear phase, the wavefront curvature is compensated after employing a 1D Stolt interpolation, and then the reflectivity map of the target can be obtained through several multiplications and inverse FFT operations. Image reconstruction for a MIMO array can be realized by coherently summing up all the SIMO focusing results. Both simulation analysis and experimental results demonstrate the effectiveness of the proposed algorithm in imaging quality and computational efficiency.

Influence of Uncertainty of Body Permittivity on Achievable Radiation Efficiency of Implantable Antennas—Stochastic Analysis

Design of medical sensor implants is very challenging due to numerous restrictions in terms of size and biological acceptability. In addition, large absorption and reflection of electromagnetic waves in body tissues significantly degrades the communication link capabilities. The usual assumption in calculating the link budget is that the permittivity and conductivity of the body tissues are known. However, biological tissues show considerable diversity in structure and consequently in dielectric properties. The first aim of this article is to determine how much the uncertainty of the body tissues’ constitutive parameters affects the prediction of the achievable radiation efficiency of the implant. The second aim is to understand the loss mechanism and thus which tissue permittivity and/or conductivity has the dominant influence on losses. The analysis is done by considering a spherical multilayer human phantom and applying spherical wave decomposition proposed in a previous article. The stochastic collocation method is used to estimate the uncertainty of power density outside the human body, and sensitivity on the uncertainty of each tissue parameter is performed using the analysis of variance (ANOVA) approach. Several test cases were considered and the results clearly indicate which constitutive parameters have dominant effect on uncertainty.

Unveiling the third dimension in morphometry with automated quantitative volumetric computations

As computed tomography and related technologies have become mainstream tools across a broad range of scientific applications, each new generation of instrumentation produces larger volumes of more-complex 3D data. Lagging behind are step-wise improvements in computational methods to rapidly analyze these new large, complex datasets. Here we describe novel computational methods to capture and quantify volumetric information, and to efficiently characterize and compare shape volumes. It is based on innovative theoretical and computational reformulation of volumetric computing. It consists of two theoretical constructs and their numerical implementation: the spherical wave decomposition (SWD), that provides fast, accurate automated characterization of shapes embedded within complex 3D datasets; and symplectomorphic registration with phase space regularization by entropy spectrum pathways (SYMREG), that is a non-linear volumetric registration method that allows homologous structures to be correctly warped to each other or a common template for comparison. Together, these constitute the Shape Analysis for Phenomics from Imaging Data (SAPID) method. We demonstrate its ability to automatically provide rapid quantitative segmentation and characterization of single unique datasets, and both inter-and intra-specific comparative analyses. We go beyond pairwise comparisons and analyze collections of samples from 3D data repositories, highlighting the magnified potential our method has when applied to data collections. We discuss the potential of SAPID in the broader context of generating normative morphologies required for meaningfully quantifying and comparing variations in complex 3D anatomical structures and systems.

A FFT-Based Millimeter-Wave Imaging Algorithm with Range Compensation for Near-Field MIMO-SAR

In this article, an improved fast Fourier transform (FFT)–based millimeter-wave imaging algorithm with range compensation is presented, which can be used to reconstruct 3D images for near-field multiple-input multiple-output synthetic aperture radar (MIMO-SAR). The frequency-domain interpolation is avoided and only one-step spherical-wave decomposition is employed in this algorithm. During the image reconstruction process, the amplitude factor is considered for the compensation of signal propagation loss, and the final target image can be obtained by FFT/IFFT and coherent accumulation steps. As demonstrated with numerical theoretical analysis and experimental results, the proposed method greatly reduces the computational load but ensures the quality of image reconstruction compared to the back-projection (BP) algorithm. Moreover, it is superior to the MIMO-range migration algorithm (MIMO-RMA) in compensating propagation loss and other performance indexes in the image reconstruction results.

Spherical Wave Decomposition Based Polar Format Algorithm for ArcSAR Imaging

Arc synthetic aperture radar (ArcSAR) is a remote imaging technology with the ability of wide field of view in the principle of ground-based synthetic aperture radar (GB-SAR). The existing ArcSAR imaging algorithms have the problems of low computational efficiency as the scene expands and reduced imaging accuracy caused by the slant-range approximation. To avoid these problems, this article proposes a polar coordinate format algorithm based on spherical wave decomposition. First, the echo signal in the form of spherical wave is decomposed into an integral of plane waves. Second, according to the integration, an angular filter can be constructed by virtue of the convolution theorem, which is used to eliminate the high-order phase error in the scanning angle direction. Next, the interpolation from the polar to rectangular coordinates on the filtered signal is performed to achieve decoupling of the scanning angle and wavenumber. Finally, the target focusing is achieved by 2-D inverse Fourier transform. In this article, the imaging process is analyzed through simulation experiments and compared with other imaging algorithms in terms of imaging accuracy and efficiency. Moreover, the actual data are used for verification.

An Efficient Algorithm for MIMO Cylindrical Millimeter-Wave Holographic 3-D Imaging

A novel cylindrical millimeter-wave holography regime using a multi-input-multi-output (MIMO) array is first introduced. More importantly, an accurate and fast 3-D imaging algorithm is developed for this regime. Although many efficient imaging algorithms for synthetic aperture radar (SAR) or circular SAR have been developed, they can hardly be used for this new regime due to the compound effects of a spherical wavefront, MIMO geometry, and cylindrical observation aperture. In this paper, we develop an efficient algorithm mainly based on the ideas of a spherical wave decomposition, circular convolution, and nonuniform fast Fourier transform. The proposed algorithm achieves similar imaging quality with the golden-standard back-projection algorithm (BPA) while costs much less time. Compared with the BPA, the proposed algorithm belongs to a kind of the frequency-domain method built upon range migration techniques. Detailed derivations are first presented. Then, several important issues including resolutions, sampling criteria, and computational complexities are analyzed. Finally, a series of simulations and experiments are carried out, and all the results verify the effectiveness of the proposed algorithm on both accuracy and efficiency.

Range Migration Algorithm for Near-Field MIMO-SAR Imaging

In this letter, a 3-D range migration algorithm for multiple-input multiple-output synthetic aperture radar imaging is proposed. The accurate expression of the signal spectrum is derived by utilizing the spherical wave decomposition. This method compensates for the curvature of the wavefront in wavenumber domain and achieves the 3-D Fourier transform of the reflectivity map through a dimension-reducing accumulation operation. Its fast Fourier transform-based imaging scheme provides high imaging efficiency. In addition, this method does not take the plane wave approximation and can be applied in near-field imaging scenes. Both theoretical analysis and experimental results show that the proposed method can reconstruct the 3-D image as accurately as the backprojection algorithm but with much lower computational load.

Sound Source Localization Using Non-Conformal Surface Sound Field Transformation Based on Spherical Harmonic Wave Decomposition

Spherical microphone arrays have been paid increasing attention for their ability to locate a sound source with arbitrary incident angle in three-dimensional space. Low-frequency sound sources are usually located by using spherical near-field acoustic holography. The reconstruction surface and holography surface are conformal surfaces in the conventional sound field transformation based on generalized Fourier transform. When the sound source is on the cylindrical surface, it is difficult to locate by using spherical surface conformal transform. The non-conformal sound field transformation by making a transfer matrix based on spherical harmonic wave decomposition is proposed in this paper, which can achieve the transformation of a spherical surface into a cylindrical surface by using spherical array data. The theoretical expressions of the proposed method are deduced, and the performance of the method is simulated. Moreover, the experiment of sound source localization by using a spherical array with randomly and uniformly distributed elements is carried out. Results show that the non-conformal surface sound field transformation from a spherical surface to a cylindrical surface is realized by using the proposed method. The localization deviation is around 0.01 m, and the resolution is around 0.3 m. The application of the spherical array is extended, and the localization ability of the spherical array is improved.

3-D Antenna Radiation Pattern Reconstruction in a Reverberation Chamber Using Spherical Wave Decomposition

It has been shown that the correlation between the radiation patterns of two antennas can be measured in a reverberation chamber (RC). In this paper, it is shown that the self-correlation coefficient of an antenna, defined as the correlation between the radiation pattern of an antenna under test (AUT) and a transformed version of itself, can also be measured in an RC. It is found that the 3-D radiation pattern of the AUT can be reconstructed from the measured self-correlation coefficient by using spherical wave decomposition. Moreover, the axial ratio of the AUT can also be measured efficiently in the RC, when the pattern is directional. Numerical simulations and measurements in the RC and in an anechoic chamber have been undertaken. Good agreement is obtained, which confirms the validity of the proposed method. Thus, this novel method can become a very useful, cost-effective, and efficient method for 3-D antenna radiation pattern measurement.

Noise source identification by using near field acoustic holograpy and focused beamforming based on spherical microphone array with random unifrom distribution of elements

With the development of techlology, noise controlling has received wide attention in recent years. Noise source identification is the key step for noise controlling. Spherical microphone array, which can locate the noise source of arbitrary direction in three-dimensional space, has been widely used for noise source identification in recent years. Conventional methods of locating noise source include spherical near field acoustic holography and spherical focused beamforming. The acoustic quantities are reconstructed by using spherical near field acoustic holography method to realize the noise source identification, while the noise source can also be located by using focused beamforming based on spherical harmonic wave decomposition. However, both these methods have their own limitations when they are used in identifying the noise source. Spherical near field acoustic holography has low resolution at high frequency with a far distance from noise source to measurement array for noise source identification, whereas the spherically focused beamforming has low localization resolution at low frequency. Noise source identification is discussed here, and a 64-element microphone spherical array with randomly uniform distribution of elements is designed. The combination methods of noise source identification by using spherical near field acoustic holography and mode decomposition focused beamforming are investigated. The performance of the proposed combination method is simulated, and an experiment on noise source identification is carried out based on the designed spherical microphone array to test the validity of proposed method. Research results show that the high-resolution noise source identification can be achieved by using near field acoustic holography when reconstruction frequency is 100-1000 Hz with a distance 0.3-0.45 m from noise source to the center of spherical array, while high resolution of noise source localization can be achieved by using spherical wave decomposition beamforming when signal frequency is 1000-5000 Hz with a distance 0.5-3 m from noise source to the center of spherical array. Spherical array with random uniform distribution of elements maintains stable identification ability in all bearings. The spherical near field acoustic holography has high-resolution distinguishing ability in near field and at low frequency, while the focused beamforming method has high-resolution distinguishing ability in far field and at high frequency. Therefore the noise source can be efficiently identified by using the proposed combination method of near field holography and focused beamforming with less elements and small aperture spherical microphone array.

Minimal mass non-scattering solutions of the focusing <i>L</i><sup>2</sup>-critical Hartree equations with radial data

We prove that for the Cauchy problem of focusing \begin{document}$L^2$\end{document} -critical Hartree equations with spherically symmetric \begin{document}$H^1$\end{document} data in dimensions \begin{document}$3$\end{document} and \begin{document}$4$\end{document} , the global non-scattering solution with ground state mass must be a solitary wave up to symmetries of the equation. The approach is a linearization analysis around the ground state combined with an in-out spherical wave decomposition technique.

Quantitative Classification of Cerebellar Foliation in Cartilaginous Fishes (Class: Chondrichthyes) Using Three-Dimensional Shape Analysis and Its Implications for Evolutionary Biology

A true cerebellum appeared at the onset of the chondrichthyan (sharks, batoids, and chimaerids) radiation and is known to be essential for executing fast, accurate, and efficient movement. In addition to a high degree of variation in size, the corpus cerebellum in this group has a high degree of variation in convolution (or foliation) and symmetry, which ranges from a smooth cerebellar surface to deep, branched convexities and folds, although the functional significance of this trait is unclear. As variation in the degree of foliation similarly exists throughout vertebrate evolution, it becomes critical to understand this evolutionary process in a wide variety of species. However, current methods are either qualitative and lack numerical rigor or they are restricted to two dimensions. In this paper, a recently developed method for the characterization of shapes embedded within noisy, three-dimensional data called spherical wave decomposition (SWD) is applied to the problem of characterizing cerebellar foliation in cartilaginous fishes. The SWD method provides a quantitative characterization of shapes in terms of well-defined mathematical functions. An additional feature of the SWD method is the construction of a statistical criterion for the optimal fit, which represents the most parsimonious choice of parameters that fits to the data without overfitting to background noise. We propose that this optimal fit can replace a previously described qualitative visual foliation index (VFI) in cartilaginous fishes with a quantitative analog, i.e. the cerebellar foliation index (CFI). The capability of the SWD method is demonstrated in a series of volumetric images of brains from different chondrichthyan species that span the range of foliation gradings currently described for this group. The CFI is consistent with the qualitative grading provided by the VFI, delivers a robust measure of cerebellar foliation, and can provide a quantitative basis for brain shape characterization across taxa.

Automated segmentation and shape characterization of volumetric data

Characterization of complex shapes embedded within volumetric data is an important step in a wide range of applications. Standard approaches to this problem employ surface-based methods that require inefficient, time consuming, and error prone steps of surface segmentation and inflation to satisfy the uniqueness or stability of subsequent surface fitting algorithms. Here we present a novel method based on a spherical wave decomposition (SWD) of the data that overcomes several of these limitations by directly analyzing the entire data volume, obviating the segmentation, inflation, and surface fitting steps, significantly reducing the computational time and eliminating topological errors while providing a more detailed quantitative description based upon a more complete theoretical framework of volumetric data. The method is demonstrated and compared to the current state-of-the-art neuroimaging methods for segmentation and characterization of volumetric magnetic resonance imaging data of the human brain.

Comparison of different approaches to the numerical calculation of the LMJ focal

The beam smoothing in the focal plane of high power lasers is of particular importance to laser- plasma interaction studies in order to minimize plasma parametric and hydrodynamic instabilities on the target. Here we investigate the focal spot structure in different geometrical configurations where standard paraxial hypotheses are no longer verified. We present numerical studies in the cases of single flat top square beam, LMJ quadruplet and complete ring of quads with large azimuth angle. Different calculations are made with Fresnel diffraction propagation model in the paraxial approximation and full vector Maxwell's equations. The first model is based on Fourier transform from near to far field method. The second model uses first spherical wave decomposition in plane waves with Fourier transform and propagates them to the focal spot. These two different approaches are compared with Miro (1) modeling results using paraxial or Feit and Fleck options. The methods presented here are generic for focal spot calculations. They can be used for other complex geometric configurations and various smoothing techniques. The results will be used as boundary conditions in plasma interaction computations. where f(x,y) is the amplitude of the field with a spatial extension size of a and k0 = /c is the wave number of the field. The field expression in the k space (spatial frequencies) with one fast Fourier transform (FFT) requires a large number of points. But for a parabolic phase lens, plane wave decomposition of the electric field in the k space with double FFT allow to reduce the spatial sampling (2048 points instead of 256000 for a = 1.2m and zf = 0.8m). The plane wave decomposition with two FFT is given by:

A NEAR-FIELD 3D CIRCULAR SAR IMAGING TECHNIQUE BASED ON SPHERICAL WAVE DECOMPOSITION

A near-fleld three dimensional imaging algorithm for circular SAR is proposed in this paper. It adopts the theory of spherical wave decomposition to transform Green function to a superposition of plane wave components. Using this relation, the image-reconstruction can be implemented in frequency domain instead of in spatial domain, which simplifles the solving process of target re∞ectivity function, and allows for the target to be near to the radar. Through compensating phase factor and flltering at each elevation, we flrstly get the ground CSAR signal of each elevation in frequency domain. Then, performing two dimensional inverse nonuniform fast Fourier transform and accumulating the results of all azimuth angles, the reconstructed two dimensional image corresponding to an elevation is achieved. Finally, using reconstructed image datum of all elevation, the three dimensional image of target is obtained. To demonstrate the imaging performance of our method, numerical simulations and experiments are conducted. By comparing the results with the focusing operator algorithm and the back-projection algorithm, it is found that the proposed algorithm is more e-cient and can obtain a good imaging performance.

A parametric study of interactions between acoustic signals reflected by the seafloor

This paper deals with the study of broadband acoustic signals reflected by the seafloor and recorded on a vertical array in shallow water areas. Only the first bottom reflected path is considered here. In previous studies (see e.g., Guillon and Holland, JASA, 122, 2974), two different aspects of the "coherence" of these signals were examined (the maximum of the cross-correlation coefficients and the phase of the cross-spectra) and it was shown that these parameters are sensitive to the geoacoustic nature of the seafloor. These results show that the interactions between signals can be used efficiently for improving geoacoustic inversion schemes or for transmission loss predictions. Before going to such applications, a detailed parametric study is needed to investigate the sensitivity of the interactions measurement to various parameters (range, geoacoustic structure,...). This is done using a numerical model, based on the spherical wave decomposition of plane waves, that simulates the signals reflected by the seafloor. The parametric study lead shows the relative importance of the various parameters and gives indications for the possibility of inverting these parameters.