Deep Shadow Region Research Articles

Geometrical Theory of Diffraction Formulation for On-Body Propagation

A geometrical theory of diffraction model for on-body propagation is developed in this paper. The exact solution to the canonical problem of a plane wave incident on an infinitely long cylinder, with arbitrary constitutive parameters, is found. The same is done for a magnetic and an electric infinitesimal dipole source of any orientation, located on the surface of the cylinder. The exact solutions are transformed with the Watson transformation to yield asymptotic expressions that are valid in the deep shadow region. These asymptotic expressions are validated by comparison to the numerically evaluated exact solution. It is found that the expressions are valid as long as the object is opaque, with a geometry down to the size of (κ/κ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> + τ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) > λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> /2, and the rays not too torsional τ/κ <; 2, where κ and τ are the curvature and torsion of the local geometry, respectively. The asymptotic expressions are found to approximate the exact solution significantly better than the asymptotic expression of an equivalent perfect electric conductor geometry. The same is the case for the impedance boundary condition asymptotic approximation for low dielectric constant materials. Finally, the asymptotic expressions are generalized so they can be applied to any convex geometry of the human body or an opaque lossy dielectric of electrically large size.

Asymptotic expansions of the Helmholtz equation solutions using approximations of the Dirichlet to Neumann operator

This paper is concerned with the asymptotic expansions of the amplitude of the solution of the Helmholtz equation. The original expansions were obtained using a pseudo-differential decomposition of the Dirichlet to Neumann operator. This work uses first and second order approximations of this operator to derive new asymptotic expressions of the normal derivative of the total field. The resulting expansions can be used to appropriately choose the ansatz in the design of high-frequency numerical solvers, such as those based on integral equations, in order to produce more accurate approximation of the solutions around the shadow and the deep shadow regions than the ones based on the usual ansatz.

Illumination normalization based on correction of large-scale components for face recognition

A face image could be decomposed into two components of large- and small-scale components, which carry low- and high-frequency contents of the original image, respectively. The illumination field mainly locates in the spectrum of large-scale components, whereas the small-scale components hold the detailed image cues, like edge, corner, etc., which are less sensitive to the illumination changes. In this paper, we proposed a new illumination normalization framework with the idea of Correction on Large-scale Components (CLC). The logarithmic total variation (LTV) technique is firstly applied to decompose the large- and small- scale components of face images. We assume that there are two main contents in the large-scale components: the smoothly varied illumination field and the large-scale intrinsic facial features. Based on this assumption, an energy minimization framework is proposed to estimate and remove the smoothly varied field of the large-scale components in an interleaving fashion. The final normalization results can then be achieved with the integration of the smoothed small-scale components and the corrected large-scale components. Experiments on CMU-PIE, Extended Yale B and CAS-PEAL-R1 databases show that the proposed method can present a very good visual quality even on the images illuminated with deep shadow and high brightness regions, and attain promising illumination normalization results for better face recognition performance.

Location and Sizing of Defects in Coated Metallic Pipes Using Limited View Scattered Data in Frequency Domain

The inverse problem of reconstructing the location and size of defects in a coated metallic pipe from single frequency limited view electromagnetic scattered field is considered. Specifically, the paper addresses the problem of assessing shape changes in the shadow region entailed by limited view data in 2D by operating in an intermediate size parameter (ka) range. The inverse scattering problem is formulated as a non-linear optimization problem solved through genetic algorithm that seeks to minimize in the least-squared sense the difference between measured data and simulated data through iterations of the solution to a forward problem. The hybrid finite element boundary integral formulations were used to solve the forward problem of coated metallic pipe with defects. The proposed inversion methodology was applied for shadow region shape change assessment to determine whether a metal pipe is coated or not, and to reconstruct the location and size of corrosion-like defect, over a range of size parameters. The study is carried out using transverse electric and transverse magnetic polarized fields. To understand the effect of coating on backscattered fields, parametric studies are conducted using numerical data. A range for size parameter \(2.0\le ka\le 4\) was found to produce the highest contrast between defect free pipe and coated metallic pipes with defects in the deep shadow region. The experiments are carried out using vector network analyzer in an anechoic chamber. The inversion results obtained using measured data were found be in good agreement with inversion results obtained using synthetic data. Estimated extent of corrosion in deep shadow region of a coated metallic pipe was found to be within 9 % of actual extent of corrosion.

Frequency-adapted Galerkin boundary element methods for convex scattering problems

We introduce a class of hybrid boundary element methods for the solution of sound soft scattering problems in the exterior of two-dimensional smooth convex obstacles. To facilitate the applicability of our algorithms throughout the entire frequency spectrum, we have enriched our Galerkin approximation spaces, through incorporation of oscillations in the incident field of radiation, into the algebraic and trigonometric polynomial approximation spaces. The resulting methodologies have three distinctive properties. Indeed, from a theoretical point of view (1) they can be tuned to demand only an$$\mathcal {O}(k^{\varepsilon })$$O(kź)increase (for any $$\varepsilon >0)$$ź>0)in the number of degrees of freedom to maintain a fixed accuracy with increasing wavenumberk, owing to the optimal adaptation of approximation spaces to asymptotic stretching (shrinking) of illuminated and deep shadow regions (shadow boundaries), and (2) they are convergent for each fixed wavenumberk, thanks to the additional approximation spaces in the deep shadow region. Perhaps more importantly, from a practical point of view (3) they give rise to linear systems with significantly enhanced condition numbers and this, in turn, allows for more accurate solutions if desired.

Estimating ground fractional vegetation cover using the double-exposure method

Fractional vegetation cover (FVC) is a key parameter in ecological models. It is important to determine the ground FVC quickly and accurately in studies of soil erosion, surface energy balance, and carbon cycling. As one of the FVC ground measurement methods, the photographic method is easy to operate with relatively high precision. However, its classification result showed poor accuracy when an image of a high-contrast scene contained a shadow region where a low signal-to-noise ratio (SNR) existed, because the single-exposure image in the photographic method did not contain sufficient surface information about both the illuminated and shadowed parts. This article presents application of a double-exposure photographic method to determine vegetation cover in the shadow region of an image. It consists of two measurements used in acquiring images (normal and over-exposure) and one image-processing part to handle the obtained images. Illuminated vegetation and soil, as well as the shadow region, was classified with the normally exposed image in the intensity, hue, and saturation (IHS) colour space, and the shadow region was further classified as shadowed vegetation and shadowed soil using the over-exposed image. The results indicate that the over-exposed image reduced the average bias of the FVC in the shadow region from 15.40% to −4.14% and the root mean square error (RMSE) from 0.174 to 0.066. The RMSE of the entire scene was 0.055 in the over-exposed image and 0.092 in the single-exposed image. The double-exposure method also showed a better classification result than the high dynamic range method in deep shadow regions. This study shows that this method is capable of distinguishing vegetation and soil in the shadow region and thus it is an effective and accurate method for ground FVC measurement.

The Contour Deformation Method for Calculating the High-Frequency Scattered Field by the Fock Current on the Surface of the 3-D Convex Cylinder

In this paper, the high-frequency diffracted waves like the creeping waves are comprehensively analyzed by the Fock currents. On invoking the contour deformation method, the highly oscillatory Fock currents are efficiently calculated. Furthermore, the workload for the calculation of Fock currents is frequency-independent. To capture the high-frequency wave physics phenomenon, the Fock current is separated into the classical physical optics (PO) current and the nonuniform (NU)-Fock current along the shadow boundary and in the deep shadow region. To calculate the highly oscillatory scattered wave fields from the Fock current, quadratic approximations of the phase functions in the integrand are adopted. On invoking the numerical steepest descent path (NSDP) method, the scattered wave fields are efficiently calculated with frequency-independent computational effort and error controllable accuracy in each frequency-independent segment. Meanwhile, the high-frequency creeping wave coming from the NU-Fock current is efficiently captured by the NSDP method. Numerical results for the Fock currents, the high-frequency NU-diffracted and scattered far fields on the convex cylinders are given to validate the efficiency of the proposed method. Furthermore, the contour deformation method for computing the Fock currents offers a clear physical picture for the high-frequency wave fields on the convex scatterer.

A Fast 3-D Deterministic Ray Tracing Coverage Simulator Including Creeping Rays Based On Geometry Voxelization Technique

A deterministic ray tracing simulator is described in this work which conveniently fulfills the requirements of a radar coverage, i.e., field distribution, simulator at 24 GHz or above. Very high performance is achieved by avoiding computational loops due to the usage of same-size matrices. The considered geometry is defined by a voxelization technique to improve the flexibility of this family of ray tracers. A reliable root finder which locates all roots of an equation simultaneously is used to efficiently find the intersections of the rays and the objects based on analytical geometry representations. Also, illumination matrices identify the contributing rays for all the observation points and simplify the process of field superposition. Creeping rays are included into the simulator for more accurate transitions from the illuminated to the deep shadow regions. Furthermore, the proposed simulator is capable of carrying out large bandwidth tasks such as channel impulse response computations. The results approve the capability of the simulator to be used as an optimization and design tool for complex and electrically large scenarios of a radar system including moving targets.

Frequency-Domain and Time-Domain Novel Uniform Asymptotic Solutions for Scattered Fields by an Impedance Cylinder and a Dielectric Cylinder

Frequency-domain and time-domain novel uniform asymptotic solutions for the scattered fields by an impedance cylinder and a dielectric cylinder, with a radius of curvature sufficiently larger than the wavelength, are presented in this paper. The frequency-domain novel extended UTD and the modified UTD solutions, derived by retaining the higher-order terms in the integrals for the scattered fields, may be applied in the deep shadow region in which the conventional UTD solutions produce the substantial errors. The novel time-domain uniform asymptotic solutions are derived by applying the saddle point technique in evaluating the inverse Fourier transform. We have confirmed the accuracy and validity of the uniform asymptotic solutions both in the frequency-domain and in the time-domain by comparing those solutions with the reference solutions calculated from the eigenfunction expansion (frequency-domain) and from the hybrid eigenfunction expansion and fast Fourier transform (FFT) method (time-domain).

Radiation Pattern Analysis of Reflector Antennas--Discussions and Hybrid Use of Physical Optics and Aperture Field Integration Method--

This paper reviews the approximation principle of Physical Optics in view of diffraction theory. Two key error factors are identified for PO, that is, 1) errors in edge diffraction coefficients and 2) fictitious penetrating rays. Improved methods named PO-AF and PTD-AF are proposed as the methods which suppress the fictitious penetrating rays from PO and PTD respectively. In deep shadow regions of the reflector antennas, PO-AF and PDT-AF approach to PO-EEC and UTD respectively, while the continuity is assured. The effectiveness is numerically demonstrated for two dimensional scatterers.

Influence of diffraction coefficient and corner shape on ray prediction of power and delay spread in urban microcells

For a low base-station (BS) antenna located on one street, signals propagate into crossing and parallel streets by reflection and diffraction at corners of buildings. Therefore, in order to accurately predict the received signals, it is necessary to properly model the diffraction coefficient at the building edge and to accurately represent the shape and the electrical properties of the building near the corner. This paper compares ray-tracing predictions to measurements of received power and root mean square (rms) delay spread and shows the need for a diffraction coefficient having larger values than suggested by the commonly used heuristic diffraction coefficient. A new heuristic diffraction coefficient is proposed that has higher diffracted field strength in the deep shadow region and in the region between the two shadow boundaries. The proposed diffraction coefficient shows better agreement with measurements of both received power and delay spread compared to the commonly used heuristic diffraction coefficient. The influence of building shape near the corner and its electrical properties on the ray-tracing predictions are also presented. The shape is shown to have an important role in accurately predicting both received power and delay spread.

Investigation into the sensitivity of the power predictions of a microcellular ray tracing propagation model

This paper investigates the sensitivity of the three-dimensional (3-D) ray tracing microcellular model presented in Astanasiadou et al. (1995, 2000). The variation of the received power is examined for different ray permutations, wall characteristics, antenna position offsets and database inaccuracies. Predictions of the different configurations in line-of-sight (LOS), non-LOS (NLOS), and deep shadow areas are compared with each other and also with narrowband measurements. The analysis illustrates that although the model produces reliable results with five orders of reflection and one order of diffraction, higher orders of reflection and double diffracted rays enhance the model's performance in deep shadow areas. It is also shown that good agreement with measured results can be obtained for wall conductivity in the order of 10/sup -3/ S/m and values of relative permittivity around five. The sensitivity analysis to the antenna positioning and database inaccuracies indicates that the receiver positions which suffer the highest power deviations are those at the boundaries of the LOS areas, as well as the positions in the deep shadow regions. In general, for antenna offsets up to 1 m, the predictions of the model are not significantly affected. Finally, the building databases with 1m maximum displacement do not have severe effects on the predictions, but databases with less accuracy can seriously degrade the performance of the model.

RCS reduction of canonical targets using genetic algorithm synthesized RAM

Radar cross section (RCS) reduction of canonical (planar, cylindrical, and spherical) conducting targets is the focus of this paper. In particular, a novel procedure is presented for synthesizing radar absorbing materials (RAM) for RCS reduction in a wide-band frequency range. The modal solutions of Maxwell's equations for the multilayered planar, cylindrical, and spherical canonical structures is integrated into a genetic algorithm (GA) optimization technique to obtain the best optimal composite coating. It Is shown that by using an optimal RAM, the RCS of these canonical structures can be significantly reduced. Characteristics of bistatic RCS of coated cylindrical and spherical structures are also studied and compared with the conducting structures without coating. It is shown that no optimal coating can be found to reduce the RCS in the deep shadow region. An in-depth study has been performed to evaluate the potential usage of the optimal planar coating as applied to the curved surfaces. It is observed that the optimal planar coating can noticeably reduce the RCS of the spherical structure. This observation was essential in introducing a novel efficient GA with hybrid planar/curved surface implementation using as part of its initial generation the best population obtained for the planar RAM design. These results suggest that the optimal RAM for a surface with arbitrary curvature may be efficiently determined by applying the GA with hybrid planar/curved surface population initialization.

An iterative current-based hybrid method for complex structures

This paper presents a general unified hybrid method for radiation and scattering problems such as antennas mounted on a large platform. The method uses a coupled electric-field integral equation (EFIE) and magnetic-field integral equation (MFIE) formulation, referred to as the hybrid EFIE-MFIE (HEM), in which the EFIE and MFIE are applied to geometrically distinct regions of an object. The HEM is capable of modeling arbitrary three-dimensional (3-D) metallic structures, including wires and both open and closed surfaces. We show that current-based hybrid techniques that utilize physical optics (PO) are an approximation of the HEM formulation. A numerical solution procedure is given that combines the moment method (EFIE) with an iterative Neumann series technique (MFIE). This permits one to effectively utilize the PO approximation when appropriate, and provides a general and systematic mechanism to correct the errors introduced by PO. Consequently, the HEM overcomes the inherent limitations of hybrid techniques which rely upon ansatz-based improvements of PO. The method is applied to the problem of radiation from objects that can be modeled using wires and metallic surfaces as fundamental elements. A representative example is given to demonstrate that the method can handle the difficult problem of a parasitic monopole located in the deep shadow region.

On the asymptotic frequency behavior of uniform GTD in the shadow region of a smooth convex surface

A number of canonical plane-wave and line-source solutions involving circular cylinders have led to a widely accepted uniform geometrical theory of diffraction (GTD) formulation for the scattered electromagnetic field in the shadow region of a smooth convex surface. The current solution does not constitute a properly formulated asymptotic high-frequency theory in the sense that it becomes increasingly inaccurate with increasing frequency. This inaccuracy results from transition-function dominance in the deep shadow region over the Pekeris caret function that is used. An improved formulation that circumvents this difficulty by avoiding use of a transition function is derived via a straightforward extension of the canonical line-source solution given by Jones (1963). This new solution takes the form of Keller-type modes with modified diffraction coefficients that result in convergence at the shadow boundary provided that the source and observation point are not both located at asymptotic distances from the scatterer.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

High-frequency surface field excited by a magnetic line source on an impedance cylinder

The evaluation of the transverse electric (TE) surface field on an impedance boundary circular cylinder, excited by a magnetic current on the same surface is discussed. The source is of infinite axial extent. The integral which describes the field due to a single surface ray is evaluated numerically and asymptotically. The results compare well with each other as well as with the eigenfunction solution. The surface ray field has a uniform representation in the sense that it remains valid in the immediate vicinity of the infinitesimal source as well as in the deep shadow region. A comparison is made with a flat impedance plane to indicate the influence of curvature on the surface field.

Experimental study of a slotted telemetry antenna array with a shaped beam for satellite communication

The far-field distribution of a travelling type triangular array of slots on a circular waveguide is evaluated experimentally. The efficacy of the antenna as a satellite onboard antenna is examined, and it is found that such an antenna can indeed be characterised as a good telemetry antenna. With the dominating mode propagating in the guide, the radiation pattern of a single slot, array of slots and array of arrays is obtained experimentally. The experimentally obtained E-plane radiation pattern of a single slot in the illuminated region compared with the theoretically obtainedresults of geometrical optics and Shafai and Hassan&apos;s modematching technique. In a similar manner GTD is used to confirm the experimentally obtained results in the transition and deep shadow regions. The comparison is found to be very good.

A uniform GTD solution for the radiation from sources on a convex surface

A compact approximate asymptotic solution is developed for the field radiated by an antenna on a perfectly conducting smooth convex surface. This high-frequency solution employs the ray coordinates of the geometrical theory of diffraction (GTD). In the shadow region the field radiated by the source propagates along Keller's surface diffracted ray path, whereas in the lit region the incident field propagates along the geometrical optics ray path directly from the source to the field point. These ray fields are expressed in terms of Fock functions which reduce to the geometrical optics field in the deep lit region and remain uniformly valid across the shadow boundary transition region into the deep shadow region. Surface ray torsion, which affects the radiated field in both the shadow and transition regions, appears explicitly in the solution as a torsion factor. The radiation patterns of slots and monopoles on cylinders, cones, and spheroids calculated from this solution agree very well with measured patterns and with patterns calculated from exact solutions.