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Second order statistical moments of scattered electromagnetic waves in the turbulent magnetized plasma slab with electron density fluctuations are calculated applying the modify stochastic smooth perturbation theory and the boundary conditions. The obtained results are valid for arbitrary correlation function of electron density fluctuations. Stokes parameters are analyzed both analytically and numerically. The theory predicts that depolarization effect caused by second Stokes parameter may be important in scintillation effects. Numerical calculations are carried out for new spectral function of electron density fluctuations containing both anisotropic Gaussian and power-law spectral functions using the experimental data. Polarimetric parameters are calculated for different anisotropy factor and inclination angle of elongated small-scale irregularities with respect to the magnetic lines of forces. The relationship between the scintillations and the polarimetric parameters is important. Web of Science 8 2 84 77

This chapter discusses some key formulations in biomedical electromagnetics (EM). Extensive work has been reported on static through terahertz coupling to bodies near fields, cell phones, specific absorption rate (SAR), narrow and UWB pulse in biological systems. The chapter considers specific absorption rate (SAR) and heat diffusion in tissues. It describes the diffusion approximation of the radiative transfer theory. In the diffusion approximation, the specific intensity has a broad angular spectrum and therefore the diffused wave cannot be focused into a small volume. There is a way to focus the diffused wave, but the focusing requires constructive interference near the focal point and destructive interference elsewhere. The chapter also discusses fundamentals of ultrasound scattering and imaging of tissues and blood. Optical coherence tomography (OCT) was introduced to obtain noninvasive images of biological images of biological tissues with resolutions of 1‐15 μm.

One of the important current problems is imaging and detection of objects hidden by obscuring obstacles. There have been extensive works reported on “Through-Wall Imaging” in recent years. This paper extends the previous works to the case where the wall is non-penetrating and the diffraction around the edge becomes important. This hard-wall imaging is related to the historical problem of “Poisson Spot” and “Anti-Podal point.” This paper makes use of the modified time-reversal technique and GTD, and shows the formulations of the multistatic data matrix, eigenvectors and steering vectors to form the imaging function. Signal processing includes the multiplicative modified time reversal technique to eliminate the unwanted extraneous images. Numerical examples include comparisons between the modified and the conventional time-reversal imaging to show the effectiveness of the hard-wall imaging method.

It has been recognized that unequally spaced arrays can offer some advantages over equally spaced arrays, mainly in the following areas: 1) thinned array by reducing the number of elements to achieve the high resolution without producing grating lobes; 2) broadbanding or wide scanning without grating lobes; 3) reducing sidelobes for the array of uniform amplitude; and 4) unequally spaced arrays on a curved surface. Historical accounts and a basic theory of unequally spaced arrays based on Poisson Sum Formula are given. Most of the analytical approach can be obtained by numerical computation. Analytical methods may show additional physical mechanisms and offer alternative approaches. This paper also discusses some additional applications on circular arrays, active impedance and arrays on a curved surface.

This paper considers the imaging of objects located close to rough surfaces such as ocean or terrain. If transmitters and receivers are also located close to rough surfaces, incident wave is no longer a plane wave nor a spherical wave in free space and it is necessary to consider Green’s functions with the point source located close to the surface, similar to the Sommerfeld dipole problem. This paper considers the near-surface imaging by making use of time-reversal imaging and surface flattening transform. Surface flattening transform converts the rough surface problem into flat surface with inhomogeneous random medium. Mutual coherence function is obtained and used to obtain imaging of point target near rough surface, making use of the multi-static data matrix, time-reversal matrix, the eigenvectors, and the steering matrix. Numerical examples are given. An important point is that integration of stochastic wave propagation and signal processing is necessary to obtain imaging through complex clutter envir...

Imaging of objects through complex environment is important in several applications, including imaging of hidden objects in obscuring media such as atmospheric and ocean turbulence, rough ocean surfaces, rain, fog, snow, and biological tissues. These media are often randomly varying in space and time, and statistical treatments are necessary to obtain images with useful spatial and temporal resolutions. In recent years, there has been increasing interest in using signal processing and correlation techniques to improve resolutions and to distinguish images from clutter. This paper presents several imaging techniques for objects in the presence of random media. Time-reversal MUSIC (multiple signal classification) imaging has excellent resolution when multiple scattering is small or moderate. Modified beamformer imaging has moderately high resolution even at large multiple scattering. We also include time reversal (TR) and synthetic aperture radar (SAR) imaging for comparison. The technique involves stochastic Green's function and mutual coherence function (MCF), eigenvectors of time-reversal matrix and pseudo spectrum. Numerical examples are given to show the effectiveness of these imaging techniques.

The mutual correlation function of the phase ∞uctuations of scattered ordinary and extraordinary waves by the magnetized plasma slab with electron density ∞uctuations and the variance of the Faraday angle is calculated by the perturbation method. Analytical expression of broadening of the spatial spectrum of scattered radiation is obtained for arbitrary ∞uctuation spectrum. Numerical calculations are carried out for the anisotropic Gaussian ∞uctuation spectrum at difierent anisotropy factor and the angle of inclination of prolate irregularities with respect to the external magnetic fleld. Isolines of the normalized root mean square deviation of the Faraday angle nonlinearly depends on the angle of inclination of prolate irregularities and increases in proportion to the anisotropy factor; two receiving antennas are located in orthogonal planes. It is shown that the broadening of the spatial spectrum of scattered electromagnetic waves

Multiple input-multiple output systems have received considerable attention because of their potential to achieve high channel capacity. This paper presents a study of the effects of a random scattering medium on channel capacity. Formulations are given including stochastic Green's functions and mutual coherence functions. Transmitter and receiver characteristics are included and analytical formulation for eigenvalues and channel capacities are given in terms of the medium scattering characteristics, optical depth, frequency, number of transmitter and receiver elements, transmitting power, and noise spectral power. As an example, we show 500 m link at 60 GHz through rain. The eigenvalues and the channel capacity are calculated in terms of SNR and the rain rate representing the optical depth. It is shown that as the rain rate increases, the correlation of waves at antennas decreases and the capacity increases. However, at high rain rate, the capacity tends to decrease due to the absorption and scattering.

In order to improve the performance of terrestrial free-space optical communication systems in adverse visibility conditions, we present a method for estimation of the atmospheric channel impulse response function which governs the optical intensity propagation. This method reduces run-time computational demands and system complexity in comparison to our previously proposed dual-wavelength channel estimation technique. We consider propagation of optical wavelengths in fog, where the droplet diameters are close to the wavelength and thus scattering and absorption effects are significant. A method for rapid calculation of a channel response function based on estimating the effective optical depth of the channel and curve-fitting is described. The channel response estimate can then be used to design a receiver-side equalizer (minimum mean-squared error linear equalizer) to correct the signal distortion due to propagation through the dispersive channel. The channel estimates are based on parametric curve-fitting functions which have been developed using the modified-vector radiative transfer theory to model the channel response. The optimal fit parameters are found using particle-swarm optimization to minimize the simulated bit-error rate of the received signal.

We analyse the problem of the estimation of the angle of arrival in discrete random scattering media. Assuming incidence of a plane wave, we derive the performance of the determination of the angle of arrival in terms of beamwidth, which reflects the ability to resolve the angle of arrival from several directions. The minimum variance beamformer or Capon beamformer is applied. We demonstrate that in random scattering media the signal arriving at the receiving array shows correlation and is modelled as a Gaussian function, and this correlation deteriorates the ability to determine the angle of arrival. A matrix compensation is introduced to improve the performance by correcting the correlation. The main parameter in compensation is the correlation length. We investigate the effect of the correlation length on the angle of arrival.

Imaging through discrete random media is an important problem in several applications such as medicine, remote sensing, and security. Discrete random media create scattering which deteriorates the quality of the image and there have been several efforts to mitigate the problem. We propose an array processing method called coherence tomography array (CTA) whose algorithm is derived from that of optical coherence tomography. We use the Monte Carlo method to simulate the imaging scenarios in random scattering media. The results show that CTA can be used to alleviate the clutter effects from discrete random scatterers.

Features of spatial power spectrum (SPS) of scattered radiation in a randomly inhomogeneous medium with strongly prolated anisotropic inhomogeneities of dielectric permittivity are investigated. In single scattering approximation, it has been shown that a pronounced gap along a direction of prolate inhomogeneities appears in SPS. Features of SPS of multiple scattered waves at oblique illumination of a boundary of randomly-inhomogeneous medium with prolate irregularities have been analytically studied using smooth perturbation method taking into account diffraction effects. Numerical calculations have shown that with an increase of a distance passing by 192 Gavrilenko et al. the wave in random media, SPS has a double-peaked shape and a gap substantially increases. Its maximum is slightly changed and the width is broadening. The results have been obtained analytically for the first time and could find extensive practical application in optics and be useful in development of principles of remote sensing of random media.

Wireless power transfer (WPT) is a popular research field in recent years and can be categorized into three approaches: inductive coupling, laser beaming, and microwave power transmission (MPT). MPT system operates at the microwave and transfers the energy over more than a few wavelengths. It has its unique advantages of supplying power to non-accessible and mobile receivers. The overall efficiency, which is the ratio between available DC power at the receiver and supplied DC power at the transmitter, depends on both circuit design and wave propagation. As a comprehensive theory of MPT system is not available, this chapter starts with the study of MPT system from the perspectives of mathematical formulation and the experiment in the indoor environment, in Sect. 3.1. The preliminary study leads to the conclusion that highly directional wireless transmitter is very useful in the MPT system for achieving high transmission efficiency. For this reason, phased array antennas with beamforming functionality are usually used to direct the electromagnetic wave toward mobile receivers, and adaptive array algorithms are implemented to enable wireless power focusing in the complex environment. Section 3.3 presents a novel beamforming algorithm, which is proven to give the optimal transmission efficiency and applies to the arbitrarily positioned unequal array based on our problem formulation. To verify this algorithm, Sect. 3.4 validates it with numerical electromagnetic simulation in different cases. The numerical comparison in these examples shows that this algorithm gives higher transmission efficiency over other optimal beamforming algorithms discussed in Sect. 3.2.

A general formulation of a theory of imaging through random obscuring layers is described. Previously we presented a theory for the temporal behavior of a short pulse scattered from a random medium and from a point target. In this paper, we generalize our study to include the imaging of objects of finite size and the actual imaging pattern at the receiver. This involves the study of two-frequency fourth order moments. Numerical examples are given to illustrate several important features, including the optical depth, backscattering enhancement, shower curtain effects, aperture size, bandwidth and target size.

A simple steerable array antenna is designed and developed using a movable dielectric phase shifter. The change of effective dielectric constant at different dielectric slab positions on a coplanar waveguide is used as the phase shifter. The impedance matching and desired phase shift conditions are satisfied at two slab heights, and the reflection is designed to be minimized at these slab positions. The low-loss dielectric material is used as the dielectric slab and is placed close to a coplanar transmission line with airgap. The 4times4 steerable array antenna with the phase shifters is designed and fabricated at 20 GHz. The H-plane radiation patterns are measured at different phase shift positions and compared with the expected results

In addition to being an outstanding theoretician, researcher, and educator, Prof. Felsen loved to write poetry, as evidenced by his Poet's Corner, which he regularly published in this Magazine. It is therefore fitting that our community, and this Magazine in particular, honor Prof. Felsen and bid farewell by having this final Poet's Corner devoted to him. We offer here a collection of 13 poems, 11 of which were contributed by family members, colleagues, friends, and admirers of Prof. Felsen. We open with three poems written by family members: Prof. Felsen's son, Michael; his daughter, Judy; and one of his grandchildren, Sam. We next present a set of nine poems, with eight of them being written by colleagues and friends of Prof. Felsen, arranged in alphabetical order by the authors' last names. One of the nine poems is a poem written by Prof. Felsen to the contributor. Finally, the last poem is one written by Prof. Felsen himself, titled "As I Look Back Upon My Life." This seems like an appropriate way to end this Poet's Comner.

It has been noted that angular and frequency correlations of the scattered wave from multiple scattering or rough surfaces exhibit the characteristics indicating that the scattered wave remembers the angular and frequency characteristics of incident wave under certain conditions. This is called the “Memory Effects” and was discussed by Feng in 1988. In July 2014 at URSI meeting in Memphis, we presented a preliminary study of the use of Memory Effects to reduce the clutter from rough surface and to improve the resolution of images of objects located near rough surface.

“Through-Wall Radar Imaging” (TWRI) has been studied extensively to reconstruct the image from the backscattered waves through the opaque dielectric wall. When the objects are located in the shadow region of the metallic wall (hard wall) where the waves can only bypass the wall via diffraction, a new problem arises as “Hard-Wall Radar Imaging” (HWRI), which has been proposed and discussed in our previous papers.

Statistical Electromagnetic Theories have been developed over many years and applied to a wide range of practical problems in remote sensing of geophysical media, biological media, medical optics, ultrasound imaging and object detection and communication in clutter. This paper gives a review of recent developments in applications of statistical wave theories. The super resolution of images occurs in random media due to the multiple scattering and the increase of apparent aperture size of the transmitter. Another interesting effect is that the scattered wave from multiple scattering remembers the direction of the incident wave and strong correlations can be observed under certain conditions. This is called the “Memory Effect”. Recent study shows that under certain conditions, the angular and frequency correlations of the scattered wave can be enhanced or reduced and this effect can be used to reduce the clutter from the rough surface. It is also noted that the coherence in multiple scattering causes the increase of radar cross sections in turbulence due to the interference between the forward and backward waves, called the “double passage effect”. This is related to the Anderson localization and the coherent backscattering.

This paper presents a theory of imaging objects behind layers of scattering media. The transmitter is a focused array or an aperture emitting a short pulse. The scattered pulse is received by a focused array or aperture. The received signal consists of two components: the pulse scattered from a random medium and from the target, and these two components can be distinguished by the use of ultra wide band (UWB) pulse. The second moment of the received signal includes the fourth-order moments of stochastic Green's functions, which are reduced to the second moments by the use of the circular complex Gaussian assumption, and of the generalized two-frequency mutual coherence function. This imaging theory is a generalization of optical coherence tomography (OCT), SAR and confocal imaging. It clarifies the relationships among resolution, coherence length, shower curtain effects and backscattering enhancement.

Most electromagnetic problems deal with media with unit permeability. However, recent interest in metamaterials necessitated studies of wave characteristics in media with arbitrary permittivity and permeability whose real parts can be positive or negative. This paper presents analysis of wave characteristics on semiinfinite metamaterials. Waves are excited by electric or magnetic line sources, and the problem is separated into the p (TM) and the s (TE) polarization, showing symmetries. The Fourier spectra of the reflection and transmission coefficients are examined and the poles, branch points, and zeros are shown in the real /spl mu/-real /spl epsi/ diagram. We clarify the location of poles in proper and improper Riemann Surfaces, and the excitation of forward and backward surface waves, forward and backward Lateral waves, and Zenneck waves, and the relations between Brewster's angle and Sommerfeld poles. We include the behaviors of the backward surface waves and the temporal backward Lateral waves.

Optical surface plasmon resonance sensors have been known for a long time. In this paper, we discuss the use of metamaterials to construct a surface plasmon sensor which can be used at microwave frequencies. We review the conditions for the existence of surface plasmon and the use of the forward and backward surface waves. A sharp dip in the reflection coefficient occurs when the propagation constant of the incident wave along the surface is nearly equal to the propagation constant of the plasmon surface wave and may be used to probe bulk material characteristics or to determine metamaterial characteristics. Numerical examples are given to illustrate the basic characteristics.

This paper presents a quasi-static analysis of a metama- terial consisting of a three-dimensional array of small tunable stacked split ring resonators (SSRRs). The resonance frequency of the pro- posed resonator structure can be controlled by adjusting the auxiliary lumped elements which are inserted between the split of each ring. In addition, the size of the ring resonator can be reduced to an order of 0.01λ that is one tenth that of the split ring resonator (SRR) by choosing the proper lumped elements. The analysis is based on the quasi-static Lorentz theory, and the generalized matrix representation of the macroscopic constitutive relations of the composite medium is calculated.

This paper presents a theory of the radar cross section (RCS) of objects in multiple scattering random media. The general formulation includes the fourthorder moments including the correlation between the forward and the backward waves. The fourth moments are reduced to the second-order moments by using the circular complex Gaussian assumption. The stochastic Green’s functions are expressed in parabolic approximation, and the objects are assumed to be large in terms of wavelength; therefore, Kirchhoff approximations are applicable. This theory includes the backscattering enhancement and the shower curtain effects, which are not normally considered in conventional theory. Numerical examples of a conducting object in a random medium characterized by the Gaussian and Henyey–Greenstein phase functions are shown to highlight the difference between the multiple scattering RCS and the conventional RCS in terms of optical depth, medium location and angular dependence. It shows the enhanced backscattering due to multiple scattering and the increased RCS if a random medium is closer to the transmitter.

The problem of polarized light propagating through scattering media can be explained using the vector radiative transfer equation. This equation is an integro-differential equation and is well-known to be unsolvable analytically. One of the approximate solutions is discrete ordinates method which is based on the discretization of the Stokes parameters and the Mueller matrix. Although it produces accurate results, it requires a lot of computational resources. In addition, there are limitations on the calculation for angles that are very close to the optical axis. The solutions at these angles are necessary for some applications such as atmospheric imaging. First-order scattering approximation has been applied to mitigate the computational resource situation. It can also be used to calculate the solution at the angles that are very close to optical axis. However, it lacks information about the cross-polarization and it is inaccurate when light encounters more scattering events. Second-order scattering approximation provides more accurate solutions and offers some information about cross-polarization. We develop the first-order and second-order scattering approximations and their solutions for the pulse wave case. We investigate the second-order approximation solutions and compare them to the solution from the complete vector radiative transfer equation in several cases.

The passage of a photon density wave through random media has been investigated extensively for medical imaging based on the diffusion approximation. In this paper, the photon density wave is studied based on the exact time-dependent vector radiative transfer theory. Both continuous and pulse photon density waves are analysed in a plane parallel medium using Mie scattering and the discrete ordinates method. The photon density wave shows superior properties over regular waves in several aspects. It has a narrower angular spectrum and maintains the original pulse shape. It also preserves the degree of polarization and increases the cross-polarization discrimination. These properties of a photon density wave suggest its potential for improving imaging. Thus, we apply the photon density wave to an imaging problem and show that it improves the quality of the images compared to other conventional imaging techniques.

The technology of “Through-the-Wall Radar imaging” (TWRI) enables us to see through the walls by reconstructing the image based on the backscattered waves passing through the opaque dielectric wall. However, when the electromagnetic waves cannot penetrate the walls (such as metallic walls), a new problem called “Hard-Wall Radar Imaging” (HWRI) emerges as we have discussed in our previous papers. Because in this problem the objects are located in the shadow region, where only diffracted field around edges can be reflected back, the conventional imaging techniques are not applicable.

Recently, there has been increasing interest in the use of spaceborne synthetic aperture radar (SAR) for measuring forest biomass. However, it is noted that conventional SAR using C-band or higher frequencies cannot penetrate into foliage, and therefore the biomass measurements require longer wavelengths, typically P-band (500 MHz). It is also known that the ionosphere is highly dispersive, causing group delay and broadening of pulses. The variance of the refractive index fluctuations due to turbulence is approximately proportional toƒ−4. In addition, the Faraday rotation due to the geomagnetic field in the ionosphere becomes significant. This paper presents an analysis with numerical examples of the following effects in the frequency range from 100 MHz to 2 GHz in order to show the frequency dependence and the effects of total electron content (TEC) of the ionosphere. First, the ionospheric turbulence can reduce the coherent length below the equivalent aperture size, and the azimuthal resolution becomes greater than D/2 where D is the antenna aperture size. Second, the ionospheric dispersion causes a shift of the imagery due to the group velocity. Third, the dispersion also creates broadening of the pulse. In addition, multiple scattering due to ionospheric turbulence gives rise to pulse broadening. Fourth, we consider the Faraday rotation effect and show that the ellipticity change is negligible, but the orientation angle changes significantly at P-band. Numerical examples are shown using typical ionospheric parameters, turbulence spectrum, and TEC values.

The correlation effect of waves scattered from random media has attracted considerable interest in recent years. In particular, the angular correlation function (ACF) of waves scattered from rough surfaces and volumes has been studied extensively, and the characteristics of the angular memory effect (AME), which was first described by Feng et al. [1988], were reported for different surface conditions. Applications of AME, including height profiling in interferometric synthetic aperture radar (INSAR) and detection of buried objects, have been proposed and studied by researchers using numerical and experimental techniques. However, most of the recent studies of AME have been confined to the area of waves scattered from rough surfaces. In this paper we will investigate the angular memory signature of volume scatterers. Numerical and experimental studies on the ACF of waves scattered from randomly distributed cylinders are presented at millimeter-wave frequencies (80–105 GHz). It has been found that the angular width of ACF for volume scattering is narrower and shorter than that for random rough surfaces.

This paper presents a theory and its experimental demonstration of an imaging technique based on three-dimensional (3D) space-time confocal imaging and circular synthetic aperture radar (SAR). The theory is an extension of the conventional straight-path SAR-to-SAR on an arbitrary curved path. Next, a general formulation for the curved SAR is applied to circular SAR geometry, which has two important features. First, it allows the maximum attainable resolution to be an the order of a wavelength. Second, it makes 3D confocal imaging possible, X-band (7-13 GHz) imaging experiments are conducted to demonstrate this technique.