Far-field Correlation Research Articles

Spatially uncorrelated two port MIMO DRA using phase gradient PRS for dual directional pattern diversity

This study presents a system utilizing a cylindrical shape ceramic along with a suspended frequency selective surface (FSS), designed for multiple input multiple output (MIMO) applications with dual ports. The proposed antenna system showcases dual pattern diversity properties introducing spatially uncorrelated pattern. Key features of the structured radiator include the arrangement of cylindrical ceramic and the incorporation of an FSS. The alumina ceramic is purposefully placed on the upper part of the dielectric with a joint ground plane. These ceramics are stimulated using circular aperture. To reduce the far-field correlation, FSS with similar phase gradients are placed at the top of DRA at a certain distance. This arrangement yields two distinct radiation patterns from the two ports, ensuring a diverse radiation pattern for the antenna. The proposed technique yields significant improvements, surpassing 10 dB in isolation and achieving a 70% improvement in correlation values. The measured results validate the applicability of this antenna structure for WLAN access point applications within the 5.15–5.35 GHz frequency range.

Far-Field Correlations Verifying Non-Hermitian Degeneracy of Optical Modes.

An experimental verification of an exceptional point (EP) in a stand-alone chaotic microcavity is a tough issue because as deformation parameters are fixed the traditional frequency analysis methods cannot be applied any more. Through numerical investigations with an asymmetric Reuleaux triangle microcavity (ARTM), we find that the eigenvalue difference of paired modes can approach near-zero regardless of nonorthogonality of the modes. In this case, for a definite verification of EPs in experiments, wave function coalescence should be confirmed. For this, we suggest the method of exploiting correlation of far-field patterns (FFPs), which is directly related to spatial mode patterns. In an ARTM, we demonstrate that the FFP correlation of paired modes can be used to confirm wave function coalescence when an eigenvalue difference approaches near zero.

Far-field correlation of palaeokarstic surfaces in Mississippian successions using high-frequency foraminiferal diversity trends

The degree to which emergent surfaces are correlated in late Asbian carbonate successions in Britain and Ireland is assessed by the integration of detailed biostratigraphy and diversity trends in foraminifers. Data are related to the Trowbarrow Quarry section in northern England, which provides a reference section for the upper Asbian because of its rich assemblages and high sampling density. Diversity trends are shown to be non-random, possess cyclic behaviour, and can be quantitatively correlated between sections. The assemblages allow stratigraphic segmentation into 13 intervals of foraminiferal diversity trends, which sub-divide the coarser-resolution biozones and sub-biozones. Similar foraminiferal trends are recognised in sections hundreds of kilometres away from Trowbarrow, in South Wales, and southeastern and western Ireland, facilitating a more precise correlation of strata. These highlight the coeval nature of emergent surfaces and rhythms between these regions, thus, establishing a precise stratigraphy. This new assessment also enables better discrimination of ‘missing beats’ and large hiatuses in the successions. The establishment of this rhythmic stratigraphy permits recognition of the late occurrence of some biostratigraphical markers, enabling amendment of biostratigraphic mismatches.

A General Method to Calculate the Source-Stirred Correlations in a Well-Stirred Reverberation Chamber

To identify the independent sample number in a platform-stirred reverberation chamber, the correlated angle of a rotating platform has to be identified. A general numerical method is proposed to calculate the farfield correlation in a source-stirred reverberation chamber. The proposed method is verified using a dipole antenna which has an analytical solution. General source antenna configurations are also investigated (e.g., a Vivaldi antenna) which show that the correlated angle is not sensitive to the radiation pattern of the source-stirred antenna for a large rotating radius.

On Near-Field and Far-Field Correlations in Reverberation Chambers

A common question for the reverberation chamber (RC) measurement is whether the Fraunhofer far-field distance is satisfied between the device under test and other objects (e.g., RC walls and mode stirrers). In this letter, it is shown that far-field sampling may not be needed for most RC measurements that rely on the statistics of the stirred field. For these kinds of measurements, measurement uncertainties in near field and far field are the same.

Experimental investigation of the turbulent density – Far-field sound correlations in compressible jets

Jet mixing noise is experimentally investigated by means of cross-correlations between density fluctuations inside the turbulent jet flow and the far-field acoustic pressure. The time-resolved density fluctuations are measured by an experimental device based on Rayleigh scattering, which is mounted in the large anechoic wind tunnel of Ecole Centrale de Lyon. An original signal processing developed in a previous study is implemented for the photon counting, combined with the use of a single photomultiplier to remove shot noise. A high-speed subsonic jet and a perfectly expanded supersonic jet with a subsonic convective velocity are considered to characterize mixing noise sources. In order to go beyond the classical Fourier analyses, conditional cross-correlations are determined, and the signature of turbulent events linked to the noise emission in the downstream direction is extracted.

Experimental study of turbulent-jet wave packets and their acoustic efficiency

This paper details the statistical and time-resolved analysis of the relationship between the near-field pressure fluctuations of unforced, subsonic free jets (0.4 ≤ M ≤ 0.6) and their far-field sound emissions. Near-field and far-field microphone measurements were taken on a conical array close to the jets and an azimuthal ring at 20∘ to the jet axis, respectively. Recent velocity and pressure measurements indicate the presence of linear wave packets in the near field by closely matching predictions from the linear homogenous parabolized stability equations, but the agreement breaks down both beyond the end of the potential core and when considering higher order statistical moments, such as the two-point coherence. Proper orthogonal decomposition (POD), interpreted in terms of inhomogeneous linear models using the resolvent framework allows us to understand these discrepancies. A new technique is developed for projecting time-domain pressure measurements onto a statistically obtained POD basis, yielding the time-resolved activity of each POD mode and its correlation with the far field. A single POD mode, interpreted as an optimal high-gain structure that arises due to turbulent forcing, captures the salient near-field–far-field correlation signature; further, the signatures of the next two modes, understood as suboptimally forced structures, suggest that these POD modes represent higher order, acoustically important near-field behavior. An existing Green's-function-based technique is used to make far-field predictions, and results are interpreted in terms of POD/resolvent modes, indicating the acoustic importance of this higher order behavior. The technique is extended to provide time-domain far-field predictions.

Spatially Robust Far-field Beamforming Using the von Mises(-Fisher) Distribution

This paper presents spatially robust far-field microphone beamformers and nullformers derived using the von Mises and von Mises-Fisher distributions to model the expected direction of arrival. Simple analytic expressions are presented for 2D and 3D far-field correlation functions and used to design spatially robust beamformers and nullformers. It is demonstrated that the spatially robust beamformers show a modest improvement in tolerating uncertainty in the target direction of arrival without incurring a significant penalty in terms of SINR performance compared with the MVDR beamformer. In addition, the spatially robust formulation shows significantly improved numerical robustness, indicating improved ability in tolerating intrinsic array errors.

How is the Balance of a Forecast Ensemble Affected by Adaptive and Nonadaptive Localization Schemes?

Abstract This paper investigates the effect on balance of a number of Schur product–type localization schemes that have been designed with the primary function of reducing spurious far-field correlations in forecast error statistics. The localization schemes studied comprise a nonadaptive scheme (where the moderation matrix is decomposed in a spectral basis), and two adaptive schemes: a simplified version of Smoothed Ensemble Correlations Raised to a Power (SENCORP) and Ensemble Correlations Raised to a Power (ECO-RAP). The paper shows, the author believes for the first time, how the degree of balance (geostrophic and hydrostatic) implied by the error covariance matrices localized by these schemes can be diagnosed. Here it is considered that an effective localization scheme is one that reduces spurious correlations adequately, but also minimizes disruption of balance (where the “correct” degree of balance or imbalance is assumed to be possessed by the unlocalized ensemble). By varying free parameters that describe each scheme (e.g., the degree of truncation in the schemes that use the spectral basis, the “order” of each scheme, and the degree of ensemble smoothing), it is found that a particular configuration of the ECO-RAP scheme is best suited to the convective-scale system studied. According to the diagnostics this ECO-RAP configuration still weakens geostrophic and hydrostatic balance, but overall this is less so than for other schemes.

On Cross Correlation in Antenna Arrays With Applications to Spatial Diversity and MIMO Systems

We develop a general approach to cross correlation in antenna systems suitable for applications to spatial diversity and MIMO systems. The far-field correlation is expressed in terms of the currents on the antennas. The basic strategy proposed here is to perform the overall evaluation of cross correlation by means of superposition integrals involving contributions emerging from all possible mutual correlations between the point sources on the antenna currents where interactions are mediated by a new cross-correlation Green’s function. The method is verified and demonstrated in several numerical examples and a design methodology aiming at maximizing the diversity gain is outlined and illustrated. It is also shown that arbitrary antenna arrays can be reduced to suitable models involving only infinitesimal dipoles, in effect enabling us to compute the total diversity gain using the cross-correlation Green’s function. The formulation provided here gives the electromagnetic aspect of spatial diversity an articulated form proper for design and development of practical communication links using multiple antenna systems.

Far-field correlation of bidirectional tracking beams due to wave-front deformation in inter-satellites optical communication links.

In some applications of optical communication systems, such as inter-satellites optical communication, the correlation of the bidirectional tracking beams changes in far-field as a result of wave-front deformation. Far-field correlation model with wave-front deformation on tracking stability is established. Far-field correlation function and factor have been obtained. Combining with parameters of typical laser communication systems, the model is corrected. It shows that deformation pointing-tracking errors θ(A) and θ(B), far-field correlation factor δ depend on RMS of deformation error rms, which decline with a increasing rms including Tilt and Coma. The principle of adjusting far-field correlation factor with wave-front deformation to compensate deformation pointing-tracking errors has been given, through which the deformation pointing-tracking error is reduced to 18.12″ (Azimuth) and 17.65″ (Elevation). Work above possesses significant reference value on optimization design in inter-satellites optical communication.

Nonuniversal Intensity Correlations in a Two-Dimensional Anderson-Localizing Random Medium

Complex dielectric media often appear opaque because light traveling through them is scattered multiple times. Although the light scattering is a random process, different paths through the medium can be correlated encoding information about the medium. Here, we present spectroscopic measurements of nonuniversal intensity correlations that emerge when embedding quantum emitters inside a disordered photonic crystal that is found to Anderson-localize light. The emitters probe in situ the microscopic details of the medium, and imprint such near-field properties onto the far-field correlations. Our findings provide new ways of enhancing light-matter interaction for quantum electrodynamics and energy harvesting, and may find applications in subwavelength diffuse-wave spectroscopy for biophotonics.

Adaptive Ensemble Covariance Localization in Ensemble 4D-VAR State Estimation

Abstract An adaptive ensemble covariance localization technique, previously used in “local” forms of the ensemble Kalman filter, is extended to a global ensemble four-dimensional variational data assimilation (4D-VAR) scheme. The purely adaptive part of the localization matrix considered is given by the element-wise square of the correlation matrix of a smoothed ensemble of streamfunction perturbations. It is found that these purely adaptive localization functions have spurious far-field correlations as large as 0.1 with a 128-member ensemble. To attenuate the spurious features of the purely adaptive localization functions, the authors multiply the adaptive localization functions with very broadscale nonadaptive localization functions. Using the Navy’s operational ensemble forecasting system, it is shown that the covariance localization functions obtained by this approach adapt to spatially anisotropic aspects of the flow, move with the flow, and are free of far-field spurious correlations. The scheme is made computationally feasible by (i) a method for inexpensively generating the square root of an adaptively localized global four-dimensional error covariance model in terms of products or modulations of smoothed ensemble perturbations with themselves and with raw ensemble perturbations, and (ii) utilizing algorithms that speed ensemble covariance localization when localization functions are separable, variable-type independent, and/or large scale. In spite of the apparently useful characteristics of adaptive localization, single analysis/forecast experiments assimilating 583 200 observations over both 6- and 12-h data assimilation windows failed to identify any significant difference in the quality of the analyses and forecasts obtained using nonadaptive localization from that obtained using adaptive localization.

Seismic Interferometry Using Non-Far-Field Sources and Removing the Spurious Arrival

Abstract Seismic interferometry using far-field correlation is a technique to obtain the Green’s function between two receivers using passive wave-field recordings, and often it is under the theoretical assumption that sources are in the far field when in fact they may not be. Using a heterogeneous medium enclosed by a closed boundary on which the sources are fired, we offer two views on the meaning of the far-field correlation. In the intrinsic view, the validity of the far-field correlation is based on the far-field approximation for wave scattering, and it is investigated by comparing various physical dimensions in the heterogeneous interior, regardless of the exterior. However, the extrinsic view centers on the medium properties in the exterior only without considering the interior. Previous studies showed that, with the correct scattering model and complete source coverage, no spurious arrivals should be generated if the illuminating sources are in the far field. We investigate the case of near-field cross correlation. This problem is considered in the context of two-dimensional space with a single embedded scatterer that is represented by a cylindrical inclusion with small radius. An analytical solution for the scattered wave is computed. However, if the sources are not in the far field, the cross-correlation kernel must be used to eliminate the spurious arrival, in addition to the correct scattering model and full source aperture. The kernel accounts for the near-field illumination of the region.

Investigation of Noise Source Mechanisms in Subsonic Jets

The precise nature of the origin of jet noise remains in question to this day. Apart from the scientific importance of gaining a better understanding of the noise sources, there is the practical consideration of our ability to alter/ manipulate the sources so as to achieve noise reduction. In this study, the sources of jet noise have been investigated with 1) the analyses of far-field spectra, and 2) the measurements of the far-field correlations, both in the polar and azimuthal directions. Two geometries were used: a round nozzle and a beveled nozzle. The acoustic characteristics of these nozzles exhibit interesting trends at different jet velocities (Vj/a), thereby permitting a better understanding of the nature of the noise sources. The far-field spectra from unheated round jets at extremely low Mach numbers conform to the large-scale similarity shape at angles close to the jet axis; there is a gradual progression from the fine-scale similarity shape to the large-scale similarity shape for all jet velocities. This seems to be a fundamental characteristic of jet noise and is a new finding. The far-field correlations indicate that there is very little correlation at the lower polar angles; in the peak aft radiation sector, high correlations prevail. It is established with both the round and beveled nozzles that low correlations are associated with fine-scale-similarity-shaped spectra and high correlations with large-scale-similarity-shaped spectra. Experimental evidence for the importance of the noise from large coherent structures even at low velocities is offered. The data indicate the existence of two independent sources in both high-speed and low-speed jets, with the coherent large structures radiating to the aft angles and the random turbulence radiating to the lower angles. It is shown that the noise reduction of the beveled nozzle is due to the alteration of the noise from the coherent structures. The beveled nozzle thus provides indirect evidence for the importance of large coherent structures.

Fourier-transform ghost imaging with pure far-field correlated thermal light

Pure far-field correlated thermal light beams are created with phase grating, and Fourier-transform ghost imaging depending only on the far-field correlation is demonstrated experimentally. Theoretical analysis and the results of experimental investigation of this pure far-field correlated thermal light are presented. Applications which may be exploited with this imaging scheme are discussed.

Ghost imaging using homodyne detection

We present a theoretical study of ghost imaging based on correlated beams arising from parametric down-conversion, and which uses balanced homodyne detection to measure both the signal and idler fields. We analytically show that the signal-idler correlations contain the full amplitude and phase information about an object located in the signal path, both in the near-field and the far-field case. To this end we discuss how to optimize the optical setups in the two imaging paths, including the crucial point regarding how to engineer the phase of the idler local oscillator as to observe the desired orthogonal quadrature components of the image. As is well known, the near-field image resolution is inherently linked to the far-field bandwidth of the image, determined by the bandwidth of the source of the correlated beams. We show how to circumvent this limitation by using a spatial averaging technique which dramatically improves the imaging bandwidth of the far-field correlations as well as speeds up the convergence rate. The results are backed up by numerical simulations taking into account the finite size and duration of the pump pulse.

Detection of a small defect on a rough surface

We report experimental results that show that the far-field correlation function is sensitive to a small local change in rough-surface geometry, where the speckle spatial correlation rather than the sample ensemble average is adopted. The angular cross-correlation function of the far-field speckles scattered by one-dimensional random rough surfaces is measured when a polarized beam of light is incident upon the rough surface from vacuum, where one part of the surface used is a thin dielectric film deposited upon a glass substrate and the other part is identical to the first except for a localized defect. We envisage application of this sensitivity property to inspection of a sample with a defect by means of speckle mapping.

Stochastic direct and inverse radiation problem on two ring random sources

A model consisting of two ring sources is developed for the study of the farfield behavior: correlation, coherence, and phase on a round jet. The sources on the rings are random and monopole with Gaussian profiles. They couple within the rings as well as between rings such that only adjacant sources correlate. Numerical results show that the sources are compact, in a broadband sense, when the farfield correlation peaks at zero time delay; otherwise, they are noncompact with respect to the acoustic wavelength. For noncompact cases the phases have a sawtooth type of distribution joined with linear ones with increasing frequency. This is the resultant interference effect. The behavior is well documented by the systematic variation of the distance between rings, diameter and the number of sources. The inverse radiation approach is in general ill‐posed in Hadmark sense; however, the asymptotic behavior of the phase function, as the frequency tends to zero and infinity, permits one to obtain explicitly the loca...

Quantum electrodynamics in the presence of dielectrics and conductors. IV. General theory for spontaneous emission in finite geometries

A quantum-electrodynamic theory of spontaneous emission in presence of dielectrics and conductors is developed. The theory makes use of the master-equation techniques and the response-function formalism of part I of this series of papers. Various observable entities such as damping coefficients (lifetimes), Lamb shifts, and frequency shifts are related to the appropriate surface-dependent response functions. The results are valid for arbitrary geometries (involving linear dielectrics) and naturally contain, as a special case, the usual results of spontaneous emission in free space. As explicit examples we consider a two-level atom (also the multilevel atom) in presence of a plane dielectric interface and between two conducting plates. Formulas for the shifts and widths are given and their asymptotic behavior for large and short distances is discussed. The behavior when the atom is embedded inside the dielectric is different than when the atom is outside the dielectric. The origin of coherence in the present model is discussed and the coherence effects in this model are contrasted with those in Dicke's model. The results are also compared with those obtained by the image method. Exact expressions for the operator radiation-reaction fields are obtained in terms of the atomic polarization operators and response functions. Approximate results for such fields are also given. The far-zone behavior of the radiation fields is obtained in terms of response functions and the polarization operators. Some of the normally ordered correlation functions are also calculated. The connection of some of the theoretical results with a recent experimental work of Carniglia, Mandel, and Drexhage is discussed. The effect of anisotropy of the dielectric function on the lifetimes as well as on the far-field correlation functions is also considered. Finally the contribution to the shifts and widths due to the excitation of surface polariton modes is computed and the results are compared with those obtained by the quantization of surface polariton field. It is found that such surface modes contribute significantly to widths.