Far-field Cross-correlation Research Articles

Measuring the topological charge of coherence vortices through the geometry of the far-field cross-correlation function.

Determination of orbital angular momentum of optical vortex beams has attracted the attention of many researchers over the last few years. For some applications, it is convenient to use a partially coherent vortex beam because of its robustness. In this work, we developed a method to measure the topological charge of a partially coherent vortex beam. Our method relies simply in the measurement of the minimum radius of a zero contour of the modulus of the cross-correlation function and in the measurement of the full width at half maximum of its central spot.

Empirical Geometrical Bounds on MIMO Antenna Arrays for Optimum Diversity Gain Performance: An Electromagnetic Design Approach

We propose a general design methodology for synthesizing surface or volume multi-input-multi-output (MIMO) antenna arrays with optimum cross-correlation diversity gain performance through engineering the array’s geometrical shape. The design algorithm is based on approximating arbitrary antenna geometrical configurations by the arrays of infinitesimal (electrically small) dipoles and then using the recently introduced cross-correlation Green’s function in order to compute far-field cross correlations without the need to explicitly measure or compute far-zone fields. After directly expressing far-field cross correlation in terms of the geometrical details of the antenna array (position and orientation), the method applies a global optimization strategy (the genetic algorithm) to find optimum positions and orientations of the MIMO antennas’ elements within a given geometrical shape, resulting in the statistically best system performance. We provide extensive numerical results, including various array topologies (both fixed and conformal), with investigations of the impact of the array density, positions, and the relative orientations of the composing antenna elements on the attainable diversity gain. This paper also outlines an expansion of the proposed design methodology in order to deal with the important special case when a ground plane is present in the MIMO environment. It is found using the proposed methods that small MIMO receiver terminals can be made to fit any geometrical shape by properly controlling the position and the orientation of each element. All the resulting arrays have dimensions that are smaller than $0.35\lambda \times 0.35\lambda$ with the diversity gain of 80% or greater. It was also found that for each antenna topology, a critical number of antennas per unit area/volume exist, such that no further improvement of the diversity gain is possible. This upper bound is geometrical in nature, but it is obtained through an electromagnetic analysis, clearly demonstrating the impact of relative antenna positioning and orientations. Various 2-D and 3-D antenna array configurations, including disk, ring, spheres, and spherical layers, were investigated and their critical array densities are tabulated. Also, a practical example of conformal arrays mounted on an avionic nose was provided. It was also found that relative orientations alone can be exploited to substantially improve the performance of MIMO arrays by considering different scenarios comparing position-alone, orientation-alone, and position-and-orientation optimization processes with random arrays in terms of diversity gain performance. The method developed in this paper can be expanded to include more complex antenna types, but it is also suitable for scalable computing analysis of continuous large radiating and receiving antenna surfaces and massive MIMO. In particular, for mmWave applications, we expect that the need to optimize large arrays of tiny antennas will increase the demand for accurate and general design algorithms, such as the one proposed in this paper.

Effect of the radial and azimuthal mode indices of a partially coherent vortex field upon a spatial correlation singularity

The existence of a spatial correlation singularity or a ring dislocation in the spatial coherence function when a vortex is present has been demonstrated recently. Here, we investigate how the spatial correlation singularity is affected by both the radial and azimuthal mode indices (p, ℓ) in a partially coherent light field. Theoretically, we find that the spatial correlation singularity may exist even in a non-vortex beam (ℓ = 0) due to the radial index. Numerical simulations show the number of ring dislocations in the far-field cross correlation function is equal to 2p + |ℓ| for the low coherence cases. This is confirmed by our experimental results. This phenomenon may occur in any partially coherent vortex wave.

Measuring the orbital angular momentum of partially coherent optical vortices through singularities in their cross-spectral density functions

By analysis of the far-field cross-correlation function (CCF) of partially coherent optical beams, we demonstrate an implicit rule that the number of ring dislocations (dark zones) of the far-field CCF is equal to the original topological charge of an optical vortex rendered partially coherent. This novel link between an optical vortex and its correlation singularity may offer an efficient method for measuring the orbital angular momentum of partially coherent optical vortices in fields such as astrophysics and astronomy, as well as atmospheric laser communication.

Digital processing of aerosonic signals

Experimental data were obtained from tests performed in the NASA‐Ames 7‐ × 10‐ft wind tunnel. A digitizing process for flow over a blunt‐edged air foil was used to compare data with an analog system. The nearfield surface‐pressure signal on the wing and the farfield aerosonic signal were cross‐correlated. Digital filtering was applied to the data to suppress unwanted signals. The results of near‐/farfield cross correlations show, using the digitized treatment, that there is substantial ringing, a relatively narrow‐band source. Analog prefiltering exhibits a shift to lower frequency, due to frequency roll‐off of the RC analog filters. It is shown that the clip‐correlation (needed for analog) and the digitized full correlation methods give similar results. But the absolute value of the correlation is lost in clipping. [Work supported by NASA‐Ames.]

Large scale model measurements of airframe noise using cross-correlation techniques

Cross-correlation techniques are used to measure the sound radiated by wing/flap airfoil configurations in the NASA–Ames 40- by 80- foot wind tunnel using a 6.7-m semispan model with three deployed flaps. The sound from the flap side edges exceeds other airframe noise sources by more than 10 dB, with the noise from the side edges of the leading flaps the strongest. The radiated sound is estimated using two formulas based on the standard aeroacoustic theory and one method using only the near and farfield cross correlation. The last method is essentially independent of such theory. The classic dipole angular distribution pattern is modified by wing diffraction effects to yield stronger radiation in the forward direction. The radiated intensity increases at slightly higher than the fifth power of the mean flow speed U0. The location of the flap track fairings is found to have a substantial effect on the radiated intensity: placing the fairings at or near the lateral edges of the flaps substantially reduces the radiated noise.

Large scale model measurements of air frame noise using cross correlation techniques

Cross‐correlation techniques are used to measure the sound radiated by wing/flap airfoil configurations in the NASA‐Ames 40‐ by 80‐ft wind tunnel using a 5.8‐m‐high model, with three deployed flaps. The sound from flap corners exceeds other airframe noise by 10 dB and more; the noise from the leading, outbound corner of the leading flap seems to be the strongest. The sound is estimated using two formulas based on standard aeroacoustic theory and one method using the near‐, farfield crosscorrelation; this last is essentially independent of such theory—all three are in fair to good agreement with one another. The classic dipole angular distribution pattern for one dipole is compared with measurements; it is found that there is qualitative but not quantitative agreement. The dependence of intensity on U0 is roughly, though not exactly, U06, where U0 is the free stream speed. The turbulence length scales on the flap surface as determined by the characteristic time of the measured correlation function and the free stream speed, are from a few to many centimeters, on the order of the flap thicknesses. Time delays from the correlation between the far field signal and the surface source are determined from the correlation functions and are in good agreement with the flow‐refraction‐corrected results.

Jet Noise Source Distribution from Far-Field Cross Correlations

HIS paper contains the development of a technique to determine the relationship between the unknown source correlation function and the correlation of the far-field acoustic pressure. Based on LighthilPs equivalent source model, a Fredholm integral equation relating the unknown source-correlation function to the far-field pressure correlation is derived. Analytically, this is a statistically inverse radiation problem. It is assumed that the source is distributed over an axisymmetric region, that is, a cylindrical region in an axisymmetric jet. This technique was developed for an application in the study of the installation effects for static and moving jets, since the spatial and temporal distribution of the source relative to the jet were required.l In the literature, several techniques are available, for example, Refs. 2 through 5, which provide information of the spatial distribution only or suitable to reproduce far-field intensity without body effects. In addition, further information can be extracted from the source field if obtained from the far-field two-point correlation.6'7 Contents Consider the propagation of an acoustic wave generated by turbulence in the jet confined in a region D in space, Fig. 1; the sound pressure in the spectral or frequency domain satisfies