Array Of Line Sources Research Articles

Generation of narrowband antisymmetric lamb waves using a formed laser source in the ablative regime

A formed laser source, using a four-element lenticular array, is used in the ablative regime to generate select, narrowband, acoustic plate waves. The arrangement of the array produces acoustical signals that have frequencies compatible with the response of the broadband capacitive air-coupled transducer used in this study. A simplified concept is presented to explain the effect of a line array source on the frequency content of acoustic waves. The analytical model for a point pulse surface displacement is derived from the point load solution to Lamb's problem. The point pulse displacement elements of a line array source are summed mathematically, taking into account all applicable propagation modes and dispersion of plate waves. The model considers only the out-of-plane displacement of the antisymmetric plate modes to represent the detection capability of the broadband receiver. The distribution function of the laser beam energy profile is modified to depict the actual energy distribution that illuminates the surface of the plate. Filtering functions are made compatible with the sensitivity of the broadband receiver so as to retain only the detected frequencies in the model. The theoretical model showed good agreement with experimental results.

Efficient computation of the 2-D Green's function for 1-D periodic structures using the Ewald method

The Ewald method is applied to accelerate the evaluation of the Green's function of an infinite periodic phased array of line sources. The Ewald representation for a cylindrical wave is obtained from the known representation for the spherical wave, and a systematic general procedure is applied to extend previous results. Only a few terms are needed to evaluate Ewald sums, which are cast in terms of error functions and exponential integrals, to high accuracy. Singularities and convergence rates are analyzed, and a recipe for selecting the Ewald splitting parameter /spl epsiv/ is given to handle both low and high frequency ranges. Indeed, it is shown analytically that the choice of the standard optimal splitting parameter /spl epsiv//sub 0/ will cause overflow errors at high frequencies. Numerical examples illustrate the results and the sensitivity of the Ewald representation to the splitting parameter /spl epsiv/.

Attenuation correction using combination of a parallel hole collimator and an uncollimated non-uniform line array source.

Attenuation correction is very important for quantitative SPECT imaging. We designed an uncollimated non-uniform line array source (non-uniform LAS) for attenuation correction based on transmission computed tomography (TCT) using Tc-99m and compared its performance with an uncollimated uniform line array source (uniform LAS) in a thorax phantom study. This non-uniform LAS was attached to one camera head of a dual-head gamma camera, and transmission data were acquired with another camera head with a low-energy, general purpose, parallel-hole collimator at 50 cm-distance apart from the source. The modified TEW using a subtraction factor of 1.0 was employed to correct scattered Tc-99m photons for transmission data. In the phantom experiment, eight TCT data were acquired with the scanning time changed from 2 minutes to 20 minutes for each LAS. The Tc-99m attenuation coefficient (mu) maps with the non-uniform LAS and uniform LAS improved the statistical count variation in the mediastinum filled with water as the scanning time got longer. The Tc-99m mu-map with the non-uniform LAS and 6 minutes of scanning time had equal quality at the center of the thorax phantom to that with the uniform LAS and 16 minutes of scanning time. In conclusion, for the TCT imaging with combination of the parallel hole collimator and uncollimated Tc-99m external source the non-uniform LAS can reduce the Tc-99m radioactivity or the TCT scanning time compared with the uniform LAS.

Steady infiltration from line sources into a layered profile

Two‐dimensional unsaturated flow emanating from an array of line sources is analyzed for a stratified soil. The present work extends earlier solutions for flow from an array of line sources into a homogeneous soil to the more complex and realistic case of layered conditions. The hydraulic conductivity is of the form Ki exp(αh) where the saturated conductivity Ki is different in each stratum considered, α is a constant in the entire flow domain, and h is the pressure head. An interesting feature of the derived solution is the use of an expression of the gradients of the stream function at the strata interfaces. This is analogous to the change in slope of path lines crossing a region of contrasting conductivities for saturated flow. For a two‐layer example, a build‐up of pressures is shown within a layer of lower permeability overlying a more conductive soil. The effect of an included finite stratum on spreading (for an inclusion layer of lower permeability) or concentrating flow (for an inclusion layer of higher permeability) is also shown using a three‐layered domain.

Generating a plane wave with a linear array of line sources

Creating a plane wave across an antenna under test is important for accurate antenna measurements. This paper optimizes the location and weightings of an array of line sources in order to approximate a plane wave at a given location in space. The amplitude and phase ripples across a desired test aperture are optimized to be much less than that of a uniform array with the same number of elements. Results are presented for a nine-element array with optimized amplitude and phase weights, with optimized weights and spacing in the x-direction, and with optimized weights and spacing in the x and z directions. The optimized approximate plane wave is a significant improvement over a uniform array or a single line source.

Narrow band laser-generated surface acoustic waves using a formed source in the ablative regime.

A narrow band laser-generated acoustic signal was created using a 4-element lenticular array. This arrangement of the array produces an acoustical signal with frequency content that is compatible with the response of a noncontact and remote broadband receiver, such as a capacitive air-coupled transducer. To support the experimental observations, a simplified concept is presented to explain the effect of a line array source on the frequency content of a surface acoustic wave. The analytical model solution for the wave front shape is derived from the point load solution of Lamb's problem that represents the displacement of a surface acoustic wave generated by an ablative line array. The distribution function, which was used for the model to represent the laser light energy, was tailored to depict the actual energy distribution that illuminates the lenticular array. Filtering functions are applied to the resultant surface displacement function to retain frequencies similar to those detected by the broadband 50 kHz-2.25 MHz receiver. The theoretical model showed good agreement with experimental results.

Quantitative planar imaging method for measurement of renal activity by using a conjugate-emission image and transmission data.

We are proposing a method to accurately measure renal activity in renography using Tc-99m labeled tracers. This method uses a conjugate-view image and transmission data for attenuation correction, the triple energy window (TEW) method for scatter correction, and background correction techniques that consider the source volume for accurate background activity correction. To examine this method in planar imaging, we performed two renal phantom studies with various uniform background activity concentrations. One study used two ideal box-shaped kidney phantoms with a thickness of 2 or 4 cm in a water tank and the other study employed two real kidney-shaped phantoms in a fillable abdominal cavity. For these studies the kidney phantom-to-background activity concentration ratio (S) was changed from 5 to infinity. The transmission data were obtained with an external Tc-99m line array source. The anterior- and posterior-view emission images were acquired with a dual-headed gamma camera simultaneously and the TEW method was used to correct scatter for the emission and transmission images. The results showed that this method with both the accurate background correction and scatter correction could give depth-independent count rates and could estimate the true count rate with errors of less than 5% for all S values. However, if either accurate background correction or scatter correction was performed alone, the absolute error increased to about 50% for the smaller S values. Our proposed method allows one to accurately and simply measure the renal radioactivity by planar imaging using the conjugate-emission image and transmission data.

Maximum-likelihood transmission image reconstruction for overlapping transmission beams.

In many transmission imaging geometries, the transmitted "beams" of photons overlap on the detector, such that a detector element may record photons that originated in different sources or source locations and thus traversed different paths through the object. Examples include systems based on scanning line sources or on multiple parallel rod sources. The overlap of these beams has been disregarded by both conventional analytical reconstruction methods as well as by previous statistical reconstruction methods. We propose a new algorithm for statistical image reconstruction of attenuation maps that explicitly accounts for overlapping beams in transmission scans. The algorithm is guaranteed to monotonically increase the objective function at each iteration. The availability of this algorithm enables the possibility of deliberately increasing the beam overlap so as to increase count rates. Simulated single photon emission tomography transmission scans based on a multiple line source array demonstrate that the proposed method yields improved resolution/noise tradeoffs relative to "conventional" reconstruction algorithms, both statistical and nonstatistical.

Efficient calculation of lattice sums for free-space periodic Green's function

An efficient method to calculate the lattice sums is presented for a one-dimensional (1-D) periodic array of line sources. The method is based on the recurrence relations for Hankel functions and the Fourier integral representation of the zeroth-order Hankel function. The lattice sums of arbitrary high order are then expressed by an integral of elementary functions, which is easily computed using a simple scheme of numerical integration. The calculated lattice sums are used to evaluate the free-space periodic Green's function. The numerical results show that the proposed method provides a highly accurate evaluation of the Green's function with far less computation time, even when the observation point is located near the plane of the array.

High-frequency analysis of an array of line sources on a truncated ground plane

A uniform high-frequency solution is presented for the field radiated at finite distance by a semi-infinite beam-scanning array of magnetic line sources located on a perfectly conducting half-plane. The field is represented in terms of Floquet waves plus their relevant singly and doubly diffracted rays, which arise from both the end of the array and the edge of the half-plane. This representation is uniformly valid also when transition conditions from propagating to evanescent Floquet waves occur. Furthermore, it provides a simple and attractive physical interpretation and is found numerically very effective, due to the fast convergence of the Floquet wave expansion for the field.

A one-sided version of the Poisson sum formula for semi-infinite array Green's functions

The Poisson sum formula provides an efficient method for transforming many slowly converging infinite summations into equivalent, but more rapidly converging infinite summations. Electromagnetic applications for this result come in the analysis of infinite arrays of periodic scatterers, such as frequency selective surfaces. However, in some applications, such as when one desires the radiation of a semi-infinite array of periodically spaced currents, the original form of the Poisson sum formula is inappropriate. For such applications, we derive a one-sided version of the formula and apply it to the radiation from a semi-infinite array of line sources with currents dictated by Floquet's theorem. The one-sided Poisson sum transformation yields enhanced convergence characteristics for certain regions of application as a result of the inverse bandwidth relationship between Fourier transform pairs. The application of it to a semi-infinite line source array also provides a plane wave representation for the fields, which makes for an extension of the solution to geometries with stratified dielectric media.

Spectral integral approach to radiation from fluid‐filled boreholes.

A hybrid model for radiation from a borehole while drilling has been developed. A numerical model for propagation in a borehole including a drill pipe has been combined with the OASES frequency–wave‐number model for propagation in layered earth media, using the concept of effective sources. Equivalent line source arrays that produce the same far‐field radiation as the borehole are first computed. These are then introduced into the layered earth model and the resultant seismic wave field is computed. The borehole modes are excited by a displacement source at the bottom, simulating bit motion while drilling. In contrast to earlier work the present model includes the drill pipe in the simulation, allowing for three propagating modes at low frequencies. The model has been applied to analysis of the role of the formation composition in the radiation from the tube modes. The fundamental differences between the radiation into soft and hard formations are discussed and demonstrated, including the formation of Mach cones along the borehole in soft formations.

Laser generation of Rayleigh and Lamb waves for ultrasonic testing

The thermoelastic generation of surface waves by a Q-switched ruby laser is investigated both experimentally and analytically. The motivation is to improve the amplitude and to control the frequency content of the ultrasonic signal by taking advantage of the tremendous flexibility that one has in controlling the size and the shape of the thermoelastic source. Waveforms have been recorded for several source geometries at the surface of an aluminum block: spot source, line source, periodic array of spot sources, and periodic array of line sources. Also, focusing effects have been measured with a periodic array of curved line sources obtained with a Fresnel lens. In all cases, the waveforms are reasonably well predicted by a simple and efficient convolution technique. Waveforms have also been generated in a 1-mm-thick aluminum plate and recorded over a distance of 50 mm at increments of 0.5 mm. Processing of these waveforms in the frequency–wave-number domain allows for the extraction of the dispersion curve and the various modes propagating in the plate. [Work supported by NSF.]

Experimental evidence of localized wave phenomena

Recent interest in creating beams that exhibit more localized behavior on the propagation axis than traditional solutions has led to many formalisms for creating and describing energy transport. One set of these solutions, the localized linear wave solution developed by Ziolkowski, has been under investigation through acoustic experiments for some time. Experiments using linear superposition to simulate two-dimensional acoustic arrays are discussed. These experiments use two methods, acousto-optics, to simulate an array of line sources and a point detector, as well as the traditional two-transducer arrangement, to simulate square arrays of point sources. Preliminary experiments with an actual two-dimensional acoustic array are also described. The technique of signal preprocessing to overcome damping problems and interelement interactions is discussed. [Work performed by the Lawrence Livermore National Laboratory under the auspices of the U.S. Department of Energy under Contract No. W-7405-ENG-48.]

Gaussian beam algorithm for bottom reflection and head waves due to extended aperture sources

Gaussian beams furnish a useful algorithm for high-frequency sound propagation in complex environments but in their paraxial implementation, they are flawed by spectral defects that obscure certain wave phenomena. Critical reflection and head wave generation due to a fast bottom belong in this category. In a separate study, methods for “fleshing out” the deficient spectrum for the prototype structure of a homogeneous ocean and a homogeneous fluid bottom, have been explored with excitation due to a line source [[X. J. Gan et al., 2nd IMACS Symposium, Princeton University (March 1989)]. In the presentation here, these methods of excitation from a continuously distributed extended aperture source and from an array of line sources have been applied. In the Gaussian beam modeling, not only are the ad hoc discretization that involves arbitrary parameters employed but the self-consistent Gabor phase space stacking are also employed. It is found that distributed sources deemphasize the above-noted spectral defects but do not remove them entirely. [Work supported by ONR.]

Diffraction Tomography with Arrays of Discrete Sources and Receivers

We present both theory and numerical simulations of diffraction tomography for arrays of line sources. The approach taken is applicable to a wide range of imaging problems where discrete sources and receivers are located near the object to be imaged rather than in its far field. As such, these new results tie into the vast body of research on inverse scattering, which to date is based largely on planewave sources. Our derivation implicitly includes a method for synthesizing plane waves; this method leads to inversion formulas based on the generalized projection-slice theorem. Although related techniues for synthesizing plane waves from discrete arrays are known, it is helpful to have available a theory that incorporates the synthesis directly into the scattering theory. The formulation is presented for propagating fields satisfying the Born and Rytov approximations in weakly inhomogeneous media and provides a convenient means for treating both forward and inverse scattering problems. Through a numerical example, we illustrate two important features of diffraction tomography inversion, i. e., 1) the effects of limited view and 2) results of probing with different signal frequencies. The example utilizes data generated by an exact forward modeling technique thus providing strong evidence supporting the usefulness of weak scattering approximations for inversion problems.

A Numerical Method for Near-Field Array Synthesis

A numerical method for near-field array synthesis is developed for arbitrary array geometries. The intended application is for generating a planar field in a test volume for electromagnetic susceptibility testing, but the method is valid for arbitrary field distributions. A uniqueness theorem is utilized to allow the field conditions to be enforced on the surface of the test volume rather than throughout the volume. The synthesis method is a least-squares solution with a constraint on the source norm; the constraint keeps the field small outside the test volume. Numerical results are shown for the case of synthesizing a plane wave in the near field of an array of line sources.

Design Nomographs for Trickle Irrigation Systems

Nomographs relating discharge rate, plant uptake and soil water potential at a reference point are developed for trickle irrigation systems. The hydraulic conductivity K is assumed to be related to pressure head h by K\do EXP (αh) in which K\do and α are empirical constants representative of the specific soil. Point or disc sources located at the soil surface as well as arrays of line sources located at the soil surface or buried at depth d are considered. For point or disc sources, the plant water uptake is from a cylindrical volume or a buried horizontal disc. For line source arrays, however, a one-dimensional uptake is assumed. The reference point for line sources is chosen at depth z\dM midway between the line emitters. For disc or cylindrical uptake, the reference point is located at the outer edge of the maximum depth of withdrawal. The nomographs are easy to use and provide answers without performing tedious computations.

Impedance-match and element-pattern constraints for finite arrays

It is shown how an N -element antenna array may in principle be impedance matched by means of a specially designed interconnecting feed network to N real generators (for arbitrary excitation of these generators). The resulting element patterns for a single excited element (a single generator) in the terminated-array environment are then calculated. It is shown that for closely spaced regular arrays a condition of partial match, as contrasted with perfect match for all excitations, is the more appropriate design objective. The theory is illustrated through application to a uniform array of line sources. Element patterns obtained with an appropriately matched finite array are compared with those from the corresponding matched infinite-array model, the latter patterns having been obtained previously by an independent technique. The range of finite-array parameters to which the infinite-array model approximately applies is discussed.

Analysis of an array of line sources above a finite ground plane

A simplified analysis which gives insight into and physical interpretation on the radiation mechanism of an array of line sources above a finite ground plane is presented. Computations have been restricted to an array of two line sources since data are available for comparison. Results on the variation of the maximum field intensity, the angle of maximum field intensity, and the field intensity at the axis of the counterpoise as functions of the size of the ground plane are presented. Variations of the maximum field intensity and the angle of maximum field intensity as functions of the distance of the source above the ground plane are also illustrated. These data become very important in the design of antennas for aircraft navigation taking into account the presence of the finite counterpoise which otherwise could lead to erroneous designs.