One-half Wavelength Research Articles

Evaluation of the radiation pattern of a split aperture linear phased array for high frequency imaging

Developing transducer arrays for high frequency medical imaging is complicated because of the extremely small size and spacing of the array elements. For example, a 50 MHz linear phased array requires a center-to-center spacing of only 15 microm (one-half wavelength in water) to avoid the formation of grating lobes in the radiation pattern of the array. Fabricating an array with these dimensions is difficult using conventional technology. A split aperture design that permits much larger element spacing (3 to 4 times) while avoiding the formation of grating lobes is described. The 3-D radiation pattern of a 1.9x1.4 mm, 50-MHz split aperture linear phased array with 33 transmit elements and 33 receive elements has been evaluated theoretically. The azimuthal beam width is 90 microm at a distance of 4.0 mm. Grating lobes are suppressed by at least 60 dB at distances >4.0 mm (~f/2). The elevation beam width is 220 microm at 4.0 mm, and a useful depth of field over the axial range from 4 to 10 mm is obtained.

A tonpilz projector for use in an underwater horn

Tonpilz transducer head piston diameters are usually about one-half wavelength in diameter, so that “ρ-c” radiation loading will be approximately achieved. However, for this underwater tracking application, the transducer is required to fit inside the throat of a 360-degree horn. The piston diameter is limited to 1 in. (25 mm), or about 0.22 wavelength at the resonance frequency, 13 kHz. The design is based on a lumped-element model. The lead zironate-titanate (PZT-8) ring stack is 2.1 in. (53 mm) long with an outer diameter of 0.49 in. (12.5 mm) and an inner diameter of 0.24 in. (6.0 mm). The head mass is 0.25-in. (0.635-mm)-thick aluminum, and the tail mass is wolfram (tungsten), with a mass of 93 g. The transducer is isolated from its cylindrical housing with a syntactic foam spring. An O-ring piston seal is used, and a similar O-ring provides support for the tail mass. The results of free-field measurements are used to determine the parameters of a lumped-parameter equivalent circuit model, which is then used to predict the performance after installation in the horn.

A demountable interconnect system for a 50/spl times/50 ultrasonic imaging transducer array

A novel Pad Grid Array (PGA) system allows microminiature coaxial conductors to be electrically connected to a one-half wavelength, 50/spl times/50 element transducer array suitable for diagnostic ultrasound at 2.5 MHz. In order to achieve the desired one-half wavelength interconnection spacing present at the backing of the transducer module, an intermediary flexible printed circuit and other custom structures provide a transitional architecture between 42 AWG coax and inline interconnect pads at a 300 /spl mu/m spacing. Due to critical alignment requirements, special processes are needed for fabrication and the successful connection of the fine-pitch circuit elements. A conductive anisotropic elastomeric material acts as the medium to effect the final interconnect between the PGA and transducer module. Because the anisotropic medium provides a separable interface, the interconnect system allows repeated connection. Acoustic performance indicates suitability for diagnostic imaging.

Broad-bandwidth radiation patterns of sparse two-dimensional vernier arrays

The fabrication of a dense (one-half wavelength element spacing) two-dimensional (2D) transducer array suitable for medical ultrasound imaging is unrealistic using existing technology. Consequently, there is interest in developing sparse 2D transducer arrays. In this paper, we present the results of a study looking at the broad-bandwidth radiation patterns of 72 different sparse 2D vernier arrays. Suppression of grating lobes is achieved by choosing a different arrangement of transmit and receive elements using an analogy with a vernier scale. The broad-bandwidth radiation patterns were investigated by simulating volumetric sector scan of a point target. We summarize these results by deriving a set of design curves that predicts the minimum number of elements, element spacing, and apodization required for a desired beam width and maximum secondary lobe. The results show that a sparse vernier array can be designed with significantly lower average and peak secondary lobes compared with a sparse random array with the same number of elements and aperture size.

The Effects of Leaf Pruning and other Stresses on Sex Determination in the Oil Palm and their Representation by a Computer Simulation

Oil palms produce an inflorescence in each leaf axil. These show irregular cycles of gender with occasional abortions. Physiological stress is known to induce a higher frequency of males and abortions, but it is not known how such factors interact with endogenous cycles nor is/are the developmental state(s) when sex is determined known with accuracy. A computer simulation model, based on published results of field experiments to define critical timings of sex determination and stress generation, with feedback loops generating “stress” one-half wavelength ahead of the sex determination and abortion stages, produced oscillations of male, female and abortion cycles. The model assumes that female inflorescences are formed unless the stress exceeds a specified threshold level, when males are formed. At higher stress levels abortions occur. The model predicts that in the absence of external stimuli there is a natural sex cycle the duration of which depends on the timing of sex determination. A shorter abortion cycle 24 nodes in duration interacts to modify the sex cycle. Annual stress cycles (e.g. drought) can over-ride the endogenous cycles and synchronize them. The response obtained to a transient stress simulating leaf pruning resulted in extra males and abortion but depended on when the stress was applied in the natural flowering cycle. Simulations of irrigation experiments are presented and disbudding experiments discussed. The model allows wide flexibility of inputs. The examples shown are based on sex determining stages at a variety of times between leaf axil −5 (spikelet initiation) and leaf axil −27 (first bract initiation) with the signal generated during bunch development. Abortions occurring at leaf axial +10 are also induced by a signal from developing bunches. The timing of these stages can be changed at will. By changing the stress threshold levels at which females, males and abortions occur, it was found that this double loop feedback model gives good simulations of the endogenous cycles. The loop timings used are consistent with published data on the critical stages of oil palm floral development. The effects of pruning stress on two oil palm clones with different flower-cycle characteristics were only partially simulated, and deeper understanding of the sex determination processes is needed. Several predictions are made which would allow the model to be tested experimentally.

A small antenna consisting of short‐ended parallel stubs and capacitors

A small antenna for mobile communication is proposed in which the ends of the shorted parallel plates are folded inward to generate a capacitive load between the gap. The balanced feed happens at an appropriate position on the parallel plates. When dual parallel plates are used, the antenna can be used at dual frequencies. This antenna is considered to ba a kind of small loop antenna and can be used at the electric field null (or the peak of the magnetic field) generated near the metallic furniture, a column with internal conductors and walls. In this paper, the far-field radiation pattern and the input impedance of this antenna are computed and the results are compared with the measured results. This comparison demonstrates that the method cannot quantitatively evaluate the antenna characteristics but can be useful for finding the tendency of these characteristics. Next, the design guideline of the antenna is presented according to the analysis method. Miniaturization limitations of the present antenna are discussed. The antenna proposed in this paper has a measured gain of G = −0.3 dBi and a bandwidth of 5.6 percent for a return loss of less than −10 dB with a maximum dimension of one-half wavelength. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 1, 80 (4): 83–95, 1996

190-GHz radiation from a quasioptical Josephson junction array

At 190 GHz, 0.36 /spl mu/W has been detected from an 11/spl times/58 array of niobium Josephson junctions. The power is radiated directly into free space above the surface of the two-dimensional array of junctions. Detection is made by a commercial bolometer outside the array cryostat. The junctions in the array are closely spaced in the y-dimension, but spaced by more than one-half wavelength in the x-direction. This asymmetry results in mutual phase-locking between adjacent junctions suitable for the production of y-polarized radiation. The resonance anti asymmetry also results in a reasonable impedance match between the Josephson junctions and the free-space radiation mode.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On the spontaneous lifetime change in an ideal planar microcavity-transition from a mode continuum to quantized modes

The spontaneous emission lifetime of an atom is known to be influenced by its environment. In general, the lifetime will be different if the atom is suspended in free space than if it is placed inside a cavity. A simple cavity geometry in which to explore this effect is the planar cavity. In a paper by Brorson, Yokoyama, and Ippen, the authors derived the minimum lifetime in a planar cavity to be one-third of the free space (no cavity) lifetime, and the appropriate mirror spacing was found to be one-half wavelength. In a paper by Yamamoto, Machida, and Bjork, it was concluded that the lifetime for a half-wavelength-long cavity was only two-thirds of the free space lifetime. In this paper, the discrepancy between these results is clarified and it is shown that the shortest lifetime is indeed one-third of the free space lifetime; but to achieve this, the cavity has to be slightly longer than one-half wavelength. This will influence the emission mode pattern in a way that, in general, is undesirable for a surface emitting laser. It is also shown that a strictly half-wavelength-long cavity has a lifetime of two-thirds of the free space lifetime. The model employed has the attractive feature that if allows a smooth transition from a fully open system with the atom interacting with a mode continuum, to the fully closed system with quantized photon modes.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Scattering by finite wires

For a conducting wire of finite length illuminated by an incident electromagnetic wave, induced surface current is represented as the sum of a driven term and resonant traveling waves, for which free-space propagation behavior is slightly modified by a perturbation m. Requiring current to vanish at the ends of the wire, both m and the resulting amplitude are obtained for normal incidence by applying Galerkin’s method to the resulting trial function. In the Rayleigh limit cross sections are expressed analytically. For wires up to one-half wavelength long, we find equivalence with Tai’s variational results [J. Appl. Phys. 23, 909 (1952)]. Beyond this point, the driven term goes over to the infinite cylinder current, as wire length increases. At the same time, for highly conducting wires one finds an explicit formula for m, in which ‖m−1‖≪1; for moderate conductivity, m reduces to the attenuated propagation behavior found by Sommerfeld [J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), pp. 524ff] for infinite-length wires.

I-slot characteristics

I-shaped slots will fit entirely on the rectangular waveguide narrow wall without wrapping onto the broad wall. This slot type is suitable for single plane scan-phased arrays where element spacing, in the scan plane, is equal to or less than one-half wavelength. The method of moments solution for the I-slot is presented. Comparison of computed results with measured data illustrates the validity of this solution. To facilitate future designs, the waveguide scattering parameters and the radiation characteristics of I-slots are included. >

Analysis of phase-focused near-field testing for multiphase-center adaptive radar systems

Airborne or spaceborne radar systems often require tests before deployment to verify how well the system detects targets and suppresses clutter and jammer signals. The radar antenna diameter can be large and thus the conventional far-field test distance is impractical to implement. The theory and simulations of phase-focused near-field testing for adaptive phased array antennas is discussed. With near-field source deployment, standard phased-array near-field phase focusing provides far-field adaptive nulling equivalent performance at a range distance of one aperture diameter from the adaptive antenna under test. Both main beam clutter sources and sidelobe jammer sources are addressed. The phased array antenna elements analyzed are one-half wavelength dipoles over the ground plane. Bandwidth, polarization, array mutual coupling, and finite array edge effects are taken into account. Numerical simulations of an adaptive antenna that has multiple displaced phase centers indicate that near-field and far-field testing can be equivalent. >

Improved technique for determining complex permittivity with the transmission/reflection method

The transmission/reflection method for complex permittivity and permeability determination is studied. The special case of permittivity measurement is examined in detail. Robust algorithms for permittivity determination that eliminate the ill-behaved nature of the commonly used procedures at frequencies corresponding to integer multiples of one-half wavelength in the sample are presented. An error analysis yielding estimates of the errors incurred due to the uncertainty in scattering parameters, length measurement, and reference plane position is presented. Equations for determining complex permittivity independent from reference plane position and sample length are derived.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A subarray approach to matched-field processing

A simplified approach is presented for matched-field processing of large vertical arrays in typical ocean environments. The large array is divided into subarrays such that a plane-wave decomposition of the signal field is a good approximation over each subarray. A simple rule, based on the sound-speed profile, is presented for subarray sizing. Plane-wave beamforming is then performed to provide multiple beams from each subarray. For long-range situations, only those beams need to be formed that are steered to receive rays that are not strongly bottom interacting. When elements are spaced at one-half wavelength, the typical result of considering only these beams is a significant reduction in the size of the problem with far fewer beams required than elements. This first step is very robust and does not require a detailed knowledge of the signal field, or an assumption of signal coherence across the full array aperture. Beam outputs can then be combined to achieve full matched-field processing. The relative performance of suboptimal approaches such as incoherent combination of beam outputs or simply choosing the best beam is also examined. It is shown that full optimum coherent matched-field processing in spatially white noise yields an output signal-to-noise ratio that depends only on the total signal power intercepted by the aperture, and not on the details of the signal field. For an array that spans the full water column, this can be estimated simply on the basis of cylindrical power flow and falls off as the reciprocal of range. Detailed results are presented for a Pacific winter profile at three widely separated ranges. A small percentage of the beams is found to contain almost all of the signal power. The ray angle diagram (RAD) is used to relate rays, normal modes, and subarray beams, providing insight into the underlying principles. It is shown that the signal field has a fixed number of degrees of freedom and can be represented by that number of beams or normal modes.

Length error analysis for impedance tube measurements

Length error analysis of the transfer function method and improved standing wave ratio (SWR) method for impedance tube measurements is presented in this letter. The error of measuring the complex reflection coefficients R is caused by errors in measuring the positions of the two microphones (or the two pressure points for the improved SWR method). Results agree with Abom and Boden’s [J. Acoust. Soc. Am. 83, 2429–2438 (1988)] conclusions, i.e., errors will be large if s, the separation distance of the two microphones, is about one-half wavelength and will be small if s is about one-quarter wavelength. Results also show that in order to reduce the amplitude error of R, it is better to locate one microphone near a minimum pressure point and the other near the adjacent maximum pressure point. To reduce the phase error of R for the transfer function method, preference of the two microphone locations depends on the combination of length errors Δl1 and Δl2. Phase error reduction for the improved SWR method requires an accurate measurement of the minimum pressure point.

Generalized holography and computational solutions to inverse source problems

The inverse source problem for one- and two-dimensional coherently radiating sources is studied within the framework of generalized holographic imaging. It is shown that the image field produced from a generalized hologram of a one-dimensional source contains a complete description of the source. For such sources, structure larger than one-half wavelength is accurately imaged, whereas information on smaller scales can be obtained from a linear operator applied to the image field. The image fields of two-dimensional sources are shown to contain only partial information about these sources. It is shown, however, that perfect imaging is possible for the class of sources satisfying the homogeneous Helmholtz equation. This class is shown to be identical with the class of minimum energy sources recently encountered in connection with the inverse problem for three-dimensional sources. For noisy images there are serious practical limitations on source detail obtainable from any imaging system; the generalized hologram achieves near-ideal performance when the image is noisy.

Determination of source parameters by wavefield extrapolation

The extrapolation of an observed (seismogram) wavefield backward in time produces an image, in both time and space, of the source. This concept is implemented through a finite difference solution of the two-dimensional acoustic wave equation. The seismograms themselves are used as time-dependent boundary values that drive the finite difference mesh, Numerical examples illustrate the determination of hypocentre location and origin time for point sources and of source extent, orientation and rupture velocity for finite sources in both homogeneous and heterogeneous media. Spatial resolution of source parameters is typically one-half wavelength of the dominant frequency generated by the source.

Miniaturization of wide-band VHF filters by using spiral resonators

The miniaturization of a wide-band VHF filter composed of distributed resonators has been studied. The miniaturized filter was realized with spiral resonant lines and lumped capacitors. The filter was designed using a prototype filter circuit composed of only series-resonant lumped-constant circuits. Each resonant circuit is transformed to another resonant circuit consisting of a spiral resonant line and two capacitors. One capacitor is connected to each end of the spiral resonant line. With this technique, the line length becomes very short, e.g., one-twentieth wavelength, in comparison with the line length in conventional resonant lines of one-half or one-quarter wavelength. A filter which has a 160-185 MHz passband and a volume of 3 × 4 × 10 cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> was realized with 10 spiral resonators. The filter exhibits superior characteristics with very little volume.

A multiple frequency array for improved diagnostic imaging

Cost and complexity of phased array diagnostic ultrasound imaging systems is related to the number of parallel channels during both transmit and receive. If the total numberofa ctive elements within a given aperture is reduced so that fewer parallel channels are required, grating lobes may result if the spacing of elements within the array is greater than one-half wavelength. These grating lobes may produce image ambiguities in the form of multiple images and reduced dynamic range. These grating lobes can, however, be reduced if transducers of large bandwidth are utilized. A novel broadband array is described which consists of two transducer arrays of different frequencies (one at 1.5 MHz, the other at 2.5 MHz) mounted one above the other. This method of construction avoids the usual compromise between sensitivity and bandwidth. Experiments indicate a reduction of 5 dB in the off-axis response in the transmit operation when compared to a single frequency array (2.5 MHz) with similar dimensions (16 elements within a 19.7-mm aperture). The routine diagnostic utilization of this array resulted in improved image quality in terms of reduced image artifacts and improved contrast as well as better target acquisition.

Currents and Charges Induced in an Arbitrarily Oriented Electrically Thin Conductor with Length up to One and One-Half Wavelengths in a Plane-Wave Field

Distributions of induced current and charge per unit length are displayed for electrically thin antennas not longer than one and one-half wavelengths that are illuminated by an incident plane wave. It is shown that the distributions of current and charge have significant even and odd parts which vary with the angle of incidence.

Edge diffraction effects on acoustically baffled, phased arrays

The two-dimensional scattering of plane waves by a thin, semi-infinite plate with either Neumann boundary conditions over both surfaces or mixed Neumann/Dirichlet conditions on opposing sides may be readily calculated. Since wave components in any plane parallel to the barrier edge undergo specular reflection, the two-dimensional formulation may be easily extended to three dimensions. The distribution of the total pressure amplitude and phase on both sides of the barrier as a function of aspect angles is shown in this paper for both types of boundary conditions. The effects of edge diffraction on acoustic array performance is demonstrated first in the calculated receiving patterns of a summed five wavelength array steered towards the baffle edge and then away from it, and second in the calculated beam patterns of a two element, two and one-half wavelength array used for phase detection. The estimated bearing error versus bearing for the null array is shown for different tilt angles and different distances of hydrophones from the baffle edge.