Sum Mode Research Articles

Instrumental corrections of peak areas in gamma-ray sum-peak counting

Direct activity measurement by the γ-ray sum-peak method with two NaI(T1) crystals operating in the summing, coincidence and anticoincidence modes is demonstrated for 88Y and 207Bi. Estimates of γ-spectrum peak areas are described in detail. Instrumental corrections of the peak areas for pile-up, dead time and random summing are derived theoretically and verified experimentally for all three modes of operation.

Null shift and beam squint in circularly polarized offset-reflector antenna

A formula for the null shift of the difference mode pattern of an offset-reflector antenna is derived. It is shown that this null shift and the beam squint of the sum mode pattern have different values. Such a phenomenon must be considered in the design of a two-channel tracking system.

Constrained optimization of monopulse circular aperture distribution in the presence of blockage

A method of synthesizing aperture antenna excitations to obtain optimum performance in the presence of aperture blockage is presented. The problem of optimizing the performance indices such as directivity and angular sensitivity is formulated as an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> -dimensional minimization problem, with constraint on the sidelobe level. In most cases, the objective function is nonlinear with multiple minima which does not yield readily to gradient methods. A simplex search method is used in the study for optimizing the performance index. The sidelobe level (SLL) constraint has been incorporated using the penalty function method. The method is applied to circular monopulse aperture distribution with circular blockage to obtain maximum directivity factor (DF) in the sum mode and maximum angular sensitivity factor (ASF) in the difference mode, with sidelobe level constraint. The effect of blockage on the maximum directivity and maximum angular sensitivity is studied for various sidelobe level constraints.

Resonant scattering by fluid-filled cavities

abstract Interaction of seismic energy with a fluid-filled cavity results both in scattering by the cavity and in excitation of its normal modes. The normal modes contain information about the properties of the fluid that fills the cavity and its size. In the frequency domain, each mode in the cavity response can be decomposed into a sum of two spectra; the “background” scattering from an empty cavity and the resonant coupling between the fluid cavity filler and the surrounding matrix. Synthetic seismograms are computed by Fourier transformation and summing modes. The theory is applied to a water-filled crack in granite, a model for the core of Mars, and a magma chamber.

Plane wave spectrum scattering analysis of near-field obstacle effects on directive antenna patterns

A plane wave spectrum scattering analysis of the effects of a near-zone obstacle on the pattern performance of a directive antenna is discussed. The free-space azimuth monopulse antenna is characterized by its sum and difference mode plane wave spectra, and a computed plane wave scattering dyad is used to characterize the scattering by a metallic right circular cylinder when it is excited by the incident antenna spectra. An efficient computer algorithm has been developed to compute the far-zone scattered and total fields for the antenna/cylinder system. Extensive experimental data have been obtained, and the patterns calculated using the present analysis are in agreement with the measured data.

Boxcar controller for low-repetition-rate use

We present a simple digital circuit which will control a Princeton Applied Research Corporation (model No. 164) boxcar integrator and thereby allow full utilization of the linear sum mode. This provides for improved signal-to-noise ratios and shorter data acquisition times for short signals [10-50 ns occuring at moderate repetition rates (1-20 Hz)]. This provides significant data acquisition time savings for low-repetition-rate, high-time-resolution measurements. It also increases the signal-to-noise ratio in many circumstances.

Arbitrarily polarized slot radiators in bifurcated waveguide arrays

The feasibility of obtaining arbitrary polarization in both one- and two-dimensional arrays of slots in dual mode bifurcated Waveguides has been demonstrated. The radiating element consists of a pair of crossed slots in the sidewall of a bifurcated rectangular waveguide that couple to even and odd waveguide modes. One linear polarization is excited by the even or "sum" mode and the orthogonal linear polarization is excited by the odd or "difference" mode. By superposing the sum and difference modes in the proper amplitude and phase, any arbitrary polarization can be realized. A two-dimensional array consisting of eight waveguide linear arrays, ferrite phase shifters for scanning in the plane normal to the linear arrays, and a feed network for power distribution and polarization control was constructed. Good radiation performance for various polarizations was obtained. In the case of linear polarization, the cross polarization component was on the order of -25 dB and in the case of circular polarization, the axial ratio was on the order of 1 dB. The polarization was controlled with a ferrite phase shifter. Close-in sidelobes of better than 20 dB were obtained for all polarizations. The preceding performance characteristics were obtained over a scan range of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\pm20\deg</tex> and over a 6 percent frequency band.

Multiphonon infrared absorption spectra of MgO and CaO

The multiphonon absorption spectra of MgO and CaO single crystals have been recorded, and analysed in terms of the infrared active sum modes of lattice vibrations. A critical point analysis was carried out using the dispersion curves obtained from previous neutron scattering studies and the 'breathing shell' model, and it produced similar mode combination patterns for both substances. The two main peaks I and II (846.5 cm-1 and 981 cm-1 for MgO; 628 cm-1 and 738 cm-1 for CaO) in the two- phonon region are interpreted as the sum modes W'2+W3 at W and Sigma 1LO+ Sigma 3TO near X respectively, in both crystals. Three- phonon bands were observed for both MgO and CaO and a four- phonon band in MgO, all at wavenumbers in agreement with theoretical predictions.

Preliminary Study of a Germanium Three-Dimensional Camera for Positron Emitting Radioisotopes

A preliminary feasability study of a camera for imaging of positron emitting radioisotopes based on two arrays of Ge detectors operated in coincidence has been carried out. Efficiency, effects of energy resolution, and timing characteristics have been studied. It has been found that Ge can compete favorably with NaI in efficiency if Compton signals can be admitted for imaging. Analysis of the effect of scattered radiation indicates the advisability of having some moderate energy resolution in the system. A method is devised which allows the use of the Compton signals of the Ge detectors in a summing mode and, therefore, maintain very good energy resolution. A study of the timing properties of small Ge detectors indicates that count rates as high as one order of magnitude more than those possible with NaI detector arrays should be possible. Also, for the first time, it appears realistically possible that tomography by time-of-flight techniques can be carried out with a camera. It is concluded that a small prototype camera section should be built and investigated further.

Corrugated waveguide for monopulse feed

Abstract Monopulse feeds which allow an independent optimization of the performance of the sum and difference modes have received much attention in the literature. This paper presents some experimental results obtained with a corrugated feed horn designed to operate at the focus of a paraboloid having θ0 = 60°. The present. indication is that a near-optimum performance in both the sum and difference modes can be achieved.

A flat-feed technique for phased arrays

A recently developed phased-array feed configuration offering significant advantages over the conventional space, corporate, and series feed techniques is described. This technique, referred to as the flat feed, allows power division for monopulse sum and difference pattern illumination functions in a feed depth of less than a half-wavelength with low loss. The technique used to extract energy from the power divider, which consists in part of a radial transmission line, results, in its simplest configuration, in a circular grid of antenna elements. Relations governing the circular grid array geometry design are derived which relate the angular locations of attenuated grating lobes to the spacing between the rings of radiating elements. Experimental S -band hardware, built to prove the feed technique, is described. It includes a multimode launcher with measured coupling between circular wavegulde sum ( TM_{01} ) and difference ( TE_{11} ) modes of less than -37 dB; a seven-ring 1:195 radial power divider measured across a 10-percent band to have insertion loss of 0.1 dB and rms phase and amplitude deviations of less than 3.5\deg and 0.47 dB; a 144-element array whose measured sum and difference beam radiation patterns are compared with calculated patterns for scan angles out to 60\deg and whose sum port VSWR, measured across a 10-percent band, was under 1.8:1 with the array steered to broadside, and under 1.5:1 for other scan angles out to 60\deg .

Intensity Summation of Modes and Images in Shallow Water Sound Transmission

An earlier paper [J. Acoust. Soc. Amer. 41, 161 (A) (1967)] gave a simple expression for predicting the transmission loss in shallow water under conditions of downward refraction when incomplete environmental knowledge precludes the use of elaborate theory. The present paper considers the case of near-isovelocity water with parallel lossy boundaries. Summing modes on a computer intensity-wise, assuming random phase between modes, yields a set of prediction curves for the loss in terms of normalized range r/H and normalized water depth H/λ with boundary reflection loss, expressed in decibels per degree grazing angle, as a parameter. The random phase assumption is justifiable, as a practical matter, by the effects of natural environmental irregularities, by the smallness of mode interference effects when many modes are trapped and by the interest of the engineer in only the average sound field at a distance. Summing discrete modes and images in this way, as well as integrating a continuous distribution of modes and images, leads to identical values of loss when H/λ is large. Comparisons of the prediction curves with field data reported in the literature are made.

Monopulse Operation with Continuously Variable Beamwidth by Antenna Defocusing

Monopulse tracking operation with continuously variable beamwidth may be obtained by antenna defocusing. To demonstrate this property, antenna patterns (including phase) of a square aperture for large amounts of defocusing have been computed by diffraction theory for the case of highly tapered illumination in both the sum and difference antenna modes. From an examination of the computed patterns over a 10 to 1 beamwidth range, it is shown that with the increasing defocusing, the patterns in the sum and difference modes exhibit smoothly increasing width. Some change of shape is noted, but the pattern amplitudes and phase relationships are still suitable for on-axis tracking or off-axis location by monopulse techniques. To achieve monopulse operation with the defocused patterns two modifications to ordinary monopulse receivers are necessary. A phase shifter, inserted in the difference or sum channel and ganged to the amount of defocusing, is needed to cancel the phase variation with defocusing. In addition, amplitude correction is required to keep the error-signal slope constant.

Monopulse Networks for Series Feeding an Array Antenna

Series networks for feeding an array antenna are attractive because they can be designed compactly. A series "ladder" network is available which is particularly applicable for feeding a monopulse array antenna since it has complete independent control of the sum and difference excitations, minimum dissipative loss, and physical symmetry. This network consists of primary and secondary transmission lines feeding two sets of directional couplers that are interconnected to resemble a ladder. To obtain physical symmetry, the ladder is fed at the center by two hybrid junctions and an additional directional coupler. An experimental array fed by a ladder network was fabricated and tested. The design objectives of 25 dB sidelobe suppression for the sum and difference mode patterns were achieved.

Lattice vibrations of wurtzite structure crystals

In this article we present expressions based on the general shell model of lattice dynamics, for all important long wavelength properties of the lattice vibration spectrum of a wurtzite structure crystal and for the vibration frequencies having wave vectors along the hexagonal axis of the first Brillouin zone. The dynamics of the wurtzite structure is discussed in terms of sum and difference mode parameters. The dynamics of the sum modes in wurtzite is closely related to the dynamics of a sphalerite structure crystal which has been given previously by Kaplan and Sullivan. In an effort to evaluate some of the parameters of our model by fitting our theoretical expressions to available experimental data, we have made two approximations; (1) The non-Coulomb force constants are limited to interactions with the four nearest neighbors. (2) The dynamics of the sum modes is made equivalent to the dynamics of a sphalerite crystal. The latter approximation is most simplifying and the experimental data indicates that for those wurtzite compounds having nearly ideal structure the approximation is reasonable. Even using this simplifying approximation we were unable to make a unique determination of the parameters of our model, the difficulties being the same as those encountered in the analysis of the sphalerite structure. Selection rules for first and second order phonon absorption of infrared radiation and for fundamental Raman scattering are also considered.

Optimum feeds for all three modes of a monopulse antenna I: Theory

In a monopulse antenna for use in a tracking radar, the requirements for the sum and difference modes are not the same. For the amplitude-comparison type of monopulse having an antenna whose main aperture is illuminated by a feed, these independent requirements can be met by a feed designed to fulfill two conditions. One is that excitation of the feed aperture in the difference modes be effectively about twice as wide as in the sum mode. The other is that the shapes of all the feed excitations be free of any avoidable irregularities. The amount of improvement available when these conditions are met depends on the optimization point desired for each mode, as well as the design of the reference antenna. In a typical case, the gains and slopes in the difference modes should increase by several db. Furthermore, the near sidelobes and the spillover radiation in the difference modes should decrease by an order of magnitude. A small increase of gain in the sum mode is also available, and finally, the criticalness of positioning the feed may be appreciably reduced.

Optimum feeds for all three modes of a monopulse antenna II: Practice

In an amplitude-monopulse antenna whose main aperture is illuminated by a feed, it is desired to control the feed excitation independently in the sum, azimuth difference, and elevation difference modes. It is possible to describe a feed system, comprising an infinite array of radiators and hybrid junctions, which demonstrates the principle of complete independent control of the three modes. There are several practical feeds which approach a hypothetical ideal one in varying degrees. One representative type is the "twelve-horn feed;" although it has some disadvantages, it is versatile and quite useful. However the most attractive type for many applications appears to be one having a combination of multiple-horn excitation in one plane and multimode-waveguide excitation in the other. With a simple form of the "multihorn-multimode" feed, the ideal is substantially realized, and a major improvement in monopulse performance can be obtained.