Linear Grid Research Articles

Climate Simulations with a Spectral, semi-Lagrangian Model with Linear Grids

ABSTRACT Semi-Lagrangian, semi-implicit, spectral transform atmospheric models do not require conventional quadratic unaliased Gaussian grids because advection is not expressed as an Eulerian quadratic product in their formulation. The conventional T42 quadratically unaliased grid with 128 (64) points in longitude (latitude) supports a T63 spectral truncation, and similarly for other resolutions. We refer to these types of truncation/grid combinations as aliased or linear grids, since they can be considered as being aliased for quadratic products or unaliased for linear terms. In this paper, climate simulations based on linear grids are compared with ones based on quadratic unaliased grids. It is shown that for spectral resolutions above T42, the spectral truncation, rather than the transform grid on which the physical parametrizations are calculated, dominates the accuracy of simulations. Thus the linear grid provides a 50 percent increase in resolution of both horizontal dimensions at a negligible additional cost.

On the existence of solutions of synthesis problems for radiating systems in terms of a prescribed amplitude directional pattern

We study two variational formulations for nonlinear inverse problems applied to the synthesis of radiating systems, and we derive nonlinear operator equations that follow from the necessary condition for the functional to have a minimum. On the basis of the properties of these functionals we prove theorems and exhibit an existence domain for solutions of this class of problems. Using the example of a linear grid, we exhibit the transition from the variational formulation of a problem to nonlinear integral equations of Hammerstein type.

ALGEBRAIC GRID FRONT MARCHING METHODS

The transfinite interpolation formula of grid generation that employs the Hermite interpolation formula is improved by the addition of a grid front marching method embedded with a simple grid smoother. In the test cases, the proposed method preserved approximate grid orthogonality around all the boundaries and eliminates grid nonsmoothness, grid slope discontinuity, and grid overlapping that occurred with the original method. The required CPU time is about 2.2 times more than the CPU time required by the original method and is at least one order of magnitude faster than the elliptic grid solver employed as a grid smoother. The method was also applied to the linear grid system to improve grid smoothness, but its computing time is about 4 times greater than the original method and is of the same order as the elliptic grid smoother. For cases with boundary discontinuity, the grid front marching method is applied to only a few grid levels inward, the remaining grids are generated via the original transfinite interpolation formula, and the required computing time is only slightly longer than that of the original formula.

Numerical solution of the synthesis problem of a linear equidistant grid in a given frequency range

Using the example of a linear grid we study problems of phase and amplitude-phase synthesis in a given frequency range: finding the frequency-dependent currents in radiators that guarantee optimal mean-square approximation of the amplitudes of the given and the synthesized diagrams; finding the averaged frequency-independent currents. The problems reduce to nonlinear integral equations that can be solved numerically by the method of successive approximations.

Device for facilitating precise alignment in bedside radiography.

The difficulty associated with achieving precise alignment in a bedside radiographic setting has led many departments to abandon the use of a grid and forfeit the improved contrast it affords. The authors describe a method of alignment that has proved successful in overcoming the hazards of grid cut-off in a bedside setting. The method affords obtainment of reproducible high-quality bedside radiographs with a 10:1 linear grid.

Resistive grid image filtering: input/output analysis via the CNN framework

The cellular neural network framework developed by L.O. Chua and L. Yang (IEEE Trans. Circuits Syst., vol.32, Oct. 1988) is used to analyze the image filtering operation performed by the VLSI linear resistive grid. In particular, it is shown in detail how the resistive grid can be cast as a CNN, and the use of frequency-domain techniques to characterize the input-output behavior of resistive grids of both infinite and finite size is discussed. These results lead to a theoretical justification of one of the so-called folk theorems commonly held by researchers using resistive grids: resistive grids are robust in the presence of variations in the values of the resistors. An application to edge detection is proposed. In particular, it is shown that the filtering performed by the grid is similar to the exponential filter in the edge detection algorithm proposed by J. Shen and S. Castan (1986). >

Digital phase-step interferometry: a simplified approach

In a two-beam optical interferometer, introduction of a tilt between the beams produces a set of nominally straight and equispaced fringes. The phase information represented by deformations in this fringe pattern can then be calculated at each point in a video image by using intensity samples from a group of neighbouring positions. Deformations of a linear grid pattern as encountered in moiré methods can be analysed in the same manner. This procedure of spatial phase stepping has been implemented on a fast microcomputer, enabling quantitative results to be obtained in a particularly simple qay.

Point-source location using a millimetre wave focal-plane array radar

The problem of point-source location using a multibeam focal-plane staring array radar is addressed. A maximum likelihood approach to position estimation is adopted and analytic expressions are derived for the error in position estimation due to noise as a function of the signalto- noise ratio (in a high signal-to-noise ratio approximation) and as a function of the array configuration. These expressions are evaluated for different array arrangements (linear array, square grid and triangular grid). The implementation of a maximum likelihood position estimation algorithm in a particular experimental millimetre-wave staring array radar is described. The performance of the radar is predicted using the theoretical calculations and results of experiments are then compared with these predictions. Good agreement indicates that the theoretical analysis may be used as a design tool for focal-plane arrays.

Simple method for the defect control in X-ray mask fabrication

In a 1:1 X-ray mask with structures of about 0.5 micron defects ⩾ 0.15 - 0.2 micron perturb whereby printing defects are of interest only. It needs a tight defect control of the fabrication process to keep the defect density within a reasonable range. This paper describes a method for the measurement of the density of printed mask defects by simple means. It uses a linear grid as the mask pattern, which is printed twice on the same wafer with a mask displacement inbetween. Measurements with this method showed a considerable increase of the density of printed pinspots with the proximity gap decreasing from 100 microns down to 50 microns. A measured size distribution of printed pinspots confirms the expected exponential increase of the defect density down to 0.15 micron defect size.

Continuous lateral shearing interferometer

A simple lateral shearing interferometer based on the use of gratings is discussed, which facilitates the display of the spatial complex degree of coherence (CDC). A first version consisting of two identical gratings inclined relative to each other was used to demonstrate the working principle. For this purpose partially coherent light was used which was generated by imaging different object distributions on a rotating scatterer (e.g., double-slit or linear grid patterns). Furthermore, an achromatic lateral shearing interferometer based on the use of three gratings in a series arrangement is discussed and a theoretical proof for the achromatism of this arrangement is given.

Artifacts produced by moving grids.

Anti-scatter grids reduce the amount of secondary radiation contributing to the image and improve the signal-to-noise ratio. However, they may also lead to the creation of linear artifacts representing the shadows of the radiopaque septa. Grid motion perpendicular to the septa during the exposure can cause blurring of the artifacts; however, the wider septa of recently proposed grids increase the difficulty of suppressing the artifacts entirely. Physical characteristics which affect perceptibility of grid-line artifacts and the conditions needed for their elimination are analyzed. Sufficient grid movement can eliminate overlap artifacts, while synchronization of linear grid motion with exposure time can suppress artifacts for relatively small grid movements.

Moiré pattern of a linear grid with a lenticular grating

It is shown that, when a certain space exists between a linear rectangular grating and a lenticular grating, the resulting moiré pattern is a linear rectangular grid. An analysis of the phenomenon is provided, and some of its applications to moiré analysis are demonstrated.

A method to analyze the motion of the endocardium during contraction.

Regional segmental wall motion analysis assumes a linear or radial grid system. In this study, motion patterns of points on the canine endocardium were evaluated. Radiopaque endocardial and epicardial markers were inserted along the anterior and posterior descending coronary arteries. Postoperative cine radiography showed that the endocardial markers did not move along either linear or radial grids. The endocardial and epicardial markers were shown to have different patterns of movement.

A new type of grid.

A new type of grid is discussed. It is anticipated that it will have the same primary transmission as and will eliminate scatter more efficiently than a conventional linear grid of equal thickness and lead content. The construction of the new type of grid is similar to a conventional one except that the lead strips are arranged in zigzag rather than linear pattern. Geometrically ideal "zigzag" and linear grids were constructed and their performance tested. The scatter transmitted by the ideal zigzag grid was one-half that of the comparable ideal linear grid. The implications regarding the improved scatter-eliminating capabilities of a practical zigzag grid are discussed.

Computer Processing and Presentation of Discrete Transducer Directivity Data

Different interpolation techniques were used to generate a continuous transducer directivity function from a series of response data measured at discrete points over a plane area. The problem of the presentation of such information is discussed. A contour plot was used as a compact way to present all of the data in a form that can be examined rapidly for practical information about the transducer-beamwidth, side-lobe levels, and side-lobe locations. However, examination of such contour plots proved to be an unsatisfactory way to compare them accurately. The technique used for this purpose was to compare corresponding plots of response versus elevation at various azimuths. The most practical format for the contour plots appears to be a linear grid of elevation versus azimuth. A CDC-3200 computer was used to perform all data processing, including generation of the contour plots.

Determination of “Three-Dimensional” Directivity Patterns of a Transducer from Discrete Response Measurements

An experimental program was undertaken to study the measurement and and presentation of “three-dimensional” directivity patterns of an underwater acoustic transducer. The output of a fixed transducer was sampled discretely and recorded on paper tape as a small projector was scanned over a plane aperture in the farfield. This was done to simulate the use of an array of small probes to measure directivity of a shipboard transducer. The spacing between data points was a variable parameter. The data were reduced on a CDC-3200 computer; interpolation techniques were used to generate continuous directivity functions. A useful presentation of the data consisted of contours of equal response plotted on a linear grid of elevation versus azimuth. The contour plots for different spacings are compared; these plots are also compared with equivalent plots generated from a series of conventional directivity patterns. The accuracy of the plots was surprisingly good in the case of relatively widely spaced data—for example, with the spacing equal to about one-third, the half-power beamwidth of the major lobe of the transducer pattern. This would indicate that measurement of relatively few discrete response data and computer processing can provide a useful means of determining transducer directivity.

Splitting Phenomena of a Liquid Drop by a Linear Grid

Splitting Phenomena of a Liquid Drop by a Linear Grid

The Reactance-Tube Oscillator

The reactance-tube oscillator is a combination reactance-tube circuit and oscillator circuit which uses but a single tube. It has two forms-one derived from the capacitive reactance-tube circuit and one from the inductive reactance-tube circuit; with slight variations the first may be made to resemble the Hartley oscillator circuit, and the second the Colpitts oscillator circuit. Experiments with this oscillator have shown that linear frequency variation versus grid voltage change with constant output amplitude may be obtained over a range of more than five per cent in the region of 1 to 4 Mc.