A description, history and the capabilities of an ionospheric sounder in the auroral zone near Tromsø, Norway are presented, together with some scientific applications. The sounder, which is of the dynasonde type, has provided a data set which has improved dramatically in quantity, quality and information content. A similar sounder is planned to be installed in the polar cap near Longyearbyen on Spitsbergen.

An algorithm is presented which can be used to outline ellipses, circles, or any of the other conic sections on a hexagonal lattice. The basic algorithm requires just one test and three add operations in the inner loop, though an additional test is required to detect a change in the overall direction between two adjacent sectants.

The problem of identifying echoes in digital ionosonde observations is discussed, starting with an off‐line simulation of the procedure long used in real time by the dynasonde. In that method, echoes are defined as amplitude‐modulus peaks from rapid (10‐μs) sampling of receiver quadrature outputs; coincidence of peak time among a small number (4–8) of repeated pulses has served well to reject impulsive noise while deciding the complex‐amplitude samples to be retained for off‐line analyses. This paper presents a new method of echo recognition dependent on all of the phase information contained in the same rapid sampling. No change is made in basic sounding function, but conversion to physical parameters is done first, for all 10‐μs samples; the consistency of these parameters in five dimensions over four or more samples defines an echo, or at least a partial “glint.” In an example recording, the new method recognizes about 60% more echoes and glints, giving better trace continuity than the earlier method. Measurement resolution among proximate echoing regions is improved. Weighted means of the physical parameters within their defining samples yields better accuracy. Almost incidentally, these results would be available immediately in a real‐time implementation of the method.

Splines based on four-point Bezier cubic arcs show some disadvantages compared to general conic arcs. Efficient rendering and data fitting algorithms require that the cubic be expressed in algebraic form, but there are problems in the conversion from the parametric form because of a singularity associated with a special case, the parabola. In conversion from the general conic to the Bezier cubic format, on the other hand, the authors note that the arcs of an ellipse can be well approximated, but not sharply turning hyperbolic arcs

The arithmetic mean, and sample variance, are the most common summary statistics of a data set. There are circumstances (within computational loops, and in real-time data analysis, for examples) where it is desirable to maintain a current estimate of the mean and variance. The ''lossy'' (sometimes called the ''running'') mean and variance are frequently useful also. We present an algorithm for these applications, and show the provisions necessary for use with cyclical (e.g. phase-angle) data.

We consider the interpretation of “spread F” ionograms, particularly those echoes that determine most of the radio bandwidth of the phenomenon. We compare expectations based on total internal reflection with theoretical descriptions based on underdense scattering. We conclude that “Rayleigh,” “Bragg,” and “diffuse multiple-refractive” radio scattering theories are not consistent with observed properties of these echoes. The total-reflection interpretation is shown to be consistent with rocket and satellite data. Evidence for multiple refractive scatter is found, but it neither greatly nor subtly extends the observed radio bandwidth. Ionograms therefore indicate comprehensively the range of plasma densities within view of the ionosonde, even in conditions of spread F. Using digital ionosonde observations, much can be learned of the spatial structures of plasma density responsible for spread F at auroral and equatorial latitudes. As an example, we suggest how contemporary theory and simulations of the equatorial “bubble” phenomenon may be reconciled with the distinctive equatorial spread F pattern.

Two mathematical descriptions of outlines which have found acceptability and widespread usage are the Bézier cubic and the general conic forms (which include the distinctive parabolic format). Though there are good reasons for employing just the general conic, PostScript characterises fonts in terms of splines based on four-point Bézier cubics. In order to improve the efficiency with which these PostScript fonts can be rendered, the equation of the Bézier cubic is here reduced to the non-parametric form required to exploit an efficient cubic tracking algorithm first presented in 1968. Although successful in most cases, the occasional breakdowns are both spectacular and disastrous. The cause of the problem is analysed, and possible solutions suggested.

Line-of-sight Doppler velocity V∗ and three-dimensional apparent echolocation (XL, YL, ZL), are among the principal parameters available for each ionospheric echo from most observing modes of the dynasonde. An ensemble of three or more echoes containing diverse XL, YL, ZL is sufficient to determine the full vector velocity VX, VY, VZ common to the ensemble. We present a procedure based on weighted least-squares, which may be applied to an entire recording or to suitably selected parts of it, to yield ‘best’ estimates of VX, VY, VZ and their confidence limits. Each observation is weighted according to an r.m.s. phase error incurred in the estimation of XL, YL, ZL and V∗. A measure of the fraction of observed Doppler variance expressed by the analysis is useful to decide if spatial or temporal variabilities are significant within the ensemble. Often at Tromsø the results are directly applicable to the estimation of prevailing electric fields with high (⪢10 s) time resolution.

The accuracy and efficiency with which radio echo parameters may be estimated by a programmable ionosonde of high resolution depend upon software‐designed strategies of pulse set design and receiving antenna layout. All of the echo parameters, except amplitude and time of arrival (thus three components of echolocation, Doppler, polarization rotation, and an average phase angle) are determined by phase angle differences. The solution is conveniently expressed as a least squares estimation, provided that more than six independent phase measurements are available. Since the observed phases are necessarily obtained modulo 360°, from 12‐bit complex amplitude data, each parameter is subject to aliasing ambiguities which must be anticipated in each strategy, and minimized.

This paper presents efficient algorithms for generating points on the circumference of a circle, based on extensions to an ellipse-drawing algorithm attributed to Minsky. The algorithms have direct use in the control of the path of machine tools, particularly through their acceleration and deceleration phases.

A structural algorithm is proposed which used Euclid's algorithm to control two symmetric production rules which can construct the ‘best-fit’ incremental line. The output is identical to that produced by Bresenham's algorithm but is, in general, produced in fewer subtract operations. The correctness of the algorithm is established, and a formula conjectured for the behaviour of the subtractive version of Euclid's algorithm.

An algorithm is presented which evaluates the area of the triangles formed by the intersection of a straight‐line boundary with pixel elements, yet involves only tests and additions.

The sequence of plotter moves generated by Bresenham’s algorithm for a single straight line can be expressed recursively as a sequence of repeated patterns. A similar pattern can be seen in the flow of Euclid’s algorithm if it is applied to find the highest common factor of the two integer parameters defining the gradient and end point of the given line. The analysis suggests a simple extension of Bresenham’s algorithm which provides an automatic shortcut (Computer Journal 25, 114).

Simulation des perturbations de la region F provoquees par une explosion au sol. Des mesures montrent que la vitesse du son a 280 km est d'environ 900 m/s