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High angular resolution is a desirable property of mapping and reconnaissance radar systems. The synthetic-aperture principle reduced the beamwidth of airborne radar by as much as two orders of magnitude. Notwithstanding the long interest in the subject, a quantitative relationship is lacking between beamwidth and resolution. This paper is an attempt to overcome this deficiency. Among its several results, it is shown that the angular resolution of synthetic-aperture radar can be considerably poorer than expected. It is also shown that a modest tapering of the synthetic aperture in those cases offers significant improvement.

The problems of low-angle tracking over the earth's surface are explored in the light of rough-surface scattering theory. A detailed model of diffuse scattering is constructed which agrees with available test data and which permits the power distributions in radar coordinates to be estimated. Using this model, the potential performance of various techniques proposed for avoidance of multi-path is evaluated, Several are found effective in maintaining tracks of reasonable accuracy down to one-fourth beamwidth above the horizon, but no generally practical solution to height measurement below that angle appears available.

RF pulses are used in radar and sonar to detect and locate targets in extended media. Short RF pulses (and impulses) can be used to find buried objects or voids by echo sounding, or can be used to probe snow fields or the depths of the earth. Although similar to radar in principle, there are important differences in these applications that can lead to significant variations in the design approach. A novel system is described, with a computer-programmed tunable RF source, that tunes rapidly through all the frequencies of a nanosecond pulse spectrum, makes individual "CW" measurements, stores them, and finally computes a synthetic echo. Target signatures can be "recognized" by calculating correlation functions. Experimental results are presented.

The scattering matrix of a target generalizes the scattering properties to include a description of their dependence upon radar polarization. The matrix may be determined directly through two successive transmissions at orthogonal polarizations, with reception of each at both of the polarizations. In the laboratory, it is possible to eliminate the requirement for phase measurement by an indirect technique using successive measurements at six polarizations (five of which may be linear). In the case where results are to be applied to linearly polarized radars, it is sufficient to determine the "linear restricted matrix" by six linear measurements. Analysis is provided and measurement technology described and evaluated for both classes of indirect measurement.

This paper describes the design of an extremely high range resolution FM/CW X-band radar and discusses some measurement data taken with this radar. The Delta radar system employs a 35 per cent bandwidth and was built as a research tool for scattering investigations at Cornell Aeronautical Laboratory under Bell Telephone sponsorship.[1] This equipment has demonstrated a range resolution of 3.0 inches as measured at the signal spectrum half-power points. The primary design objective of the radar is to provide the capability to measure radar cross section of scaled models with a range resolution equal to a small fraction of the target's length. Radar cross-section measurements made with this radar have permitted the separation and identification of the individual scattering contributions on several target bodies. Data from three types of radar targets are presented and discussed. Particular theoretical interest centers on the measurement of the sphere-capped cone, for which the measurements bear out simple arguments of electro-magnetic theory to demonstrate that: 1) Discontinuities of geometric surface curvature on a metallic body are pronounced scatterers. 2) There is no scattering from the optical shadow boundary. 3) There is now good evidence of the "creeping wave" contribution to the scattered field.

Experiments have been performed in which the radiation from a CO 2 laser was coherently detected after being scattered from a moving diffuse reflector. This is generally the configuration of an infrared laser radar. The power-spectral-density of the heterodyne signal was measured and its width was shown to agree with the calculated value based on a theoretical model for the process. Expressions are obtained for the ratio of heterodyne signal bandwidth to heterodyne frequency for the cases of focused radiation, unfocused radiation, and for a typical radar configuration. In most cases, the heterodyne signal is found to possess a narrow-band character. The probability density of the signal envelope was also measured for a known scatterer (providing Gaussian scattered radiation) and was found to be Rayleigh distributed, as expected. The power-spectral-density and envelope probability distribution provide information about a scattering medium or target which cannot be obtained from average-value measurements of the heterodyne signal-to-noise ratio. This information is useful for communications applications, infrared radar, and heterodyne spectroscopy experiments. Finally, a simple and direct method of obtaining information about the statistics of an incident radiation field (which does not involve photocounting) is discussed.

The methods now in the literature for calculating the terrain-backscattered radar-altimeter echo utilize the antenna power-gain patterns and the terrain radar cross section per unit area, usually designated σ 0 . In this paper, the polarization characteristics of the antennas and the echo depolarization by the terrain are taken into account for the first time. The formulas for the backscattered return are presented in terms of antenna and terrain parameters that can be measured directly or calculated from other measurements. These parameters are the four transmitting- and receiving-antenna gain patterns for the orthogonal polarization components, the two functions giving transmission- and reception-phase difference between the polarization components, the terrain-depolarization factor that accounts for the average backscattered power cross polarized with respect to the incident wave, and the radar cross section σ 0 per unit area. It is shown that the older formulas used for radar return from the near vertical are correct only when both antennas are linearly polarized and have the same direction of polarization. The errors that result from failure to consider polarization effects are illustrated by examples.

The use of the scattering matrix leads to a formulation of radar reflectivity that is independent of radar polarization, target range, and target rotation about the line of sight. The resulting formulation is applied to the problem of object recognition in free space. Experimental results for right circular cones are presented.

The scant two-decade existence of radar astronomy has seen important contributions by this new technique to positional astronomy, to the metrics of the solar system, and to the study of lunar and planetary surfaces. The role of millimeter wavelengths in this new astronomy is discussed and the problems unique to these short wavelengths defined. Brief mention is made of the importance of correlation of active and passive measurements and important new millimeter wave component requirements are listed. The implementation of an eight-millimeter radar capable of detecting the moon is described. At the eight-millimeter wavelength, the moon is found to be generally rough and has a radar cross section of about seven percent of its projected geometrical area. Methods of improving these measurements and their feasibility are outlined. Future equipment configurations capable of extending millimeter wave measurements can be implemented, given critical component development success.

The application of Thomson (or incoherent) Scatter observations to the study of the earth's ionosphere is described. Those aspects of theory of Thomson Scatter that have been put to practical use in ionospheric investigations are reviewed briefly and the type of radar equipment constructed for these investigations is discussed. Methods of measuring electron density, electron and ion temperatures, and ionic composition are then reviewed. Other applications of the technique--to the study of the neutral density and temperature of the upper atmosphere, drift motions, the flux density of fast photoelectrons, and the orientation of the earth's magnetic field--are also described.

Two approximate methods have been developed for calculating the radar cross sections of nonconducting bodies. The superposition approximation used to obtain the radar cross sections of dielectric clad bodies requires that the scattering properties of the component parts be known. The modified geometrical optics method, which yields the radar cross sections of dielectric bodies, requires no such initial information. These methods can be applied to some bodies with shapes that cannot be treated by means of the classical boundary-value solutions. Furthermore, the computations required are usually considerably simpler than for the boundary-value solutions even when the latter are obtainable.

The rapid variabilty of pulsar signals and the dispersive nature of the interstellar medium introduce a number of problems which are not inherent in other radio-astronomical observations. These problems are discussed and some of the techniques currently being used to cope with them are described.

In recent literature radiation emitted or reflected from a body or surface has been modeled as equivalent radiation from a collection of individual discrete radiators. This model has application to the analysis of forward and backscatter from rough surfaces, clutter and chaff models for radar, and cavity emissions at optical frequencies. In this paper we investigate radiation using a generalization of the above radiator ensemble. We allow some degree of coupling to exist between individual radiators, and we assume each radiator emits random energy bursts as a Poisson process. Analysis is confined to power spectral densities and first-order statistics of the resulting scalar radiation fieid. The results indicate that the pulsed radiator model can account for many properties of radiation. A by-product of the analysis is a filter model for dispersive channels, applicable to radar design problems. Theoretical results are compared with previously reported experimental results wherever possible. Some consideration is given to a relativistic interpretation of the radiator ensemble.

Three distinct methods of making high-range resolution radar cross-section (RCS) measurements are discussed. Comparisons are drawn for nanosecond pulse, FM/CW, and frequency-stepping methods of measuring location and magnitude of discrete scattering sources. The effects of using wide bandwidth transmissions on RCS amplitude level and fine structure are quantitatively estimated, and analytical results are presented. The three techniques are effective and yield the desired information about the magnitude and location of discrete scattering sources. Minor differences in data format and convenience of operation are noted, and it is concluded that a need for additional investigation of wide-band scattering phenomena is necessary.

Observations of radar echoes from the clear atmosphere are presented and the scattering mechanisms responsible for the two basic types of clear-air echoes are discussed. The commonly observed dot echo originates from a point in space and usually shows little variation in echo intensity over periods of about 0.1 second. The results of the most recent investigations of these clear-air dot targets are consistent with the conclusion that most, if not all, of the dot echoes are caused by insects or birds. The second type of clear-air radar echo appears diffuse in space, and signal intensities vary considerably over periods of less than 0.1 second. The echoes often occur in thin horizontal layers or as boundaries of convective activity; these are characterized by sharp gradients of refractive index. The reflectivity-wavelength dependence of these echoes is consistent with the theory of scattering by fluctuations in refractive index, and the signal intensities can be accounted for by the spectral characteristics of refractive-index variations observed directly. Some features of clear-air atmospheric structures as observed with radar are presented. These structures include thin stable inversions, convective thermals, Benard convection cells, breaking gravity waves, and high tropospheric layers which are sufficiently turbulent to affect aircraft.

The use of coherent detection can theoretically allow optical radar systems employing laser transmitters to achieve considerably improved receiver sensitivity, particularly in conditions of high background radiation. However, there are many practical factors that can limit sensitivity in coherent optical detection, which are described. It is shown that to achieve an efficient coherent optical radar, one would generally like a pulse width less than 10 µsec and a spectral line width less than 10 Mc.

A review is given of detection and estimation methods in current use in radio and radar astronomy. Methods of determining position and brightness distribution of radio sources by narrow-beam antennas, interferometry or lunar occultations are discussed. Observational procedures for the estimation of frequency spectra are explained. The fundamental problem in radar astronomy, viz., that of mapping, is reviewed, and several methods for the removal of ambiguities are considered. Schemes for the determination of range and velocity of a planet are also described.

The output of an array of sansors is considered to be a homogeneous random field. In this case there is a spectral representation for this field, similar to that for stationary random processes, which consists of a superposition of traveling waves. The frequency-wavenumber power spectral density provides the mean-square value for the amplitudes of these waves and is of considerable importance in the analysis of propagating waves by means of an array of sensors. The conventional method of frequency-wavenumber power spectral density estimation uses a fixed-wavenumber window and its resolution is determined essentially by the beam pattern of the array of sensors. A high-resolution method of estimation is introduced which employs a wavenumber window whose shape changes and is a function of the wavenumber at which an estimate is obtained. It is shown that the wavenumber resolution of this method is considerably better than that of the conventional method. Application of these results is given to seismic data obtained from the large aperture seismic array located in eastern Montana. In addition, the application of the high-resolution method to other areas, such as radar, sonar, and radio astronomy, is indicated.

A new approach is presented to the formulation and understanding of the problem of electromagnetic scatter from a slightly perturbed continuous medium. The problem is expressed in terms of periodic functions instead of conventional power series. From this formulation, specular properties are observed that are not obtainable from older considerations. The approach was verified with a laboratory experiment using microwave transmission lines with length-dependent, slowly varying dielectric cross sections. Further experiments were carried out using backscatter from a radar designed to detect clear air turbulence. The primary result shows that a turbulent medium can be replaced for the purposes of scatter calculation by a structure of finite periodicities because the medium acts as a lumped insertion loss, the stopping characteristics being determined by a spectral scale in the turbulence. The formulation defines the limits of knowledge about the medium and shows that, although it is not unique, some knowledge of the structure is obtainable. Insight is gained into the work needed to understand and interpret remote probe experiments.

Electromagnetic field waveforms produced by scattering of transient plane waves from finite objects are related to those produced by an impulsive plane wave. Properties of the impulse response waveforms at great distances from the target, particularly in the backscattering direction, are discussed. Various methods for approximation of impulse response waveforms using time and frequency domain concepts are suggested and illustrated. Other applications of response waveforms to target identification and to prediction of radar echo pulse waveforms are suggested.

Master oscillator requirements for coherent radar applications are derived from a consideration of the mainlobe width and sidelobe level objectives of the Doppler aperture function of the overall radar system. These parameters are related to the linewidth and sideband level of a carrier as modulated by the differential oscillator phase during a signal transit time. Both periodic and random phase modulation are considered. For the latter, techniques are given and illustrated by example for transforming oscillator stability characteristics measured in the time domain into a spectral form useful for radar design.

A series of radar cross-section measurements has been performed on flat base dielectric cones. Curves are presented showing radar cross section as a function of 1) cone size (angle constant) and 2) cone angle (diameter constant). A curve for a thin (0.07λ) conical dielectric shell as a function of circumference/wavelength ratio is also shown. The data are compared to that for metal cones.

A simple physical model that predicts the error associated with the monostatic-bistatic equivalence theorem for the case where coupling is significant between sources of scattering is presented. The analysis is discussed in terms of both monochromatic-wave and short-pulse scattering. Experimental verification of the results is provided by isolating the coupling components through use of a high-resolution radar.

The variational method of computing radar scattering cross sections has been applied to the bistatic scattering cross section for chaff dipoles. The average cross section was calculated for three distributions of dipole orientation; uniform, horizonal, and vertical. The geometry considered was for dipoles located near one terminal of a two terminal radio link such that the azimuth and elevations angles of the far terminal were small. Measured values of bistatic cross section were within about 3 dB of predicted values for measurements at a frequency 5652 MHz. Fading rates from 5 Hz to 25 Hz were measured. Space diversity distances were of the order of 2 to 5 feet for this particular 50-mile link.

Meteorological radar targets such as raindrops, refractivity perturbations, etc., are being studied using scattering angles other than 180° (back scattering). An analysis, analogous to that of Probert-Jones, yields a radar equation that is applicable, for a bistatic radar system, over all of space excluding the region near the line joining the two antennas.

The short-pulse radar return of a cone-sphere was measured to determine the contribution of individual scattering elements to the total scattered field. Experimental results are presented which show the existence of the creeping-wave contribution and also demonstrate it to be the predominant contribution to the return from this body at nose-on incidence.

The radar cross-section measurement equipment described in this paper was designed as a research tool for use in radar discrimination studies. Measurements of the radar scattering matrix made for various bodies were then used to predict the radar cross section of the body for any arbitrary polarization. All measurements were made at X-band with both metal and dielectric covered models scaled to simulate radar returns at UHF and L-band frequencies. A unique closed loop measurement system was employed to measure amplitude and relative phase to considerably greater accuracy than usual. The results show clearly that it is possible to use the radar scattering matrix to predict accurately the return from a body at any polarization.

Curves are presented for the sequential detection of slowly fading and constant cross section radar targets. These results assume the use of a biased, square-law detector and were obtained by means of a digital computer simulation.

Calculations have been made of the radar cross sections of imperfect spheres to circularly polarized radiation. The matrix method of Waterman was used and only imperfections having axial symmetry were considered. Some results for spheres with an equatorial cylindrical section are given for spheres up to six wavelengths in diameter.

Two probability density functions (pdfs) for the power from a Rayleigh target are compared empirically. Swerling's one-dominant pdf is shown to be approximately valid for a unit dominant-to-background scatterer power ratio. The power form of the Rice pdf is used to define the input signal fluctuations in the calculation of detection probability.

In order to determine ionospheric winds from meteor trails observations, one needs a sensitive radar operating near 30 MHz which can provide a precise localization of the target as well as detect slow target motions. Since, at these frequencies, very short pulses and directional antennas are both impractical, a CW bistatic radar was designed in which direction of arrival, distance, and Doppler measurements are all affected by means of phase comparisons. The precisions obtained are of the order of 0.2 degree, 300 meters, and 1 meter per second, respectively, for an S/N ratio of 25 dB. This was done using three receiving antennas for the angle measurements, three frequencies for the distance measurement, a vertically polarized link to transmit the direct ground wave, and cancelling the backward feedthrough of the transmitting antenna. Experimental results are displayed on a panel, from which they can be read directly.

The IMP-6 spacecraft was detected at 140 000 km using a 430-MHz radar. Several radar observables were measured.

It is shown that at fast scanning speeds the radar antenna beam contains frequency components other than the transmitted frequency, resulting in a frequency spread in the echo from a fixed target which is distinct from that arising from finite time on target.

A simple method to measure backscatter cross sections of live insects at 10-cm wavelength using an ultra-high resolution scanning FM-CW tropospheric radar sounder is described. The technique involves suspending an insect along a line between two metal spheres and comparing insect and sphere cross sections.

The hologram matrix, which is a more elementary quantity than a conventional microwave hologram and contains much more information, is defined. Its application to a microwave holographic radar is described. This radar determines the distance by the spatial distribution of the scattered wave and differs from all other radars which determine the distance by the lapse of time. Some promising results were obtained from the computer simulation of such a radar.

The physical optics approximation is not applicable to the determination of electromagnetic scattering from obstacles that are not both large and smooth. In this paper, the second-order Born approximation has been utilized to determine the radar cross section of a fairly large, perfectly conducting finite cone. This method leads to radar cross-section values of proper magnitude for such cones, whereas the usual physical optics method yields cross-section values in error by an order of magnitude.

A ripple tank study of wave motion associated with the wave formation in the vicinity of a cone-sphere is discussed. The experimental test facility is described. Included in the interpretation of the ripple tank experiments are the wave formations in the shadow region of the cone-sphere showing traveling and creeping waves.

Literature references dealing with the radar cross section of a dipole target contain a possible source of confusion in that two definitions of cross section have been used. To clarify this situation, the radar cross section of a randomly oriented half-wave dipole is considered using both definitions.

A radar system for imaging a spetially limited object at long range is described. The geometry consists of a large array (100 km square) of widely separated receivers, each containg its own local oscillator. The reference signal is derived by scattering a low-frequency wave from the object.

A new type of scattering range is described in which the radar reflection properties of objects are measured by inserting them into a transmission line. The theoretical justification for this technique is presented on the basis of the reciprocity theorem. The results of a testing program are used to indicate the advantages and limitations of the transmission line scattering range.