After a brief history of near-field antenna measurements with and without probe correction, the theory of near-field antenna measurements is outlined beginning with ideal probes scanning on arbitrary surfaces and ending with arbitrary probes scanning on planar, cylindrical, and spherical surfaces. Probe correction is introduced for all three measurement geometries as a slight modification to the ideal probe expressions. Sampling theorems are applied to determine the required data-point spacing, and efficient computational methods along with their computer run times are discussed. The major sources of experimental error defining the accuracy of typical planar near-field measurement facilities are reviewed, and present limitations of planar, cylindrical, and spherical near-field scanning are identified.

An overview of near-field antenna measurements

The general problem concerning the interaction of a probe antenna with the near field of an arbitrary antenna is considered. The application of the Lorentz reciprocity theorem to the problem of determining antenna characteristics, including the far-field pattern, is presented. The data required to correct for the directional effects of the probe, the effect of probe correction on the measured data, and the attendant mathematical computations in rectangular systems are described. Extensions to cylindrical and spherical systems are discussed.

Basic theory of probe-compensated near-field measurements

An alternative method is presented for computing far-field antenna patterns from near-field measurements. The method utilizes the near-field data to determine equivalent magnetic current sources over a fictitious planar surface that encompasses the antenna, and these currents are used to ascertain the far fields. Under certain approximations, the currents should produce the correct far fields in all regions in front of the antenna regardless of the geometry over which the near-field measurements are made. An electric field integral equation (EFIE) is developed to relate the near fields to the equivalent magnetic currents. The method of moments is used to transform the integral equation into a matrix one. The matrix equation is solved with the conjugate gradient method, and in the case of a rectangular matrix, a least-squares solution for the currents is found without explicitly computing the normal form of the equation. Near-field to far-field transformation for planar scanning may be efficiently performed under certain conditions. Numerical results are presented for several antenna configurations. >

Planar near-field to far-field transformation using an equivalent magnetic current approach

In many cases, it is impractical or impossible to make antenna pattern measurements on a conventional far-field range; the distance to the radiating far field may be too long, it may be impractical to move the antenna from its operating environment to an antenna range, or the desired amount of pattern data may require too much time on a far-field range. For these and other reasons, it is often desirable or necessary to determine far-field antenna patterns from measurements made in the radiating near-field region; three basic techniques for accomplishing this have proven to be successful. In the first technique, the aperture phase and amplitude distributions are sampled by a scanning field probe, and then the measured distributions are transformed to the far field. In the second technique, a plane wave that is approximately uniform in amplitude is created by a feed and large reflector in the immediate vicinity of the test antenna. And in the third technique, the test antenna is focused within the radiating near-field region, patterns are measured at the reduced range, and then the antenna is refocused to infinity. Each of these techniques is discussed, and the various advantages and limitations of each technique are presented.

Determination of far-field antenna patterns from near-field measurements

Presented here is a method for computing near- and far-field patterns of an antenna from its near-field measurements taken over an arbitrarily shaped geometry. This method utilizes near-field data to determine an equivalent electric current source over a fictitious surface which encompasses the antenna. This electric current, once determined, can be used to ascertain the near and the far field. This method demonstrates the concept of analytic continuity, i.e., once the value of the electric field is known for one region in space, from a theoretical perspective, its value for any other region can be extrapolated. It is shown that the equivalent electric current produces the correct fields in the regions in front of the antenna regardless of the geometry over which the near-field measurements are made. In this approach, the measured data need not satisfy the Nyquist sampling criteria. An electric field integral equation is developed to relate the near field to the equivalent electric current. A moment method procedure is employed to solve the integral equation by transforming it into a matrix equation. A least-squares solution via singular value decomposition is used to solve the matrix equation. Computations with both synthetic and experimental data, where the near field of several antenna configurations are measured over various geometrical surfaces, illustrate the accuracy of this method.

Near-field to near/far-field transformation for arbitrary near-field geometry utilizing an equivalent electric current and MoM

A new method is developed for determining the farfield pattern of an antenna from probe compensated near-field measurements over the surface of a right circular cylinder enclosing the antenna. The method is derived by first expanding both the field radiated by the antenna and the field radiated by the measurement probe, when it is used as a transmitter, into cylindrical wave expansions. The Lorentz reciprocity theorem is then used to solve for the field radiated by the antenna from the probe output voltage. It is shown rigorously that the antenna pattern can be determined independently of the characteristics of the measurement probe provided that certain calibration data are known. A method for determining these data from the measured far field radiated by the probe is described. It is shown that the necessary numerical integration can be performed with the fast Fourier transform algorithm. Experimental results are presented to validate the theory and to demonstrate its practicality from a measurement and computational viewpoint.

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Probe compensated near-field measurements on a cylinder

A novel and numerically efficient method of far-field evaluation from measurements taken on a cylinder is based on the representation of both the antenna and the probe fields as superpositions of plane waves. A system of two integral equations are established whose unknown functions are the azimuthal and elevation components of the antenna pattern and whose known terms are the set of measurement data taken with two different probes-the second probe in most practical instances being simply the same probe with a different geometrical orientation. The equations express the known data-for each angular position of the antenna under measurement-as the integrals of the products of the corresponding components of the unknown antenna and known probe patterns multiplied by a phase term. The convolutional nature of the integral equations makes their solutions straightforward. If, as is virtually always the case, the probe has small or moderate size so that the axis of rotation of the antenna mount is in the far field of the probe, the intervention of asymptotic techniques makes the solution numerically very efficient. The agreement of calculated and experimental patterns is excellent.

W. Leach

Papers

Basic theory of probe-compensated near-field measurements

Probe compensated near-field measurements on a cylinder

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