NBSIR 79-1602

A QUALITATIVE SURVEY OF NEAR-FIELD

ANALYSIS AND MEASUREMENT

Paul F. Wacker

Electromagnetic Fields Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

June 1979

NBSIR 79-1602

A QUALITATIVE SURVEY OF NEAR-FIELD

ANALYSIS AND MEASUREMENT

Paul F. Wacker

Electromagnetic Fields Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

June 1979

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

A QUALITATIVE SURVEY OF NEAR-FIELD ANALYSIS AND MEASUREMENT

PAUL F. WACKER

Abstract--This first paper in a series on a new unified theory of near-field analysis

and measurement serves as an introduction to and a summary of some of the forthcoming

papers in the series. Further, it describes the advantages and limitations of near-field

scanning and compares various techniques, as well as corrects many of the conceptual errors

of the literature. Being firmly based upon generalized scattering matrix theory and both

relativistic and gauge invariance (Wigner's extended inhomogeneous Lorentz group [1964]),

the theory is rigorous and very comprehensive, general, and fundamental, yet it provides

the detailed bases of extremely efficient computer programs for reduction of both electromagnetic and acoustic measurements on planar, circular cylindrical, and spherical scanning

lattices, as well as provides the basis for the most accurate method of calibrating standard gain horns (described in the series). For both the probe correction and ideal probe

cases, the theory yields a series of general -but-expl icit formulas which apply to the

aforementioned and other lattices (including plane-radial) and to a wide variety of physical systems; plug-in expressions (given by the theory) depend upon the type of lattice and,

in the spherical case, parametrically upon the physical system. The efficiency of the

spherical EM programs (based upon a paper in the series) is indicated by the fact that

probe-corrected least squares values of the complex coefficients of 50,000 exact global

solutions of Maxwell's equations in spherical coordinates and the associated far field may

be computed in a few minutes.

I. INTRODUCTION AND SUMMARY

During the past 25 years, scanning on planes [9], [8], circular cylinders [10], [26], and

spheres [4], [5] has been developed to obtain far-field patterns of antennas. These procedures have many practical advantages and can yield accuracies equalled only in a small

number of far field measurements. The currently-used Cartesian-planar data-processing is

extremely efficient and cylindrical moderately so. The present series of papers describes

highly efficient processing of spherical data ([8], [21], Paper V), plane-radial scanning

[22], Paper III), improvements in cylindrical processing (Paper IV), and the (author's)

theory of the extrapolation method for gain and effective area ([18], [11], Paper VI). The

latter is the most accurate method of calibrating standard gain horns; the values calculated from the horn geometries are usually outside the limits of error of measurements made

with this technique at the National Bureau of Standards (NBS) [11].

The planar, cylindrical, and spherical analyses were originally developed in different

laboratories and the treatments particul arized for each surface. However, due to the

complexity of the spherical analysis, it is highly desirable to have a panoramic view of

near-field scanning and a common notation for the various scanning surfaces and physical

systems. Then both general and detailed comparisons can be made, facilitating (a) the

transfer of understanding from one surface or physical system to another, (b) the translation of computer programs from one physical system to another (say EM to acoustic in a gas, liquid, or solid), (c) insurance that all available computational efficiencies are utilized, (d) emphasis upon fundamentals rather than a morass of detail, (e) generalization

and extension to other scanning lattices and physical systems, (f) defining the limits of

the techniques, (g) eliminating unnecessary repetition in presentation, and (h) clarification of concepts. ( Ad hoc studies of particular systems have led to many conceptual errors

in the literature; see Section III A.) To achieve these ends, the presentation (Paper II)

is in terms of a unified theory in which spherical, Cartesian planar, plane radial, cylindrical, and other types of scanning and both electromagnetic and acoustic systems are treated as mere special cases. Only parts of the unified theory and unified notation are

evident from Cartesian planar or cylindrical theory because of their simplified nature;

details which are so simple in the Cartesian planar case that they may be barely considered

may be extremely complicated in the spherical case, e.g., transformation of the modal

coefficients under translation normal to the measurement surface. However, spherical

theory does provide such a basis, Cartesian planar and cylindrical being limits of the

spherical on the equator and pole, respecti vely, as the radius becomes infinite [16].

This first paper provides a non-mathematical introduction to and summary of some of the

subsequent papers in the series. It first discusses the advantages and limitations of

various measurement procedures and compares them. Then it provides a non-mathematical
summary of near-field analysis.

In general, the antenna or other transducer is treated as a black box as far as the

formal analysis is concerned, with no consideration of its shape or current distribution;

however, known or assumed symmetry of the transducer may be used in reducing the measurement and computational effort, and qualitative information concerning the pattern or design

is useful in choosing measurement conditions and the modes used to represent the data.

Minimal assumptions, idealizations, and approximations are made, leading to highly accurate

results, even for systems many wavelengths across. This is to be contrasted with techniques in which various approximations are made (see [6] for some of them); the accuracy

and reliability of the results of such treatments of course depend upon the specific problem and approximations made, but are commonly less than satisfying. This series of papers

emphasizes rigorous rather than approximate treatments, in particular, exact global solutions of the differential equation(s) (Maxwell's in the EM case), their exact transformations under change of coordinates, and natural orthonormal ities of the transformation

coefficients with respect to summation on the measurement lattice ; it also makes full use Xsee Papers 1

1 - V and VII) of the Discrete Fast Fourier "Transform" (DFFT) (here rigorously

exact), even for spherical scanning. (An "exact global solution" here means an exact

solution valid everywhere in space for a given infinite medium .) The approximate procedures usually do not use the DFFT and so are usually no faster if as fast; further, many of

them break down for large systems (see Paper II). The rigorous theory is very comprehensive, general, and fundamental. The general statements made in these papers apply in

particular to Cartesian planar, circular cylindrical, spherical, and some types of planeradial scanning; various other possible and proposed scanning procedures will be discussed

relative to the preceding norms. Apart from obvious exceptions, the statements also apply

to the extrapolation method, which involves a linear (one-dimensional) scan as the transducers are separated. Since the analysis and computer programs are in large part independent of the physical system, the statements made also apply to many physical systems,

including electromagnetic, heat flow, and acoustic systems, acoustic scanning having been

in operation at the NBS since 1975 [7].

The rigorous three-dimensional theory of near field analysis and measurement was pioneered by the National Bureau of Standards, which has been engaged in near-field analysis

since 1953, with a definitive paper on Cartesian planar scanning being published by Kerns

and Dayhoff in 1960 [9], including full treatment of the probe pattern and multiple reflections to all orders. In 1963, Baird [1] described the operation of the NBS 50 GHz scanner

and preliminary measurements of the near field of a horn-lens antenna 100 wavelengths on an edge. Brown and dull [2] described an azimuthal scanning procedure in 1961, but assumed

the pattern to be independent of the z coordinate. Leach and Paris [10] described circular

cylindrical scanning in 1973. The author first presented his extrapolation method for gain

and effective area in 1969 [17], [18], and Newell and Kerns incorporated his procedure in

their description of the three-antenna method in 1971 [13], [11], Jensen described spherical scanning in 1970 [4],L5], and the author presented the scheme for practical reduction

of spherical data with and without correction for the probe pattern in 1974 [19], [21]. The

author first described his unified theory in 1974 [20], [21], The early history of scanning

is discussed by Kerns [8].

II. ADVANTAGES, LIMITATIONS, AND COMPARISONS OF MEASUREMENT TECHNIQUES

A. Advantages

The suitability of a given method of determining a transducer pattern of course depends

upon the transducer and the use of the data. For a transducer which is small both physically and in terms of wavelength, say a probe, near-field techniques seldom compete with

conventional methods. However, for larger transducers, near-field techniques have the

following distinct advantages.

First, near-field measurement systems are closely coupled and therefore subject to laboratory-type control, making for high accuracy [1 1 ] ,[12] ,[14].

Second, the data are expressed as linear combinations of exact global solutions (modes)

of the appropriate differential equation(s) (Maxwell's in the EM case) for the given infinite medium ; small angle, scalar, or Kirchhoff diffraction theory approximations are not

used. Hence, (a) every computed field is consistent with the differential equation(s), (b)

measurement and computational efforts are not wasted determining information available from

the differential equation(s), etc., and (c) various auxiliary tools become more effective.

Thus, complex vector solutions are much more effective for interpolation, statistical tests

2
of significance, and smoothing than are arbi trari ly-chosen real scalar polynomial or sinusoidal basis functions. Further, optional application of additional a priori constraints

becomes more effective; e.g., (a) rejection (on a priori grounds) of high transverse spatial frequencies in the near field (evanescent and high-order supergain modes), (b) symmetry of the transducer for possible reduction of measurement and computational effort, (c)

finite size of the transducer in the extrapolation method, spherical scanning, and (to some

extent) circular cylindrical scanning, and (d) frequency dependence of the pattern, related

to the Singularity Expansion Method and dispersion (causality, Kronig-Kramers) theory.

Hence, many superficial ly plausible interpretations of measurement errors are rejected,

often automatically, and the measurement data effectively used. Far-field amplitude measurements are not subject to such stringent theoretical constraints.

Third, each and every measurement (commonly tens or hundreds of thousands) is used to compute the pattern for each and every direction. Hence, random error and ambient noise

are quite unimportant, particularly since the signal -to-noi se ratio is high in a closely

coupled system.

Fourth, full correction for proximity effects is made, which is especially important for

high accuracy measurements. However, minimization of proximity error in conventional measurements can be burdensome; to reduce the proximity error for a typical standard gain horn

to 0.05 dB requires a separation of 32 (not 2) a^/A, where a is the largest transverse

dimension and A is the wavelength. Further, with contoured pattern antennas, the required

measurement distance may be ten times that normally required [24], [25].

Fifth, ground reflections and grazing-incidence reflections of an "anechoic" chamber are eliminated since the test transducer and probe are close together and the absorber can be

placed essentially perpendicular to the radiation. In conventional measurements, ground

reflections are often significant even for very high towers. Their importance is illustrated by observations with our extrapolation method; we not infrequently observe ground re- flections with antennas of 20 dB or more gain, yet the ratio of tower height to antenna

separation is never less than 15 percent. (Such reflections cause no error in the extrapolation method at microwave frequencies.)

These observations, combined with the separation required to eliminate proximity

error, indicate that very long ranqes and especially high towers are required for highaccuracy conventional measurements. (Fifteen percent of 32 a

2 /A yields 4.8 a2 /A for a desirable tower height.) Reflections in chambers are also larqer than is commonly believed.

Thus, in a "good" anechoic chamber, the apparent gain may vary by 2 dB (at L band) as the

antenna pair is rotated with respect to the chamber walls, and the field in the volume later

occupied by the test antenna may vary by as much as 1 or 2 dB, particularly in a rectangular

chamber [3]. The low reflections and the lack of problems with random error and ambient

noise thus make near-field techniques quite attractive for determining low-level sidelobes

and the depth and shape of the "null" of a monopulse antenna operating in the difference

mode.

Sixth, near-field scanning qives quite detailed information. The far-field amplitudes

and polarizations are commonly given for 10,000 or more directions. Given sufficiently

close spacing in the near field, arbitrarily fine spacing in the far-field pattern can be

obtained with a minor increase in computational effort in the spherical case (and for the

azimuthal dependence in the cylindrical case); the computations are padded with zeros prior

to taking the final (inverse) DFFT. A similar technique may be used for planar scanning.

Further, the phase and amplitude of each component of the electromagnetic six-vector can be

obtained as functions of position in the far, intermediate, and near field. Hence, nearfield interactions, say common site interference, can be determined from near-field data

[27], but not from far-field amplitude data.

Seventh, assuming that a computer is available, the cost of a near-field range is much

less than a far-field range or anechoic chamber capable of giving equal accuracy on com- parable antennas. In fact, for an antenna mounted on a model, azimuth-over-elevation, or elevation-over-azimuth mount, no probe transport system is needed for "spherical" scanning;

this is of course quite attractive for an inexpensive system and for large steerable dishes.

Eighth, for production line testing and adjustment, the antenna need not be transferred

to a tower on a range between adjustments. Further, measurements of satellite antennas can

be made in a clean room. Ninth, the all-weather character of near-field work is an obvious advantage, near-field

measurements being independent of moisture in the ground, foliage on trees, and weather

conditions. Further, the method may be used to determine the patterns of antennas in

atmospheric absorption bands, e.g., in a water absorption band, and has been used for highly

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accurate measurements in the 0 2 band at 60 GHz [11]; these frequencies may, of course, be

used for communication between satellites.

Tenth, a complete satellite may be considered as an antenna, automatically including

scattering by other parts of the satellite. Similarly, a terrestrial antenna can be measured on site, automatically including the effects of the mount and permitting computation

of ground reflection effects.

Note that near-field techniques (a) can qive absolute measurements including mismatch

corrections, (b) need not involve approximations other than truncation of the infinite set of basis functions, and (c) apply to nonreciprocal transducers (say arrays with ferrite

phase shifters or isolators), whether transmitting, receiving, or scattering. Further, an absolute near-field measurement combined with pattern integration can be used to determine

the losses in a transducer, e.g., a radiometric antenna. Note further that scanning is

useful for moderate accuracy requi rements; thus, if the error in the far-field amplitude can

be increased by a factor of five, the errors in the real and imaginary parts of the near

field can be increased by a factor of five. From a single physical scan, the patterns for

many different steerinq directions may be obtained for an array, or patterns for many

different frequencies can be obtained for a broadband antenna; the steerinq direction or frequency is merely stepped rapidly durinq the scan, and the data unscrambled in the computer.

I

B. Limitations

Near-field measurements are somewhat limited by the availability of absorbers, say

below a few hundred megahertz for antennas; however, the antenna may be directed toward the

zenith and ferrite absorbers used, consistent with their cost. Further, at very high

frequencies, measurement of phase as a function of position becomes more difficult, particularly measurement to a small fraction of a cycle over a large area, all referred to a single reference. (This limitation does not apply to the author's extrapolation method,

since it does not require phase measurement.) Nevertheless, we have accurately determined

the patterns of 60 GHz antennas 100 wavelengths in diameter using only a simple positioner.

With our currently used laser fringe-countinq technique for measuring probe position, the

positional accuracy for planar scanning is limited only by the straightness, parallelism,

and planarity of the scan lines; with servo mechanisms, measurements could be made even in

the far infrared. Further, servo mechanisms and a fringe-counting system should permit

accurate measurements to be made on physically large antennas using a relatively flimsy

probe-transport system.

For electrically large antennas, large numbers of measurements and considerable data

processing are required. However, near-field measurements and processing appear feasible

even for antennas for which accurate far-field terrestrial measurements are impractical, and

the near-field range is much less expensive than a large conventional range or anechoic

chamber. We have already processed 500 2 x 2 = 500,000 real values for a single planar scan

of given polarization and, in the spherical case, routinely obtain least squares values of

the complex coefficients of the 50,000 exact solutions of Maxwell's equations in spherical

coordinates, used as basis functions, with full correction for the pattern of the probe.

Moreover, symmetry, directional probes, and other technioues may be used to reduce the

required data-taking and data-processing.

Transverse scanning provides very detailed pattern information, but (unlike the extrapolation method) it is not very economical for determining gain in a single direction.

C. Comparison of Near-Field Scanning Techniques

Which near-field technique is most appropriate depends upon the nature of the pattern,

the physical size of the antenna, the nature of the available mount and/or probe transport

system, and the transverse physical size of the near field (where the amplitude is significant).

In mechanical terms, the "spherical" scan is most convenient because no probe transport

is required. This is particularly attractive for inexpensive implementation and for physically large transducers mounted on elevation-over-azimuth or azimuth-over-elevation mounts.

(If the transducer cannot be tipped, azimuthal rotation and a probe on a gantry arm may be

used.) Circular cylindrical and plane-radial scanning are next simplest, requiring only an azimuthal rotator and a linear probe transport. Circular cylindrical is useful for an azimuthally symmetric antenna on a tower. Cartesian planar scanning requires the most

complicated probe transoort system.

4
In terms of data processing, Cartesian planar scanning is by far the simplest, circularcylindrical and plane-radial next, and spherical is the most complicated of the methods

being used. The probe correction is almost trivial for the planar case, not trivial for the

cylindrical case, and quite complicated for the spherical case, yet commonly needed for a wide-angle scan. If the wide-angle radiation is negligible or of no interest, a directional

probe can be used with planar scanning, permitting wider spacing of measurements and truncation of the measurement area, thus reducing both the measurement and data-processi ng effort.

For a well -collimated pencil beam significantly smaller in cross section than an available scanning system, planar scanning is very well suited. Similarly, cylindrical

scanning is quite effective for a fan beam and, with a directional probe, in determining the

sidelobes of a transducer. Spherical and plane-polar scanning are well suited to a transducer with simple azimuthal dependence. For a transducer which radiates in (or is steered

to) wide off-axis angles, spherical scanning is much better suited. In fact, if there is

much radiation making a small angle with the scanning plane or cylindrical axis, planar and

cylindrical scanning require unreasonable scanning areas and involve a marked degradation of

measurement accuracy. In principle, planar scans may be made on a series of canted planes

using a directional probe (with a probe correction), but this tends to be unwieldy.

III. DESCRIPTIVE SURVEY OF NEAR FIELD ANALYSIS

The unified theory is based upon generalized scattering matrix theory and symmetries

arising from relativistic and gauge invariance. Hence, the theory is very comprehensive,

general, and fundamental and involves few assumptions, idealizations, and approximations.

Nevertheless, it provides the detailed bases for extremely efficient computer programs.

For simple systems, many data reduction techniques may be used, but for highly accurate

results on transducers many wavelengths across, the most efficient available techniques are

required. Further, particularly for the latter systems, few approximations can be made

because (a) the far field pattern is obtained by (sophisticated) extrapolation of nearfield data perpendicular to the measurement surface and (b) good values of high-order modal

coefficients are commonly required. For all types of near-field scanning, the data reduction commonly involves tens or hundreds of thousands of (a) complex simultaneous equations

(one for each measurement), (b) complex unknowns (one for each exact global solution (mode)

used in fitting), and (c), for the probe-pattern correction case, transformations of the

set of modal coefficients (one transformation for each probe position and orientation).

(This is true for Cartesian planar and cylindrical scanning as well as spherical and planeradial, although it may not be so evident in the first two cases due to the simplicity of

the analysis.) The transformations are carried out, the equations solved, and the complexvector far field calculated (from the coefficients) for a like number of directions, all in minutes or even seconds; these times apply for the EM case, despite the complexity of the

radial transformations for exact global solutions of Maxwell's equations in spherical

coordinates. (Conventional techniques for the solution of simultaneous equations are completely avoided in the scalar case; sets of two equations in two unknowns remain in the

planar and cylindrical EM cases, but even these may be eliminated in the spherical EM case.

)

The assumptions and idealizations are three in number: (i) The system is assumed to be

mathematically linear, but the treatment is easily extended to nonlinear transmitting

transducers for fixed input levels, (ii) The medium is assumed to be invariant under

certain translations, rotations, reflections, and/or inversion(s) , depending upon the

scanning procedure, but no assumption is made concerning losses. ( i i i ) The appropriate

differential equation(s) (Maxwell's in the electromagnetic case) are assumed to be obeyed.

Actually, the last two assumptions are expressed in terms of symmetries and much of the

analysis, particularly the orthonormalities on the measurement lattice and the DFFT, applies to systems for which the differential equations are unknown. (Except as limited by

the properties of the medium and apart from some optional simplifications, all the symmetries used in this series of papers follow from relativistic invariance (Wigner's ex- tended inhomogeneous Lorentz group [23], even for non-linear media and differential equation^).) The symmetries explain the similarities between different physical systems

(including the occurrence of the same special functions) and provide (a) general expressions in which various scanning lattices are mere special cases, (b) the modal transformations, (c) the measurement lattices, (d) the natural orthonormalities with respect to summation on the measurement lattices for both "the ideal probe and probe correction cases,

and (e) justification for the use of the DFFT; in fact, for mathematically linear systems,

5
the symmetries provide all the (measurement) lattices on planar, circular cylindrical, and

spherical surfaces which yield natural orthogonalities with respect to summation of the

exact solutions and of the transformation coefficients of their addition theorems (required

for efficient processing of the ideal probe and probe-correction cases, respectively) [22].

Although symmetry can be completely avoided for any specific physical system and scanning

lattice, it is basic to a unified theory.

There are no approximations in the theory, which includes all the transmitting, receiving, and scattering properties of each transducer and both proximity and multiple reflection effects without approximation. However, two approximations are made in the numerical

computations (in addition to those of the complex exponential subroutine and rounding in

the computer (say after 48 mantissa bits)): (i) The infinite set of exact global solutions

of the differential equation(s) is truncated. However, for spherical scanning, the set of

modes actually used in the numerical computations is mathematically complete (for the given

differential equation(s) and finite transducers) except for insignificant supergain modes,

(ii) In transverse scanning (i.e., for measurements on a surface), multiple reflections

between the transducer under test and the probe are minimized experimentally and neglected

in the computations. However, they are fully treated in the extrapolation method, as are

the reflections between each transducer and its source or load, even in transverse scanning. As used for Cartesian planar, plane radial, circular cylindrical, and spherical

scanning, the DFFT involves no approximations beyond the al ready-mentioned truncation of

the solution set, since only the coefficients of a finite Fourier series need be determi ned.

These techniques give absolute values without physical standards such as standard gain

horns. A pair of transducers (transmitting and receiving) is considered to constitute a two-port and substitution measurements are made, yielding the four complex elements of the

2x2 scattering matrix as functions of the separation and relative orientations of the

transducers. The patterns of the individual transducers are determined in the absol ute sense with the aid of the three antenna method [13], [11], which starts with three transducers of unknown gain and polarization.

The data processing consists primarily of sophisticated curve fitting, ordinarily supplemented by a rigorous form of extrapolation (in computing the far field). Since the

basis functions used in fitting the experimental data are confined to exact global solutions of the differential equation(s), pattern measurements may be confined to a surface

and (in the EM case) to two vector components [15]. In the extrapolation method, spherical

scanning, and the azimuthal part of cylindrical scanning, finite dimensions of the transmitting and receiving transducers are also assumed; this causes the mathematically complete

sets to be discrete in these cases. Since the modes are discrete in the spherical case and

the higher order modes (with high transverse spatial frequencies) are supergain modes, the

finite set actually used is mathematically complete except for insignificant supergain

modes. Actually, supergain modes present no special problem beyond the total number of

modes, the required spacing of the measurements, and the resulting increase in measurement

and computational effort; hence, the pattern of a practical supergain antenna can be ac- curately determined if desired. The use of exact global solutions means that no effort is

wasted in determining information available from the differential equation(s) or (in the

aforementioned cases) from the finite size of the transducers. These modes of course make

far more effective use of measurements or computations (in a theoretical problem) than

segmented ad hoc basis functions such as those used in the moment method or Simpson's rule.

At NBS, full correction is routinely made for the probe pattern, proximity effects, the

complex mismatch factor (multiple reflections between each transducer and its source or load), and (for the extrapolation method) multiple reflections between the two transducers.

The probe may have arbitrary directivity (even for spherical scanning), be either transmitting or receiving (even if nonreciprocal), and (in a vector field) have arbitrary on-axis

polarization (ell ipticity) . Further, least squares fitting of the data is routine for the

spherical and extrapolation methods and is optional for Cartesian planar, plane radial, and

circular cylindrical scanning; truncation of the basis set provides a convenient means of

rejecting high transverse spatial frequencies (e.g., supergain modes) inconsistent with the

transducer design. For spherical scanning and the extrapolation method, there is automatic

discrimination against not only random errors but also against some types of consistent

(bias) errors; in particular, modes inconsistent with finite transducers are rejected, as are isotropic modes in spherical scanning of electromagnetic systems. Further, in the

scanning of EM systems, the use of exact global solutions permits measurements to be confined to two components [15] if the propagation across the surface is only outward or

i nward.

6
A. Conceptual Errors

Unfortunately, a considerable number of conceptual errors occur in the existing literature. Some of them are corrected before presenting the mathematical analysis in the next

paper. A linear combination of plane waves (or of circular cylindrical or spherical) can represent an arbitrary field, including the near, intermediate, and far zones and supergain, evanescent, and reactive modes, even in a lossy medium, to arbitrary accuracy in the

mean, provided that the total energy of the field (or the portion represented) is finite.

(The plane wave representation includes evanescent waves which are exponentially damped

perpendicular to the scanning plane and therefore inhomogeneous.) Like supergain modes,

evanescent and reactive modes present no fundamental problem in representation , but it is

usually convenient in the determination of far-field patterns to have the probe far enough

from the transducer under test so that the evanescent modes are insignificant, permitting

wider spacing of the measurements and reduced computational effort. The far-field wave

impedance is not assumed for the near, intermediate, or far zone, except asymptotical ly in

the latter case. Multiple reflections are fully treated in the theory, although (as previously mentioned) those between the two transducers are not included in the computations

of transverse scanning (except perhaps to first order). The magnetic pickup of the probe

is not neglected; in fact, an ideal electric dipole probe may be used to determine the full

pattern of a so-called shielded loop antenna.

According to the literature, planar, cylindrical, and spherical scanning must be based

upon reciprocity. On the contrary, unless one wishes to express the receiving properties

in terms of the transmitting properties or vice versa, reciprocity of the transducers is

completely irrelevant . (Although burying the essential parts of a proof in a maze of

famil iar-but-irrelevant material may comfort the casual reader, it decreases understanding.)

The transducers can be arrays containing ferrite phase shifters and isolators. Moreover,

Cartesian-planar and plane-radial scanning theory and computational techniques apply to anisotropic, non-reciprocal, magnetoelectric, biaxial, birefringent, and piezoelectric

media ; only the mechanical properties of the medium restrict application to a general

mathematical ly-1 inear perfect crystal. However, with identical probes equally-spaced in a planar surface and time-windowing to avoid multiple reflections, these techniques could be

used for geophysical prospecting (EM or acoustic) in an anisotropic medium; further, the

analysis and computer programs described in this series would provide for correction for

the pattern of the individual probes in both the transmitting and receiving arrays (which

may be the same).

In addition to explicit errors, there are erroneous implications in the literature. In processing spherical data, it is not assumed that the probe pattern approximates that of a short dipole; the probe may have arbitrary directivity. According to the literature, an exact solution in the spherical wave case is impractical because the solution of many

simultaneous equations is required. In fact, for Cartesian planar, plane radial, circular

cylindrical, and other types of scanning, as for spherical, there is a complex simultaneous

equation for each probe position and orientation, but in the efficient processing procedI

ures, conventional techniques for the solution of the equations are largely avoided through

decoupling based upon symmetry. However, for the electromagnetic problem, only in the

spherical case can the decoupling be complete so that conventional techniques can be avoided completely; Cartesian planar, plane radial, and circular cylindrical require ordinary

solution of sets of two equations in two unknowns. As for exact solution being impractical

in the spherical case, the set of solutions used to express the pattern of the test transducer in numerical computations is mathematically complete (except for insignificant supergain modes), but such a set is impractical for both planar and cylindrical scanning.

Conceptual errors concerning reactive and evanescent modes and domains of convergence will

be corrected in the forthcoming paper on the General Theory of Near-Field Scanning (Paper

II).

B. Data Processing

There are two parallel treatments of scanning data; one assumes an ideal probe and the

other corrects for the effect of the probe pattern upon the measured signal. In each case,

the computations consist essentially of the DFFT, supplemented by matrix multiplication in

the spherical case. (These multiplying matrices are independent of the test transducer,

the detailed nature of the probe, the frequency, radius of the sphere, and both the number

and angular positions of the measurements.) These computations supplant: evaluation of

7
the point matching matrix and its inverse, matrix inversion, ordinary solution of simultaneous equations (at least in more than two unknowns), ordinary numerical integration,

evaluation of functions of direction (even in the computation of the far field), timeconsuming orthogonal ization, and (in the Cartesian planar, plane radial, and circular

cylindrical cases) even matrix multiplication. The procedure may be considered to involve

numerical integration in which the basis functions are constrained to be exact global

solutions of the differential equation(s) and perhaps otherwise constrained; therefore it

is highly efficient in terms of the use of experimental data. All of these data processing

schemes may be considered to be techniques of determining the response to synthetic plane waves, but this point of view provides no new computational or experimental techniques.

In a scalar field an ideal probe measures the field at a point, while in a vector field

an ideal dipole measures a component (of a given polarization) at a point; thus for the

ideal probe case, efficient data reduction requires orthonormal ities between solutions on the measurement lattice. However, in the probe correction case, simple expressions are obtained only if the patterns of the two transducers are expressed in the same coordinate

system; hence, the set of modal coefficients for one or both of the transducers must be

transformed from its coordinate system to another. These transformations occur in each of

the simultaneous equations which are solved in fitting the experimental data (one equation

and transformation for each probe position and orientation). The transformations are the

main source of the algebraic complexities, the radial transformation being particularly

complicated in the spherical case. Efficient data reduction is then obtained if the

transformation coefficients are orthonormal with respect to summation on the measurement

Tattice (weighted summation in the spherical case). For transverse scanning, the nominal

axis of the probe is ordinarily kept perpendicular to the scanning surface, simplifying the

transformations and mechanical design. The transformations are split into two parts, one perpendicular to the measurement surface and the other on or parallel to the surface. The

former is carried out once and for all for a given probe, surface, and frequency, greatly

simplifying the computations in the spherical case and increasing the efficiency in the

cylindrical case beyond that of the published [10] program. The transformations on or parallel to the surface are supplanted by orthonormal ities with respect to summation on the

measurement lattice (see Paper II on the general theory of near-field scanning); in the

Cartesian planar, circular cylindrical, and spherical cases by DFFTs, supplemented by a matrix multiplication in the spherical case.

C. Unified Theory

As previously mentioned, the unified theory is based upon symmetry analysis (theory of

group representations) and generalized scattering theory. It yields explicit formulas

valid for a wide range of physical systems and for various coordinate systems and scanning

lattices. It also yields explicit functions which are plugged in the general formulas and

which vary according to the the type of scanning lattice and, in the spherical case, parametrically according to the physical system. These formulas of course facilitate both

general and detailed comparisions between various scanning and physical systems, facilitating transfer of understanding and translation of computer programs from one physical

system to another.

Given enough symmetry operations (translations, rotations, reflections, and/or inversion), symmetry alone gives all the familiar modal indices for rectangular, circular cylindrical, and spherical coordinates. These are symmetry indices, like even and odd, and

include: the propagation constants k , k , and k ; the cylindrical and spherical radial

x y z constants kp and k ; m and n of Pm

(cos 9) exp(im0); the angular frequency w; and the TE,TM

designation. Further, symmetry g^ves the explicit modal expressions including the special

functions and their definitions. Moreover, symmetry gives explicit expressions for the

transformations of the modal coefficients under coordinate change, during both the scanning

operations and motion perpendicular to the scanning surface; determination of f(-x) from

f(+x) for f even or odd is a familiar example of this process. Furthermore, symmetry

specifies the measurement lattices and gives the orthonormalities of both the solutions and

transformation coefficients with respect to summation on the lattice, as well as justifying

the approximation-free use of the DFFT. (The author knows of no general constructive

procedure which is not based upon symmetry, yet provides orthogonal i ty of the transformation coefficients.)

8
ACKNOWLEDGEMENT

The discussion of advantages, limitations, and comparisons of various measurement techniques distils decades of experience in the NBS Antenna System Metrology group and various

predecessor units; it is quite impossible to determine the origin of many conclusions of

Section II and quite possible that some of them were either suggested or independently

arrived at by others such as Dr. David M. Kerns, Dr. Ramon C. Baird, or Allen C. Newell.

REFERENCES

[1] R. C. Baird, "Fresnel Zone Diffraction Effects at 50 Gc/sec Determined from Measured

Aperture Field Data," IEEE AP Digest 1963 Meeting , pp. 171-173, 1963.

[2] J. Brown and E. V. Jull , "The Prediction of Aerial Radiation Patterns from Near-Field

Measurements," Proc . IEE , vol . 108B, pp. 635-644, November 1961.

[3] M. L. Crawford, Natl. Bur. Stds., Private Communication, 1977.

[4] F. Jensen, " Electromagnetic Near-Field Far-Field Correlations , Dissertation LD-15,

Technical University of Denmark, Lyngby, 1970.

[5] F. Jensen, "On Probe Compensation for Near-Field Measurements on a Sphere," Archi

v

fur Electronik und Ubertragungstechni

k

, 1975.

[6] R. C. Johnson et al., "Determination of Far-Field Antenna Patterns from Near-Field

Measurements," Proc . IEEE , vol. 61, pp. 1668-1694, December 1973.

[7] D. M. Kerns, "Scattering-matrix Description and Nearfield Measurements of Electroacoustic Transducers, J_. Acoust . Soc . Amer . , vol. 57, pp. 497-507, February 1975.

[8] D. M. Kerns, "Plane-Wave Scattering-Matrix Theory of Antennas and Antenna-Antenna

Interactions," NBSIR 78-890, Natl. Bur. Stds., Washington, 1978; to appear as Monograph No. 162.

[9] D. M. Kerns and E. S. Dayhoff, "Theory of Diffraction in Microwave Interferometry, " J_. Res . NBS , vol. 64B, pp. 1-13, January 1960.

[10] W. M. Leach, Jr. and D. M. Paris, "Probe-compensated Near-Field Measurements on a Cylinder," IEEE Trans . Antennas Propagat ., vol. AP-21 , pp. 435-445, July 1973.

[11] A. C. Newell, R. C. Baird, and P. F. Wacker, "Accurate Measurement of Antenna Gain and

Polarization at Reduced Distances by an Extrapolation Technique," IEEE Trans . Antennas

Propagat . , vol. AP-21, pp. 418-431, July, 1973.

[12] A. C. Newell and M. L. Crawford, "Planar Near-Field Measurements on High Performance

Array Antennas, NBSIR 74-380, Natl. Bur. Stds., Washington, 1974.

[13] A. C. Newell and D. M. Kerns, "Determination of Both Polarization and Power Gain of

Antennas by a Generalized 3-Antenna Measurement Method," Electron . Lett . , vol. 7, No.

3, pp. 68-70, February 1971.

[14] G. P. Rodrigue et al .

,

"An Investigation of the Accuracy of Far-Field Patterns Determined from Near-Field Measurements," Georgia Institute of Technology, Atlanta, 1973.

[15] J. A. Stratton, Electromagnetic Theory . New York: McGraw-Hill, 1941, pp. 486-488.

[16] J. D. Talman, Special Functions : A Group Theoretic Approach . New York: W. A. Benjamin, 1968, pp. 206-209.

L 1 7 ] P. F. Wacker, "Proximity and Multiple-Reflection Corrections for Antenna Gain and

Pattern Measurements," URSI 1969 Fall Meeting, pp. 5-6, 1969.

[18] P. F. Wacker, "Theory and Numerical Techniques for Accurate Extrapolationof Near-Zone

Antenna and Scattering Measurements," Report 10 733, Natl. Bur. Stds., Washington,

April 1972.

[19] P. F. Wacker, "Near-Field Antenna Measurements Using a Spherical Scan: Efficient Data Reduction with Probe Correction," in Conference on Precision Electromagnetic Measure - ments , IEE Conference Publication No. 113, IEE, London, July 1974.

L20] P. F. Wacker, "Near-Field Measurements of Antennas and Electroacoustic Transducers: A General Treatment," URSI Meeting, pp. 122-123, October 1974.

[21] P. F. Wacker, "Non-Planar Near-Field Measurements: Spherical Scanning," NBSIR 75-809,

Natl. Bur. Stds., Washington, June 1975.

[22] P. F. Wacker, "Plane-radial scanning techniques with probe correction; natural orthogonalities with respect to summation on measurement lattices," Digest 1979 AP-S Int . Synip . , Univ. of Washington, Seattle, WA, June 1979.

[23] E. P. Wigner, "Unitary Representations of the Inhomogeneous Lorentz Group Including

Reflections," pp. 37-80 in Group Theoretical Concepts and Methods in Elementary Par- ticle Physics , Feza Gu'rsey, ed. New York: Gordon and Breach, 1964.

[24] P. J. Wood, "The Prediction of Antenna Characteristics from Spherical Near Field

Measurements, Part I Theory," Marconi Review, vol. XL, pp. 42-68, 1977.

9
[25] P. J. Wood, "The Prediction of Antenna Characteristics from Spherical Near Field

Measurements -- Part II, Experimental Validation," Marconi Review, vol . XL, pp. 117-

155, 1977.

[26] A. D. Yaghjian, "Near-Field Antenna Measurements on a Cylindrical Surface: A Source

Scattering-Matrix Formulation," Tech. Note 696, Natl. Bur. Stds., Washington, Sept.

1977.

[27] A. D. Yaghjian and Carl F. Stubenrauch, "Efficient Computation of Coupling between Co^ sited Antennas from the Far Field of Each Antenna," URSI Meeting, p. 167, November

1978.

10
HBS-114A IREV. 9-78)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 79-1602

2. Gov't Accession No. 3. Recipient's icCfcssicm No,

——....

v \

!V'"-

4. TITLE AND SUBTITLE

A Qualitative Survey of Near-Field Analysis and Measurement

5. Publication Date June 1979

7. AUTHOR(S)

Paul F. Wacker

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

li. Contract/Grant No. None

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City, state, zip) 13. Type of Report & Period Covered

;15. SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

16. ABSTRACT (A 200-word or less factual[ summary of most significant information. If document includes a significant bibliography or

literature survey, mention it here.) This first paper in a series on a new unified theory of nearfield analysis and measurement serves as an introduction to and a summary of some of

the forthcoming papers in the series. Further, it describes the advantages and limita

tions of near-field scanning and compares various techniques, as well as corrects many

of the conceptual errors of the literature. Being firmly based upon generalized

scattering matrix theory and both relativistic and gauge invariance (Wigner’s extended

|

i nhomogeneous Lorentz group [1964]), the theory is rigorous and very comprehensive,

general, and fundamental, yet it provides the detailed bases of extremely efficient

computer programs for reduction of both electromagnetic and acoustic measurements on

planar, circular cylindrical, and spherical scanning lattices, as well as provides the

basis for the most accurate method of calibrating standard gain horns (described in

the series). For both the probe correction and ideal probe cases, the theory yields a series of genera 1 -but-expl i c i t formulas which apply to the aforementioned and other

lattices (including plane-radial) and to a wide variety of physical systems; plug-in

expressions (given by the theory) depend upon the type of lattice and, in the spherica

case, parametrically upon the physical system. The efficiency of the spherical EM

programs (based upon a paper in the series) is indicated by the fact that probecorrected least squares values of the complex coefficients of 50,000 exact global

solutions of Maxwell's equations in spherical coordinates and the associated far field

may be computed in a few minutes.

7. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name;

separated by semicolons)

Acoustics; antenna gain; antenna patterns; computer programs; cylindrical scanning;

electromagnetic theory; group representations; near-field analysis; near-field

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