PROCEEDINGS OF THE I-R-E

Antenna-Scattering Measurements byModulation of the Scatterer *

H. SCHARFMAN, ASSOCIATE, IRE, AND D. D. KING, MEMBER, IRE

Summary--An indoor method for measuring the radar cross sec-tion of objects by modulating the position of the object is described.The use of synchronous detection and employment of a substitutiontechnique wherein the scattering from an object under test and aknown object are measured and compared simultaneously reducemeasurement error to ± 2 per cent. The characteristics of the sys-tem are discussed, and its advantages and limitations are comparedwith other systems. Measured curves for the back-scattering cross-section of dipoles for lengths from O.4X to 1.6X show good agreementwith other published theoretical and experimental curves. Methodsfor measuring back-scattering and off-angle scattering from irregularobjects by extension of this technique are indicated.

I. INTRODUCTIONAS A CONSEQUENCE of its importance in the

radar equation, the absolute value of the back-scattering cross section

l Power scattered back to Source/unit solid angle\= ~ Power Incident Power density /

of many objects has been studied both theoreticallyand experimentally for many years. The inherentmathematical difficulties in the determination of o- forall but the simplest objects place a premium on precisemethods of measurement.

Several techniques have been used for the meas-urement of a- and related parameters. In recent yearsattention has turned to the use of an image plane forsuch measurement. Image plane methods have the ad-vantage that errors caused by reflections and lenseeffects of supports are circumvented. King' has employedthis device for determination of absorption gain andback-scattering cross section of dipoles. Dike and King2used a similar method for the study of the dipole, andSevick3 and Aden4 made measurements on coupled di-poles and water spheres by means of this technique.

For many purposes these and simpler measurementschemes are adequate. However, use of the image-planetechnique limits the investigation to objects having atleast one axis of symmetry. Thus scattering investiga-

* Decimal classification: R537.4. Original manuscript received bythe I.R.E., August 1-1, 1953; revised manuscript received December30, 1953.

The work described in this paper was supported by ContractAF 33(616)-68 between the Wright Air Development Center and theRadiation Laboratory, Johns Hopkins University. This paper ispart of a thesis submitted to The Johns Hopkins University by H.Scharfman in partial fulfillment of the requirements for the D.S.in E.E.

t Radiation Lab., Johns Hopkins University, Baltimore, Md.I D. D. King, "The measurement and interpretation of antenna

scattering," PROC. I.R.E., vol. 37, pp. 770-777; July, 1949.2 S. H. Dike, and D. D. King, "The absorption gain and back-

scattering cross-section of the cylindrical antenna," PROC. I.R.E.,vol. 40, pp. 853-860; July, 1952.

3 J. Sevick, "An experimental method of measuring back-scatter-ing cross-sections of coupled antennas," Cruft Lab., Harvard Uni-versity, Cambridge, Mass, Report 151, May 28, 1952.

4 A. Aden, "Electromagnetic scattering from metal and waterspheres," Cruft Lab., Harvard University, Cambridge, Mass., Report106, 1950.

tions of the objects are confined to study of the back-scattering cross section.

In addition, it has been difficult to achieve high ac-curacy with the image-plane technique for severalreasons. Errors arise due to drift of the source power andfrequency, detector sensitivity variations, and noise.Reflections from surrounding objects and walls as wellas the finite size and imperfections in the ground planealso cause errors.As a result, errors of 5 per cent or more are quoted for

previous measurements of back-scattering cross section(1, 3). The system described below avoids many of thesources of error mentioned, and also has the capabilityof measuring both a. and off-angle scattering from ir-regular objects.

CW SOURCE

PHASESNIFTER

MATCHEDLOAD

H TUNER

HR AXIS OF MAIN LOBEE ---

-- --- ~~~~~~~~~~~~~--

__-4 TUNER

IAHO

SWITCHING RELAYS

Fig. 1 System block dia

COMMUTATIONREGION

FOR EACHOBJECT

STANDARD

__ OB_ECT VERTICAL DRIVESHAFT AND

-"(_4L , / %COMMUTATOR

MOTOR ANDI;s / GEAR REDUCER

A4_ WHORIZONTAL/ e STYROFOAM COLUMN

/ %UNKNOWN OBJECT

/

agram.

II. THE MEASURING APPARATUSThe measurement system is shown in block diagram

form in Fig. 1; photographs of the actual equipmentset up are shown in Figs. 2, 3, 4 and 5. Referring to Fig.1, a cw source feeds a slightly unbalanced hybrid tee;the power is divided about equally between the loadand horn arms with a small amount of oscillator powerentering the detector arm. The power emitted by thehorn impinges on a rotating column of styrofoam (di-electric constant z 1.03) in which are embedded astandard such as a metal sphere and opposite it, theobject whose a- is to be determined. A synchronousmotor and gear reducer drives a vertical wooden shaftwhich supports the styrofoam column. The horn islocated so that its main lobe falls on only one objectat a time while the rotation center is kept near the firstnull of the horn pattern.As the styrofoam column rotates, each object in

turn passes into the main lobe of the horn and scattersback to the horn a quantity of power proportional to its

854 _;-fay

1954 Scharfman and King: Antenna-Scattering Measurements by Modulation of the Scatterer 855

- s &Fig. 2-View of styrofoam column and drive. Fig. 3-Close-up of motor, gear reducer, and commutator.

t 'l: ' , . : , _ ,

Fig. 4-View of oscillator and waveguide assembly.

I _

Fig. 5-View of horn and metering equipment

PROCEEDINGS OF THE I-R-E

back-scattering cross section. The portion of this signalreaching the detector arm mixes with the oscillator sig-

nal and is detected by a crystal. As an object moves into,through, and out of the main lobe, the power scatteredback to the horn will vary in amplitude because of thelobe shape and the changing distance, but more im-portant, the phase of the scattered field with respect tothe oscillator field will change by 7r radians for eachquarter wavelength of motion parallel to the axis of thehorn. For a styrofoam column that is long compared toa wavelength, many phase reversals will occur over thesemi-circular swing of the object through the main lobe.Thus, the phase of the back-scattered signal in the de-tector arm will vary rapidly with respect to the oscilla-tor signal in that arm. The two signals are mixed anddetected in the crystal, producing an audio signal cor-

responding in frequency to the doppler shift caused bythe relative motion of the horn and object. In this case

the detection process is that of a superheterodyne re-

ceiver with an IF equal to the doppler frequency andhas been termed Synchronous Detection.5'6 Under theseconditions, the detector response is linear in that theamplitude of the audio voltage is proportional to theamplitude of the back-scattered field, and the sensitivityis about 30 db better than for direct video detection.The output of the crystal over a full revolution of the

styrofoam column consists of two signals each corre-

sponding to the movement of one of the objects passingthrough the main lobe of the horn. These signals are in-dependent of each other as only one object is in themain lobe at a time. Double reflection effects and thecontribution from objects passing through the sidelobes of the horn were observed to be negligible.The combined signal from the crystal is amplified and

the parts corresponding to the standard object and theobject to be measured separated by means of relays anda commutator mounted on the vertical drive shaft ofthe styrofoam column. Commutation is arranged tooccur at the time that objects are entering and leavingthe main lobe. The separated doppler signals are recti-fied and averaged over many revolutions of the supportcolumn by a long time-constant filter. The two resultingdc voltages appear on a pair of vacuum-tube voltmeters.Each voltage is proportional to the back-scattered fieldof its respective object. Taking the square of the ratioof the voltages removes the proportionality constantsand yields the ratio of the back-scattering cross sectionof the two objects. The standard scatterer (usually a

metal sphere) has a o- that is known exactly7'8,9 and thefor the object under test is determined directly from

the measured ratio and known value for the standard.

5 M. E. Brodwin, C. M. Johnson, and W. M. Waters, TechnicalReport 18, Radiation Laboratory, The Johns Hopkins University,Baltimore, Md.; March 31, 1952.

6 M. E. Brodwin, C. M. Johnson, and W. M. Waters, "Low levelsynchronous mixing,"1953 I.R.E. Convention Record, part 10, p. 52.

7J. A. Stratton, "Electromagnetic Theory," p. 563 ff, McGraw-Hill Book Co., New York, N. Y.

8 L. N. Ridenour, "Radar System Engineering," p. 64, McGraw-Hill Book Co., New York, N. Y.

9 D. Kerr, "Propagation of Short Radio Waves," p. 453, McGraw-Hill Book Co., New York, N. Y.

IIJ. CHARACTERISTICS OF THE SYSTEM

The system as outlined above has several importantadvantages over others previously employed. As onlythe ac output of the crystal corresponding to movingobjects is amplified and metered, only objects movingthrough the beam are detected. Reflections from sta-tionary objects including the walls affect only theinitial adjustment of the Tee unless the object ap-proaches so close to a highly reflecting object thatmultiple reflections cannot be neglected. The lattereffect is made small by keeping the styrofoam columnmany wavelengths from the nearest wall and lining thewall opposite the main lobe with absorbing material.The reflected power from this wall is at least 17 db be-low the incident power at normal incidence. In addition,the specular reflection from the wall opposite the hornwas reduced by suitable orientation of the horn withrespect to the wall and the styrofoam column.

Potential sources of error arising from variations inoscillator power, detector sensitivity, line voltage andaging effects are avoided by using the previously de-scribed time-sharing technique. The scattered field fromeach object is subject to the same drift effects, and theseare eliminated when the ratio of the voltage readings istaken in the process of calculating oUteSt/0standard. Short-time perturbations are removed by the long-time con-stant filters at the rectifier outputs.As described above, synchronous detection is used in

the measurements, and this inherently leads to severaladvantages. It has been shown5'6 that about 1 dbm ofreference power in the detector arm is needed for goodsynchronous detection, and that the detection sensitiv-ity is essentially constant over a wide range of referencepower. The leniency of these conditions allows the Teeto be properly adjusted by tuning a phase shifter in thematched load arm. This adjustment is insensitive andindicates that the system can be used over wide fre-quency bands with minor modifications. The crystaldetector mount is the only relatively narrow-band ele-ment in the system, and this is readily modified for usein different ranges.By virtue of its linear response, the synchronous de-

tection process indirectly reduces other errors in thesystem. The crystal-output voltage is proportional tothe back-scattered field strength rather than power (asin low-level video detection) and, consequently, the re-quired linear dynamic range of the amplifiers, rectifiers,and voltmeters is reduced. Errors arising from non-linearities in the latter devices are thus reduced.

IV. LIMITATIONS AND SOURCES OF ERROR

It has been stated above that this system is inherentlywide band; the frequency limits will now be considered.The lowest frequency is limited by the physical size ofthe available range, for the object must always be keptin the Fraunhofer zone (unless one wishes to specificallymeasure Fresnel-zone scattering). Lower frequencies gen-erally mean physically larger objects and more cumber-some means of getting the standard and unknown ob-

May856

Scharfman and King: Antenna Scattering Measurements by Modulation of the Scatterer

jects in and out of the beam. For outdoor ranges, pro-vision must be made to keep moving objects out of themain lobe, and consideration must be given to the effectof moving objects close to the transmitter in its sidelobes. These considerations would appear to limit theminimum frequency to roughly 1,000 mc.The limitation at high frequencies lies in the support

column which inevitably reflects energy and may act asa lens on the standard and unknown objects. At 9,000mc styrofoam exhibits both of these faults, but measure-ments at 3,000 mc indicate negligible effects due to thestyrofoam. The high frequency limit for high accuracymeasurements, therefore, might be about 5,000 mc al-though usable results could perhaps be obtained athigher frequencies with a specially made support column.

Errors caused by curvature in the phase front of theincident wave over the objects are partly removed whenthe ratio of the meter readings is taken. This arisesfrom the fact that slight curvature of the phase frontwill reduce the measured back-scattered signal for bothobjects.10 As the error in each signal is in the same direc-tion, the error in their ratio will be smaller than theerror in either signal. For objects of approximately the

NOTE: 0/A IS NOT THE

1.0SCHARFMAN-KING (EXPERIMENTAL)

.8

.6/

.4

2

0

path traced by the scatterer are also partially cancelledby taking the ratio U test/0U standard.

Errors which cannot be excluded are due to non-linearity of the rectifiers and meters and the meter-reading error which combined should be less than 2 percent. From intercomparison tests and the excellent re-peatability, the over-all probable error in the ratio ofthe readings for two objects is estimated to be less than± 1 per cent. As this ratio must be squared to obtain theratio of the back-scattering cross section, the probableerror in the latter ratio is less than ±2 per cent. Theresidual errors become more significant for values ofU/X2 less than 0.1.

V. EXPERIMENTAL RESULTSThe system of Fig. 1 was set up at 3,000 mc, and the

back-scattering cross section of copper dipoles oflengths varying up to 3X/2 was measured as comparedto a silver-painted sphere of radius 1.50 inches. Thevalue of the back-scattering cross section for a sphereas given in the literature8'9 was used as the standard.Back-scattering from various sizes of silver-paintedspheres was also measured as a check.

1.2 1.3 1.4 1.5 1.6 1.7 1.8 9 2.0r L

Fig. 6-Back-scattering cross section versus dipole length.

same scattering cross section, the errors tend to cancelcompletely with high resultant accuracy in the ratio ofthe signals. By varying the range, it was found that forthis system negligible error was incurred if

(D + d)2

D = maximum. dimension of horn in wavelengthsd =maximum dimension of scatterer in wavelengthsX= wavelengthR = distance from horn to object on axis of main lobe.The effects of nonuniform incident amplitude over the10 E. H. Braun, "Gain of electromagnetic horns," PROC. I.R.E.,

vol. 41, pp. 109-115; January, 1953.

In Fig. 6 the measured curve of back-scattering crosssection versus dipole length in the vicinity of the firstresonance is plotted together with the measured curvesof Sevick" and King' as well as the theoretical curve ob-tained by Sevick" and Tai"l using the variational method.

In Fig. 7 a measured curve covering the first two di-pole resonances is presented along with the measuredcurves of Dike and King,2 Sevick," and a theoreticalcurve by Tai.'2 The absence of a dip before the second

1 J. Sevick, "Experimental and theoretical results on the back-scattering cross-section of coupled antennas," Cruft Lab., HarvardUniversity, Cambridge, Mass. Report 150; 1952.

12 C. T. Tai, "Electromagnetic back-scattering from cylindricalwaves," Jour. of Appi. Phys., vol. 23, pp. 909-916; August, 1952.

1954 857

PROCEEDINGS OF THE I-R-E

I.0

.8

.6

o/*.4

.2

0

NOTEa/A IS NOT THE SAME FOR EACH CURVE

/a/X:3.18 X10 (SCHARFMAN-KING) COPPER WIRE MEAS.o --a/XA 10.2 X 103 DIKE MEAS. (RELATIVE SCALE)i\ aX= 3S X0 SEVIGK SILVER-PLATED STEEL\ I1/\\ 3.5 X105 ROD MEAS. S

2--/a:-go900 TAI CALCULATED VARIATIONALMETHOD |

1.0

11' °,If

o'i

2.0 3.0 4.0 5.07rLx

Fig. 7-Back-scattering cross section 'versus dipole length.

resonance in Sevick's data is ascribed to the high prob-able error at low values of u- reported by Sevick.

VI. EXTENSIONS OF THE MEASUREMENT METHOD

The technique described above for the measurementof back-scattering cross section has the limitation incommon with image-plane techniques that only objectshaving at least one axis of symmetry can be measured.

COMMUTATION REGIONFOR EACH OBJECT

/

Fig. 8-System for measuring back-scattering fromirregular objects.

This restriction is lifted when the commutation period isreduced so that only the signal generated near the cen-

ter of the main lobe is applied to the rectifier. Scatteringfrom irregular objects may be measured, as indicated inFig. 8. The orientation of an object with respect to thehorn is almost constant from A to B, and the error in-troduced by slight change in orientation from A to C toB can be varied by changing the commutation periodwithin limits or by increasing the distance from horn to

object. Off-angle scattering for arbitrary angles withrespect to the horn may be measured by separating thelocation of receiving and transmitting horns. Referencepower for synchronous detection is then supplied from adirectional coupler to the remote receiver, and no hy-brid junction is required.The technique of modulating the scatterer is also ap-

plicable to image-plane systems. For absorption andloading measurements, as well as for freedom from sup-port problems, the image system is preferable. Thestandard and test objects would then be mounted in arotating disk in the image surface, or passed through thebeam in some other fashion.

VII. CONCLUSIONS

It has been shown that the system of modulating thescatterer removes many sources of error in back-scattering measurements. Using the described tech-nique, the room-reflection problem is reduced, much ofthe usual adjustment and tuning difficulties areavoided, and drift caused by electrical and atmosphericchanges is eliminated. In addition, the method can beapplied over a wide band of frequencies, and has highsensitivity. Data taken on dipole scattering confirmthe accuracy of the method, and is in substantial agree-ment with the results of previous investigations.With modification the system could be used to meas-

ure off-angle scattering, and, by combining some of thefeatures of an image plane, the absorption cross sectionand the back-scattering cross section of terminated an-tennas could be measured.

VIII. ACKNOWLEDGMENT

C. F. Miller, M. E. Brodwin, and C. H. Graulingmade valuable suggestions to the authors in the courseof the work.

858 May