IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-19, NO. 4, NOVEMBER 1970

to standard resistors to within 4 1 ppm, and to resistancethermometer calibrations within 0.01°C.

This automatic system has extensive RF- and micro-wave-measurement capabilities using a network analyzer[2], [3]. It has been used to measure attenuators, directionalcouplers, and terminations. Programs have been preparedthat perform measurements and calibrations automaticallyand semi-automatically. Calibrations of manually op-erated instruments and devices have been performedusing computer-corrected measurement and stimuli,operator instructions, and tolerance decisions. Examplesof computer-aided manual-instrument calibrations havebeen found to reduce instrument calibration time typicallyto - that of manual test methods.

CONCLUSIONThe development of this automatic self-certification

process has shown that it is possible to verify rapidlyand automatically the measurement and stimulus per-formance of an automatic test system over a wide dynamicrange with reference to a few fixed value standards.Use of such a process enables an automatic test system

to be used having uncertainties limited by the short-term precision of the component instrumentation andby the process uncertainty of the automatic self-certifi-cation. Typically, the accuracy specifications normallyassociated with digital equipment may be improved byas much as one order of magnitude, by using it in thecomputer-corrected mode.

ACKNOWLEDGMENTThe authors wish to thank M. Shelton and G. Marshall

for their assistance in preparing and modifying thesystem software and programming.

REFERENCES[1] W. G. Eicke and J. M. Cameron, "Designs for surveillance of

the volt maintained by a small group of saturated standardcells," NBS Tech. Note 430, October 9, 1967.

[2] R. A. Hackborn, "An automatic network analyzer system,"Microwave J., vol. 2, pp. 45-52, May 1968.

[3] B. P. Hand, "Developing accuracy specifications for automaticnetwork analyzer," Hewlett-Packard J., pp. 16-19, February1970.

[4] M. Mondress, "Laboratory evaluation unit for the automaticcalibration system," IEEE Trans. Aerosp. Electron. Syst.,vol. AES-4, pp. 569-579, July 1968.

Automated Precision Polarimeter for theHF-VHF Range

T. C. GREEN, MEMBER, IEEE, AND W. B. TARVER, MEMBER, IEEE

Abstract-An automated system for Stokes parameter-polar-ization analysis over the HF-VHF range is described. Axial ratio,orientation angle, polarization fraction, and polarization sense aredetermined by amplitude measurements using a conventional field-intensity receiver. Six amplitude measurements from four crossednonresonant dipoles, including quadrature sum and difference,eliminate the requirement for phase measurement. The antennadoes not use active components and is adaptable for mobile orstationary operation. VSWR measurements on the antenna outputcables show less than 1.2:1 (50 ohms) over the 2-70 MHz range.The antenna aperture increases from 1 X 10-5 square meters at2.0 MHz to 0.019 square meters at 70 MHz.A solid-state sequencer processes each amplitude measurement

separately through the receiver and digital conversion circuits(providing BCD output) to an incremental tape recorder. The Stokesparameter analysis is performed by an off-line digital computerusing the magnetic tape data.

This analysis permits computation of total received power fromeither set of orthogonal element measurements. When combinedwith the measured antenna aperture, power density (or fieldstrength) also can be derived. Polarization fraction measurementsfor locally controlled signals show a mean of 1.02 as compared to a

Manuscript received June 3, 1970.The authors are with the Southwest Research Institute, San

Antonio, Tex.

theoretical value of 1.00 (standard deviation of 0.1) over the 2-70MHz range and polarization results consistent with propagationpredictions.

INTRODUCTION

T HIS PAPER describes a recently developed antennaand data-logging equipment that allows the auto-matic sampling of an incident electromagnetic

wave to determine its complete polarization charac-teristics and total incident power. The polarimeterantenna was designed to operate in the 2-70 MHz fre-quency range against plane electromagnetic waves froma generally known direction (i200). For the local gen-eration of electromagnetic waves in the HF-VHF range,a complete polarization analysis allows detailed studyof propagation effects as well as the measurement oftotal received power [1]-[3].The amplitude polarization technique [4] was chosen

in order to use a broad-band calibrated single-channelEMI receiver. A calibrated single-channel receiver-oriented polarimeter allowed the calculation of totalpower and polarization, eliminating the requirements

252

GREEN AND TARVER: AUTOMATED PRECISION POLARIMETER

for a twin-channel phase and gain matched receiverand phase meter. Polarization and power results areobtained from off-line processing of the digitally recordedpolarimeter measurements.

POLARIZATION ANALYSIS

For evaluating the polarization characteristics of anincident electromagnetic wave, it is convenient to describethe polarization ellipse shown in Fig. 1 in terms of fourparameters. These are the axial ratio r, polarizationsense (right or left hand), orientation angle x, and thepolarization fraction m. The axial ratio is the ratio ofthe ellipse minor axis to major axis and is at the extremes,zero for linear polarization and equal to unity for acircularly polarized wave. Polarization sense representsthe direction of rotation of the resultant E vector (vectorialsum of EX and EV) whose locus describes the polarizationellipse.The IEEE convention of a counterclockwise-rotating

wave approaching being right handed -r is used in thisreport. The orientation angle x describes the angularposition of the major axis of the ellipse with respectto the X axis as measured counterclockwise. Polarizationfraction measurements, used quite commonly in radioastronomy polarization studies, determine the percent-age of unpolarized electromagnetic energy comparedto the total power received.The Stokes' parameter analysis develops equations

for the axial ratio r, the orientation angle x, and thepolarization fraction m in terms of the four variablesQ, U, V, and I (the Stokes' parameters). These variablesare closely related to antenna measurements. Theseequations are

(Q + u2 + V2)"2m- I

sin 2 = r =tanfd

tan (U)

For the amplitude sampling technique using X and Y,S and T, and R and L orthogonal inputs as shown inFig. 2, the expressions for Q, U, V, and I are [4]

Q =EE-EU E2ESET2

I = EX+ EY.

The total received power is represented by I and can

be obtained from the vector sum of any of the threeorthogonal antenna pairs. It should be noted that whilesix amplitude measurements are obtained, only fourare necessary to solve for Q, U, V, and I. For example,EX, ES, EL, and ER would suffice with the other twomeasurements being redundant. These redundant mea-

Fig. 1. Polarization ellipse of an electromagnetic wave.

ES

II

ET

POLARIMETER OUTPUTS

Fig. 2. Amplitude polarimeter for determining polarization charac-teristics of an electromagnetic wave.

surements can, however, be used as averaging factorand as a check on the polarimeter.

SYSTEM DESCRIPTION

The automated polarimeter system is designed formobile polarization measurements with the polarimeterand console mounted on and within an appropriatevehicle. Design emphasis was on automation of thesix amplitude measurements using a solid-state sequencercontrol circuit. Antenna amplitudes and peripheraldata were recorded on magnetic tape for off-line processing.A slow antenna-switching rate was used for the initialdesign to accommodate the long detector-time constantof the EMI receiver (approximately 2 seconds).A series of polarization and total-power measurements

can be accomplished by a single operator in the vehicle.Four modes of operation of the polarimeter system areavailable to the operator. These are 1) calibrate, 2)auto-matic, 3) manual data entry, 4) test. The desired modeis selected from a front-panel rotary switch. The calibratemode allows individually controlled sampling of eachantenna output (including sum and difference outputs)and adjustment of in-line RF attenuators. The operatoradjusts the RF attenuators for the maximum antenna

253

a

ETES.11

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, NOVEMBER 1970

amplitude in order to produce a signal level at the receivernear the dynamic range limit. Automatic sampling willthen have 40 dB of dynamic range for measurements.Two attenuators are used in series providing continuouslyadjustable attenuation in 1-dB steps from 0-79 dB.Each position of the RF attenuators is automaticallyencoded and recorded on the incremental tape recorderin a controlled sequence. Using the calibrated EMIreceiver outputs and the attenuation settings, the softwarepackage can compute the total power received by thepolarimeter antenna.Antenna selection is shown by the single-digit display

shown on the front panel. Automatic data acquisitionprovides for automatic sampling and recording of theantenna amplitudes and manually set peripheral dataupon activation of START command. Manual data entryallows the operator to manually sequence error-codedata (3 digits maximum) into the recorder after completionof an automatic data acquisition. Test-mode operationis used for diagnostic evaluation of the system. A record/monitor switch on the front panel allows observationof the sequencer operation without writing on the mag-netic tape.The data-logging console that includes the antenna

sequencer and the incremental tape recorder is shownin Fig. 3. The polarimeter antenna is shown in Fig. 4.Also included in this console is peripheral equipment(interface assembly) that allows for the direct transferof the data on magnetic tape to paper tape for preliminarycheckout and verification of the recorded data. Theperipheral circuits include a tape-search routine foridentifying end of records existing on magnetic tape.A detailed block diagram of the automatic polarimeter

containing the antenna and sequencer circuits is shownin Fig. 5. The system can be divided into six majorfunctional groups as shown below:

1)2)3)4)5)6)

polarimeter antenna assembly,RF processing and relay switching,EMI receiver,receiver analog output to digital-code converter,digital measurement and data recording sequencer,incremental tape recorder.

A radial array of dipole antennas was conceived toform the polarimeter antenna assembly. Eight linearelements spaced at 450 radially around the hub are

used to form the four-dipole element array as shownin Fig. 5. The dipole elements were conservatively madeelectrically short (less than 2 X) over the design band-width to minimize the effects of mutual coupling betweenthe adjacent antenna elements and the resultant deterio-ration of the polarization measurements. For the designbandwidth of 2-70 MHz, the dipole element lengthused was 50 inches, which is one-half wavelength (freespace) at 117 MHz.Each dipole antenna (two elements) is terminated

in a wide-band balun transformer that provides a single-ended output (four total) for routing the signal to the

Fig. 3. Data-logging console that includes the antenna sequencerand the incremental tape recorder.

Fig. 4. Polarimeter antenna.

antenna sequencer. Resistive shunting is used to providean antenna output VSWR of less than 1.2-1 over 2-70MHz. Low VSWR antenna output transmission lineswere necessary to assure proper operation of the quad-rature hybrids.The RF processing consists of switching the six ampli-

tudes to a single RF output using a sequencer-controlledsix-position coaxial relay. Selection of the high-band(30-70 MHz) or low-band (2-32 MHz) quadraturehybrid is also accomplished by the remote switching ofcoaxial relays.Input to the EMI receiver is controlled by the preset

RF attenuators. A logarithmic-detector circuit is usedin the receiver to provide a linear varying dc voltageproportional to decibels above 1 uV at the input to thereceiver. Analog-digital conversion is obtained by adigital panel meter that provides a four-digit BCD output

254

GREEN AND TARVER: AUTOMATED PRECISION POLARIMETER

Fig. 5. Block diagram of the automatic polarimeter.

representing the receiver analog output. A digital gatecontrolled by the master sequencer selects, in predeter-mined sequence, the digitized receiver output representingeach antenna amplitude, the attenuator settings, andthe outputs for manually set thumbwheel encoders.Each BCD character is sequenced out of the digitalgate and recorded sequentially on a magnetic incrementaltape recorder. Data display lights are provided on thefront panel showing the data being transferred to therecorder.The manually set thumbwheel encoders allow the

operator the option of entering information (codednumbers) into the recorded data for identifying parametersrelated to the measurement. A complete frame of datathat includes the six amplitude measurements and theauxiliary information is recorded automatically in a10-second period. Frame length was 37 or 40 BCDcharacters depending upon the optional selection of a3-character error code by the operator. Faster framespeeds in the order of 1 per second could be obtainedwith the existing sequencer using a fast time-constantdetector in the EMI receiver.

On-line recording was provided by a digital incrementalmagnetic read-write tape recorder. The recorder usesan 81-inch reel (1200-foot tape capacity), and 7-trackmagnetic tape at a density of 200 bit/in and a maximumrate of 300 Hz. The maximum incremental reading rate is150 Hz. All write-control functions and data inputs tothe recorder come from the digital sequencer. Output

data lines and read-control busses are connected to theinterface assembly. The data code chosen for recordingwas IBM-compatible binary-coded decimal (BCD).

SOFTWARE DEVELOPMENT

Fig. 6 illustrates the functional process for off-linedata reduction of the polarimeter data. All data pro-cessing was accomplished using a time-sharing computerfacility remote from our laboratory. The magnetic tapecontaining the raw data could be sent to the remotecomputer facility by mail or transferred to punchedpaper tape and transmitted on teletypewriter terminals.The raw data file is verified and edited to ensure that

no erroneous data are used in the computation program.Tests performed in the verify and edit program causedeletion of any record that does not meet the test con-ditions. Then a listing is obtained on the teletype outputalong with the cause of the deletion. Data errors dueto sequencer malfunction, magnetic tape flaws, teletypetransmission errors, etc., can therefore be detected andcorrected if necessary.

For repeated sampling of an incident wave, the dataare automatically averaged in the verify and edit pro-gram. Polarization and total power computations areperformed on the verified and edited data using a separateprogram. The computation program was written so thatexperimental parameter data, which might be oftenchanged, could easily be entered in the computations.Data such as transmitter frequency, transmitter-receiver

255

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, NOVEMBER 1970

SwRI TIME - SHARE COMPUTER SERVICE

POSTALMANETCSERVICE

( TAPE EDIT

|~~~~~~TELEPHONE FIL(PAPER TTY s

TAPEI { DT EI

PRINT - OUT | ll, VRFs-UT

W______JI POLARIZATION

i t POWERAND COMPUTERI POWER

! | COMPUTATIONSPLOT

ROUTINESL----JFig. 6. Software data-flow chart for automatic polarimeter.

ARE THERE ANY CHANGES IN FREO..APR OR RPD SINCE THELAST RUN? ANSWER YES BR NB AS APPROPRIATE: YES

OLD FREQ2 : 70.000MHZNEW FREQ.: 060.000OLD APR: .01645000000NEW APR: .00600000000BLD RPD= .00000048400NEW RPD= .00000084000ARE THERE ANY CHANGES IN DISTANCES SINCE THE

LAST RIJN? ANSWER YES BR NB AS APPROPRIATE:ENTER DATE: 04 13 70ENTER RUN NO. 002ENTER XMIt HoS-lrl0N: LAB

NO

IS INPUT FROM DISC FILE? IF SB,RETURN CARRIAGE ANDGIVE NAME BF FILE. IF INPUT IS FRBM TAPEPRETURN CARRIAGE

AND ANSWER "TPT" .

OPENING FILE 2, SYMBOLIC INPUTS NAME: /KADATA2/R lN 2 DATE 4/13/70 FREQ 60. 000 MHZSITE 0B DBX DBY P-F. A.R. CHI DIST. APF(O)

1 16 24 16 1.04 -0.38 79 379 1.042 21 38 20 1.01 -0.08 85 524 1.003 15 27 15 0.99 -0.01 76 320 0.994 18 22 19 0.87 0.69 91 250 0.885 7 1 1 7 1.08 0.05 123 225 1.066 6 6 15 1.07 0.26 15 229 1.047 11 18 12 1.00 -0.13 65 316 1.028 4 5 10 1.06 0.10 30 130 1.039 1 2 9 1.14 0.12 24 100 1.10

10 0 0 6 1.06 0 .12 158 92 1.0111 3 4 3 1.04 0.15 130 151 1.0112 4 3 17 1.09 -0.16 4 177 0.9913 2 4 5 0.88 0.85 167 287 0.8814 8 7 14 1.08 0.18 156 244 1.0115 14 18 16 0.86 0.35 54 184 0.9016 14 13 24 1.10 0.03 162 207 1.0217 9 8 19 1.10 -0.22 176 225 0.9718 14 17 17 1.09 -0.12 44 314 1.06

Fig. 7. Sample teletype (TTY) listing.

APF I)1 .171.181.140.981.191.101.131.141 .231 .10I .1 41 .090.991 .120 .961 .171 .091 .20

distance (DIST), effective antenna aperture (APR), andreference power density (RPD) can all be changed inthe program through the TTY terminal.

Vertically (DBY) and horizontally (DBX) polarizedpower components as well as total power (DB) were

calculated for each site. The power computations were

listed in decibels relative to a standard field measure-

ment. For the polarization description, the polarizationfraction (PF), axial ratio (AR) and orientation angle(CHI) were calculated for each site. Listings of theoutputs resulting from these computations for a samplerun at 60 MHz are shown in Fig. 7.A plot routine named RADIAL is used to plot site

locations on each radial along with the values of attenua-

tion (relative power), polarization fraction, axial ratio,and orientation angle corresponding to each site. A sampleplot from this routine is shown in Fig. 8.

POLARIMETER EVALUATIONMeasurement of the aperture of the polarimeter antenna

for a known standard field was accomplished by dividinga measured RPD (standard field) by the measuredpolarimeter power output. Fig. 9 shows the plot of theaperture in square meters versus frequency. Samplemeasurements on the unshunted dipoles show fieldstrengths with an average 6-dB increase in sensitivity.Sensitivity is defined in this case as a 20-dB (S+N)/Nratio on the receiver-detected output.

APF (2)0 .920.840.840.750.981 .060.841 .021 .101 .080 .971 .200 . 761 .120.701 .101 .251.01

256

GREEN AND TARVER: AUTOMATED PRECISION POLARIMETER

-Z1.~-080

-221.41-0.07so

-Z10899-0.1188

-21.-ago

O OEGftEES t.B. FRIEO: 8.000 MHZRUNs 8ORTEt 4_ 20 70SCRLE& 1-170'

-t 1.17 -121.23 00 1.200415 86 -0.05121 89

0.98 i-.q0.19 -0.05

'Z -2322 1.18[.07 -0.08

89

-2

-23

I-~~~~~~~00

1.30 1.12~~~~~~~~~~~~~~~1

0.05 -0.1~~~~~~~~~0.0

90 87-25 -21

.0789

-ZZ1 .23-0.0788

21.190.09

21.160-11

N

wa:

a:wa-

1 .cu-0.08as

KEY;rWr lON

r.tRlhrim Iriwtcrm1RXiaL mriJ08ierNr ImN RNC (0r08xs1

Fig. 8. Sample computer plot. The location of the receiver siteon each radial is indicated by the small diamond. The radialscale is indicated at the top and the measured attenuation,polarization fraction, axial ratio, and orientation angle are listedat the end of each radial.

Evaluation of the polarization response of the auto-matic polarimeter was accomplished using a targettransmitter with linear antenna elements. Transmittingelements were oriented and configured for various polar-izations and the polarimeter response automaticallyrecorded. Evaluation of the computed polarizationparameters against the orientation and polarizationconfiguration of the target emitter must be temperedby the unknown exact polarization profile of the emittedwave and the propagation effects on this wave betweenthe target emitter and polarimeter. Fig. 10 illustratesrelative positions of polarimeter and target antenna.

Fig. 11 shows the computed polarization ellipses forfour target-antenna orientations at 70 MHz. Resultsare in close agreement with the orientation of the source.

Note that only slight ellipticity is shown for the verticallyoriented emitter and none for the horizontal orientationwhile increasing ellipticity is shown for the obliquelyoriented emitters. The phasing noted for the obliquelytransmitted wave results from the different ground-reflection coefficients for the horizontal and verticalcomponents of the radiated energy.A circular polarization experiment was conducted at

70 MHz using two quadrature-fed crossed resonantdipoles. Polarimeter measurements shown in Fig. 12for the circularly polarized sources show elliptical polar-

10 100FREQUENCY IN MHz

e 10 o

a:IIz

I Z

._ c

too0N

a:0U.

-_2

j 1,000I I--

zwa:C,)

0-JW

10,000 U.

1000

Fig. 9. Plot of effective antenna aperture and sensitivity versusfrequency.

ization received with the proper sense. The orientationangles of the ellipses are near the 450 or 1350 positions.This response is produced by equal amplitude X and Ycomponents in the incident wave with a phase componentthat is neither zero nor quadrature related. The changein phase relationship of the launched wave is to be ex-pected in these frequency ranges.A linear polarization experiment was conducted for

frequencies from 2-70 MHz. Polarization ellipses com-puted from the data are shown in Figs. 13 and 14. Theresults are in good agreement with propagation theoryin this frequency range. For frequencies 20 MHz andbelow, the resultant polarization ellipse is verticallyoriented with only slight ellipticity. This results fromthe attenuation of the horizontally propagated com-ponent and the predominance of the vertically polarizedcomponent regardless of the orientation of the targetantenna. Such propagation conditions can be expectedwhere the transmitting antenna and the polarimeterantenna are less than 1 X above ground for frequenciesbelow 60 MHz. Horizontal propagation becomes in-creasingly difficult as the frequency is decreased underthese conditions.Above 20 MHz there is a rapid change in the received

polarization. At 30 MHz, the polarimeter response showsa near horizontally oriented wave with only slight el-lipticity for all orientations of the target antenna. Thiseffect is apparently from the polarimeter antenna beingin the first null-zone fringe where the direct and reflected

257

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT NOVEMBER 1970

TARGET ANTENNA POSITION1. ORTHOGONALITY TESTS

(BATTERY OPERATED)

POLARIMETER

EQUIPMENTVAN

) 3.mWU F

TARGET ANTENNA POSITION1. COMPARISON TESTS2.POLARIZATION MEAS.

6m

27m

TRANSMITTER(115 VAC)

Fig. 10. Diagram of the experimental arrangement of the transmitting and receiving antennas.

TARGET ANTENNACON FIGURATION _ /

POLARI METERRESPON SE

1, TARGET ANTENNACONFIGURATION \_-X"S N\ 3

POLARI METERRESPONSE

+ _+ +

5 6 7 8

Fig. 11. Computed polarization ellipses of four target antennaorientations at 70 MHz, linear polarization.

1t

901

z0

F-

z

w 00

0

w

CD

4r4 5*

tL

2

35

Fig. 12. Polarization measurements as in Fig. 11 but for circularlypolarized waves.

lI

t

t

tL

4 8 10 15 20

FREQUENCY/ MHz

Fig. 13. Computed polarization ellipses for linearly polarizedwaves at frequencies between 2 and 20 MHz.

RUN NO. 3 4 RUN NO.

---i s v

_a l.52 m

258

9--i

t

GREEN AND TARVER: AUTOMATED PRECISION POLARIMETER

i900

z0

I-

z

0

4

45,

35e

Et9

+(X

+30 40

FREQ

Fig. 14. Same as Fig. 13 but at frequenl

rays of the vertically propagated]or 180° out of phase. Previousrwrsler;mfov e n r ;fFnT-n"4 C,4,cnioh

f)/ t to determine the precision of the polarimeter response.W - W Polarization fractions should compute to unity for a

completely polarized electromagnetic wave. Sets ofmeasurements on locally controlled signals have con-sistently shown polarization fractions with a mean ofapproximately 1.0, with a standard deviation near 0.1

+ + _

over the 2-70-MHz range.

U\A e~2~ 4w~, CONCLUSIONS- - - An automatic data-logging polarimeter for the 2-70-

MHz range, using a single-channel amplitude-measuring, t \ receiver has been developed and demonstrated. Polar-

ization measurements of axial ratio, orientation angle,+ +

7 polarization sense, and polarization fraction are consistent50 60 70

UENCY/ MHz with propagation theory. The use of the amplitude-cies between 30 and 70 MHz. measurement Stokes' parameter analysis provides total

power measurements of the incident wave. Encodingof the antenna measurements automatically in digital

modeasremintscaclltont format has eliminated the laborious tasks of extractingbmeasurements on the

data from analog records.poiarliiieter at a uiiiereiiu 16iiu S1au 6iiowil goo0u re6oumuof vertical-to-horizontal modes of propagation at 30 MHz.For frequencies above 30 MHz, the polarimeter responsesshow decreasing difference between the polarimeter-computed orientation angle and the target antennaorientation. Polarization measurements on the oblique-oriented target antennas show considerable deviationbelow 60 MHz because of the different characteristicsof the vertical and horizontal modes.

Since the polarization analysis as described by Cohen [5]permits the computation of the total received powerfrom any of the three orthogonal dipole-pair amplitudemeasurements, it is convenient to use the total powermeasurement and the polarization fraction computation

ACKNOWLEDGMENT

The authors wish to thank W. M. Sherrill for hishelpful comments and suggestions.

REFERENCES[1]

[21

[3]

[4]

J. D. Kraus, Antennas. New York: McGraw-Hill, 1950,pp. 464-485.H. G. Booker, V. H. Rumsey, G. A. Deschamps, M. L. Kales,and J. I. Bohnert, "Techniques for handling elliptically polar-ized waves with special reference to antennas," Proc. IRE,vol. 39, pp. 533-552, May 1951.S. Chandrasekhar, Radiative Transfer. London: Oxford Uni-versity Press, 1955, pp. 24-35.M. H. Cohen, "Radio-astronomy polarization measurements,"Proc. IRE, vol. 46, pp. 172-183, January 1958.

259