PROCEEDINGS OF THE IRE

Measurements of Solar Radiation and AtmosphericAttenuation at 4.3-Millimeters Wavelength*

ROBERT J. COATESt

Summary-Solar radiation and atmospheric attenuation weremeasured at 4.3-mm wavelength The sun was scanned with a radiotelescope consisting of a 10-foot precision paraboloid antenna (6.7-minute beamwidth) and a Dicke-type radiometer. Atmosphericattenuations were determined from the change in received solarradiation with changing elevation of the sun and from direct meas-urements of the thermal radiation from the atmosphere. The meas-ured attenuations at the zenith for clear sldes were between 1.6 and2.2 db.

At 4.3-mm wavelength, the sun (when it is free of sunspots)appears to be a uniform disk nearly one per cent larger than its opticalsize. From a large number of measurements over a period of 6months, the solar brightness temperature was found to be 7000 "Kwith an uncertainty of about 10 per cent. Sunspot regions are slightlybrighter than the quiet areas; the largest observed enhancement is2 per cent.

INTRODUCTIONN July, 1956, a program of absolute measurementsof solar radiation and atmospheric attenuation wasinitiated at a wavelength of 4.3 mm at the U. S.

Naval Research Laboratory. The observing wavelengthis in the atmospheric window between the 5-mm oxygenline' and the 1.7-mm water-vapor line,2 and conse-quently, there is considerable atmospheric attenuationfrom the wings of these lines. The sun and the moonare convenient signal sources for the measurements ofsuch atmospheric attenuation.

Theoretical studies of the sun3'4 have shown thatsolar radition at millimeter wavelengths originates inthe ionized solar atmosphere at a level a few thousandkilometers above the visible surface of the sun. This isthermal radiation from the ionized gas, and therefore,the results of the absolute measurements of this radia-tion can be used to calculate the characteristics (suchas the electron temperature) of the emitting region.

THE RADIO TELESCOPE

The radio telescope (Fig. 1) used for these observa-tions has a half-power beamwidth of 6.7 minutes of arc.The antenna reflector is an aluminum paraboloid 10feet in diameter with a focal length of 35.8 inches. This

* Original manuscript received by the IRE, October 3, 1957. Thispaper was chapter III in the author's Ph.D. dissertation for TheJohns Hopkins University, Baltimore, Md.

t Radio Astronomy Branch, U. S. Naval Res. Lab., Wash., D. C.I J. H. Van Vleck, "The absorption of microwaves by oxlygen,"

Phys. Rev., vol. 71, pp. 413-424; April 1, 1947.2 J. H. Van Vleck, "The absorption of microwaves by uncon-

densed water vapor," Phys. Rev., vol. 71, pp. 425-433; April 1, 1947.3 J. P. Hagen, "Temperature gradient in the sun's atmosphere

measured at radio frequencies,' Astrophys. J., vol. 113, pp. 547-566; May, 1951.

4 S. F. Smerd, "Radio-frequency radiation from the quiet sun,'Aust. J. Sci. Res. A., vol. 3, pp. 34-59; March, 1950.

Fig. 1-10-foot radio telescope for 4.3-mm wavelength.

was cast in one piece and machined to sufficient toler-ance for use at 4.3-mm wavelength.A small horn is used to feed the reflector. A specially

designed low-loss waveguide section connects the feedhorn at the focus of the reflector to the receiver on theback of the antenna. This 4.5-foot section consists of a16-inch tapered transition from 0.074X0.148 inch IDwaveguide to 0.170X0.420 inch ID waveguide, then along run of the large-size waveguide, followed by asecond taper down to the small waveguide. The meas-ured attenuation of this 4.5-foot waveguide section is1.3 db as compared to 5-db attenuation measured forthe same length of the small waveguide.The polar mount for the antenna is an old radar

pedestal, appropriately mounted. The hour-angle driveis controlled with a servosystem and the declinationdrive is operated manually.The 4.3-mm receiver on the back of the antenna is a

Dicke-type radiometer,' consisting of a superheterodynereceiver preceded by a calibrated attenuator and amotor-driven attenuator wheel (which modulates theincoming signal), and followed by an audio amplifier,a synchronous detector, and a recording meter. This

' R. H. Dicke, "The measurement of thermal radiation at micro-wave frequencies,' Rev. Sci. Insir., vol. 17, pp. 268-275; July, 1946.

122 January

Coates: Measurements of Solar Radiation at 4.3 MM

TOANTENNA

Fig. 2-Diagram of 4.3-mm radiometer.

arrangement is shown in the block diagram of theradiometer (Fig. 2) and in the photograph (Fig. 3).When an observation is made with the radiometer,

the signal from the antenna passes through the wave-guide switch and is modulated by the attenuator wheelat a frequency of about 29.3 cps. The calibrated at-tenuator is set at zero attenuation and the modulatedsignal passes through to the balanced mixer consistingof the hybrid ring and the matched pair of crystals.The output from the mixer goes to the IF amplifier,which has a center frequency of 30 mc and a bandwidthof 5.5 mc. The audio output from the detector stage ofthe IF amplifier is amplified and detected in the syn-chronous detector. The synchronous-detector output isrecorded on a Leeds and Northrop "Speedomax" re-corder.

During calibration, the receiver is connected to thegas-discharge tube noise source6 thPrough the waveguideswitch. This noise source was calibrated against amatched waveguide termination maintained at a uni-form temperature of 620°C.

MEASUREMENTS

The observational program was designed to obtainscans across the sun for determining the brightness dis-tribution, and to measure the atmospheric attenuationand the solar antenna temperatures for determining thesolar brightness temperature. When observing, the an-tenna was pointed ahead of the sun and locked in posi-tion, and the radiometer output was recorded con-tinuously as the earth's rotation carried the sun throughthe antenna beam. After the sun was past the antennaand the sky radiation had been recorded for a few min-utes, 40 db of attenuation was inserted with the attenua-tor to give a zero-input reference reading. The receiver

6 A. I. Reynard, "Precision Instruments for Calibrating Radiom-eters at 4.3 Millimeters Wavelength," Naval Res. Lab., Washington,D. C., Rep. 4927; May, 1957.

Fig. 3-4.3-mm radiometer.

was next switched to the gas-discharge noise source formeasuring the receiver gain. After the gain measure-ment, the receiver was switched back to the antenna,the antenna was set ahead of the sun, and the sequencewas repeated. In the middle of each sun scan, the sunwas photographed through the optical sighting telescopewith a 35-mm camera to record the path taken on eachscan. The measurements were started when the sun waslow in the sky and continued until the sun had passedthe meridian. The series of measurements was brokenonce or twice for a complete radiometer calibration;7several times during a sequence of measurements therecording of the sky radiation was followed by sev-eral measurements of the radiation from an ambientblack-body enclosure placed over the feed horn. Thisenclosure was a metal can lined on the inside with non-reflecting material. There was a small hole in the lid to

T The radiometer calibration procedure was as follows: the re-ceiver was switched to the gas-discharge noise source, and the re-ceiver attenuator was set to produce approximately a full-scale read-ing on the recorder. The output of the noise source was then at-tenuated in successive small steps by the calibrated attenuator be-tween the noise source and the receiver, and the receiver output wasrecorded for each step covering the range between the zero level andfull scale. A transcription of these readings gave a graph of input noisetemperature vs recorder reading.

1231958

PROCEEDINGS OF THE IRE

permit placement over the antenna feed horn. The walllining was selected and mounted so that the impedanceof the feed horn was the same with or without the cansurrounding it. This is important because a differentimpedance would cause an error in the recording of theradiation from the can with respect to the recordings ofthe sky and the sun.

ANALYSISThe power received from a thermal source usually is

given in units of antenna temperature T, defined8 as thetemperature of a matched termination for which theavailable power at its terminals, in a frequency bandbetween f and f+df, is equal to the received power P atthe antenna terminals; i.e., P = kTdf, where k is Boltz-mann's constant. Antenna temperature is a convenientunit because the radiometer is calibrated by replacingthe antenna with a matched noise source at a knowneffective temperature.At a given wavelength, the brightness of a source is

often specified in terms of a "brightness temperature,"defined as the temperature of a black body at the sourcelocation for which the brightness of the thermal radi-ation would equal that actually observed.When the antenna is pointed at the sun, the antenna

temperature Taun is given by

ATsun-= ag J -[touna + teaY + (1 --at)tsky]dQ

4r 47r

+ (1 -a)g (1)

where ag and tg are the transmission and temperature,respectively, of the waveguide between the feed hornand the receiver; A is the gain pattern of the antenna;a is the transmission of the atmosphere; t.u0 is thebrightness temperature of the sun; t, is the brightnesstemperature of the ground; tky is the effective tempera-ture of the atmosphere; and dQ is an element of solidangle. A, t8un, a, te, and tsky are functions of position.Radiation from radio stars and galactic background hasbeen neglected, because at wavelengths as short as 4.3mm this radiation is exceedingly small, as one can verifyby extrapolating the radio source spectra9 to shortwavelengths. To date, radio stars have not been de-tected at millimeter wavelengths.When the antenna is pointed at the sky, the antenna

temperature Tky is given by

T8k y [tea + (1 a)tsky]dQ + (1 ag)tg. (2)

In the series of sun scans just described, the antennawas fixed in position during each sun scan and a record-ing was made of both the sun and the sky at the same

8 J. L. Pawsey and R. N. Bracewell, "Radio Astronomy," OxfordUniv. Press, London, Eng., p. 21; 1955.

9 N. G. Roman and F. T. Haddock, "A model for nonthermalradio-source spectra,' Astrophys. J., vol. 124, pp. 35-42; July, 1956.

position. The antenna temperature T.., with the sunin the center of the antenna beam, and the antenna tem-perature TXk with only sky in the beam, were deducedfrom the records for each sun scan with the aid of thecalibration curve, gain measurements, and the ambientmeasurements. Thus, values of T... and Tsk, were ob-tained at many antenna positions starting at a largezenith angle and ending at the minimum zenith angleat the meridian.At each antenna position, a can be considered as con-

stant over the angle subtended by the sun; and therefore,subtracting (2) from (1),

ATsun- T8ky = a0a J - tgundQ = aga(sun

s.un 4r

where Ou. is the antenna temperature for the sun in theabsence of atmospheric and waveguide losses.

For a uniform clear sky and zenith angles z less than800, a can be expressed in terms of the zenith trans-mission oa0 by a =ao0secz. It follows that

log (T8un- T8ky) = sec z log ao + log (ag5sun).Thus the attenuation at the zenith (-10 log ao) is ob-tained from the slope of a plot of log (T8 - T8ky) vssec z, and the value of 0. is obtained from the ex-trapolated intercept at sec z = 0. A typical plot is shownin Fig. 4.

--

SUNRISE OBSERVATIONX - 4mm. 1 OCT 1956

0I ,I II IUU 0.5 I.U 1.5 Z.0 Z.5SEC

Fig. 4-Plot of log (T...- T8ky) vs sec z for October 1, 1956.

Atmospheric attenuation also was calculated fromthe magnitude of the thermal emission from the atmos-phere given in (2). With a narrow beam antenna thathas very low side lobes, such as used in this investiga-tion, the integral of the antenna pattern over the mainbeam and the first few side lobes is much larger thanthe integral over the remaining part of the 47r solidangle. The thermal radiation from the sky is relativelyhigh at X 4.3 mm because of the large attenuation.Therefore, for a first approximation, only the main beamand first few side lobes need be considered, and theatmospheric attenuation is essentially constant over

3.5

3.4

LOG(Tsun-Tsky)

3.

3.2

3.6.

124 January

Coates: Measurements of Solar Radiation at 4.3 MM

this small angle. With this approximation, (2) may bewritten

T8ky = a,(1 - aosec z)tsky + (1 - ag)tg. (3)

In practice, it is very difficult to determine the abso-lute value of Tky with high accuracy, because the radi-ometer output is affected by the impedance at theradiometer input. With a properly balanced mixer, awell-matched antenna, and a well-matched noise source,this effect is small but still not negligible. With the sunscans, T5un and T5k, were measured in succession, andthe impedance at the input of the radiometer was thesame for both measurements. Therefore the errors re-sulting from the impedance effect were the same andcanceled out in the reduction of the data when T8k, wassubtracted from Tsun-

In order to cancel the impedance error in the meas-urement of the radiation from the atmosphere, theblack-body enclosure at temperature t6 was placed overthe antenna feed horn and the recorded antennatemperature T. was subtracted from T.k,. SinceTc=agt+(I -ag)tg, subtracting T. from (3) gives

TC - T.k, = ag [tc - (1 - aosee z)tsky].

This equation was used to compute a0 from the meas-ured values. Since the major part of the absorptionoccurs near the ground, the effective sky temperaturetsky was assumed to be approximately the air tempera-ture near the ground.The atmospheric attenuation at the zenith, deduced

by both methods, and the values of the zero-loss antennatemperature for the sun are listed in Table I for severalseries of measurements made over a period of 6 months.Also included in Table I are results obtained from ameasurement of a moonrise.10 The measured verticalatmospheric attenuations for 4.3 mm were between 1.6and 2.2 db for clear skies.A few cloud observations, made by tracking the sun

as clouds passed over, indicate additional attenuationsof about 0.7 db for fair weather cumulus clouds. Furthercloud measurements are in progress and the results willbe reported at a later date.The average of the solar measurements gives 5605°K

for the observed solar antenna temperature, after cor-recting for atmospheric and waveguide attenuation. Inorder to convert this value to a solar brightness tem-perature, one must consider the directional character-

10 This moonrise observation was at a lunar phase of two daysbefore full moon. The procedure used for this observation was identi-cal to that described for the sun; i.e., repeated scans were madeacross the moon starting with the moon on the horizon and con-tinuing until it passed the meridian. The scans were asymmetricaland showed that at 4.3-mm wavelength the sunlit part of the moon'ssurface is brighter than the dark part. The antenna temperaturegiven in Table I was determined from the peak of each scan. Scansof the moon also have been made at a phase of 5 days before newmoon, and the asymmetry of these scans verifies that the sunlit cres-cent is brighter than the dark portion. These observations are con-tinuing and a more detailed analysis will be made after the comple-tion of measurements for all phases of the moon.

TABLE I

MEASURED ATMOSPHERIC ATTENUATIONSAND ANTENNA TEMPERATURES

Vertical Atmospheric Cor-Attenuation rected

Source Date A) Sunrise B) Atmos- Antennaand Moon- pheric Ra- em-

rise Measure- diation Meas- peraturements urements

Sun September 10, 1956 1.8±0.3 db 53300KOctober 1, 1956 1.9 ±0.1 2.0 ±0.2 db 5620October 12, 1956 2.2±0.3 5956November 15, 1956 1.6±0.2 1.7 ±0.3 5250December 4, 1956 1.6±0.2 1.8 ±0.3 5594February 12, 1957 - 1.9 ±0.2 5880

Moon November 15, 1956 1.7 ±0.3 1.8 ±0.3 2020K

Average O..=5605'K.

istics of the antenna. If the antenna were completelysurrounded by a source at a certain brightness tem-perature, then the antenna temperature would be equalto the brightness temperature. When the source doesnot completely surround the antenna, then the ratiobetween the antenna temperature and the brightnesstemperature is equal to the ratio of the integral of theantenna pattern over the source to the integral of theantenna pattern over 4r solid angle. The 10-foot ah-tenna at 4.3-mm wavelength has a beamwidth of 5 thediameter of the sun. Thus, the main beam and the firstside lobe are entirely on the Sun, and the rest of the sidelobes are off the sun.By considering the antenna pattern, the antenna tem-

peratures for the moon, and longer wavelength meas-urements with the Naval Research Laboratory 50-footantenna, it was estimated that the observed antennatemperature is about 20 per cent lower than the solarbrightness temperature. Therefore, dividing 56050 by 0.8gives a value of 70000 + 700°K for the 4.3-mm bright-ness temperature for the central region of the sun. Theuncertainty is due mainly to the estimate of the 20 percent factor.

THE SOLAR BRIGHTNESS DISTRIBUTION

Since July, 1956, numerous scans with the 4.3-mmtelescope have been made across the solar disk undervarious sunspot conditions. Fig. 5 shows a scan acrossan active sunspot region on February 18, 1957, in whichthe increase in radiation from the active area is quiteapparent. This is the largest sunspot enhancement ob-served at this wavelength. Scans across many othersunspots showed no detectable increase. Future researchwill investigate the characteristics of this enhancedradiation.Only scans made across areas free from sunspots are

usable for determining the brightness distribution forthe quiet sun. The best scans for this purpose weremade on February 12, 1957, and one of them is shownin Fig. 6(a). The path of that scan [illustrated in Fig.

1958 125

PROCEEDINGS OF THE IRE

6(b) ] was across the center of the solar disk, and there-fore it was well suited for determining the brightnessdistribution and the solar diameter at 4.3-mm wave-length.

SUN SCAN 18 FEB. 1957

X 4.3mm. 10 ft. ANTENNA

Fig. 5-A 4.3-mm scan across an active region onthe sun on February 18, 1957.

SUN SCAN 12 FEB. 1957

X *4.3mm. 10 ft. ANTENNA

(a)

(b)Fig. 6-(a) A 4.3-mm scan across a quiet region of the suII.

(b) Map of scan path showing positions of sunspots.

1.0-

RECEIVED POWER

0.5-

0-

Several theoretical sun scans were calculated for com-parison with the observations. This involved integratingthe antenna pattern over the sun [as set up in (1)1 atsuccessive positions of the sun relative to the antenna.Scans were calculated for a range of different solardiameters and brightness distributions. Fig. 7 shows acomparison between the observed solar scan, and onecomputed for a uniform sun equal in diameter to theoptical disk. This comparison indicates that the 4.3-mmsun is larger than the optical sun. The best fit to theobservations is obtained with a uniform disk one percent larger than the optical disk. The scan for thismodel fits the observed scan within the experimentaluncertainty over the entire curve. The agreement be-tween this calculated curve and the observed curve, andthe difference between it and the optical-disk curve,lead to the conclusions that the diameter of the 4.3-mmsun is 1.01 + 0.005 relative to the optical diameter, andthe brightness temperature distribution is essentiallyuniform. The average brightness temperature of any 7-minute diameter area does not differ from the rest of thequiet sun by more than one per cent.

Since the above observations indicate that at 4.3-mm wavelength the sun is a uniform disk with a bright-ness temperature of 7000°K and a diameter about oneper cent larger than the optical disk, the 4.3-mm radi-ation must originate in the lower chromosphere atheights less than 6000 km above the photosphere. Fromthese data it may be concluded that the electron tem-perature of the emitting gas is of the order of 7000°Kor less.

ACKNOWLEDGMENTThe author expresses his appreciation for the steady

encouragement and valuable advice given by Dr. D. E.Kerr, Associate Professor of Physics of The Johns Hop-kins University. Appreciation is also expressed to Dr.J. P. Hagen of the Naval Research Laboratory whooriginally suggested this area of research. Acknowledg-ment is made to A. E. Reynard for the development ofthe standard noise sources used to calibrate the 4.3radiometer and to S. Edelson who helped operate the4.3-mm radio telescope.

SCAN

SIZE

I lII-40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 50 35 40

SEPARATION OF SUN AND ANTENNA CENTERS (min. of arc)

Fig. 7.-The observed 4.3-mm sun scan compared to a calculated scan for a uniform sun equal in diameter to the optical disk.

126 January