C A L I B R A T I O N O F A N T E N N A T E M P E R A T U R E F R O M

T H E R A D I O E M I S S I O N O F A B S O L U T E L Y B L A C K B O D I E S

W H I C H A R E S I T U A T E D A T F I N I T E D I S T A N C E

S. A. P e l y u s h e n k o , L . K. R o m a n y c h e v a , a n d K. S. S t a n k e v i c h

UDC 523.164:621.396.67

Correct ions to the antenna tempera ture are considered for calibration of received signals according to the radio emiss ion f rom absolutely blackbodies situated at finite distances.

The best accuracy in rad io -as t ronomy measurements of the intensities of d iscre te sources is achieved using the intrinsic radiation f rom an absolutely black body to calibrate the antenna temperature .

Absorptive bodies must be situated at a distance R >> D2/~ in order to maintain identity of antenna gain at infinity and a t the spot the standard is situated. This factor was noted in [1] in considering the effect of the displacement of the exciter f rom the focus along the symmet ry axis of the m i r r o r on the an- tenna gain. However, in that paper and in [2] the change in normalizat ion of the radiation pattern as a function of the distance R was not considered.

Fo r our subsequent analysis we shall make use of the normalizat ion of the pattern FR (0, (p) measured at the distance R and shall set the total radiated power equal to unity. If severa l bodies having tempera tures T n are located in the antenna field and a re situated at different distances R n f rom the aperture , then the antenna tempera ture Ta is equal to

S TnFnn(O' ~) d~

T a = x u" (1)

n S Fan (0, ~) de 4~

For Eq. (1) it is charac te r i s t i c that each body situated at a distance Rn is incorporated with its normalization. Since in the recept ion of radio emiss ion f rom the sky and emiss ion f rom a thermal standard the a r rangement of the other bodies near the antenna is not al tered, the cor rec t ion to the sky tempera ture due to calibration at a finite distance wil l be determined by the factor

S (0, ?) de S p (0, aQ A = % 4~ (2)

f an f (0, ,+) an' d d % 4x

and for the gain along the axis we have

A = , - ,, ,~:

d~O Fa (0) 4~

Foo (0) S FR (0, ~o) dU 4g

= OR (3) Goo '

w h e r e G R i s the antenna gain.

Scient i f ic-Research Radiophysics Institute, Gor 'ki i University. Translated f rom Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 13, No. 5, pp. 684-687, May, 1970. Original ar t ic le submitted April 16, 1969.

�9 1973 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without permission o[ the publisher. A copy of this article is available [rom the publisher for $15.00.

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| k (.e.,R}

U fl

o,"~ ., o.~

0'7 tx/8~ 0,7

I,,4,1 0,6 | [ [~12 0,5 .o , , , , i

U~ , ,~ o,5 ,,o ,,~ 2,0 ,Vc , :a ' )

" I [ Uni,ormdistr,lu lon

J , 0,5 ,,o , , 5 ~ ' , ' x

|Ta(RVTa(2)

O1 , , . , 0,5 - (o L5 2,o R~-/11 ~

Fig. 1 Fig. 2 Fig. 3

In order to calculate the radiat ion patterns of an antenna having a c i rcu la r aper ture with a radius a when a quadratic phase e r r o r ~ is present on the edge of the aper ture and the dis tances R f rom the plane of the aper ture vary, we shall make use of the resul ts of [3] according to which the antenna field is equal to

1 E (8, R)= e -:ike (~.ei(~-v/2) .f ,rp (~) j,, (u ~) e i~o-~)':2 ~dr., (4)

0 where y = l~2/R, u = ka sin0, r is the field distribution over the aperture. The presence of a phase e r r o r in the aper ture plane is equivalent to the substitution "y ' = y + 2~.

The rat io G ~ / G R is included in Eq. (2), and in order to find it one must integrate over the pattern within the l imits of the total solid angle 4v. The method of calculation on the basis of (3) does not allow the radiation pattern in the r e a r hal f -space to be found. Therefore, for purposes of normal izat ion we make use of the fact that

o = o ~ (1 - - ~ o ) , (5)

where G~2 ~ is the antenna gain in the stipulated solid angle ~2, while fl~0 is the scat ter ing outside the solid

angle ~0. We choose the angle corresponding to u = 12 as the solid angle ~20. In pract ice the sca t ter ing outside the principal beam of the d iagram (corresponding to Upr = 4) flpr = 0.2-0.3 [4] for pract ical ly all parabolic antennas. Consequently, with an e r r o r of at wors t 10% it may be assumed that the rat io between the gains is equal to

G~(4.':) .~. 0~o(.%)

Figure 1 shows the curves A(~, R) which charac te r i ze the rat io of the gains along the antenna axis. A compar ison of them with the analogous curves in [1] and for ~ = 0 in [2] shows that considerat ion of the normal izat ion of the pat tern at a finite distance I~ leads to a reduction of the ra t io G R / G ~ by 20% for the most frequently used distances 0.3D2/~ < R < 2D2/~. Under these conditions the gain rat io G R / G ~ on the axis pract ical ly coincided, unlike the case of [t], for uniform and Gaussian amplitude distributions over the aperture.

The calculations car r ied out for sources which close the antenna radiat ion pattern produced for uni- fo rm excitation of the aper ture at the levels S = 0.7, 0.5, and 0.3 show that the functions A(~, R) differ ve ry little f rom the gain rat io G R / G ~ on the axis. The onset of a noticeable difference between these curves s ta r t s for c losure of the radiat ion pat tern at the 0.1 level; the corresponding functions A(~, R) a re displayed in Fig. 2.

For a Gaussian distribution of ~(~) in the plane of the aper ture the curves for GR/G~o may likewise be used to calculate A(~, R) when the source closes the radiat ion pattern at the 0.5 level. It follows f rom

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the calculations which have been conducted that for negative e r r o r s ~ the functions A(~, R) have points R 0 at a finite distance at which A(~, R0) = A(~, oo). By placing the calibration standard at the distance R 0 one can avoid gain correct ions . When an antenna with parabolic ref lec tors is used the conditions c~ < 0 may always be satisfied by displacing the exciter f rom the focus. However, in the case of horn and ho rn -pa ra - bolic antennas the phase e r r o r s in the plane of the aper ture a re positive, and such a position of R 0 does not exist for the standard. Therefore, only one possibility remains: to introduce a correc t ion reflecting the difference between antenna gains at infinity and at the spot the absolutely black body is located in accordance with the calculation procedure expounded above.

In order to check the theory the following experiment was carr ied out: the antenna tempera ture due to the intrinsic radiat ion f rom the absorptive disk was measured for its displacement relat ive to the antenna along the axis over a distance 0.5 -< R ~ / D 2 ~ 2. The measurements were car r ied out at a wavelength = 15 cm with a horn-parabol ic antenna having an aper ture diameter D = 45 cm. The phase distribution was obtained in the plane of the aper ture , and the quadratic phase e r r o r on the edge of the aper ture was found to equal ~r/4. The absorptive standard in the form of a disk had a diameter d = 73 cm. In Fig. 3 the c rosses show the experimental values of the antenna tempera ture for various positions of the disk, normal - ized to the antenna tempera tu re corresponding to R = 2D2/~.. For simplici ty in calculation the antenna radiation pat tern was approximated by a Gaussian curve having a dispersion determined by the measured half-width of the pattern. Then the rat io between the antenna tempera tures for different values of the distance R f rom the disk is equal to

Ta(R) {ffP 11.18 (Od(R)/0o.5)]} ~ OR (~/4) T,(2D'~I),~ = {r [1.18 (0d(2D'l),)/0o, s)]}2 Goo(~/4) ' (7)

where @(x) is the probability integral.

The resul ts of the calculation according to Eq, (7) a re displayed by the points on the graph, which i l lustrate the ve ry good agreement with experimental data.

1~ 2. 3. 4.

L I T E R A T U R E C I T E D

K. S. Stankevich and N. M. Tseitlin, Radiotekhnika i Elektronika, 11, No. 3, 451 (1966). Centimeter-Wave Antennas [Russian translation],Vol. 1, Izd. Sov. Radio (1950). M. K. Hu, J. Res. Nat. Bur. Standards, 65D, No. 2, 137 (1961). N. M. Tseitlin, Application of Radio-Ast ronomy Methods in Antenna Engineering [in Russian], Izd. Sov. Radio (1966).

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