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ISSN 0010 9525, Cosmic Research, 2014, Vol. 52, No. 5, pp. 393402. © Pleiades Publishing, Ltd., 2014. Original Russian Text © Yu.A. Kovalev, V.I. Vasil'kov, M.V. Popov, V.A. Soglasnov, P.A. Voitsik, M.M. Lisakov, A.M. Kut'kin, N.Ya. Nikolaev, N.A. Nizhel'skii, G.V. Zhekanis, P.G. Tsybulev, 2014, published in Kosmicheskie Issledovaniya, 2014, Vol. 52, No. 5, pp. 430439.

The RadioAstron Project: Measurements and Analysis of Basic Parameters of Space Telescope in Flight in 20112013
Yu. A. Kovaleva, V. I. Vasil'kova, M. V. Popova, V. A. Soglasnova, P. A. Voitsika, M. M. Lisakova, A. M. Kut'kina, N. Ya. Nikolaeva, N. A. Nizhel'skiib, G. V. Zhekanisb, and P. G. Tsybulevb
b

Astro Space Center, Lebedev Physical Institute, Moscow, 119991 Russia e mail: ykovalev@asc.rssi.ru Special Astrophysical Observatory, Russian Academy of Sciences, Nizhnii Arkhyz, Russia
Received December 16, 2013

a

Abstract--The results of a large number of the antenna radiometric measurements at bands of 92, 18, 6.2, 1.35, and 1.71.2 cm are presented by the data of the standard telemetry system of the Spektr R spacecraft. Both special sessions of calibration object observations in the mode of a single space radio telescope (SRT) operation and numerous observations of researched sources in the mode of the groundspace interferometer were used. The obtained results agree with the first results of Kardashev et al. (2013), i.e., within 1015% at bands of 92, 18, and 6.2 cm and 2025% at the band of 1.35 cm. In the main, the measurements for the eight subbands at wavelengths of 1.71.2 cm indicate a monotonic increase in the spectral system equivalent flux density (SEFD) of noise radiation with a frequency consistent with the calculated estimates for the discussed model. The sensitivity of the groundspace interferometer for the five subbands at wavelengths from 1.35 to 1.7 cm can be higher by a factor of 1.5, and for the three subbands from 1.35 to 1.2 cm lower by a factor of 1.5 than at the band of 1.35 cm. The SRT contribution to the interferometer sensitivity proportional to the square root of SEFD is close to the design one at the bands of 92 and 18 cm and decreases the design sensitivity approximately by a factor of 1.5 and 2 at the bands of 6.2 and 1.35 cm, respectively. These differences of imple mented values from the design ones were not significantly affected the scientific program implementation. DOI: 10.1134/S0010952514050074

INTRODUCTION The description of the Spektr R spacecraft, the space radio telescope (SRT), scientific equipment, and ground tests are given in [13]. The results of flight tests, the technique and the first results of the antenna measurements of the basic telescope parame ters using the radio astronomy methods in the radio metric mode at the bands 92, 18, 6.2, and 1.35 cm are presented in [46] for the effective area, the noise temperature, the radiation pattern, pointing error at a source, etc. In this paper, we report new results of periodic tests of the basic SRT parameters in flight obtained in 20112013. The antenna measurements are per formed both in special sessions of observations of cal ibration astronomical objects and during the current sessions of scientific observations in the mode of the groundspace radio interferometer. The results of the antenna measurements are first presented for eight subbands of the frequency band of 1825 GHz using in the mode of multifrequency image synthesis in further operation with the radio interferometer. To calibrate these measurements over flux, besides the known extended primary calibration sources (Cassiopeia A, Cygnus A, Crab, Virgo A), sev eral quasi point for SRT strong variable extragalactic

objects (3C 84, 3C 273, 3C 279) have also been used, the spectral radiation flux density of which were mea sured on close dates relative to known secondary cali brators on the RATAN 600 radio telescope of Special Astrophysical Observatory (Nizhnii Arkhyz, Russia) and the 100 m telescope of the Max Planck Institute for Radio Astronomy (Effelsberg, Germany). 1. MEASUREMENTS The measurements of the antenna parameters are based on the relative measurements of spectral system equivalent flux density (SEFD) of the noise radiation Fsy s [Jy] relative to astronomical calibrators. The equivalent noise temperature of the system (radio tele scope) Tsys was measured relative to the antenna tem perature and considered to be known for onboard noise generators (in degrees K) that belong to each sci entific receiver. The onboard scientific complex includes four radio astronomical superheterodyne receivers at bands of 92, 18, 6.2, and 1.35 cm. The receiver at the band of 1.35 cm also provides a signal that receives from eight switchable subbands at 1.71.2 cm by choosing one of the subbands with corresponding commands. Units of input low noise amplifiers (LNAs) of receivers for all

393

394

KOVALEV et al. CasA/ch1 CasA/ch2 Crab/ch1 Crab/ch2 CygA/ch1 CygA/ch2 VirA/ch1 VirA/ch2

(a) 4.0 (ch1) = (ch2) = (ch1) 3.5 (ch2) 3.0 2.5 2.0 1.5 1.0 2011.5 2012 2012.5 2013 2013.5 2014 2.5 2011.5 2012 21 200 Jy +/2% 19 400 Jy +/5% = 230 K+/2% = 210 K+/5%

(b) (ch1) = 3180 (ch2) = 3260 (ch1) = 47.2 (ch2) = 48.4 Jy +/2% Jy +/2% K+/2% K+/2%

[108.7 K]

Fsys [kJy]; Tsys [14.9 K]

4.5 4.0 3.5 3.0

F

sys

[10 kJy]; T

sys

2012.5

2013

2013.5

2014

Fig. 1. SRT parameters measured using calibrators at the bands of 92 cm (a) and 18 cm (b) in 20112013. Channel 1 (ch1) cor responds to receiving left circular polarization, channel 2 (ch2) to right.

bands, except 92 cm, are installed in open space on a cold plate cooled to a temperature of 130 K by radia tion. Each receiver consists of two identical channels on which the input from the antenna through the antenna feed assembly (AFA) with polarization split ter, radiation arrives in the left and right circular polar izations. Each channel has two parallel outputs, i.e., (1) a radiometric output with the detected signal, which arrives at the spacecraft telemetry system and is used in the antenna measurements, and (2) an inter ferometric output with a signal at intermediate fre quency, which, after subsequent transformation, is used in the groundspace interferometer operation. Special sessions of observations of calibration objects were usually carried out in the mode of the sin gle telescope operation. Then, after buffer recording and storing in the onboard memory, the telemetry data were transmitted to the Earth during the day via the narrow beam antenna by the service spacecraft telem etry radio channel. When interferometric observing researched sources the telemetry system data are sequentially placed in the headers of each frame of the data stream for the interferometer and transmitted online to the Earth through the narrow beam antenna with the diameter of 1.5 m via the scientific high data rate radio channel. This makes it possible to allocate the telemetered radiometric signal from the interfero metric data stream from SRT. In this manner, in this work, the results of the antenna measurements were obtained for sources studied with the interferometer in the scientific programs. The results of all measure ments and analysis are summarized in Figs. 13 and Table 14.

2. DISCUSSION OF MEASUREMENTS 2.1. The 92 , 18 , 6.2 , and 1.35 cm Bands A measurement analysis shows that almost all basic antenna parameters vary from measurement to mea surement. We associate the main reason for these vari ations with variations in the temperature conditions of the antennafeeder tract and the receiver. Physical temperatures of the elements of antennafeeder tract and LNA on the cold plate can vary due to variations in the angle between the directions to the Sun and the measurement object from session to session. The closer the angle to the design boundary (110°) of the permitted SRT operation, the larger the expected deviations of the physical and noise temperature from their average values. In this case, the contribution to the equivalent noise temperature of the system should be varied versus the losses in the antenna feeds with polarization splitters. Therefore, significant variations in the noise equivalent temperature TNS of the calibra tion signal should also be expected. This signal from the internal noise generator arrives at the receiver tract at the LNA input and is reduced to the recalculation of the telescope input through all elements of the antennafeeder tract. Therefore, to further simplify the analysis, the con dition of the constancy of the mean values TNS and the effective area Aeff was assumed to be fulfilled. Then, all of their real variations automatically refer to variations in Tsys. Note that this procedure does not affect the correctness of the astronomical calibration of the measurements using the parameter Fsys (SEFD) depending on the ratio of Tsy s Aeff . In this case, the results presented below for the mean square devia tions Tsys and Fsys for calibration and studied sources,
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THE RADIOASTRON PROJECT: MEASUREMENTS AND ANALYSIS (a) 250 Tsys_SRT [K] 200 150 100 50 0 1.XI 11 1.III 12 1.VII 12 1.XI 12 1.III 13 1.VII 13 18 1.35 92 6.2 cm cm cm cm Tsys_SRT [K] (b) 250 200 150 100 50 0 1.XI 11 1.III 12 1.VII 12 1.XI 12 1.III 13 1.VII 13

395

Fig. 2. SRT parameters measured using studied sources in 20112013: (a) channel 1 for right circular polarization at the band of 1.35 cm, left for remaining bands; (b) channel 2 for left circular polarization at the band of 1.35 cm, right circular polarization for the remaining bands.

SEFD = 2 k T_sys /A_eff [kJy]

which do not exceed approximately 13%, can be used to substantiate this condition. Within the measurement errors, the obtained results for the mean values of the system temperature Tsys and the flux density Fsys (SEFD) at bands of 92, 18, 6.2, and 1.35 cm (Figs. 1, 2 and Tables 1, 2), taking into account the various contributions of sky back ground, which agree for both the calibration and researched sources, as well as with the first results pre sented in [5]: within (2025)% at the band of 1.35 cm and (1015)% at other bands. Approximately half of these values can be associated with slow systematic evo lution of the parameters including their calibration. A significant contribution to the observed spread of values Tsys relative to the mean can give variation of the LNA mismatch with the AFALNA input tract and variations associated with that of the LNA noise coef ficient, which depend on the physical temperature of AFA and LNA (usually, there is no decoupling at the LNA input to reduce the noise temperature of the receiver). 2.2. The 1825 GHz Band The band is intended for use in the mode of the mul tifrequency interferometer synthesis and consists of the eight following subbands (with indicated central fre quencies) spaced one after the other at 960 MHz [5]: F 4 (18 392 MHz), F 3 (19 352 MHz), F 2 (20 312 MHz), F 1 (21 272 MHz), F0 (22 232 MHz), F1 (23 192 MHz), F2 (24 152 MHz), F3 (25 112 MHz) (Fig. 3). Values of the center frequencies may be 4 MHz more or less than indicated depending on the given mode of operation of the scientific equipment. The measurement results of Fsys (SEFDSRT) in these subbands shown in Fig. 3, and the estimate of the interferometer sensitivity in Table 3 confirm the theo retically expected monotonous "course" of SEFDSRT
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and the interferometer sensitivity with increasing fre quency except, perhaps, of their behavior at the extreme frequencies, near 18 and 25 GHz. The sensi tivities given in Table 3 are calculated according the known formula [5]

GBT SR T

=b

SEFDGBTSEFD 2 IF t

S RT

,

(1)

55 50 45 40 35 30 25 20 4 3 1 2 1 0 Number of band F 2 3

Fig. 3. Results of measurements of the SRT system equiv alent flux density (SEFD) for eight subbands from F 4 to F 3 at frequencies from 18.4 to 25.1 GHz for the 3C 84 galaxy in 20112012. Signs with measurement errors are the data for channel 1 (right circular polariza tion) at the left of vertical line with the number of band F and for channel 2 (left circular polarization) at the right. Solid curve is the calculated estimate in the model of phase distortion.

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Table 1. Results of mass measurements (rows 1.1 2.2) and calculated estimations (rows 3.1 3.12) when observing the cal ibration and studied sources in the left (LCP) and right (RCP) circular polarizations in 20112013 1.35 cm Parameter LCP; RCP 1. Calibrators 1.1. Tsys, K 1.2. Fsys, kJy 2. Other objects 2.1. Tsys, K 2.2. Fsys, kJy 3. Calculation of T
sys

6.2 cm LCP; RCP 133 ± 17; 10.5 ± 1.1; 147 ± 8;

18 cm LCP; RCP 47.2 ± 1.0; 48.4 ± 1.0

92 cm LCP; RCP 230 ± 5; 210 ± 11

98 ± 13; 82 ± 11 36.0 ± 3.6; 30 ± 3.0 127 ± 8; 100 ± 10 and F

3.18 ± 0.06; 3.26 ± 0.07 21.2 ± 0.42; 19.4 ± 1.0 41.0 ± 1.0; 43.5 ± 4.0 145 ± 15; 147 ± 15

46.7 ± 3.0; 36.8 ± 3.7 11.6 ± 0.6;
sys

2.76 ± 0.27; 2.93 ± 0.27 13.3 ± 1.4; 13.5 ± 1.4

3.1. Transmission coefficient: Cable K 3 t AFA K 2 t
2 3

0.99/157 0.76; 0.84/175 0.98/200 45/140 61; 55 2 56; 34 4 3 126; 98 46.4; 36.1

0.94/157 0.68/175 0.98/200 26/140 42 15 84 4 3 148 11.7

0.95/157 0.95/175 0.98/200 15/140 17 8.9 9.4 4 3 42.3 2.85 3+5 42.3 + 5 3.18

0.98/233 0.83/175 0.98/200 39/290 49 6 36 4 3 + 50 98 + 50 13.6 3 + 120 98 + 120 19.5

Antenna K 1 t1 3.2. Trec t 4, K 3.3. Trec, K 3.4. Tcable, K 3.5. TAFA, K 3.6. TA, K 3.7. Tsky , K 3.8. Tsys, K 3.9. Fsys, kJy Calibrators: 3.10. Tsky, K 3.11. Tsys, K 3.12. Fsys, kJy

Measurements of calibrators at the bands of 1.35 and 6.2 cm are given for 20112012. Errors of the scale of spectral flux density are not included. In rows 3.33.6 and 3.7 (3.10), we present estimates of contributions in Tsys from noise temperatures of receiver Trec, cable (waveguide at the band of 1.35 cm) Tcable, antenna feed assembly TAFA, antenna TA, and sky background Tsky, respectively.

where b = 1/0.637, SEFDGBT = 23 Jy (for the HPAO radio telescope at Green Bank), IF = 16 MHz is the band of recorded frequencies, t = 5 min is the time of signal integration. Depending on the operating mode of the interferometer, signal recording is also possible at the band IF = 32 MHz [5]. The value IF = 16 MHz is used for uniformity with [6]. Based on the data in Fig. 3 and Table 3, it is possible to take interferometric measurements at five long wave subbands from F 4 to F0 with asensitivity of no lower than in F0 at a frequency of 22 GHz (with a wave length of 1.35 cm). At three short wave subbands F1, F2, and F3, the sensitivity can be lower than in F0 by a factor of 1.5 because of the strong contribution of the phase errors at wavelengths less than 1.35 cm. This

wavelength is close to the so called minimum design wavelength of the telescope use min (1620) 18 = 1.39 cm at the design value = 0.77 mm (for details, see [5, 810] and chapters 3.2 and 3.3 further). 3. NUMERICAL INTERPRETATION OF THE MEASUREMENTS RESULTS 3.1. Equivalent Noise Temperature of SRT System Tsys To explain the measured values Tsys, we numeri cally estimate the parameters of the antenna, antennafeeder system, and receivers that affect Tsys. Usually, the SRT system in each of the polarization channels can be represented as a block diagram of four
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THE RADIOASTRON PROJECT: MEASUREMENTS AND ANALYSIS Table 2. Basic SRT parameters according to [5] and mass measurements of F circular polarizations in 20112013 1.35 cm Parameter LCP; RCP SRT in flight, 20112013: LCP; RCP LCP; RCP
sys

397

and T

sys

in the left (LCP) and right (RCP) 18 cm 92 cm LCP; RCP

6.2 cm

1. (

0.5

± 5%) (0.5 ± 5%)
2

6.0 в 13 7.5 0.1 127; 100 46.7; 36.8 368 1.2 ± 0.2 <1.5 2.5

25 35 0.45 147; 11.6; 78.9

72 41 0.52 41.0; 43.5 2.76; 2.93 67.3

6°.1 30 0.38 145; 147 13.3; 13.5 92.0

2. Aeff ± 10%, m

3. AE = Aeff Ageom ±10% 4. T
sys

± 13%

5. Fsys ± 10% (SEFD), kJy 6. Amplification, Jy/K 7.
S

8. S 9. P 10.
SVLB I

, mJy (at t = 5 min; = 16 MHz)
0.5

17; 15 1.29 в 2.80

5; 1.17

3; 3 1.16

14; 14 1.16

11. D = (

0.5) D/

In rows 111, we present the width of the main lobe of the radiation pattern at half power (1); the effective area (2); aperture efficiency (3); system equivalent noise temperature (4); system equivalent flux density (5); telescope amplification (6); systematic error when scanning the sky area over two coordinates (7) and (8) after entering constant correction (9) in pointing the telescope; sensitivity of the interferometer SRT Green Bank Telescope by (1) and [6] (10); the ratio of measured width to ideal width /D of the main lobe of the radiation pattern (11).

sequential units [5], i.e., (1) an antenna, (2) an antenna feed assembly (AFA) with an input polariza tion splitter on the left and right circular), (3) a VHF cable/waveguide that connects units (2) and (4), and (4) a receiver with input a low noise amplifier (LNA). Then, the equivalent noise temperature Tsys reduced to the input of this system can be written as follows: Tsys = Tsky + T1 + T2L1 + T3L1L2 + T4L1L2L3, (2) Ti = ti(Li 1), Li 1/Ki , i = 1, 2, 3. (3) Here, Tsky is the antenna temperature of the sky at the antenna input; Ti is equivalent noise temperatures of four units reduced to the input of own unit, including the antenna (i = 1), AFA (i = 2), cable (i = 3), and receiver (i = 4); and ti , Li, and Ki are the physical tem perature and coefficients of losses and power transmis sion for ith unit, respectively. Each summand in (2) reduces (recounts) the unit noise temperature to the antenna input, i.e., to the input of the entire SRT system and, thus, allows one to estimate the contribu tion of the corresponding unit in the complete noise temperature of the radio telescope system. In this case, to simplify it is assumed that the losses Li have only
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active component, and all units are perfectly matched with each other. Note that AFA contributes to three out of five sum mands in (2) (due to difference of L2 = 1 K 2 from the ideal case of the absence of losses, when L2 is equal to
Table 3. Estimate of sensitivity GBT SRT of the interferom eter SRTGreen Bank Telescope for 8 subbands Band 1. 2. 3. 4. 5. 6. 7. 8. F F F F F F F F 4 3 2 1 0 1 2 3 Frequency, GHz 18.392 19.352 20.312 21.272 22.232 23.192 24.152 25.112

SEF DSRT , kJy
26 28 31 34 37 41 46 51

1

GB T SRT

,

mJy 12 13 14 14 15 16 16 17

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KOVALEV et al.

Table 4. Typical values of losses, AE, and Aeff estimated by the method for reflectory antennas [8] Parameter 1. Aeff = AEA
geom,

1.35 cm 21

6.2 cm 36 0.46 0.96 0.85 0.834 0.976 0.96 0.935 0.773

18 cm 39 0.50 0.96 0.90 0.834 0.997 0.96 0.935 0.773

m2
2

2. AE = 12479101 2.2. 2 (at absorption) 2.3. 4 (at overradiation)

0.28 0.96 0.85 0.834 0.598 0.96 0.935 0.773

2.1. 1 (losses at reflection)

2.4. 7 (at rms mirror error) 2.5. 9 (at shading from AFA) 2.6. 10 (at scattering on four rods) 2.7. 12 (at radiation nonuniformity)

one). Therefore, losses in AFA are the most consider able losses when forming the overall noise telescope temperature. Lower values of L2 are obtained when the matching calculated and measured noise telescope temperatures are close, (within approximately 10%) to typical values in ground feeds of this type and caused by the compactness and coaxiality of feeds, as well as their association with polarization splitters in united four frequency unit. Additional losses in AFA at the band of 1.35 cm can occur when formed and propa gated in higher types of waveguide modes due to the increased diameter of the circular input waveguide (to provide the requirement for feed operation in the extended frequency band at 1825 GHz needed to synthesize the interferometric mode of the frequency). Usually, the physical temperature in the real ses sions of radio astronomy observations with SRT were supported by the thermal control system within t 4 = 130150 K for LNA on the cold plate and t2 = 150 200 K for AFA using radiative cooling of the cold plate. For numerical estimates of the values in (2) and (3), for all bands, we take the following: t 4 = 140 K (t 4 = 290 K for the band of 92 cm), t2 = 175 , t3 = (t 2 + t 4 ) 2 , t1 = 200 , Tsky = 3 K, and K1 = 0.98 (the design value). Then, for these values and the val ues of other parameters, depending on the band, as discussed below, we obtain estimates of Tsys and the corresponding contributions from the receiver, ele ments of antennafeeder tract, and sky background, which are summarized in Table 1. 3.1.1. The 92 cm Band Tsys (K2 = 0.83; K3 = 0.98; T4 = 39 K) = 3 + 4 + 36 + 6 + 49 = 98 K. Here and below, five numerical sum mands correspond to the contributions from the five summands in (2). It can be seen from here that the

main contribution to the system temperature without the Galactic background makes contributions from AFA (third summand, 36 K) and LNA (fifth summand, 49 K). Assuming that the difference of the measured system temperature (Table 1) and this one is mainly determined by anisotropic radiation of the Galactic background, we obtain Tsky 50 ; Tsys 150 K for the researched sources in the interferometric sessions; and Tsky 120 , Tsys 220 K for calibrators. To test this hypothesis, a detailed analysis is required that takes into account the individual observational conditions. 3.1.2. The 18 cm Band Tsys (K2 = 0.95; K3 = 0.95; T4 = 15 K) = 3 + 4 + 9.4 + 8.9 + 17 = 42.3 K. Due to the relatively low losses, the LNA noise, cables, and AFA (summands from fifth to third) make the main contributions. The small difference between measured Tsys when observing calibrators and other objects can be referred to the cor responding background excess near the Galactic plane because the most studied sources are extragalactic. 3.1.3. The 6.2 cm Band Tsys (K2 = 0.68; K3 = 0.94; T4 = 26 K) = 3 + 4 + 84 + 15 + 42 = 148 K. It was noted in [5] that, in this band, there is an approximately twofold excess of the mea sured noise temperature over the expected value. It can be seen that the measured value can be formally explained by increasing active losses in AFA over the design. The measurements for calibrators and other objects coincide within errors. However, taking into account that the stable operation in flight was found to only be possible at separate operation with channels of left and right polarizations (otherwise both channels were in the off scale level due to the self excitation of one or both channels [5]), a mechanism is also possi
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399

ble at which, because of the temperature sensitivity of the LNA and AFA characteristics (with polarization splitters) when cooling from 300 to 130150 K, during flight, the coordination of LNA and AFA with the tract worsened and reactive losses and LNA noise coefficient increased such that the operating conditions of one or both channels were found to be close to the conditions of self excitation. However, the operation with chan nels was still individually stable. 3.1.4. The 1.35 cm Band Tsys (K2 = 0.84; K3 = 0.99; T4 = 45 K) = 3 + 4 + 34 + 2 + 55 = 98 K is for channel 1. Tsys (K2 = 0.76; K3 = 0.99; T4 = 45 K) = 3 + 4 + 56 + 2 + 61 = 126 K is for channel 2. As before, to explain the average measured values Tsys, it is sufficient to admit the presence of active losses in AFA with the average values of the AFA transmission coefficient indicated here and in Table 1 with other variables that affect Tsys being fixed. In the general case, the reactive losses, variations in the LNA noise coefficient and increases the active losses L3 = 1/K3 due to a reduced conductivity of the coating of waveguide walls over time should also be taken into account. The spread of individual measurements rela tive to the average is naturally obtained by varying physical and noise temperatures, as well as other parameters that enter into ratios (2)(3). Individual variations in these parameters depend on the physical temperature of the elements of the antennafeeder tract, i.e., on the conditions of temperature control, and, therefore, are primarily determined by variations in the orientation of the space radio telescope relative to the Sun in individual observational sessions. The difference in the measured average values Fsys and Tsys for calibrators and other objects (about 2025%, see Table 1), except for measurement errors, can include the effect of different temperature conditions for observations of these objects on average. 3.2. Effective Area and Radiation Pattern The effective area Aeff at wavelength is associated with so called effective solid angles A of the antenna radiation pattern, beam of main lobe of the radiation pattern, and lobe outside the main lobe by known ratios as follows:

A =

4

D(, )d =

beam

+

lobe

= 2 Aeff ,

(4) (5) (6)

beam

=

beam

D(, )d k00.50 5, =

lobe

lobe

D(, )d ,

beam lobe + = 1. A A
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(7)

In (4), (5), and (6), the radiation pattern D(, ) is integrated over solid angles within 4, of the main lobe and outside the main lobe, respectively, lobe = 4 - beam; 0.5 and 0.5 is main lobe width at half power for mutually perpendicular directions and , and the coefficient k0 = 11.15 depends on the shape of mirror irradiation (k0 = 1 at the uniform dis tribution of the electric field over the aperture, k0 = 1.13 at the Gaussian distribution [7]). The first sum mand in (7) is usually designated as the coefficient of radiation pattern using and the second is designated as the coefficient of radiation scattering outside the main lobe. One should note the rather common mistake even among specialists according to which the measure ments of the main lobe can supposedly yield the value of the effective area. In fact, from (4)(7), the only correct conclusion is that, without knowing informa tion on the portion of radiation dissipated by the antenna in the effective solid angle lobe (as in this case), it is not possible to do this correctly. We estimate values of the SRT effective area, which can be expected for typical accepted phase errors in the antennafeeder system. For this, we consider the aperture efficiency AE = Aeff Ageom , where Aeff and Ageom = 75.8 m2 are effective and geometric areas of the SRT mirror aperture, respectively, and we use the AE representation through seven main of twelve usually used coefficients [7, 8], each of which describes one of the typical causes of area losses for reflector antennas (see rows 2.12.7 in Table 4; we assume that the remaining five coefficients are equal to 1). Comparing the obtained typical estimates of the effective area and AE shown in Table 4 with the results of measurements (Table 2), it is seen a good agreement for the bands of 6.2 and 18 cm. The difference between the typical design value of 21 m2 and the measured value at the band of 1.35 cm is connected with addi tional phase errors in the mirror aperture, an analysis of possible causes of which is presented in our paper [5] and will be continued below. The typical AE estimate for the band of 92 cm was not carried out, since the ratio of wavelength to the diameter of the mirror is not low enough for the correctness of using values of the typical coefficients, and the reliability of this estima tion does not seem high. Flight tests of the RadioAstron telescope [4, 5] showed agreement between the basic measured char acteristics with the design characteristics at the bands of 92 and 18 cm and their difference from the design characteristics for the equivalent noise temperature of the system at the band of 6.2 cm and for a width of the main lobe and the effective area at the band of 1.35 cm. At the minimum wavelength of 1.35 cm of design using the space radio telescope the main lobe of the radia tion pattern was found to be considerably asymmetric (wider by a factor of 2 than the design value in one of the mutually orthogonal sections) that indicated to the

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corresponding errors of the phase distribution of the field in the antenna aperture. As a consequence, these phase errors led to a decrease in the effective area and, as a result, to an increase in SEFD and a decrease in the SRT and interferometer sensitivities [5]. Further measurements and analysis, on which we will report in this paper, confirm these results. 3.3. Model of Phase Distortions One possible reason for these phase distortions is considered in [5], i.e., the system astigmatism due to the features of the phase feed radiation pattern. Another reason is estimated here as follows: astigmatism caused by a slight variation in the SRT mirror shape, which in the first approximation transforms the para bolic mirror with the circular aperture of diameter D and focal length F into a slightly elliptical aperture with the principal axes of the ellipse D1 and D2 close to D, and corresponding centers of focusing F1 and F2 in mutu ally orthogonal sections. This deformation of the mir ror shape seems possible if residual stresses in tension for rods to 27 hard mirror lobes are various and exceeds the design characteristics. It can be expected that stronger tension leads to smaller profiles of the quasiparabolic surface in the corresponding sections of the mirror with a shift in the centers of focusing in the directions from the mirror. To simplify the numerical estimates in any sections that contain the mirror axis, we propose to maintain the axis position and the parabolic profile of the cross section with the design ratio a = F/D. Then, the vari ations in the aperture size in this cross section from D to D1(D2) leads to a mismatch of the focus F with F1(F2) in this cross section, i.e., to astigmatism of the mirror, and the feed fixedly installed on the Earth on the calculated focus F is found to be shifted in flight relative to F1 and/or F2 that for the system of 27 lobes give the total phase errors in the aperture and the broadening of the telescope radiation pattern. Let us consider this effect quantitatively using the results of Kuhn's monograph [9] in order to associate the maxi mum quadratic phase error at the edge of the para bolic mirror with the feed shift from focus along the focal axis at wavelength :
1. = 4 1 + (4a)2

(8)

According to [5], in (8), we assume that 1.5, = 1.35 cm, a = 0.43 (the design value for SRT), as well as taking into account for this case = F = aD, F F1 - F2, D D1 - D2, D2 = 10 m, we obtain 2.0 cm, D = /a 2.0/0.43 4.7 cm and the eccentricity E of the ellipse E = D1/D2 10.047/10 1.0047. Thus, under these assumptions, a small defor mation of the SRT mirror shape that transforms the circular aperture with a diameter of 10 m into elliptical with eccentricity E 1.0047 (the major axes of the

ellipse are equal to about 10 m and 10.047 m), can cause astigmatism of the mirror that leads to the observed features of the measurement results of the SRT characteristics at the band of 1.35 cm. In eight subbands, for the mode of frequency syn thesis, we can expect smooth variations in the shape of the main lobe of the radiation pattern and the tele scope effective area that correspond to variations of phase error (8) from 1.1 to 1.6 at the fre quencies of 1825 GHz. For the remaining standard bands of SRT ( 6.2 cm), the phase error (8) is the value /3.3 close to /4, which is generally considered to be the permissible phase error. Let us numerically estimate the influence of phase errors in the antennafeeder system to variations in the effective area Aeff at frequencies of 1825 GHz. In this case, using typical values of the area equal to 21 m2, according to Table 4 and the product of three coefficients k1(), k2(), and k3(), we perform the following: Aeff /A0 = k1()k2()k3. Here, A0 = 21/7 = 35 m2 corresponds to a typical effective area in the total absence of phase distortions (7 = 0.598 from Table 4); k1() = exp[(4/)2] [8] takes into account the known contribution from random phase errors at the root mean square deviation of the mirror sur face profile from the ideal parabolic mirror (k1() = 7 = 0.598 at = 1.35 cm, = 0.77 mm); k2 = [( = 0)( = )]1/2 at () = 6.55(1.01 0.2 cos )/(5.3 + 2) [10] gives an estimate of the contribution from the effects considered above with quadratic phase error (8) of the mirror. Here, k3 0.73 is taken as the value of the contribution from the phase error of mirror irradi ation, including the difference of the AFA phase radi ation pattern from ideal (see in detail [5, 8, 10]). Then, at = 1.35 cm, Tsys = const = 100 K, the design value = 0.77 mm, 1.5, we obtain k2() = 0.49, Aeff = 21k2()k3 m2 = 7.5 m2, SEFDSRT = 37 kJy and numerical dependence of SEFDSRT on the fre quency, which is shown in Fig. 3 by a solid line. It can be seen that the calculated estimate agrees with the measurements for all subbands except extreme within accuracy. The deviations of calculated values relative to those measured at the extreme frequencies near 18 and 25 GHz can be explained by the violation of the assumption Tsys = const in these subbands. The corre sponding estimates of the expected interferometer sensitivity for eight subbands are shown in Table 3. Thus, the results of the antenna measurements in eight subbands at frequencies of 18 to 25 GHz (the noise temperature of the system, the effective area, the system equivalent flux density (SEFD), and their dependence on the frequency) can be concordantly explained in the model of phase distortion developing the model considered in [5]. According to our estimates of loss coefficients (see Table 4) by the known method [8], the typical effective area at the band of 1.35 cm should be close to 35 m2 at the absence of any phase distortions and to 21 m2 at the presence of only design phase losses k1 of the area
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due to the random errors of the mirror surface; in this case, the aperture efficiency is about 0.45 and 0.27, respectively. In the model, coefficient k2 0.49 reduces the typ ical design area of 21 m2 by a factor of two due to astig matism and the quadratic phase error of the mirror surface, assuming that the circular aperture of the mir ror with diameter of 10 m was the quasi elliptic with the principal axes of 10 m and 10.047 m, and the coef ficient k3 0.73 decrease further by a factor of about 1.5 due to the phase distortions of mirror irradiation similar to [5]. As a result, the effective area of 35 m2 (at 7 = k1 = k2 = k3 = 1) or 21 m2 (at 7 = k1 = 0.598) decreases to the measured value Aeff 7.5 m2, and an asymmetry of the main lobe of the radiation pattern arises due to the system astigmatism and the total phase errors in the antenna aperture. Similar phase errors and losses in the antenna feeder system distorting the radiation pattern and reducing the effective area, the cases of the self excita tion of the receiver are a typical, well known situation for ground based telescopes, especially at the begin ning of operation at short wavelengths close to the minimum wavelength of the telescope operation. The reasons for these effects are usually partially excluded by additional surface adjustment and correction of mirror exposure, corrections of focusing, debugging or replacing elements of the antennafeeder system and the receiver, and improving their coordination with each other. Formally, in the discussed model, it is possible to reduce astigmatism caused by the deviation of the par abolic mirror shape from design by reducing the resid ual forces of lobe tension through the cable and a rod of mirror opening mechanism using commands from the Earth. However, the utility of this operation is questionable up to finishing observations on the main priority scientific goals. The main reasons for doubt are as follows: (1) upon failure, there is no guarantee that the antenna will be returned to the previous position; (2) we must perform new labor intensive antenna measurements; (3) a gain in the effective area can be accompanied by losses, e.g., in pointing the antenna, which today are nearly absent, also because of the broadening of the main lobe of the radiation pattern. New inevitable errors can partially or completely compensate for expected improvements at the band of 1.35 cm, i.e., increasing the SRT effective area up to a factor of two (due to variations of k2 from 0.5 to 1) and the interferometer sensitivity up to a factor of 1.5 according to (1). CONCLUSIONS New results of the radiometric measurements of the space radio telescope parameters in 20112013
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using the calibration objects with the single SRT and a large number of the researched sources in the interfer ometer mode agree with the first results obtained by Kardashev et al. [5] within 1015% at the bands of 92, 18, and 6.2 cm and 2025% at the band of 1.35 cm. The main contribution to SEFD and the SRT sen sitivity at the bands of 92, 18, and 6.2 cm make noise of the receiver and antenna feed unit and, at the band of 1.35 cm, makes losses of the effective area due to phase errors in the antennafeeder system. The SRT contribution in the sensitivity of the groundspace interferometer proportional to the square root of mea sured values SEFD is close to the design at the bands of 92 and 18 cm, and reduces the design sensitivity approximately by a factor of 1.5 and 2 at the bands of 6.2 and 1.35 cm, respectively. The measured SRT con tribution increases the sensitivity of the interferometer to a factor of up to 1.5 in five subbands at frequencies of 2218 GHz and reduces it by a factor of 1.5 in three subbands at frequencies of 2225 GHz relative to the sensitivity at 22 GHz. The main contribution to the SRT equivalent noise temperature makes the receiver and the antenna feed assembly (AFA) with polarization splitters. The spread in values of the noise temperature through the depen dence on the physical temperature of LNA and AFA can be associated with the variations in the SRT orien tation relative to the Sun in individual observational sessions. The obtained results and SRT operating experience can be useful when designing future space projects (Millimetron, etc.), especially taking into account that the SRT antenna is probably the largest construc tion project to date opening in space. These results indicate the need to optimize the design of the phase errors of the surface and the mirror exposure and minimize the losses in both individual elements and the antennafeeder system with the receiver as a whole. To reduce the phase distortion near the mini mum wavelength of the telescope operation it can be appropriate the additional design lack of irradiation of the mirror edge reducing known optimum level by sev eral times. ACKNOWLEDGMENTS The RadioAstron project is performed by the Astro Space Center of Lebedev Physical Institute of the Russian Academy of Sciences (RAS) and Lavochkin Scientific and Production Association according to the contract with the Russian Space Agency together with many scientific and technical organizations in Russia and other countries. This work was supported in part by the Program for Basic Research of the Divi sion of Physical Sciences of the RAS (OFN 17 "Active Processes in Galactic and Extragalactic Objects") and the Russian Foundation for Basic Research, projects nos. 13 02 12103 and 13 02 00460. Used in the anal ysis of the antenna observational measurements on the

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KOVALEV et al. 5. Kardashev, N.S., Khartov, V.V., Abramov, V.V., et al., RadioAstron A telescope with a size of 300000 km: main parameters and first observational results, Astron omy Reports, 2013, vol. 57, pp. 153194. 6. RadioAstron User Handbook. http://www.asc.rssi.ru/ radioastron/documents/rauh/en/rauh.pdf 7. Kraus, J.D., Radio Astronomy, McGraw Hill, 1966. Translated under the title Radioastronomiya, Moscow: Sov. Radio, 1973. 8. Esepkina, N.A., Korol'kov, D.V., and Pariiskii, Yu.N., Radioteleskopy i radiometry (Radio Telescopes and Radiometry), Moscow: Nauka, 1973. 9. KЭhn, R., Mikrowellenantennen, Berlin: Veb Verlag Technik, 1964. Translated under the title Mikrovolnovye antenny, Moscow: Sudostroenie, 1967. 10. Tseitlin, A.M., Antennaya tekhnika i radioastronomiya (Antenna Technology and Radio Astronomy), Mos cow: Sov. Radio, 1976.

RATAN 600 (SAO RAS) were carried out with the financial support of the Ministry of Education and Science of the Russian Federation (project nos. 16.518.11.7062 and 14.518.11.7054). REFERENCES
1. Khartov, V.V., A new stage in the development of robotic spacecraft for fundamental space research, Solar System Research, 2012, vol. 46, pp. 451457. 2. Kardashev, N.S., Aleksandrov, Yu.A., Andreyanov, V.V., et al., RadioAstron (the Spektr R project): A radio tele scope much larger than the Earth. Basic parameters and tests, Solar Systen Research, 2012, vol. 46, pp. 458 465. 3. Kardashev, N.S., Aleksandrov, Yu.A., Andreyanov, V.V., et al., RadioAstron (the Spektr R project): A radio tele scope much larger than the Earth. Ground segment and key science areas, Solar System Research, 2012, vol. 46, pp. 466 475. 4. Avdeev, V.Yu., Alakoz, A.V., Aleksandrov, Yu.A., et al., The RadioAstron space mission. First results, Vestnik FGUP NPO im. S.A. Lavochkina, 2012, no. 3, pp. 421.

Translated by N. Topchiev

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