Mutual coupling effects on antenna radiation pattern: An experimental study applied

Transcription

1 Radio Science, Volume 33, Number 6, Pages , November-December 1998 Mutual coupling effects on antenna radiation pattern: An experimental study applied to interferometric radiometers A. Camps, F. Torres, I. Corbella, J. Bar{t, and P. de Paco Department of Signal Theory and Communications, Universitat Polit cnica de Catalunya, Barcelona, Spain Abstract. Antenna pattern mismatches are one of the most important error sources in planned Earth-observation interferometric radiometers. From a low Earth orbit, the wide field of view, about ñ30 ø, leads to the use of antennas with a large beam. In addition, antennas must be closely spaced to avoid, or at least minimize, aliasing effects in the formation of the synthetic brightness temperature images. The accuracy demanded of these systems requires the precise knowledge of all the antenna radiation voltage patterns (amplitude and phase), which may differ from their theoretical values due to mechanical and electrical tolerances in the manufacturing process and which can change due to the proximity of other structures, i.e., other antennas of the array or the mechanical support. Two approaches are found in the literature to interprethe impact of antenna mutual coupling on the performance of an interferometric radiometer: (1) a modification of the antenna voltage pattern and (2) a mixing of the cross correlations measured between the signals collected by the antennas. The main contribution of the present work is a detailed theoretical analysis of the impact of mutual coupling effects showing the equivalence between both approacheso Theoretical results are corroborated with a set of experimental measurements with two kinds of antennaso Theoretical and experimental results can be used n the design of the antennas of interferometric radiometers in order to predic the mpact of mutual coupling on the systemus performance and point out the importance of an accurate antenna pattern characterization. 1. Introduction Global soil moisture and ocean salinity data required by global climate models can be obtained by passive observations L band with 0.5-K radiometric resolution, 10-km spatial resolution, and 1-3 days revisit time [LeVine et al., 1989; European Space Research and Technology Centre (ESTEC), 1995]o While this requirement is difficulto achieve by classical radiometers due to the large antenna size, aperture synthesis interferometric radiometers can achieve this by processing the so-called visibility samples V 2(u,v). The visibility samples are the complex cross correlations of the signals collected by each pair of antennareceiver channels of a sparse array, called channels I and 2 [Thompson et al., 1986; Camps et al., 1997a] Copyright 1998 by the American Geophysical Union. Paper number 98RS /98/98RS where (,v) is the baseline, that is, the distance between the position of antennas 2 and 1 normalized to the wavelength v (O and v2(o are the analytic signals of the voltages at the output ports of channels 1 and 2 loaded with an impedance Z0, TB([, I) is the brightness temperature; ([,rl)=(sin0 cos, sin0 sin ) are the director cosines with respect to the (X,Y) axes and 2+ 12< 1; F.,2([, 1) is the normalized antenna voltage pattern; [' 1,2 '- 4x / 112, F,,2(0, ) d is the equivalent solid angle of the antennas; and r' 2 (z) is the so-called fringe-washing function that accounts for spatial decorrelation effects, which is related to the receivers' overall frequency response normalized to unity 1543

2 1544 CAMPS ET AL.: ANTENNA PATTERN COUPLING EFFECTS _d2 for + measured on the final structure are revised theoretically, showing that both approaches are equivalent. It is found that, with the?12(z) = e f H,,(fiH,2* ej2 f df (2) /B1 B2 0 required accuracies [ESTEC 1995], antenna coupling effects can be accounted for with higher precision from the measurement of where f0=c/z0 is an arbitrary center frequency usually chosen the antenna voltage patterns (amplitude and phase) and their use close to the channel's center frequency. Note that the visibility in a suitable inversion algorithm than by correcting the measured function evaluated at the origin (u,v) = (0,0) equals the antenna visibility samples with the C matrix computed from the Z matrix temperature Ta, and, in the case of identical antenna patterns and calculated from the measured S parameters of the multiport negligible fringe-washing effects (F 2( :) z 1 ), it is related to formed by the antennas [Camps et al., 1997a]. Finally, two sets the brightness temperature by a Fourier transform of experiments with different antenna types are presented to point out the importance of the impact of mutual coupling and loading IF.(,rl)l 2 = F - [V(u,v)] (3) conditions on the measured antenna radiation voltage patterns and the interference patterns. In a real case, the inversion process requires more sophisticated methods. The G-matrix method was devised in NASA's one- 2. Mutual Coupling Effects on the Measured Visibility Samples: Theoretical Study dimensional intefferometric electronically steered thinned array radiometer (ESTAR) which is based on the measurement of the impulse response for each baseline [Rufet al., 1988; LeVine et al., 1989; Le Vine et al., 1990; Ruf, 1991; Tanner and Swift, 1993]. In the European Space Agency's (ESA) two-dimensional Figure 1 shows a circuit model of the antennarray treated as a multiport, each port corresponding to a receiving antenna [Camps et at, 1997a]. This model can be used whenever decorrelation effects are negligible between coupled antennas intefferometric microwave imaging radiometer by aperture synthesis (MIRAS) the much larger number of antennas makes IF(-Ar,,x/c) I_> 0.99: B=20 MHz, Arm =2.3 m, and array the application of the G-matrix method difficult, and so Fourier- length=4.6 m for 0m =- :30 ø (Figure 2). The complex values of based iterative methods have been proposed [Mart[n-Neira et al., the parameters in the impedance matrix depend on the array 1994; Martln-Neira et al., 1996; Martin-Neira and Goutoule, geometry, on the antenna separation, on their relative pattern, and 1997; Camps et al., 1998]. Both methods rely on a direct or on their orientation. The elements in the diagonal of the Z matrix, indirect accurate measurement of the radiation voltage pattern of Zmm. are the input impedances of the isolated antennas. The offthe antennas, which must be precisely measured when embedded diagonal elements, Z,,, are the mutual impedances between in their final positions in the interferometer. antennas m and n. In the far-field region r,, n > 2 L 2 In the following sections, the impact of mutual coupling on the being the antenna separation between antennas m and n, L measured visibility samples and the antenna voltage pattern 0.9,t0 being the maximum antenna size, and o being the wave- / o (rm I1 Zl 1 + ( - ie Zln In E gj n In+ v/ / '. I 5 V[i Figure 1. Interferometer antenna array as a multiport for antenna coupling analysis. Superscript zero denotes open circuit voltage, ZL is load impedance, M is the number of antennas, and i,j are particular elements of the array.

3 CAMPS ET AL. ø ANTENNA PATTERN COUPLING EFFECTS 1545 d V V // V, 1 m 77 V ( -.) V Figure 2. Evaluation of the voltage induced in open circuit at each antenna. Equation (7) shows that the measured voltages are a linear combination of the voltages that would be measured in opencircuit conditions. Substituting equation (7) into (1) L* 0 O* VmS-1E[v Vn ] V mn-1 E[ Vmvn ] (8) 2z0 2z 0 the ideal and measured visibilities can be related by the C matrix, _ i E[,,.] 2Zo = -I 1 E[ o oh]( -I)H (9) 2Zo _. 17o( -1)H length), mutual impedances can be approximated by [Cardama where the superscript H indicates transposed and conjugated. et al., 1993, equations 1.4 and 4.100] Equation (9) shows that the measured visibility samples are also 1 a linear combination of all the visibility samples that can be Z = /D m (On, 4)n ) Dn (Om, 4)m ) mn 211; (Pmn/ 3.0 ) synthesized by the array measured in open-circuit conditions. /Rmr n R nn e -J2 n (rmn/ 3'O) (4) Camps et al. [1997a] performed a detailed analysis of the errors induced by antenna coupling using this formulation. where Dm(0.,.) and Dn(Om,( m ) are the directivities of antennas m and n, in the direction of antennas n and m, and Rmm and Rr are their radiation resistances. Even though these parameters can be numerically computed for simple antennas, such as dipoles, in practice, reflections on the array structure, etc., may alter them significantly, and their measurement, when all the antennas are mounted in the array, is much more accurate. _ V m Zmrn i m Ii =0 Vp,rn Zrnn _ in m Ii =0 Vp,n (5) Using this circuit model (Figure 1), Camps et alo [1997a] have related the voltage ljlmeasured at the load connected to port rn to the voltage v, that would be measured at the same port, when all the antennas were open-circuited and no mutual coupling effects appear (equation(5)), an assumption implicit in the derivation of equation (1) [Thompson et al., 1986]. v!l 1 + Z11 Z12 o = L Z z22 V = = 2-' Z1M ZL u ZL M ZMM (6) (7) 3. Mutual Coupling Effects on the Antenna Voltage Pattern: Theoretical Study Antenna coupling has also been studied from the point of view of its impact on the interference or fringe pattern measured in the ESTAR prototype [Ruf, 1991]. LeVine and Weissman [1996] successfully checked the voltage antenna radiation patterns measured in the ESTAR prototype following the numerical techniques used by Kelley and Stutzman [1993] and the S parameters measured between the arrays of dipoles forming the ESTAR antennasø The impact of the mutual coupling on the antenna pattern can also be derived from equation (7). The voltages induced at the antennas in open-circuit conditions Vøm (Figure 2) are 0 leff m jk(m-1)dsin(o) Vm' 1 M Vm = 'ELnc I e '"" (10) where the vector l,ff, is th effective length of antenna m and includes its polarization properties [Cardama et al., 1993] ø /eff m Rmm m o = ' - m Fn (0,(D) (11) ion m ( J) is the normalized antenna radiation voltage pattern measured in free-space conditions, Rmm is the antenna rn radiation resistance, and,l=120g ohms is the vacuum wave impedance. Assuming that all the antennas have the same Rmm and Dm, and

4 CAMPS ET AL.: ANTENNA PATTERN COUPLING EFFECTS substituting equations (10) and (11) into (7), the antenna voltage pattern measured under loading conditions is M F%L(O,O) = icvqfn/(o,o ) e jk(q-v)dsin(ø) (12) q=l where ic m is the (p,q) element of the inverse of matrix C. In order to simplify the mathematics involved and gain insight in the phenomenon, let us compute the voltage pattern of the first antenna under coupling conditions,. (0,4)), assuming that all the antennas are identical, Fø.v( ½)= -'Onq (, ½), and that = ZqqaZl,, and Z,=Z azl for all p and q. In this case, matrix C in (6) can be rewritten as Z L Z L +Zin where I is the identity matrix. Matrix C can be approximately inverted by retaining the first two terms of the Taylor development of the inverse matrix. That is, (l+x) X + Zin+ZL Z L +Zin ß " (14) The ZL/(Zi,,+Z ) factor corresponds to the voltage divider formed by the antenna impedance and the antenna load and can be neglected for comparison purposes between V m and Om o The identity matrix, zero-order term, corresponds to Vt'm-----vO m, no an tenna = coupling effects, while the first-order term, [Z- Ztn I] / (Ztn + Zz), shows the direct coupling between two antennas. Higher-order terms in the development of (14) can be understood as coupling effects through multiple reflections in other antennas, for example, a signal can be couple directly between antennas m and n, or indirectly between antennas m and p, and then from p to n... Consequently, the voltage at the first antenna v under loading conditions will be given by / 0 t Zin + ', + Zin where Z m is the mutual impedance between the first antenna and the antenna m, which can be determined from network analyzer measurements. The antenna voltage pattern measured under mutual coupling,f L. (0, ), is then ZL { F ø(0, ) Fn, L(O' 4)) = ZL + Zi n n, - Z m (16) That is, the antenna radiation voltage pattern measured in the presence of other antennas is a linear combination of the freespace antenna radiation voltage pattern and other terms that are proportional to the mutual coupling and are weighted by an exponential term at the same spatial frequency as the baseline formed by the coupled antennas. Note that when the antennas are different, a similar development can be carried out from (7), (10) and (11), but the exact values of icm have to be retained instead of the approximate ones (equation(14)). < ,.-%..:.:.... a) b) Figure 3. Partially filled circular waveguide (PFCW) antennas mounted on the support forming the baseline d=

5 CAMPS ET AL.: ANTENNA PATTERN COUPLING EFFECTS 1547 Table lo Mutual Coupling and Matching for the Partially Filled Circular Waveguides (PFCW) and the Array of Microstrip Patches, 0.89X I PFCW z-52 ø z 12 ø z 32 ø z-166 ø z-7 ø S21 (Sl <-30 db) (-30.7 db) (-40 db) (-46 db) (-48 db) (-60 db) Patches z-72 ø L-61 ø L-28 ø 0ø027 z 7 ø z 47 ø (S <-18 db) (-24.7 db) (-26.6 db) (-28.2 db) (-31.4 db) (-34.4 db) S parameters accuracy of +0.5xl 0'39 andf = GHzo The mutual coupling effect in an interferometric radiometer can now be understood from two points of view: as a mixing of all the visibility samples that can be synthesized by the array (equation(9)), or as a modification of the radiation voltage pattern of the antennas with ripples at all the spatial frequencies (baselines) that can be synthesized from the arrayo These errors are then translated into errors in the visibility samples [Camps et al., 1997a, appendix 1 ]o In section 4 a series of experiments that were conducted to show the effects of mutual coupling are presented. Since for mutual coupling smaller than about 25 db these effects require very accurate measurements to become apparent, we have not measured the changes in the visibility samples of natural scenes (equation(9)), because they are masked by noise for typical integration times [Camps et al., 1997b]. We have selected the approach of the variation in the antenna radiation voltage pattern (equation(16)) and in the interference pattern, that is, the response to a noise point source at different angles. 4. Mutual Coupling Effects: Experimental Study The effect of mutual coupling on the antenna voltage pattern has been studied for two kinds of antennas. The first type consists of a circular waveguide with an external diameter of 0.89,1,, the same as required for MIRAS antennas [Martin Neira et al., 1996; Martin Neira and Goutoule, 1997] that are partially filled with a hollow dielectricylinder (Figure 3a) (PFCW means partially filled circular waveguide). These antennas have been optimized to have a very low coupling (Table 1), together with a wide halfpower beam width, and to be very similar in the E and H planes (Table 2)ø The second antenna type consists of an array of six microstripatch antennaspaced 0.85,1, apart which also have a wide antenna beam but a higher coupling. Tables 1 and 2 summarize the main parameters of these antennas. 4.1o Effect on the Antenna Voltage Pattern Equation (16) has been checked with following procedure: 1o The E planes (PFCWs) and the H planes (microstrip patches) of the isolated antennas were measured, both in amplitude and phase. The accuracy computed from 25 consecutive measure ments was better than 4xl 0 '3 and 0.5 ø, in the margin +50 ø from boresight 2. The antenna radiation voltage pattern was measured again, but other antenna(s) was (were) placed near it, modeling an interferometric array (Figure 3b)o In the case of the PFCW, at each measurement the second antenna was moved to form different baselines (Figure 4a). In the microstripatch array, Table 2. Radiation Pattern Properties of the Partially Filled Circular Waveguides and the Array of Microstrip Patches (f= GHz) Half-Power Beam Width E-plane H-plane Cross-Polar Level PFCW Patches Here GHz. 77 ø 68 ø - 25 db 71 ø 75 ø -19 db

6 1548 CAMPS ET AL.: ANTENNA PATTERN COUPLING EFFECTS Antenna Isolated d 2d 3d 3d 4d 5d 4d lllll 5d llllll a) Figure 4o (a) Positions occupied by the PFCWs and (b) Positions of the patch antennas not covered by the strip of absorbers Effect on the Interference Pattern' different baselines were formed by covering with a thin microwave absorber the patches not used (Figure 4b). Figure 9 shows three interference patterns measured between 3. Finally, for the PFCW the difference between the antenna microstrip path antennas I and 3. voltage pattern measured in steps 1 and 2 was computed. For the 1. The first pattern is the ideal one, that is, the one that would microstrip patch array, the effect of the nth antenna, the one be measured without mutual coupling. It is computed from the whose absorber cover was removed, was computed by subtractantenna patterns measured in isolated conditions and the expoing the antenna voltage pattern of the first antenna measured nential phase terme -ik{m- )dsin{ (equation (12) with ic t= 6tn ). when antennas I to n were not covered, from the same pattern 2. The second is the measured one, when all the antennas that when only antennas I to n-1 were not covered. are not forming the baseline are left in open circuit, that is, Figures 5 and 6 show the different amplitudes of the antenna antennas 2, 4, 5, and 6. radiation voltage patterns for the PFCW and microstrip patch 3. The third is measured one, when the former antennas are antennas, respectively. Figures 7 and 8 show the measured and loaded with a 50-1' matched load. theoretical contributions of each term in equation (16), corre- From these curves it is apparenthat the interference pattern sponding to the coupling of a new antenna. Theoretical contribunumber 2 is closer to the ideal one (number 1) than interference tions have been evaluated from the Z parameters computed from pattern number 3, due to the multiple coupling effects that appear the measured S parameters (Table 1). Note that there is good when the antennas are loaded. However, as the real interferomeagreement between them, in the number of fringes and their ter operates in the conditions of 3, the coupling effects must be amplitude, especially for the shortest baselines (the ones that are taken into account in the same loading conditions to reduce errors more coupled) and for the patch antennas. Noise and residual in the recovered image. calibration errors during the measurement of the S parameters with the HP 8510 C network analyzer (Table 1) are more 5. Conclusions important when measuring weak antenna coupling (long baselines) leading to larger discrepancies in the predicted antenna The impact of mutual coupling on the antenna voltage pattern pattern deviation. Other discrepancies in the amplitude measured and in the cross correlations (visibilities) measured by interferonear +90 ø are mainly due to reflections at the rear wall of the metric radiometers has been analyzed theoretically in detail and anechoic chamber when the transmitter and the baseline were experimentally verified. It has been shown that provided the aligned. In any case, the interest of these measurements lies in the relative bandwidth is small, so as to neglect spatial decorrelation agreement in both the number of fringes, measuredeviations effects r 2 = 1, the analyses found in the literature [LeVine and and theoretical predictions, and the decreasing amplitude of the Weissman, 1996; Camps et al., 1997a] are both equivalent. The fringes with smaller coupling. study performed allows the prediction of the antenna pattern

7 CAMPS ET AL.: ANTENNA PATTERN COUPLING EFFECTS 1549 o.o..., !... ;t!... '...'..., " - ; 1 c,,i; ;,f...! i i './': i ]_X,.. _ i-- IFlt I (O)l, ant. #2 at 2 d!! i.// 'i! 'i. :---lien, (0)l, ant. #2 at 4 : : : :I// ', : ;,,., :... IFn, (#)l ant. at 5 d u... u_ ß u... u a ;... ;.... _ : : ::... i---/;"---i... i... i... i I I I I I I I I I O0 Figure 5. Measured antenna voltage pattern (,amplitude) of a PFCW at position 1, isolated and modified by the presence of the other PFCW. I I I ',,, :-- IFn, (P)l isolated IFn i (#)1, ant. # 2 IFn (P)l, ant. #2,3 _._ IFnl (#)l, ant. #2,3, 4 IFn (#)[, ant. #2,3, 4,5 :;.::.n;_(o)l, ant. # 2, 3, 4,5, , -... i... i !......!... I I I I I Figure 6. Measured antenna voltage pattern (amplitude) of a microstrip patch position 1, isolated and modified by the presence of other patchesø

8 1550 CAMPS ET AL. ø ANTENNA PATTERN COUPLING EFFECTS 0.0( (5 00( o!-: o o -: -- o : -.o,o.oo.o.o.o I ' i i I -01 I i i i I.o,- o b'.o, - o o o - o o o - o o o - o o o i ,, ,0 0 0 " ' 0.o.o.oo.o.o I, i i I I i i i I Figure 7 Measured and theoretical PFCW antenna pattern deviations for different baselineso Theoretical deviations computed are from equation (15). Subscripts indicate the positions of the antennas on the array: F,,0(0 ) is the antenna voltage pattern of the antenna at the ith position when there is another antenna atjth position. d=0.89zo h?)- h(e) (o)- ( ) (o)- ( ) (o)- _( ) (o)-. ( ) :M ' O o i o o o Figure 8. Measured and theoretical microstri patch antenna pattern deviations for different baselineso Theoretical deviations are computed from equation (15). Subscripts indicate the positions of the antennas on the array: F,,os:..(O ) is the antenna voltage pattern of the antennat the ith position when there are other antennas at thejth, kth... positionsø d=-0.85,o

9 CAMPS ET AL.: ANTENNA PATTERN COUPLING EFFECTS 1551 BASELINE 1 T 3 d ,'-...,'-...,'-...,'-... " ' ' ' e 0.5 J,t i o i -loo o loo Figure 9. Effect of the mutual coupling and antenna matching conditions on the real and imaginary parts of the normalized ideal interference pattern (no coupling); (d=-0.85.)o Dashed lines denote ideal interference pattern, dotted lines denote measured interference pattern with other antennas in open circuit, and solid lines indicate measured interference pattern with other antennas loaded with 50 fl. deviations as a function of the mutual coupling and loading be pointed out that the antennas located at the center of the array conditions. In turn, these deviations can be used to evaluate the would probably exhibit a more similar pattern, and this fact could impact on the radiometric accuracy when a particular type of be used for an optimum assignment of the redundant baselines. antenna is going to be used in an interferometric radiometerø However, it is not clear that their patterns would be similar The importance of mutual coupling has been experimentally enough to avoid an individual measurement of each antenna verified with the measurement of the changes in the antenna pattern. These voltage patterns can then be used in a suitable voltage pattern, which are of the order of 5-10% (peak values) for inversion algorithm, such as (1) the G-matrix method [Rufet al., a 0.85Z baseline formed by two microstrip patch antennas 1988] or (2) an iterative Fourier-based algorithm [Camps et al., coupled about -25 db, and of the order of 5% (peak values) for 1998] that corrects antenna pattern mismatches after a proper a 0.89Z baseline formed by two PFCW antennas coupled about calibration of receiver errors [Torres et al., 1996]. The trade-off -31 dbo Since even these small mutual coupling value effects are not negligible at all, and coupling cannot be arbitrarily reduced (equation(4)), other antenna parameters can be improved instead (pattern intersimilarities, matching, etc.). In addition, in the case that the Nyquist criterion is not satisfied, that is, d > ) o/2 for onedimensional (l-d) and 2-D rectangular (u,v) sampling, or d > ZoA/3 for 2-D hexagonal (u,v) sampling, the antenna size L (L<d) could be somewhat reduced to enlarge the alias-free field of view. It has been demonstrated that antenna mutual coupling effects can be accounted for with an accurate antenna voltage pattern measurement at the same conditions of operation as the interferometer: loading impedances, relative positions of the antennas and surrounding structures (e.g., the host platform, etc.). It should will be based on the feasibility of the measurement of the baseline interferogram (G-matrix) or the embedded antenna pattem. In our experimental work standard deviations smaller than 4x10 ' (48 db) in amplitude and 0.5 ø in phase have been estimated after 25 consecutive measurements. These accuracies are at the upper limit required for future high-performance nterferometdc radiometers [ESTEC 1995; Camps et al. 1997a]o Finally it should be pointed out that antenna patterns and mutual impedances can be measured with sinusoidal signals, provided their variation over the noise bandwidth is negligible, which is usually the case for the relative bandwidths allocated for passive observations. However, at higher frequencies, if larger relative bandwidths are available, so that those parameters change

10 1552 CAMPS ET AL.: ANTENNA PATTERN COUPLING EFFECTS within the band, a characterization with noise signals would then be required. Initial results in the development of a synthetic aperture microwave radiometer, IEEE Trans. Geosci. Remote Sens., 28(4), , 1990 Martin-Neira, M., and J.M. Goutoule, MIRAS: A two-dimen- Acknowledgments. This work has been supported by the Spanish Ministry of Education under grant CICYT TIC 96/0879, sional aperture-synthesis radiometer for soil-moisture and and the European Space Agency in MIRAS Calibraction System ocean salinity observation, ESA Bull., 92, , November Definition activities. The authors express their gratitude to the anonymous referees, whose suggestions contributed to the clarity Martin-Neira, M., Y. Menard, J.M. Goutoule, and U. Kraft, of the manuscript. MIRAS: A two-dimensional aperture synthesis radiometer, in Proceedings of the International Geoscience and Remote References Sensing Symposium, IGARSS '94, ppo , IEEE Press, Piscataway, N.J., Camps, A., J. Bar Fo Torres, I. Corbella, and J. Romeu, Impact Martin-Neira, M., et al., Integration of MIRAS breadboard and of antenna errors on the radiometric accuracy of large aperture future activities, in Proceedings of the International Geosynthesis radiometers, Radio Sci., 32(2), , 1997a science and Remote Sensing Symposium, IGARSS '96, ppo Camps, A., F Torres, I. Cotbella, J. Barfi, and X. Soler, Calibra , IEEE Press, Piscataway, N.J., tion and experimental results of a two- dimensional interfero- Ruf, C.S., Error analysis of image reconstruction by a synthetic metric radiometer laboratory prototype, Radio Sci., 32(5), aperture interferometric radiometer, Radio Sci., 26(6), , 1997b. 1434, Camps, A., J. Barfi, F. Torres, and I. Corbella, Extension of the Ruf, C.S. C.T. Swift, A.B. Tanner, and D.M. LeVine, Inteffero- CLEAN technique to the microwave imaging of continuous metric synthetic aperture radiometry for the remote sensing of thermal sources by means of aperture synthesis radiometers, the Earth, IEEE Trans. Geosci. Remote Sens., 26(5), Prog. Electromagn. Res., PIER 18, 67-83, Cardarea, A., LI. Jofre, J. Romeu, J.M. Rius, So Blanch, Antenas, Tanner, A.B. and C.T. Swirl, Calibration of a Synthetic Aperture ed. of Univ. Politic. de Catalunya, Barcelona, Spain, 1993 Radiometer, IEEE Trans. Geosci. Remote Sens. 31(1), 25% European Space Research and Technology Centre, Conclusions 267, and recommendations from the SMOS and summary reports Thompson, A.R., J.M. Moran, and G.W. Swenson, Inter romeof the working groups, in SMOS: Consultative Meeting on try and Synthesis in Radio Astronomy, John Wiley, New Soil Moisture and Ocean Salinity: Measurements and Radi- York, ometer Techniques, Rep. ESA WPP-87, pp. 6-11, Eur. Space Torres, F., A Camps, J. Barfi Io Corbella, and R. Ferrero, On- Res. and Technol. Cent., Noordwijk, Netherlands, board phase and module calibration of large aperture synthesis Kelly, D.F. and WL. Stutzman, Array antenna pattern modeling radiometers. Study applied to MIRAS", IEEE Trans. Geosci. methods that include mutual coupling effects, IEEE Trans. Remote Sens., 34(4), , Antennas Propag., 41(12), , LeVine, D.M. and D.E. Weissman, Calibration of synthetic J. Bar i, A. Camps, I. Corbella, P. de Paco, and Fo Torres, aperture radiometers in space: Antenna effects, in Proceedings Department of Signal Theory and Communications, Universitat of the International Geoscience and Remote Sensing Sympo- Polit cnica de Catalunya, Campus Nord, D4-016, Barcesium, IGARSS '96, pp , IEEE Press, Piscataway, N.J., lona, Spain. ( tscjbt eupbl.upc.es; camps voltoroupc.es; corbella voltor.upc.es; depaco voltor.upc.es; torres LeVine, D.M., T.T. Wilheit, R.E. Murphy, and C.T. Swift, A voltor. upc.es) multifrequency microwave radiometer of the future, IEEE Trans. Geosci. Remote Sens., 27(2), , (Received March 4, 1998; revised July 29, 1998; LeVine, D.M., M. Kao, A.B. Tanner, C.T. Swift, and Ao Griffs: accepted August 27, 1998.)