Single reference, three target calibration and error ... - IEEE Xplore

Single Reference, Three Target Calibration and Error Correction for Monostatic, Polarimetric Free Space Measurements ~

~

WERNER WIESBECK, SENIOR MEMBER, IEEE, AND DANIEL

All free-space polarimetric radar cross section (RCS) and antenna measurements are subject to errors like coupling and residual reflections. The modeling of these errors results in a 12-term error correction. The procedure for the error correction with three linear independent calibration targets and an isolation measurement is shown. Based on the philosophies in network analysis, a single reference calibration is introduced. This single reference calibration requires the precise calculation of only one reference target. As single references, spheres or frat plates are used. The references of the other targets are determined by the calibration procedure. The single reference calibration is suitable for all narrow and wideband, complex, polarimetric RCS, and antenna measurements. Measurements are shown for different targets which demonstrate the benefits of the single reference calibration.

I. INTRODUCTION Calibration and error correction are inherent problems in measurements implying free space propagation. For linear polarizations sufficient techniques have been developed recently in antenna and radar cross section (RCS) measurements [l], [2]. The evolution of polarimetry added another degree of complexity to the calibration of free space measurements. Several procedures have been proposed, especially for remote sensing [3]-[5],but these are still either rather complicated or not suitable for high precision antenna and RCS measurements. On the other hand, for the support and verification of antenna, RCS, and electromagnetic wave propagation theories, regarding polarization effects, highly accurate measurements are absolutely mandatory. This paper presents for the first time a single reference calibration technique for monostatic, polarimetric free space measurements. Single reference means that only one calibration standard is relevant for absolute amplitude and phase calibration, while the other standards only have a relative character. In network analysis for guided waves, single reference calibrations, known Manuscript received May 8, 1991; revised March 8, 1991. The authors are with the Institute fur Hochstfrequenztech and EIektronik, University Karlsruhe, 7500 Karlsruhe, Germany. IEEE Log Number 9103560.

KAHNY, STUDENT MEMBER,

IEEE

as TRL calibrations, have been introduced several years ago [6]. The single reference calibration presented in this paper is based on the calibration scheme published in [7]. In Section I1 the problems and limitations in polarimetric calibration of RCS measurements are listed. A 12-term error correction, developed in Section 111, is necessary for the solution. From the large number of possible calibration objects the most suited ones have been selected. They are reviewed in Section IV for their characteristics. The procedure of the single refirence calibration based on the 12-term error correction is given in Section V. It can be anticipated that this single reference calibration for polarimetric free space measurements will improve antenna and RCS measurements as much as the TRL calibration has improved network analysis. 11. LIMITATIONS IN HIGH PRECISION POLARIMETRIC

RCS MEASUREMENTS In the following sections the understanding and the algorithms will be developed for RCS measurements. Without loosing generality the philosophy is also applicable to antenna and other free space measurements [8]. For a certain frequency and aspect angle, a radar target’s scattering behavior is defined by the complex polarimetric RCS matrix:

[a]=

[E E vhh,

avv Eh..].

(1)

Notice that on account of simplicity throughout the whole paper the orthogonal linear polarizations, vertical (w) and horizontal ( h ) ,are used as a basis for (1). The results are valid for any orthogonal polarizations. Complex values are underlined (-). The main limitations originate from: statistical errors due to amplitude and phase noise; systematic linear errors, like - errors induced by the frequency response and mismatches in internal and external equipment like

0018-9219/91$01.00 0 1991 IEEE

PROCEEDINGS OF THE IEEE, VOL. 19, NO. 10, OCTOBER 1991

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lsml

Table 1 Relative Measurement Errors Au in dB due to a Finite Polarization Purity of -20 dB, ( o h v = U , h ) Correct RCS-matrix values

Relative measurement error

uhh

uhu

UUU

Auhh

Auhu

AUuv

IdBsm

/dBsm

IdBsm

/dB

/dB

/dB

0

-30 -20 - 10 0 -20 -20 -20

0 0 0 0 $10 $20 $30

0.05

17.2 9.5

0.05 0.17 0.53 1.57

0 0 0

0 0 0

0.17 0.53

1.57 0.35 0.90 2.43

4.3 1.57 14.2 21.45 30.45

XO XO XO

synthesizer, detectors, cables, switches, antennas, couplers etc.; - polarization coupling in the transmit and receive channels, i.e., mainly due to finite polarization purity of the antennas, but also coupling in the microwave signal paths; - isolation errors due to coupling from the transmit to the receive paths and residual reflections in the anechoic chamber; systematic nonlinear errors on the basis of non ideal active devices in the transmitting and receiving part of the measurement system. This paper deals with systematic, linear errors. Statistical errors may be reduced by "averaging" over several measurement cycles. With coherent integration, the residual noise floor is reduced by the square root of the number of measurements. Dydamic errors of the system are usually improved by an internal calibration using look up tables. The systematic errors are primarily caused by the polarization coupling [9]. In Table 1, some examples for the relative errors due to polarization coupling are shown. One task for the calibration procedure is to reduce the errors listed in Table 1 in free space measurement systems. The second task is to render absolutely calibrated values in the complex RCS matrix [a].The handling of errors according to their origins and the requirements for calibration targets are derived in the following sections.

111. 12-TERM ERRORCORRECTION

This section deals with the mathematical description and correction of the above mentioned systematic, linear errors [lo]. Figure 1 shows the simplified block diagram of a coherent polarimetric RCS measurement system. The regarded RCS measurement systems are measuring voltage or power-waves . Therefore the object's scattering behavior is described by a complex polarization scattering matrix [SI,which is related to the complex RCS matrix [a1 by

a 0

LCoherent Yulillrequency TransmiVReceivB System

Fig. 1. Schematic block diagram of a polarimetric RCS and antenna measurement system.

where Ro denotes a fixed reference radius for the target. Note that the root in (2) has to be taken for each matrix element. In Fig. 1 the measurement equipment is completely housed in block 1. The object of interest is shown by 3. The transmit and receive paths are represented by 2 and 4, respectively. The measurement equipment 1 has no direct access to the target. The radar system is only able to measure the transmitted power-waves ah and a, and the received waves bh and b,. The measured scattering matrix [S"],results from the incident and reflected power-waves as

(3) The errors listed in Section I1 are inherent in the blocks 2, 4, and 5 in Fig. 1. The transmit, receive, and coupling paths may be represented by their scattering matrices. This leads to a relation between the measured scattering matrix [S"], and the correct target scattering matrix [$"I, see Fig. 1:

The mathematical representation (4) shows that the correct target scattering matrix [g] is erroneous by the additive matrix [I]and the multiplicative matrices [E]and The [B]and [TI matrices are the ray transmission matrices for transmit and receive, including CO- and cross-polarization. Thus the measured scattering matrix [S"]is subject to twelve error components, the isolation errors le,,, the transmit errors Et,,, and the receive errors Be,,, four each. The indexes E and 7 are defined as arbitrary linear polarization states. If the twelve error coefficients are known, it is possible to calculate the correct matrix [S"] by inversion of (4):

[r].

[$"I

=

[ B p* {[S"]- [I]}* [Er1.

(5)

The determination of the unknowns is based on the measurement of reference targets for which the scattering matrices [S"]are well known. The determination of the four 1552

PROCEEDINGS OF THE IEEE, VOL. 79, NO. 10, OCTOBER 1991

additive error coefficients LEV is simply performed by an isolation measurement (empty room) for which [SI= [O] by definition. With [S"]= [O], ( 5 ) becomes

[S" I

= [I].

(6)

The remaining 8 unknowns REVand T E scan be determined by additional measurements with two calibration targets, each one resulting in four complex scattering parameters. For the two additional calibration targets l and 2 with their known scattering matrices [S"']qnd [SC2], (7) can be derived:

[sml] - [I]= [M'] = [B]* [S"']* [TI [sm2] - [I]= [ M 2 ]= [B]* [SC2] * [TI.

+

unknown complex error coefficients is 16 4 = 20 in (10). With (8) it is possible to represent the 16 unknown coefficients cijby eight out of them, because of their nonlinear relation. Starting from (lo), error coefficients cij can be eliminated step by step by sequential substitution through other error coefficients cij.Numerous solutions exist for this procedure, but only a few are advantageous with respect to practical considerations. Equation (1 1) gives one possible advantageous solution, for which the knowledge has been used that copolarization terms are large compared to crosspolarization. Other solutions may lead to larger sequential errors in the computation of the error coefficients cij.

(79 (7b)

cz 2

From multiplication of the matrix products and ordering the square matrices in vector form the following expression results:

e2 2

: 3

-

Luv

2 2

e42

Equation (11) leads to a homogeneous system of equations with 8 unknowns that is solvable. Therefore theoretically two reference targets, with four linear independent scattering coefficients &,each, would be sufficient. Up until now no such target is available. Therefore a solution with three reference targets, with the scattering matrices [Scl], [Sc2], and [Sc3]is proposed. The only condition imposed on the three reference targets, not on the objects to be measured later, is S v h = For the three reference targets ( i = 1,2,3) the (10) and (11) result in the error coefficients ct3. With the coefficients ca3known, the scattering matrices of unknown targets can be measured and error corrected for the object related matrices [SI.NQ restrictions concerning target characteristics are imposed. The inversion of (10) leads to:

zhv.

For simplification the formal error matrix in (8):

[C]is introduced

[S"I - [I]= [NI= [Cl [ S I . '

The explicit formulation of (9) replace the products by the formal coefficients cij:

(9)

REV* T E V

In the following, the coefficients ca3are called error coefficients. Four error coefficients e,, are additive, while the 16 error coefficients ca3 are multiplicative. The additive coefficients czo,which are identical to the L E V ,represent the isolation error and the residual reflections, they have been already determined with the empty room calibration in (6). The coefficients cz3 result from products of the transmit and receive scattering coefficients T E sand RE?. Especially the elements in the diagonal of [Cl,ca3represent the polarimetric frequency response error of the system. The matrix elements cl,, cZl,G ~and , Q~ result from the crosscoupling in the two orthogonal polarized channels. While in (4) the total number of unknowns is only 12, the number of

[s"]

IV. CALIBRATION TARGETCHARACTERISTICS In the past, numerous calibration objects have been used for free space measurements. For high precision polarimetric measurements only a few are suitable. Several out of them are reviewed for their characteristics. For theoretical and practical reasons the following requirements have to be fulfilled by the calibration targets: linear independence of the scattering vectors; precisely calculable over the whole frequency range; steady over the whole frequency range; reproducibility in hardware. A. Isolation Calibration (Empty Room)

The "empty room" measurement is a standard calibration. It determines the four isolation coefficients cia, as theoretically the empty room has to have zero reflectivity. The "empty room" calibration improves the isolation by about 30 dB. This requires that no changes take place between calibration and object measurements. It should be noted

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that a further reduction of about 30 dB to 40 dB is possible by range-gating. B. Metallic Sphere

The best suited calibration target is a sphere for the following reasons. Due to its symmetry the positioning is only critical in location, because of the phase reference, it is uncritical in all other aspects. The sphere can be produced with very high precision ( A R < 5 pm) over a wide range of diameters; for reproducible measurements gold plating is recommended. The sphere generates only a copolarized reflected signal, with phase and amplitude independent of incident linear signal polarization. The RCS matrix for a sphere has the form:

"4

"A

Fig. 2. Top: Finite length cylinder in the plane of the incident wave; a) d = Oo b) 4 = Go.Bottom: Dihedral corner reflector in the plane of the incident wave; a) 19 = Oo b) 19 = 4.5'.

The exact theory is known since 1908 [ l l ] , and many computational algorithms are published [2], [12], [13]. At the surface of the sphere the phase of the reflected wave changes by 180'. For completeness the equations for the calculation of a sphere are given in (14) for the monostatic case:

with the complex Mie coefficients

A,, B,:

D.Finite Length Cylinder For metallic as well as for dielectric cylinders the scattering behavior is sufficiently precise enough calculable. Other than for the disk and the sphere the scattering coefficients depend on the rotation angle in the incident plane. For a configuration according to Fig. 2(a) and linear orthogonal polarizations its scattering matrix has the form:

what satisfies the postulations for linear independence to spheres and disks. If the configuration is rotated in the incidence plane by 4.5" (Fig. 2(b)), (16) results:

and

x = k . a; a = Radius; k = wave number, j , : spherical Bessel function, hn: spherical Hankel function, [ 1' : derivation of [ ] with respect to x .

C . Circular Metallic Disk

The metallic disk of zero thickness exhibits characteristics like a sphere, (13), for normal incident waves. The exact solution for the ideal conducting disk of zero thickness is known since 1950, [14]. In [lS] a numerical solution of this scattering problem is given. As a result of thick edges, unwanted edge effects may show up. This has especially to be faced for wider angle bistatic measurements, for which a metallic disk is also suited. To reduce edge reflections, the edges are cut back with good results for edge angles less than 20". Compared to the sphere the RCS of a disk is high at normal incidence. The metallic disk may only 1554

be alternatively used to the sphere because of the linear dependency of the scattering coefficients.

and

Numerous solutions for the scattering of metallic and dielectric cylinders are known, so here only a few can be referred to [ 161-[18]. For dielectric cylinders the complex dielectric constant is usually not exactly enough known. Therefore metallic cylinders are preferred. E . Corner RePectors

Out of the numerous configurations of corner reflectors the dihedral corner is best suited as a precise calibration target. In spite of this, for airborne and spaceborne synthetic aperture radars (SAR) trihedral corner reflectors are preferred because of their wide 3-dB beamwidth. Like the finite length cylinder the dihedral corner is an excellent PROCEEDINGS OF THE IEEE, VOL. 79, NO. 10, OCTOBER 1991

target for cross polarization calibration. Positioned like in Fig. 2(c), (17a-d) apply, while positioned at 4S0, see Fig. 2(d), (16a-b) apply. With this two positions 8 error coefficients can be determined. The calculation is based on [19] for a rectangular corner with infinitely thin edges:

= A,

A,,

]

of C,alibration

(,tart

measureddata

em calculateddata I

+ A2

with

e3 End of Calibration

Fig. 3. Flow diagram of the standard, direct 16 term polarimetric error correction and calibration.

+ 4)) + sin(45' +4)

sin(ka cos(45' k a cos(45"

'

A, -

+ (j)e-jka

C445O+d)

sin(ka cos(45' - 4)) kacos(45' - 4 )

kal

= -j-{sin(45'

x

+ 4 ) + sin(45" + 4 ) } .

(17d)

A, represents the direct scattering, while the optical double reflection is formulated by A, and A3. Equations (17a-d) satisfy the conditions cvv

# ahh

and

ah, = c v h = 0.

(18)

The most important advantage of the dihedral corner is the only coopolarized return in the position of Fig. 2(c) and only cross-polarized return in the position of Fig. 2(d). This is very important for single reference calibration. It means that both calibration target positions (see Fig. 2(c)-(d)) result in linear independent scattering coefficients. A cylinder or the dihedral corner have to be used alternatively, as for both, the same (16)'s apply. In order to realize the ultimate results the dihedral corner has to be prepared accordingly. Gold plating, as recommended for the sphere, is necessary. Otherwise errors up to 0.2 dB may be observed. The theory for the calculation of its S-matrix is based on infinitely thin edges. In practice the edge angles have to be less than 20'. V. SINGLE-REFERENCE CALIBRATION (SRC) In a standard calibration the solution of (10) implies the measurements of three different calibration targets, each with a theoretically exact known RCS matrix, as given in Section IV. In contrast to this, the single reference algorithm, denoted as SRC in the following, allows the computation of all error coefficients in (10) with the knowledge of the scattering matrix of only one target. In the following first the standard direct calibration procedure is given as an introduction. Starting from there the SRC procedure is deduced.

A. Standard, Direct Calibration, and Error Correction

The standard, direct 12-term error correction and calibration [lo] follows the scheme shown in Fig. 3. First the scattering matrices of all reference targets are calculated. Then the measurements are performed. The "empty room" measurement provides all four isolation error coefficients cia. This is followed by: measurement of the sphere or the flat plate; measurement of the veftical dihedral corner reflector or cylinder; measurement of the 45' inclined dihedral corner reflector or cylinder. After the completion of the three measurements the error coefficients cig are calculated according to the equation in Section 111. With the error coefficients determined, the error correction can be applied to any measured target thereafter. B. Single Reference Calibration Algorithm

The drawbacks of the standard error correction in Section V-A are the problems in precise calculation of the reference target scattering matrices, as well as problems in positioning due to different phase references for the targets. Therefore, the SRC algorithm was developed to minimize all possible errors which could occur in a calibration procedure. In the following the ideas and theoretical background are given for this algorithm. Initially it is assumed that only targets are measured, for which the cross-polarization is negligible (e.g., spheres, circular disks), which means the scattering matrix has the form:

Note that this assumption is only relevant for the first two reference targets and not for the later measurements. With this assumption (10) can be simplified to:

[

= [:lo]

+

[.:, ]

[q.

O . (20) 0 d 2 -vu All not included coefficients are negligible because of the above assumptions. The remaining four error coefficients S U U

WIESBECK AND KAHNY CALIBRATION AND CORRECTION FOR FREE SPACE MEASUREMENTS _-

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can be determined by the measurement of only one known reference target and the isolation (empty room). For this purpose a sphere is well suited, because its scattering matrix is exactly known (see Section IV). The error induced by the polarization coupling, which is not considered in this case, is smaller than 0.05 dB according to Table 1, if S,, M Shh. Such a calibration is called response & isolation calibration (R&I). In Section IV the dihedral corner reflector was recommended as second calibration target, because of its ability to totally depolarize the incident field for a rotation angle of 6 = 45". For a rotation angle 19 = 0", i.e., vertical position, see Fig. 2(c), the scattering matrix of a corner reflector has the form:

which means that the cross-polarization is zero. The scattering matrices of the sphere (13) and the dihedral corner reflector (21) are of the same form as (19). Therefore the scattering matrix of the dihedral corner reflector in the position of Fig. 2(c) can be measured using the response and isolation calibration with the sphere as reference target and the inversion of (20) according to (12). The result is the error corrected scattering matrix [Sc2]for the dihedral corner in the 19 = 0' position, without the calculation of the theoretical scattering behavior of this target. From this matrix the scattering matrix [Sc3]at 6 = 45", see Fig. 2(d), can be calculated using the basis transformation as given in (22), which is the general for of (16):

[Sc3]= [RI-' . [Z3]. [RI with cos 19

[RI = [sin 19

-sin 6 cos 6

1

with 6 = 45". Thus all reference scattering matrices are gained by the only theoretical knowledge of one reference target. The precision of better than 0.05 dB, according to Table 1 for systems with the there given characteristics. Using these targets the calibration as shown in Section I11 can be performed. The SRC procedure, see Fig. 4, is based on the standard procedure of Section V-A. In the first step only the SRtarget scattering matrix [SC1] is calculated. The measurements are the same as in the standard procedure. Using just [TI], [ I ] and , [Sml]the (R&I) calibration is performed, to determine the coefficients in (20). From this results the calibrated scattering matrix [Z2]for the 29 = 0' position The basis transformation with the measured matrix [Sm2]. of (22) applied to [Z2]gives the error corrected reference By this all reference matrices are known and matrix [p]. the standard 12-term error correction can be performed. C. Considerations

The most critical part of the SR-calibration is the misalignment error between the measurements of the 2. and 3. Target. The misalignment error angle A is defined as the difference of the rotation angle from 6 = 45' in the Fig. 2(d). 1556

measured data

SR-target

e3 End of Calibration

Fig. 4. Flow diagram of the single reference polarimetric error correction and calibration.

To show the influence pf this error on the calibration accuracy a SR-calibration was completely simulated, assuming a system with a polarization purity of 20 dB and an isolation error of -55 dBsm. The relative error of the cross-polarization measurement as a function of A is plotted in Fig. 5, which shows, that the alignment is absolute uncritical. This can be explained by inspection of (10) in more detail. It shows that the measurement of the third target is mainly responsible for the determination of the amplitude error of the cross-polarization. The basis transformation (22) for the cross-polarization results in: = cos(45'

+ A) . sin(45' + A)

For a misalignment error of A = 5" the relative error is:

which proves, that even 5' misalignment are uncritical. VI. RESULTSAND SINGLE REFERENCE CALIBRATION BENEFITS The SRC has been implemented in state of the art hardware measurement equipment [7]. The features, that result from this calibration type are: Amplitude accuracy < 0.3 dB Phase accuracy < 3" Cross-polarization purity (type) > 50 dB. PROCEEDINGS OF THE IEEE, VOL. 79, NO. 10, OCTOBER 1991

-25 -30

$ -35

m

5 -40 0

cc -45 -50 -55

5

6

7

8

9

10

11 12 f I GHz

13

14

15

5

6

7

8

9

10

11

13

14

15

Fig. 5. Relative error in cross-polarization, due to misalignment of the corner reflector in the calibration procedure.

This performance can be reached over several octaves in frequency. The improvement in cross-polarization purity is in excess of 25 dB compared to a standard response and isolation calibration. In practice the SRC leaves the measurement problems to dynamic range, time and temperature stability. To illustrate the performance for different calibration steps, results for a metallic sphere (diameter: 36 mm) and a metallic cylinder (length: 150 mm; diameter: 1.2 mm) are shown. These two targets were chosen due to their typical radar characteristics, which are theoretically and experimentally well known. The calibration was performed with a metallic sphere (diameter: 150 mm) and a metallic 90" dihedral corner reflector (all dimensions 100 mm) as reference targets in the frequency range from 5 to 15 GHz. Figure 6(a) shows the magnitude of c~~~ for the sphere. The lower solid curve is the totally uncalibrated response. The typical scattering of the sphere is hardly visible. Additionally, there is an offset of 25 dB. The fully calibrated magnitude of a,, (solid upper curve) matches excellent with the theoretical results (dotted curve). To visualize the cross-polarization purity the ratio of the magnitudes a,, to a , , is plotted in Fig. 6(b) in a logarithmic scale for the same target. The dashed curve represents the totally uncalibrated cross-polarization purity. The value of approximately 25 dB corresponds to the cross-polarization purity of the antennas. Performing a response calibration, neglecting the polarization errors, result in the upper solid curve of Fig. 6(b). This type of calibration does not improve the cross-polarization purity at all. By performing a full SRCcalibration an improvement of 25 dB can be observed, with a typical cross-polarization purity of 50 dB. An important measure for the quality of a calibration is the balance of the cross-polarization channels a,, and ah, for reciprocal targets. As test target the metallic cylinder inclined by 45" was used. Figure 7(a) and 7(b) show this balance in magnitude and phase, respectively. Here only the curves for the SRC calibrated data are shown, because the uncalibrated data are far away from being balanced. Over the whole frequency range a balance of better than 0.1 dB in amplitude and 1.5" in phase are reached.

12

f I GHz

Fig. 6. (a) Magnitude of E,,,.for a, metallic sphere with 36-mm diameter. -SRC-calibrated (upper curve); --uncalibrated (lower curve); O 0 O 0 theoretical. (b) Cross-polarization purity of the system, determined with a sphere with 36-mm diameter. -response and isolation calibrated (upper curve); -SRC-calibrated (lower curve); - - - - uncalibrated.

1

rg

08 0.6

;

0.4

> 0.2 0

$

:

0

-0.2

U

2 -

-0.4 -0.6

5

6

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8

9

10

11

12

13

14

13

14

15

f I GHz

(a)

5

6

7

8

9

10

11

12

15

f I GHz

( b) Fig. 7. Cross-polarization channel balance (a) amplitude and (b) phase.

WIESBECK AND KAHNY: CALIBRATION AND CORRECTION FOR FREE SPACE MEASUREMENTS

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VII. CONCLUSION The evolution of complex, polarimetric free space measurements, as used in RCS-techniques, has to be based on new technologies for error correction and calibration. One prerequisite are high precision, computable reference targets, the other is an effective calibration procedure. With the single reference calibration an up to now unreached accuracy in the CO- and cross-polarization measurement is possible. Furthermore a reliable, calibrated cross-polarization purity of typical 50 dB can be reached. This high quality RCS-measurements improve significantly the verification of theoretical scattering phenomena, where especially numerical techniques like method of moments, finite difference or conjugate gradient method have to be tested. In addition to RCS any other polarimetric free space measurements like antenna measurements or electromagnetic compatibility measurements can be improved by the proposed single reference calibration. ACKNOWLEDGMENT

The authors wish to thank Dipl. Ing. Eberhardt Heidrich and S. Riegger for their extremely helpful contributions to this paper. REFERENCES [ l ] D. L. Mensa, “Wideband radar cross section diagnostic measurement,” IEEE Trans. Instrum. Meas., vol. IM-33, pp. 206-214, 1984. [2] G. T. Ruck, D. E. Barrick, W. D.Stuart, and C. K. Krichbaum, Radar Cross Section Handbook. New York-London, U.K.: Plenum, 1970. [3] J. D. Klein, “Calibration of quadpolarization SAR data using backscatter statistics,” in Proc. Intl. Geosci. Remote Sensing Symp.; Vancouver, Canada, pp. 2893-2896, 1989. [4] J. van Zyl, “A technique to calibrate polarimetric radar images using only image parameters and trihedral corner reflectors,” in Proc. Int. Geosci. Remote Sensing Symp., Vancouver, Canada, pp. 2889-2892, 1989. [5] H. A. Yueh and J. A. Kong, “Calibration of polarimetric radars using in-scene reflectors,” Proc. PIERS, Boston, MA, 1989. [6] “Applying the HP8510B TRL-calibration for non-coaxial measurements,” Hewlett Packard Product Note 8510-8. [7] S. Riegger and W. Wiesbeck, “Wide-band polarimetry and complex radar cross section signatures,” Proc. IEEE, vol. 77, pp. 652-658, May 1989. [E] E. Heidrich and W. Wiesbeck, “Features of advanced polarimetric RCS antenna measurements,” in Proc. IEEE AP-S Int. Symp. URSI Radio Science Meeting, San Jose, CA, vol. 11, pp. 1026-1029, June 1989. [9] F.T. Ulaby, R.K. Moore, and A.K. Fung, Microwave Remote Sensing: Active and Passive. Boston, MA: Addison-Wesley, 1986, pp. 1234-1237, vol. 111. [lo] W. Wiesbeck and S. Riegger, “A complete error model for free space polarimetric measurements,” IEEE Trans. Antennas Propagat.

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[ l l ] G. Mie, “Beitrage zur Optik triiber Medien, speziel kolloidaler Metallosungen,” Annalen der Physik, vierte Folge, band 25, 1908. [12] T. B. A. Senior, “Scattering by a sphere,’’ Proc. Inst. Elec. Eng., vol. 111, no. 5 , pp. 907-916, 1964. [13] D. Deirmendjan, Electromagnetic Scattering on Spherical Polydispersions. New York: American Elsevier, 1969. [I41 J. Meixner and W. Andrejewski, “Strenge Theorie der Beugung ebener elektromagnetischer Wellen an der vollkommen leitenden Kreisscheibe,” Annalen der Physik, 1950. 1151 D. B. Hodge, “Scattering by circular metallic discs,” IEEE Trans. Antennas Propagat., vol. AP-28, pp. 707-712, Sept. 1980. [ 161 H. C. Van de Hulst, Light Scattering by Small Particles. New York: Dover, 1981. 1171 A. Schroth and V. Stein, Moderne numerische Verfahren zur Losung von Antennenund Streuproblemen. Miinchen, Germany: R. Oldenbourg Verlag, Wien, 1985. [18] A. G. Papayiannakis and E. E. Kriezis, “Scattering from a dielectric cylinder of finite length,” IEEE Trans. Antennas Propagat., vol. AP31, pp. 725-731, Sept. 1983. [19] E.F. Knott, “RCS Reduction of dihedral corners,” IEEE Trans. Antennas Propagat., vol. AP-25, pp. 406-409, May 1977.

Werner Wiesbeck (Senior Member, IEEE) was born near Munich, Germany in 1942. He received the Dipl. Ing. (M.E.E.) and the Dr. Ing. (Ph.D.E.E.) degrees from the Technical University Munich in 1969 and 1972, respectively. From 1972 to 1983 he was with AEGTelefunken in various positions including head of R&D of the Microwave Division in Flensburg and Marketing Director, R&D Finder Division Ulm. During this time he had product responsibility for mm-wave radars, receivers, direction finders, and electronic warfare systems. Since 1983 he has been director of the Institute for Microwaves and Electronics at the University Karlsruhe. His present research topics include radar, remote sensing, wave propagation, and antennas. In 1989 he spent a six month sabbatical at the Jet Propulsion Laboratory, Pasadena. He is engaged in several working groups in electrical engineering.

Daniel Kahnv (Student Member. IEEE) was born in SchopfheimiBaden, Germany in ’1961. He received the Dipl. Ing (M.E.E.) from the University of Karlsruhe in 1987. Since 1987 he is with the Institute for Microwaves and Electronics at the University Karlsruhe. There he has the position of Research Assistant and is responsible for the student seminar in microwave theory. He is head of the microwave signature laboratory. His present research topics include polarimetric radar signature analysis and measurement techniques for monostatic, and bistatic polarimetric instrumentation radar systems. In 1991 he spent six months at the Institute for Remote sensing Applications of the European Communities Joint Research Centre in IspraiItaly.

PROCEEDINGS OF THE IEEE, VOL. 79, NO. 10, OCTOBER 1991