CALIBRATION OF POLARIMETRIC RADAR SYSTEM
USING
THREE PERFECTLY POLARIZATION-ISOLATED CALIBRATORS
Tzong-Jyh Chen and Tah-Hsiun Chu*
Electrical Engineering Department, National t a i w a n University Taipei, Taiwan, Republic of China
I. INTRODUCTION
an arbitrarily rotated dihedral corner reflector, by assuming the magnitudes of co-polarization terms in PSM of each calibrator to be equal.
In this paper, the calibration method in [3] is generalized such that the requirement for each polarization-isolated calibrator to have the same co-polarized RCS is not needed. Only the co-polarized terms in PSM of the first calibrator is required. The range and co-polarized RCS's of the other two calibrators and the rotation angle of the third calibrator can be derived in the calibration process and used to verify the calibration.
11. CALIBRATION ALGORITHM S' is expressed as [3]
The relation between the target PSM
S
and the measured target PSMs",v s",h R v v R v h s v v S v h [ . v . , ] = [ ~ : ~ ~ ] ' [ R h v R h h ] [ S h v S h h ] [
$:$h"]
where I is an additive isolation error matrix which can be directly measured without locating any scattering target. T and R are the transfer matrices of transmitting and receiving antennas to be characterized. With the isolation error matrix I suppressed, the measured PSM's of three perfectly polarization-isolated Cali brators are
A , = R [ ? k ] T (2)
b = R [ C L I T (3)
(4)
cos0 s i n e cos@ - s i n e
where 4, 9,
8,
h,
71, and 3 are complex constants to account for the different rmges and co-polarized RCS's of these calibrators. The third calibrator is rotated by 0 angle with respect to the radar range direction to provide cross-polarized information for use in the calibration. Equation (2)can be rewritten as
R = A , T - ~
[
0"'
k1-l ( 5 )which indicates that R can be found, as CUI and
cuz
are given and T is derived as the following. LetT = Thh
[
5"
y ]
= Thh T' (6)where 2 =Tvv Tvh, y =Thv/Thh, and W =Tvh/Thh are pX&IlleterS to be determined. Aiter pro er matrix manipulation, the following four equations can be derived from (2744)
El$
+
(E22 - El1)z - EZ1 = 0E12P
+
( 4 2 - E11)Y- E21 = 0 G5( m o t 6)2 - G,mot 6+
G7 = 0 G5(vtan6)2+
G,zutan6+
G7 = 0 (7) (8) (9) (10)where E = A1-1A2, F = A1-IA3, G5 = - C U ~ [ F ~ Z Z
+
(F22-F11)z - F z ~ ] , G6 =culz+cuz ) 4 1 (cu~+cuz)(qF~z-Fz~) - a~y+azz FZZ, and
G
= -(rz[F1zy2+
F22-F1$y -GI].
With the constraint(I
z1>>
Iy1,
z and y can solved from 7) and (8). As the range of 0 is known a priori, values of 6 and w can be obtained from (9) and (10). ThenPI,
pz,
71, and 72 can be solved in t e r m ofCUI and
cuz.
After z, y, and w in (6) derived, R in (5) can be expressed in normalized form asUsing ( l ) , (6), and (11) the correct target PSM can be calculated as S = R-1( S m - 1 ) T-1 = R'-1( S m - 1 ) TI-1 (12)
111. EXPERIMENTAL RESULTS
A flat metal plate with dimension 17 cm by 17 cm is used as the first calibrator. Since the scattering responses of a square plate for vertical and horizontal polarizations are the same, a1 is equal to cuz. A dihedral corner reflector with dimension 12 cm by 17 cm for each side is used as the second and third calibrators. Results of the rotation angle of dihedral corner reflector (third calibrator) are shown in Fig.1 in comparison with the method in [3]. The deviation of calculated rotation angle over operation band is shown significantly improved. Figure 2 shows the magnitude of co-polarization ratio &/pZ of dihedral corner reflector (second calibrator) in comparison with the theoretical results.
Measurement results of co-polarization ratio (&r/Shh) of a conducting cylinder with diameter 2.54 cm and length 128.5 cm is shown in Fig.3 in comparison with the method in [3] and the theoretical data. The discrepancy for magnitude and phase are shown about within 0.5 dB and 9 degrees over 7 to 17 GHz.
REFERENCES:
[l] S. H. Yueh et al., "Calibration of polarimetric radars using in-scene reflectors," J. Electromag. Wave Applz., Vo1.4, pp.27-48, Jan. 1990. [2] M. W. Whitt et al., "A general polarimetric radar calibration
technique, IEEE Tray? Antennas Propagat., pp.62-67, Jan. 1991. [3] T. J. Chen et al., A new calibration algorithm of wideband
polarimetric measurement system," IEEE Trans. Antennas Propagat., pp.1188-1192, Aug. 1991.
degree 25
-present method ----. method in 131
7 8 9 10 11 12 13 14 15 16 17
Frequency (GHz) Fig.1 Results of rotation angle 0 of the third calibrator.
magnitude(d6) 2 1 0 - 1 7 8 9 10 11 12 13 14 15 16 17 Frequency (GHz)
Fig.:! Results of magnitude of co-polarization ratio
PI//&
of the second calibrator.rnagnitude(dB)
:.:
. .
- 2 - l
t
- -theoretical - present method - - - method in 131
phase(degree1
- 5 -
theoretical - present method ..--- method in 131
- 4 5
-
507 8 9 10 11 12 13 14 15 16 17
Frequency(GHz1 (b)
Fig.3 Results of (a) magnitude and (b) phase of Svv/Shh of a conducting cylinder with diameter 2.54 cm and length 128.5 cm.
