PUBLICATIONS RESEARCH ARTICLE Key Points: Prior studies are on calibration; we evaluate its impact from users perspective Impact on polarimetric target decomposition is analyzed, and 25 db is concluded Its impact on SAR military target detection using polarimetric data is analyzed Correspondence to: F. Xu, fengxu@fudan.edu.cn Citation: Xu, F., H. Wang, Y.-Q. Jin, X. Liu, R. Wang, and Y. Deng (215), Impact of cross-polarization isolation on polarimetric target decomposition and target detection, Radio Sci., 5, 327 338, doi:. Received 26 SEP 214 Accepted 23 MAR 215 Accepted article online 26 MAR 215 Published online 22 APR 215 215. American Geophysical Union. All Rights Reserved. Impact of cross-polarization isolation on polarimetric target decomposition and target detection Feng Xu 1, Haipeng Wang 1, Ya-Qiu Jin 1, Xiuqing Liu 2, Robert Wang 2, and Yunkai Deng 2 1 Key Laboratory for Information Science of Electromagnetic Waves (MoE), Fudan University, Shanghai, China, 2 Institute of Electronics, CAS, Beijing, China Abstract Cross-polarization isolation is one of the key engineering parameters for a polarimetric radar system. Previous studies focused more on the calibration of cross-talk contamination. This paper presents a numerical evaluation of the requirement for cross-polarization isolation from the data users perspective, i.e., the quantitative impact of polarization cross talk on polarimetric target decomposition and the associated applications such as classification and detection. Sensitivity analyses of several commonly used target decomposition parameters suggest that a theoretical lower bound of 32 db isolation level is preferred to avoid any significant impact on these parameters. Our analyses with both simulated and real synthetic aperture radar (SAR) data show that a level of 25 db would be acceptable for general terrain surface classification. This requirement is also true for man-made target detection application. Using simulated SAR images of man-made targets in natural environment, sensitivity analyses on two polarimetric detectors, Yang and Marino, both suggest that target detection performance would break down rapidly if isolation deteriorates from 25 db to 2 db. 1. Introduction Cross-polarization isolation is one of the key engineering requirements for polarimetric radar systems. Previous studies have been focusing more on the calibration of cross-talk contamination on quad or dual polarization data [van Zyl, 199; Dubois et al., 1992; Freeman et al., 1992; Touzi and Shimada, 29]. The consensus is that cross-talk level can be suppressed down to 3 db after full polarimetric calibration [Touzi et al., 21] and 35 db for dual polarization calibration [Shimada et al., 29; Suchail et al., 1999; Uher et al., 24; Miller et al., 213]. There have been very few studies focusing on the actual impact of polarimetric channel cross-talk contamination on end applications of polarimetric synthetic aperture radar (SAR). For instance, Wang and Chandrasekar [26] analyzed the isolation requirements for weather application; Touzi et al. [21] studied this issue for ocean applications such as ship detection and wind speed retrieval. This study attempts to analyze the requirement for cross-polarization isolation from the perspective of data users, with a focus on general applications such as terrain surface classification and man-made target detection for both land and sea environments. The major objective is to complement the current literature on polarimetric calibration by presenting both theoretical and numerical analyses of the net effect of cross-talk contamination on the end applications. Several target decomposition parameters are chosen for sensitivity analyses, e.g., orientation angle, Cameron s unit disc, Cloude s alpha angle, and deorientation parameters. Theoretical derivation reveals the shifting pattern of these parameters. It suggests that the safe limit of cross-polarization isolation is 32 db, under which these polarimetric parameters are minimally affected. It matches with the 3 db level set by CEOS standards. However, for most common terrain surfaces, a 25 db isolation would be acceptable, which is supported by simulated cross-talk contamination on simulated SAR images. Terrain surface classification using the simulated SAR image shows that the classification results remain the same for cross-talk contamination of 25 db isolation. The same 25 db threshold is found applicable to man-made target detection as well. Using simulated man-made targets in rough surface environment, sensitivity test indicates that target detector performance breaks down rapidly when isolation deteriorates from 25 db to 2 db. The next section presents the theoretical derivation and analysis, while sections 3 and 4 give validation with both simulated and real SAR data for terrain surface classification and man-made target detection, respectively. Section 5 concludes the paper. XU ET AL. IMPACT OF CROSS-POLARIZATION ISOLATION 327
2. Theoretical Analyses 2.1. Problem Formulation Consider a scattering matrix contaminated by polarization channel cross talk as follows [van Zyl, 199]: S ¼ 1 δ " # Sv S x 1 δ S v þ 2δS x þ δ 2 S h S x þ δs h þ δs v þ δ 2 S x ¼ δ 1 S x S h δ 1 S x þ δs h þ δs v þ δ 2 S x S h þ 2δS x þ δ 2 S v (1) Let the isolation coefficient, δ 1, yields S v þ 2δS x S S x þ δs h þ δs v S x þ δs h þ δs v S h þ 2δS x (2) Note that we have assumed that the cross talk between two polarization channels abides by reciprocity for both transmitter and receiver. In reality, this assumption of reciprocity may not be valid, in particular for residue cross talk. After polarimetric calibration, the residue might be purely attributable to the nonreciprocity. This will affect the shifting pattern derived later; however, the general conclusion of theoretical limit is still valid. Using diagonalization, the scattering matrix can be written in the form of cosψ sinψ cosχ jsinχ λ1 cosχ jsinχ cosψ sinψ S ¼ sinψ cosψ jsinχ cosχ λ 2 jsinχ cosχ sinψ cosψ where ψ and χ represents the angle of rotation transform and elliptical transform. Many target decomposition approaches follow the first step of separating orientation information and rotation invariant information [Cameron and Leung, 199]. As revealed in Xu and Jin [25], most of these approaches are equivalent under the assumption of nonhelicity, i.e., χ =, which greatly simplifies the problem. In practice, the helicity-related portion of information is often smaller in magnitude and thus is less often used in general applications such as terrain surface classification. Thus, this paper focuses the impact of polarization cross talk on target decomposition of the nonhelicity case. Under this assumption, the derived conclusion is generally applicable to most target decomposition parameters. The scattering matrix for nonhelix targets thus becomes cosψ sinψ λ1 cosψ sinψ S ¼ sinψ cosψ λ 2 sinψ cosψ (3) (4) Apparently, the rotation invariant λ 1 and λ 2 become the eigenvalues of S, while the rotation matrix of ψ corresponds to the eigenvector matrix. From the contaminated scattering matrix, we can derive the complex eigenvalues λ 1,2 and angle: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2λ 1;2 ¼ S v þ S h þ 4δS x ± ðs v S h Þ 2 þ 4ðS x þ δs h þ δs v Þ 2 S x þ δs h þ δs v sin2ψ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðs v S h Þ 2 þ 4ðS x þ δs h þ δs v Þ 2 (5) Further, define the following parameters: A ¼ jλ 1 j g ¼ λ 2 λ 1 p ¼ sin2ψ (6) The orientation information is now conveyed in parameter p, while the rotation invariant intrinsic information is conveyed in the two eigenvalues. The overall amplitude represented by A is usually not interesting in target decomposition, as it is directly related to target s radar cross section. Following Cameron s definition, the ratio of the two complex eigenvectors g is used as the sole parameter conveying intrinsic target characteristics. XU ET AL. IMPACT OF CROSS-POLARIZATION ISOLATION 328
Under the nonhelicity condition, we can link the intermediate parameter g to well-known target decomposition parameters as follows: For Huynen s theory [Huynen, 197] g ¼ tan 2 γ expð2jνþ (7) where γ denotes the characteristic angle and ν denotes the skip angle. For Cameron s theory [Cameron and Leung, 199] z ¼ g (8) where z denotes the position on Cameron s unit disc on complex plane. For Cloude-Pottier decomposition of a deterministic target [Cloude and Pottier, 1997] where α denotes the Cloude-Pottier s alpha angle. For deorientation theory of a deterministic target [Xu and Jin, 25] cosα ¼ q j ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ gj (9) 2 þ 2jgj 2 juj ¼ 1 jgj2 1 þ jgj 2 ; v ¼ 2Reg 1 þ jgj 2 (1) where u and v denote the projected dielectric polarity and dielectric skipness [Jin and Xu, 213], respectively. To summarize, we now have three parts of polarimetric information of target: orientation ψ, shape g, and mechanism arg g. All three can be extracted from the scattering matrix and also used to represent different types of polarimetric scattering targets. The Cameron s unit disc is used as the sole metric in this paper, simply because of its unique role to link different sets of typically used polarimetric parameters. 2.2. Sensitivity The following section is to analyze the impact of polarization channel cross talk on these parameters for different targets classified by these parameters. Write g and p as a function of δ: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi gðþ¼ δ S v þ S h þ 4δS x ðs v S h Þ 2 þ 4ðS x þ δs h þ δs v Þ 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S v þ S h þ 4δS x þ ðs v S h Þ 2 þ 4ðS x þ δs h þ δs v Þ 2 (11) S x þ δs h þ δs v pðþ¼ δ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S v þ S h þ 4δS x þ ðs v S h Þ 2 þ 4ðS x þ δs h þ δs v Þ 2 To study the sensitivity of these parameters to small polarization channel cross talk, let us take their first-order derivatives of δ, which results in g 4p δ δ ðþgðþ δ p δ 21 1 þ gðþ δ p2 ðþ δ 1 gðþ δ Now let us define the perturbation of polarimetric parameters caused by channel cross talk as Δg ¼ gðþ g δ ðþ ¼ 4δpðÞg δ ðþ δ Δp ¼ ½pðÞ p δ ðþšj1 gðþj 2δ½1 p 2 ðþ δ Š 1 þ gðþ δ 1 gðþ δ j1 gðþj (13) where the factor 1 g() is applied to regularize p, i.e., p = p 1 g(), because the orientation angle becomes arbitrary as g approaches 1. (12) XU ET AL. IMPACT OF CROSS-POLARIZATION ISOLATION 329
Figure 1. Amplitude map of Δg on the Cameron s unit disc for different orientations. (The color from blue to red corresponds to to 4δ.) The conditions for parameters perturbation to be negligible can be written as jδgj 1 jδp j 1 Following equation (13), we also have Δg 4δpðÞg δ ðþ Δp 2δ½1 p 2 ðþ δ Šj1 þ gðþj (14) (15) Note that p(δ) p() is not negligible, as g approaches 1. Using the following relationship pðþ p δ ðþ 21 p 2 1 þ gðþ ðþ δ 1 gðþ δ (16) we can estimate it as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ 4k 2 þ 4kpðÞ 1 pðþ δ 2k k ¼ 1 þ gðþ (17) 1 gðþ δ Finally, it yields ( j jδgj ¼ 4δp 1gj g 1 j4δpgj else ( 2jj1 δ p 2 Δp 1 j1 þ gj g 1 ¼ 2jj1 δ j p 2 jj1 þ gj else pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ 4k 2 þ 4kp 1 p 1 ¼ ; k ¼ 1 þ g 2k 1 g δ (18) Following equations (14) and (18), the upper bound of δ for all polarimetric targets is jj δ 1=4 (19) i.e., δ <.25, which corresponds to 32 db of polarization isolation. In practice, this dictates the requirement for the net cross talk after calibration. Note that this conclusion is derived for the case of deterministic coherent target, which will be extended to the case of distributed targets later in section 2.4. 2.3. Numerical Analysis Now let us investigate the pattern of the perturbations Δg and Δp. The gradient fields of Δg plotted on the Cameron s unit disc are shown in Figures 1 and 2. As we can see, the major shift of g is from the edge to the center. This shrinking shift is proportional to orientation p and g, as can be observed from equation (18). When orientation angle is small, there is a secondary shift to occur at g 1 region. It drags g toward left. Hence, it can be interpreted as the shrinking shift preserves at g 1 region for small orientation angles. Look at the g versus p plane, where Img =. The shifts of Δp and Δg are plotted in Figure 3. The shrinking shift of g can be seen clearly as well, while the major shift of orientation occurs around the lower right region. It XU ET AL. IMPACT OF CROSS-POLARIZATION ISOLATION 33
quart-wave dihedra narrow dihedra dipol cylinder sphere quart-wave Figure 2. Quiver map of Δg on the Cameron s unit disc for different orientations. increases the orientation angle, i.e., p, for targets in these regions. Also notice that the lower left region (aligned dihedral) is immune to contamination; its polarimetric characteristics are not sensitive to δ. The perturbations to different polarimetric parameters of the typical targets are summarized in Table 1. Note that for deterministic coherent scattering, the nonhelicity assumption, in fact, excludes general nonsymmetric scattering mechanisms. Here additional sensitivity analysis is provided to evaluate the impact of cross talk on helicity angle χ. InFigure4,theerrorofχ caused cross talk at 3 db isolation level is plotted on the plane of g versus p. The helicity angle is chosen as χ =15 according to our experience with real data. It canbeseenthatδχ for most cases. The negative bias on the right edge is caused by degeneration of polarity as g 1. The largest error Δχ 8 occurs on the top edge where the orientation angle ψ 45. 2.4. Distributed Targets For distributed targets, the polarimetric information is often expressed as the correlation of individual scattering matrix. Take the eigen analysis [Cloude and Pottier, 1997] as an example, i.e., coherency matrix T ¼< k p k þ p > (2) where k H p denotes the Pauli-vectorized scattering matrix of an individual target and superscript + denotes conjugate transpose. Apparently, we have the contaminated k p vector written as 2 ðs v þ S h Þ 1 þ δ 2 3 þ 4δSx k p ðþ¼ δ p 1 ffiffiffi ðs v S h Þ 1 δ 2 6 7 24 5 ¼ QðÞk δ pðþ 2S x 1 þ δ 2 þ 2δ ð Sh þ S v Þ (21) 2 1 þ δ 2 3 2δ QðÞ¼ δ 6 1 δ 2 7 4 5 2δ 1þ δ 2 Thus, the contaminated coherency matrix is TðÞ¼Q δ ðþk δ p ðþk þ p ðþqþ ðþ δ (22) With eigen analysis, it is supposed to extract the polarimetric parameters of major individual targets, while the extracted entropy H indicates the diversity or randomness of distributed targets. The extracted major polarimetric parameters should follow the same shift as discussed in the previous sections. To discuss the shift of H, consider two extreme cases: 1. All individual targets are the same, meaning the distributed target is single, i.e., H =. In this case, all targets have the same shift, meaning the contaminated data will show the same deterministic distribution. Hence, the entropy H remains zero. 2. All individual targets are distinct, meaning the distributed target is completely random, i.e., H 1. In this case, whether H increase or decrease depends on how these targets would be shifted respectively. If the distance between these targets is compressed, then H decreases. From the gradient fields shown in Figures 2 and 3, this is very likely the case, because most shifts are toward the same direction. XU ET AL. IMPACT OF CROSS-POLARIZATION ISOLATION 331
4δ However, we believe that the changes to H is comparable to the changes to g and p. Consider the case of uniformly and randomly oriented dipoles. After contamination, the orientation distribution range will be compressed from p [,1] to p [2δ,1]. This conclusion is supported by numerical analysis given in the next section. 3. Impact on Terrain Surface Classification 2δ 3.1. Simulated SAR Image The simulated SAR image using the MPA 1δ (mapping and projection algorithm) [Xu and Jin, 26] is used as a proxy to validate the sensitivity analysis result given in the previous section. However, the case given here is rather oriented specific to that type of terrain surface classification application. Note that narrow simulated data are preferred over dihedra dihedra dipol cylinder sphere real SAR data here to avoid further complication that may be caused by the already included cross-talk aligned contamination in any real SAR data. Figure 5 is the simulated SAR image based on MPA algorithm at L band Figure 3. Amplitude maps of Δp and Δg and their quiver map on the g versus p plane. (The color from blue to red corresponds to to 4δ.) with 12 m resolution (pixel spacing is 5 m), and the scene includes urban buildings, suburban, farmland, road, river, and forests. In the figure, urban buildings, which are modeled as parallel street block with few trees, are located in the top right area. Right next to urban area, suburban region contains randomly distributed trees and small buildings. Farmland is located at the bottom left and constructed by flat area with crops. The top left and bottom right areas are forests with different species, while broadleaf trees and conifer are, respectively, in the top left and bottom right areas. Detailed descriptions of SAR image simulation are addressed in Xu and Jin [26]. Red boxes are the areas selected to analysis, from top to bottom and from left to right: forest1, farmland1, farmland2, forest2, urban, road, suburban, and river. Note that these areas are selected so that the scattering signatures are, in general, uniform within each area. The distributions of these regions are plotted on the u-h planes as shown in Figure 6. These regions are well separated in the u-v-h space. Note that suburban area involves oriented buildings and vegetation which appears much dispersed in the polarimetric space. The urban area is purposely selected to be a narrow strip of strong double-bounce scattering, and thus, it presents very low entropy H because of its purity of scattering mechanism. These regions will be collectively analyzed for the impact of cross-polarization contamination in the next section. 3δ Table 1. Perturbations of Polarimetric Parameters Caused by Channel Cross-Talk δ Target g or z p or sin 2ψ u v cos α Sphere 1 1 4δ - 4δ 1 1 8δ 1 1 2δ Dipole aligned δ/2 1 1.7.7 Dipole oriented 1 1 1 1.7.7 Dihedral aligned 1 1 1 1 1 1 Dihedral oriented 1 1+4δ 1 1 1 1-4δ 1 1+8δ 2δ XU ET AL. IMPACT OF CROSS-POLARIZATION ISOLATION 332
3.2. Quantitative Analyses In this section, the influence of crosspolarization isolation is quantitatively measured on four polarimetric parameters, namely, H, alpha, u, and v. The isolation changes from 42 db to 18 db, and δ is calculated from isolation level (db); e.g., δ =.1 corresponds to 4 db isolation. Figure 7 shows the four polarimetric Figure 4. Shift of helicity angle Δχ on the g versus p plane ( χ =15 and parameters as a function of isolation δ = 3 db). level. It can be seen that parameter changes are literally negligible when isolation is below 32 db, which is consistent with the previously derived theoretical limit. Note that u is more sensitive than other parameters. For isolation below 25 db, the maximum shift of u is less than.1, and thus, we conclude that for general natural terrain surfaces, the requirement of isolation can be relaxed to 25 db. Moreover, the shift direction agrees with the theoretic prediction given in the previous section. The change in H appears to be much smaller than u, which is also consistent with our prediction. Interestingly, the parameter v does not change too much for most terrain surfaces except forest2. Note that the alpha parameter is calculated as the averaged value of three eigenvectors of the coherency matrix of the simulated SAR image. Classification is one of the main polarimetric SAR applications. Influence of polarimetric isolation on classification accuracy is evaluated according to the deorientation scheme proposed in Xu and Jin [25], and terrain surfaces are classified into nine types in total [see Xu and Jin, 25, Figure 13]. Figure 8 shows the classification error as a function of isolation. Note that classification error is defined as the percentage of wrongly classified pixels. It can be seen that if isolation is better than 25 db, the classification accuracy remains below 1%, but when the isolation degrades from 25 db or 18 db, then the corresponding accuracy drops steeply from 1% to 44%. This result confirms the 25 db requirement for natural terrain surface classification. Figure 5. Simulated SAR image based on MPA. XU ET AL. IMPACT OF CROSS-POLARIZATION ISOLATION 333
Figure 6. The selected regions distributed on the u-v-h planes. 3.3. Analyses With Real SAR Image As a comparison, real SAR data obtained by NASA/Jet Propulsion Laboratory Uninhabited Aerial Vehicle (UAV) SAR over San Diego port are analyzed in the same way. The UAV SAR image is compared in Figure 9 with the corresponding aerial image where three regions are labeled as urban, sea, and forest. Note that the real data are already contaminated by polarization cross talk. However, it is treated as pure data in our analyses, and additional cross talk is added via simulation. In Figure 1, the simulated polarimetric parameters as a function of isolation level are plotted. It can be seen that the same conclusion of 25 db requirement can be made. a H c u 1.9.8.7.6.5.4.3.2.1 1.8.6.4.2-42 -38-34 -3-26 -22-18 -42-38 -34-3 -26-22 -18 b Alpha ( ) d v 9 8 7 6 5 4 3 2 1 1.8.6.4.2 -.2 -.4 -.6 -.8-1 -42-38 -34-3 -26-22 -18-42 -38-34 -3-26 -22-18 urban suburban road river forest1 forest2 farmland1 farmland2 Figure 7. Polarimetric parameters as a function of cross-polarization isolation: (a) H, (b) alpha, (c) u, and (d) v. XU ET AL. IMPACT OF CROSS-POLARIZATION ISOLATION 334
4. Impact on Target Detection Man-made target detection is another important application of polarimetric SAR. In this section, SAR images simulated using the BART (bidirectional analytic ray tracing) [Xu and Jin, 29] are used as sample data to validate the sensitivity analysis result from the aspect of target detection. 4.1. Polarimetric Target Detector To evaluate the influence of channel cross talk on target detection accuracy, three typical cases, namely, aircraft on airport, tank on grassland, and ship on ocean, were simulated using the Figure 8. Classification error as a function of cross-polarization isolation. BART engine. Two target detection algorithms are tested, which are respectively proposed by Yang et al. [21] andmarino et al. [212], both approaches measuring the similarity of two scattering matrix to detect target. The brief induction of two methods is given below. In Yang s method, for noncoherent targets, the similarity of two target evaluated by Mueller matrix is given as jh rm ð 1 ; M 2 Þ ¼ M 1; M 2 ij (23) k kkm 2 k F where h, iand F denote inner product and F norm of matrix, respectively. M 1 is the Mueller matrix of the target to be detected, which can be obtained by theoretical calculation or measurement of real target, while M 2 is Mueller matrix of unknown target. The similarity r is calculated, and we can assume that two targets are the same given r is greater than the threshold T. In Marino detector, normalized scattering vector is used, and it is given by M 1 F ω ¼ k= jj k (24) Figure 9. (left) UAV SAR image over San Diego port and (right) the corresponding aerial image from Google Earth. XU ET AL. IMPACT OF CROSS-POLARIZATION ISOLATION 335
(a) (b) (c) (d) Figure 1. Polarimetric parameters as a function of cross-polarization isolation: (a) H, (b) alpha, (c) u, and (d) v, as calculated using UAV SAR data. Assume that the normalized scattering vectors of target and measured object to be identified are respectively ω T and ω M. The coherence coefficient criteria are defined as [Marino et al., 212] γðω T ; ω M Þ ¼ iðω T Þi ðω M Þ 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi iðω T Þi ðω T Þiðω M Þi (25) ðω M Þ 1 þ b2 1 5b 2 t T t 1 T j t T ^t T j 2 where i ω j ¼ ω T j k; ðj ¼ T; MÞ denotes the image with scattering vector ωj, b is a complex number which amplitude is close to, and and are the scattering vectors of the target to be detected and the measured t ^t T data, respectively. Considering the noise in real measured data, a threshold T is usually adopted. Two targets can be regarded as the same when γ(ω T, ω M ) T. For more technical details of the Marino detector, the readers are referred to Marino et al. [21] and Marino [212]. 4.2. Numerical Analysis Three targets including aircraft, tank, and battle ship were selected to test the influence of cross talk on detection accuracy. As shown in Figures 11a2 11c2, there are 15 aircrafts, 3 tanks, and 3 battle ships randomly placed in airport, grassland, and sea, with, 45, 9, and 135 four types azimuth angles and 1 m resolution in both azimuth and range direction. As shown in Figure 11, for both detectors, detection accuracy decreases dramatically as the cross-polarization isolation increased beyond 25 db. For isolation better than 25 db, a detection accuracy of at least 9% can XU ET AL. IMPACT OF CROSS-POLARIZATION ISOLATION 336
(a1) (b1) (c1) (a2) (b2) (c2) Detection Error (%) 1 9 8 7 6 5 4 3 2 1 T=.9 T=.9 7 6 Detection Error (%) 5 4 3 2 1-4 -35-3 -25-2 -4-35 -3-25 -2 T=.9 7 6 5 4 3 2 1-4 -35-3 -25-2 (a3) (b3) (c3) Detection Error (%) 8 T=.987 4 T=.96 18 T=.96 7 35 16 Detection Error (%) 6 5 4 3 2 Detection Error (%) 3 25 2 15 1 Detection Error (%) 14 12 1 8 6 4 1 5 2-4 -35-3 -25-2 -4-35 -3-25 -2-4 -35-3 -25-2 (a4) (b4) (c4) Figure 11. Image simulation and influence of cross talk on target detection accuracy. Rows from top to bottom are (a1, b1, and c1) model, (a2, b2, and c2) simulated scene with targets, (a3, b3, and c3) relation of Yang s detector, and (a4, b4, and c4) relation of Marino s detector, respectively. Columns from left to right denote aircraft (Figures 11a1 11a4), tank (Figures 11b1 11b4), and battle ship (Figures 11c1 11c4). XU ET AL. IMPACT OF CROSS-POLARIZATION ISOLATION 337
be guaranteed in these particular cases, which are in accordance with the general conclusion given in the above analyses. 5. Conclusions To evaluate the impact of polarization cross talk from the perspective of target decomposition and classification, both theoretical and numerical analyses are conducted. The derived theoretical limit suggests that polarimetric signature shift is negligible if cross-polarization isolation is below 32 db. However, numerical analysis with the MPA-simulated L band SAR image of comprehensive natural scene suggests that both parameters and classification result will not be significantly affected with a minimum requirement of 25 db cross-polarization isolation. This conclusion is valid only for commonly seen terrain surfaces, e.g., vegetation canopy, bare ground/water surfaces, urban, and suburban built-up areas. Similar analyses with real SAR data confirm the observation. 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