Abstract

We report the development of a technique for adaptive selection of polarization ellipse tilt and ellipticity angles such that the target separation from clutter is maximized. From the radar scattering matrix [S] and its complex components, in phase and quadrature phase, the elements of the Mueller matrix are obtained. Then, by means of polarization synthesis, the radar cross section of the radar scatters are obtained at different transmitting and receiving polarization states. By designing a maximum average correlation height filter, we derive a target versus clutter distance measure as a function of four transmit and receive polarization state angles. The results of applying this method on real synthetic aperture radar imagery indicate a set of four transmit and receive angles that lead to maximum target versus clutter discrimination. These optimum angles are different for different targets. Hence, by adaptive control of the state of polarization of polarimetric radar, one can noticeably improve the discrimination of targets from clutter.

© 2006 Optical Society of America

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References

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  1. C. H. Papas, Theory of Electromagnetic Wave Propagation (Dover, 1988).
  2. J. J. van Zyl, C. H. Papas, and C. Elachi, "On the optimum polarizations of incoherently reflected waves," IEEE Trans. Antennas Propag. AP-35, 818-825 (1987).
    [CrossRef]
  3. F. T. Ulaby, and C. Elachi, eds., Radar Polarimetry for Geoscience Applications (Artech House, 1990).
  4. H. Mott, Antennas for Radar and Communications: a Polarimetric Approach. (Wiley, 1992).
  5. S. Huard, Polarization of Light (Wiley, 1996).
  6. A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, 1991).
  7. M. I. Skolnik, Introduction to Radar Systems, 2nd. ed. (McGraw-Hill, 1980).
  8. B. V. K. Vijaya Kumar, "Minimum-variance synthetic discriminant functions," J. Opt. Soc. Am. A 3, 1579-1584 (1986).
    [CrossRef]

1987

J. J. van Zyl, C. H. Papas, and C. Elachi, "On the optimum polarizations of incoherently reflected waves," IEEE Trans. Antennas Propag. AP-35, 818-825 (1987).
[CrossRef]

1986

Elachi, C.

J. J. van Zyl, C. H. Papas, and C. Elachi, "On the optimum polarizations of incoherently reflected waves," IEEE Trans. Antennas Propag. AP-35, 818-825 (1987).
[CrossRef]

F. T. Ulaby, and C. Elachi, eds., Radar Polarimetry for Geoscience Applications (Artech House, 1990).

Huard, S.

S. Huard, Polarization of Light (Wiley, 1996).

Ishimaru, A.

A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, 1991).

Kumar, B. V. K. Vijaya

Mott, H.

H. Mott, Antennas for Radar and Communications: a Polarimetric Approach. (Wiley, 1992).

Papas, C. H.

J. J. van Zyl, C. H. Papas, and C. Elachi, "On the optimum polarizations of incoherently reflected waves," IEEE Trans. Antennas Propag. AP-35, 818-825 (1987).
[CrossRef]

C. H. Papas, Theory of Electromagnetic Wave Propagation (Dover, 1988).

Skolnik, M. I.

M. I. Skolnik, Introduction to Radar Systems, 2nd. ed. (McGraw-Hill, 1980).

Ulaby, F. T.

F. T. Ulaby, and C. Elachi, eds., Radar Polarimetry for Geoscience Applications (Artech House, 1990).

van Zyl, J. J.

J. J. van Zyl, C. H. Papas, and C. Elachi, "On the optimum polarizations of incoherently reflected waves," IEEE Trans. Antennas Propag. AP-35, 818-825 (1987).
[CrossRef]

IEEE Trans. Antennas Propag.

J. J. van Zyl, C. H. Papas, and C. Elachi, "On the optimum polarizations of incoherently reflected waves," IEEE Trans. Antennas Propag. AP-35, 818-825 (1987).
[CrossRef]

J. Opt. Soc. Am. A

Other

C. H. Papas, Theory of Electromagnetic Wave Propagation (Dover, 1988).

F. T. Ulaby, and C. Elachi, eds., Radar Polarimetry for Geoscience Applications (Artech House, 1990).

H. Mott, Antennas for Radar and Communications: a Polarimetric Approach. (Wiley, 1992).

S. Huard, Polarization of Light (Wiley, 1996).

A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, 1991).

M. I. Skolnik, Introduction to Radar Systems, 2nd. ed. (McGraw-Hill, 1980).

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Figures (10)

Fig. 1
Fig. 1

Polarization ellipse.

Fig. 2
Fig. 2

Visible-band view of the scene used for data collection.

Fig. 3
Fig. 3

Sample of the SAR imagery of the scene shown in Fig. 2.

Fig. 4
Fig. 4

(Color online) Variation of the MACH filter's distance for target 1 (at 236.7973, 324.221) in terms of the inclination angle for the special case in which the ellipticity angle = 0 deg.

Fig. 5
Fig. 5

(Color online) Variation of the MACH filter's distance for target 2 (at 321.211, 148.5055) in terms of the inclination angle for the special case in which the ellipticity angle = 22.5 deg.

Fig. 6
Fig. 6

(Color online) Variation of the MACH filter's distance for target 3 (at 482.7191, 162.8607) in terms of the inclination angle for the special case in which the ellipticity angle = 45 deg.

Fig. 7
Fig. 7

(Color online) Composite display of all ROC plots associated with the case of corrupting polarimetric radar images with a Gaussian noise of mean of 0.001 and standard deviation of 0.0002.

Fig. 8
Fig. 8

(Color online) ROC plot for the case of radar imagery at the transmitted polarization angles of χ = 45 deg and ψ = 0 deg and the received polarization angles of χ = 45 deg and ψ = 180 deg. The corrupting Gaussian noise has a mean of 0.001 and a standard deviation of 0.0002.

Fig. 9
Fig. 9

(Color online) ROC plot for the case of radar imagery at the transmitted polarization angles of χ = 0 deg and ψ = 0 deg and the received polarization angles of χ = 0 deg and ψ = 0 deg (horizontal transmit and horizontal receive). The corrupting Gaussian noise has a mean of 0.001 and a standard deviation of 0.0002.

Fig. 10
Fig. 10

(Color online) ROC plot for the case of radar imagery at the transmitted polarization angles of χ = 0 deg and ψ = 90 deg and the received polarization angles of χ = 0 deg and ψ = 90 deg (vertical transmit and vertical receive). The corrupting Gaussian noise has a mean of 0.001 and a standard deviation of 0.0002.

Tables (1)

Tables Icon

Table 1 Optimum Polarimetric Angle Sets a

Equations (74)

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S = [ | S HH | e ϕ HH | S HV | e ϕ HV | S HV | e ϕ HV | S HV | e ϕVV ] ,
P r = k | E r E t | 2 ,
P r = k A r [ K ] A t .
A = [ E H E H * + E V E V * E H E H * E V E V * 2 Re [ E H E V * ] 2 Im [ E H E V * ] ] = [ a 2 a 2 cos 2 χ cos 2 ψ a 2 cos 2 χ sin 2 ψ a 2 sin 2 χ ] ,
E = Re { [ E H h + E V v ] e j ( κ r - ω t ) } ,
h   and   v
( κ r ω t )
[ K ]
K 11 = 1 / 2 ( | S HH | 2 + 2 | S HV | 2 + | S VV | 2 ) ,
K 12 = K 21 = 1 / 2 ( | S HH | 2 | S VV | 2 ) ,
K 13 = K 31 = Real ( S HH S HV * + S HV S VV * ) ,
K 14 = K 41 = Imag ( S HH S HV * + S HV S VV * ) ,
K 22 = 1 / 2 ( | S HH | 2 2 | S HV | 2 + | S VV | 2 ) ,
K 23 = K 32 = Real ( S HH S HV * S HV S VV * ) ,
K 24 = K 42 = Imag ( S HH S HV * S HV S VV * ) ,
K 33 = Real ( S HH S VV * + | S HV | 2 ) ,
K 34 = K 43 = Imag ( S HH S VV * ) ,
K 44 = Real ( S HH S VV * + | S HV | 2 ) ,
K i j
σ rt ( Ψ r , χ r , Ψ t , χ t ) = lim r [ 4 π r 2 ( P r / P t ) ] ,
σ ( Ψ r , χ r , Ψ t , χ t ) = 4 π A r [ K ] A t .
g ( 0 , 0 ) = x ( m , n ) h ( m , n ) = x + h ,
x   is   an   N × d
g i ( m , n )
ASM = 1 N i = 1 N m n [ g i ( m , n ) - g ¯ ( m , n ) ] 2 ,
g ¯ ( m , n ) = ( 1 / N ) j = 1 N g j ( m , n )
ASM = ( 1 / N d ) i = 1 N k l | G i ( k , l ) G ¯ ( k , l ) | 2 ,
G i ( k , l )   and   G ¯ ( k , l )
g i ( m , n )   and   g ¯ ( m , n )
ASM = ( 1 / Nd ) i = 1 N | g i - g ¯ | 2 .
m = ( 1 / N ) i = 1 N x i
M   and   X i
m   and   x i
g i = X i * h   and   g ¯ = M * h
ASM = 1 N d i = 1 N | X i * h M * h | 2
= 1 N d i = 1 N h + ( X i M ) ( X i M ) * h
= h + [ 1 N d i = 1 N ( X i M ) ( X i M ) * ] h = h + S h ,
S = ( 1 / N d ) i = 1 N ( X i M ) ( X i M ) *
ACH= ( 1 / N ) i = 1 N x + h = m + h .
h + C h
J ( h ) = | ACH | 2 ASM + ONV = | m + h | 2 h + S h + h + C h = h + m m h + h + ( S + C ) h .
( S + C ) 1 m m +
h = γ ( S + C ) 1 m ,
FSEP  = Separation = | ( m 1 m 2 ) + h | 2 ,
m 1   and   m 2
33.6   GHz
3   kHz
1.5   kHz
0.3   m
χ r = 0.393
Ψ r = 0.000 , χ t = 0.000
Ψ t = 0.785
χ r = 0.393
Ψ r = 0.000 , χ t = 0.000
Ψ t = 1.178
χ r = 0.196
Ψ r = 0.000
χ t = 0.589
Ψ t = 1.571
χ r = 0.589 ,
Ψ r = 0.000
χ t = 0.000
Ψ t = 0.785
χ r = 0.589
Ψ r = 0.000
χ t = 0.000
Ψ t = 0.785
χ r = 0.393
Ψ r = 0.000
χ t = 0.000
Ψ t = 1.178
χ = 45
χ = 45
ψ = 180

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