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On a gesture-computing technique using electromagnetic waves
SAR correlation imaging and anisotropic scattering
Department of Mathematics and Statistics, Villanova University, Villanova, PA 19085, USA |
In this paper we investigate the ability of correlation synthetic-aperture radar (SAR) imaging to reconstruct isotropic and anisotropic scatterers. SAR correlation imaging was suggested by the author previously in [
References:
[1] |
J. G. Berryman, L. Borcea, G. Papanicolaou and C. Tsogka,
Statistically stable ultrasonic imaging in random media, J. Acoust. Soc. Am., 112 (2002), 1509-1522.
doi: 10.1121/1.1502266. |
[2] |
W. M. Boerner, M. B. El-Arini, C. Y. Chan and P. M. Mastoris,
Polarization dependence in electromagnetic inverse problems, IEEE Trans. on Antennas and Propagation, 29 (1981), 262-271.
doi: 10.1109/TAP.1981.1142585. |
[3] |
L. Borcea, G. Papanicolaou and C. Tsogka,
Adaptive interferometric imaging in clutter and optimal illumination, Inverse Problems, 22 (2006), 1405-1436.
doi: 10.1088/0266-5611/22/4/016. |
[4] |
L. Borcea, G. Papanicolaou and C. Tsogka,
Interferometric array imaging in clutter, Inverse Problems, 21 (2005), 1419-1460.
doi: 10.1088/0266-5611/21/4/015. |
[5] |
L. Borcea, M. Moscoso, G. Papanicolaou and C. Tsogka,
Synthetic aperture imaging of direction and frequency dependent reflectivities, SIAM J. Imaging Sci., 9 (2016), 52-81.
doi: 10.1137/15M1036063. |
[6] |
L. Borcea, G. Papanicolaou and C. Tsogka,
Theory and applications of time reversal and interferometric imaging, Inverse Problems, 19 (2003), S139-S164.
doi: 10.1088/0266-5611/19/6/058. |
[7] |
T.-K. Chan, Y. Kuga and A. Ishimaru,
Subsurface detection of a buried object using angular correlation function measurement, Waves Random Media, 7 (1997), 457-465.
doi: 10.1080/13616679709409809. |
[8] |
R. D. Chaney, M. C. Burl and L. M. Novak,
On the Performance of Polarimetric Target Detection Algorithms, IEEE International Radar Conference, 1990.
doi: 10.1109/RADAR.1990.201114. |
[9] |
M. Cheney and B. Borden,
Fundamentals of Radar Imaging, SIAM, Philadelphia, 2009. |
[10] |
S. R. Cloude and E. Pottier,
A review of target decomposition theorems in radar polarimetry, IEEE Trans. on Geoscience and Remote Sensing, 34 (1996), 498-518.
doi: 10.1109/36.485127. |
[11] |
A. J. Devaney,
The inverse problem for random sources, J. Math. Phys., 20 (1979), 1687-1691.
doi: 10.1063/1.524277. |
[12] |
R. L. Dilsavor and R. L. Moses, Fully-Polarimetric GLRTs for Detecting Scattering Centers with Unknown Amplitude, Phase, and Tilt Angle in Terrain Clutter, in SPIE's International Symposium on Optical Engineering in Aerospace Sensing, Orlando, FL, 1994. |
[13] |
D. E. Dudgeon, R. T. Lacoss, C. H. Lazott and J. G. Verly,
Use of Persistent Scatterers for Model-Based Recognition, Proc. SPIE 2230, Algorithms for Synthetic Aperture Radar Imagery, 1994. |
[14] |
A. E. El-Rouby, A. Y. Nashashibi and F. T. Ulaby,
Application of frequency correlation function to radar target detection, IEEE Trans. Aero. Elec. Sys., 39 (2003), 125-139.
doi: 10.1109/TAES.2003.1188898. |
[15] |
E. Ertin, L. C. Potter and R. L. Moses,
Enhanced imaging over complete circular apertures, Signals, Systems, and Computers, (2006).
doi: 10.1109/ACSSC.2006.355025. |
[16] |
S. Feng, C. Kane, P. A. Lee and A. D. Stone,
Correlations and fluctuations of coherent wave transmission through disordered media, Phys. Rev. Lett., 61 (1988), 834-837.
doi: 10.1103/PhysRevLett.61.834. |
[17] |
L. Ferro-Famil, A. Reigber, E. Pottier and W. M. Boerner,
Scene characterization using subaperture polarimetric SAR data, IEEE Trans, on Geoscience and Remote Sensing, 41 (2003), 2264-2276.
doi: 10.1109/TGRS.2003.817188. |
[18] |
A. Freeman and S. L. Durden,
A Three-Component Scattering Model for Polarimetric SAR data, IEEE Trans. Geosci. Remote Sensing, 36 (1998), 963-973.
doi: 10.1109/36.673687. |
[19] |
A. C. Frery, H. J. Muller, C. C. F. Yanasse and S. J. S. Sant'Anna,
A model for extremely heterogeneous clutter, IEEE Tran. Geosci. Remote Sensing, 35 (1997), 648-659.
doi: 10.1109/36.581981. |
[20] |
I. Freund,
Correlation Imaging through multiply scattering media, Phys. Lett. A., 147 (1990), 502-506.
doi: 10.1016/0375-9601(90)90615-U. |
[21] |
J. Garnier and K. Solna, Coherent interferometric imaging for synthetic aperture radar in the presence of noise, Inverse Problems, 24 (2008), 055001, 23 pp. |
[22] |
A. Grigis and J. Sjostrand,
Microlocal Analysis for Differential Operators: An Introduction, London Mathematical Society Lecture Note Series, 196. Cambridge University Press, Cambridge, 1994. |
[23] |
M. Gustafsson,
Multi-static Synthetic Aperture Radar and Inverse Scattering, Technical Report LUTEDX, TEAT-7123, 2004. |
[24] |
J. R. Huynen,
Phenomenological theory of radar targets, Electromagnetic Scattering, (1978), 653-712.
doi: 10.1016/B978-0-12-709650-6.50020-1. |
[25] |
J. Jackson and R. Moses,
Clutter model for VHF SAR imagery, Proc. SPIE 5427, Algorithms for Synthetic Aperture Radar Imagery Ⅺ, 271 (September 2, 2004). |
[26] |
P. Li,
An inverse random source scattering problem in inhomogeneous media, Inverse Problems, 27(2011), 035004, 22pp. |
[27] |
A. Mahalanobis, A. Forman, M. Bower, N. Day and R. Cherry,
Multi-class SAR ATR using shift-invariant correlation filters, Patter Regonition, 27 (1994), 619-626.
doi: 10.1016/0031-3203(94)90041-8. |
[28] |
L. M. Novak, G. J. Owirka and C. M. Netishen,
Radar target identification using spatial matched filters, Pattern Regonition, 27 (1994), 607-617.
doi: 10.1016/0031-3203(94)90040-X. |
[29] | |
[30] |
M. Soumekh,
Synthetic Aperture Radar Signal Processing, John Wiley and Sons Inc., New York, 1999. |
[31] |
M. E. Taylor,
Pseudodiferential Operators, Princeton University Press, Princeton, NJ, 1981. |
[32] |
L. C. Trintinalia, R. Bhalla and H. Ling,
Scattering center parametrization of wide-angle backscattered data using adaptive Gaussian representation, IEEE Trans. Ant. Prop., 45(1997), 1664-1668. |
[33] |
L. Tsang, G. Zhang and K. Pak,
Detection of a buried object under a single random rough surface with angular correlation function in EM wave scattering, Microw. Opt. Technol. Lett., 11 (1996).
|
[34] |
K. Voccola,
Synthetic aperture radar correlation imaging, SIAM J. Imaging Sci., 8 (2015), 299-330.
doi: 10.1137/14096921X. |
[35] |
K. Voccola, M. Cheney and B. Yazici,
Polarimetric synthetic-aperture inversion for extended targets in clutter, Inverse Problems, 29 (2013).
doi: 10.1088/0266-5611/29/5/054003. |
[36] |
K. Voccola,
Statistical and Analytical Techniques in Synthetic Aperture Radar Imaging, Ph. D. Thesis, Dept. Math. Sciences, Rensselaer Polytechnic Institute, Troy, NY, 2011. |
[37] |
T. Webster,
Scalar and Vector Multistatic Radar Data Models, Ph. D. Thesis, Dept. Math. Sciences, Rensselaer Polytechnic Institute, Troy, NY, 2012. |
[38] |
J. L. Wong,
A model for the radar echo from a random collection of rotating dipole scatterers, IEEE Trans. Aerosp. Electron. Syst., 3 (1967), 171-178.
doi: 10.1109/TAES.1967.5408739. |
[39] |
B. Yazici, M. Cheney and C. E. Yarman,
Synthetic-aperture inversion in the presence of noise and clutter, Inverse Problems, 22 (2006), 1705-1729.
doi: 10.1088/0266-5611/22/5/011. |
[40] |
G. Zhang, L. Tsang and Y. Kuga,
Application of angular correlation function of clutter scattering and correlation imaging in target detection, IEEE Trans. Geosci. Remote Sensing, 36 (1998), 1485-1493.
|
[41] |
G. Zhang, L. Tsang and K. Pak,
Angular correlation function and scattering coefficient of electromagnetic waves scattered by a buried object under a two-dimensional rough surface, J. Opt. Soc. Am. A, 15 (1998), 2995-3002.
doi: 10.1364/JOSAA.15.002995. |
[42] |
G. Zhang, L. Tsang and Y. Kuga,
Numerical studies of the detection of targets in clutter by using angular correlation function and angular correlation imaging, Microw. Opt. Technol. Lett., 17 (1998), 82-86.
doi: 10.1002/(SICI)1098-2760(19980205)17:2<82::AID-MOP3>3.0.CO;2-E. |
[43] |
G. Zhang, L. Tsang and Y. Kuga,
Studies of the angular correlation function of scattering by random rough surfaces with and without a buried object, IEEE Trans. Geosci. Remote Sensing, 35 (1997), 444-453.
doi: 10.1109/36.563283. |
show all references
References:
[1] |
J. G. Berryman, L. Borcea, G. Papanicolaou and C. Tsogka,
Statistically stable ultrasonic imaging in random media, J. Acoust. Soc. Am., 112 (2002), 1509-1522.
doi: 10.1121/1.1502266. |
[2] |
W. M. Boerner, M. B. El-Arini, C. Y. Chan and P. M. Mastoris,
Polarization dependence in electromagnetic inverse problems, IEEE Trans. on Antennas and Propagation, 29 (1981), 262-271.
doi: 10.1109/TAP.1981.1142585. |
[3] |
L. Borcea, G. Papanicolaou and C. Tsogka,
Adaptive interferometric imaging in clutter and optimal illumination, Inverse Problems, 22 (2006), 1405-1436.
doi: 10.1088/0266-5611/22/4/016. |
[4] |
L. Borcea, G. Papanicolaou and C. Tsogka,
Interferometric array imaging in clutter, Inverse Problems, 21 (2005), 1419-1460.
doi: 10.1088/0266-5611/21/4/015. |
[5] |
L. Borcea, M. Moscoso, G. Papanicolaou and C. Tsogka,
Synthetic aperture imaging of direction and frequency dependent reflectivities, SIAM J. Imaging Sci., 9 (2016), 52-81.
doi: 10.1137/15M1036063. |
[6] |
L. Borcea, G. Papanicolaou and C. Tsogka,
Theory and applications of time reversal and interferometric imaging, Inverse Problems, 19 (2003), S139-S164.
doi: 10.1088/0266-5611/19/6/058. |
[7] |
T.-K. Chan, Y. Kuga and A. Ishimaru,
Subsurface detection of a buried object using angular correlation function measurement, Waves Random Media, 7 (1997), 457-465.
doi: 10.1080/13616679709409809. |
[8] |
R. D. Chaney, M. C. Burl and L. M. Novak,
On the Performance of Polarimetric Target Detection Algorithms, IEEE International Radar Conference, 1990.
doi: 10.1109/RADAR.1990.201114. |
[9] |
M. Cheney and B. Borden,
Fundamentals of Radar Imaging, SIAM, Philadelphia, 2009. |
[10] |
S. R. Cloude and E. Pottier,
A review of target decomposition theorems in radar polarimetry, IEEE Trans. on Geoscience and Remote Sensing, 34 (1996), 498-518.
doi: 10.1109/36.485127. |
[11] |
A. J. Devaney,
The inverse problem for random sources, J. Math. Phys., 20 (1979), 1687-1691.
doi: 10.1063/1.524277. |
[12] |
R. L. Dilsavor and R. L. Moses, Fully-Polarimetric GLRTs for Detecting Scattering Centers with Unknown Amplitude, Phase, and Tilt Angle in Terrain Clutter, in SPIE's International Symposium on Optical Engineering in Aerospace Sensing, Orlando, FL, 1994. |
[13] |
D. E. Dudgeon, R. T. Lacoss, C. H. Lazott and J. G. Verly,
Use of Persistent Scatterers for Model-Based Recognition, Proc. SPIE 2230, Algorithms for Synthetic Aperture Radar Imagery, 1994. |
[14] |
A. E. El-Rouby, A. Y. Nashashibi and F. T. Ulaby,
Application of frequency correlation function to radar target detection, IEEE Trans. Aero. Elec. Sys., 39 (2003), 125-139.
doi: 10.1109/TAES.2003.1188898. |
[15] |
E. Ertin, L. C. Potter and R. L. Moses,
Enhanced imaging over complete circular apertures, Signals, Systems, and Computers, (2006).
doi: 10.1109/ACSSC.2006.355025. |
[16] |
S. Feng, C. Kane, P. A. Lee and A. D. Stone,
Correlations and fluctuations of coherent wave transmission through disordered media, Phys. Rev. Lett., 61 (1988), 834-837.
doi: 10.1103/PhysRevLett.61.834. |
[17] |
L. Ferro-Famil, A. Reigber, E. Pottier and W. M. Boerner,
Scene characterization using subaperture polarimetric SAR data, IEEE Trans, on Geoscience and Remote Sensing, 41 (2003), 2264-2276.
doi: 10.1109/TGRS.2003.817188. |
[18] |
A. Freeman and S. L. Durden,
A Three-Component Scattering Model for Polarimetric SAR data, IEEE Trans. Geosci. Remote Sensing, 36 (1998), 963-973.
doi: 10.1109/36.673687. |
[19] |
A. C. Frery, H. J. Muller, C. C. F. Yanasse and S. J. S. Sant'Anna,
A model for extremely heterogeneous clutter, IEEE Tran. Geosci. Remote Sensing, 35 (1997), 648-659.
doi: 10.1109/36.581981. |
[20] |
I. Freund,
Correlation Imaging through multiply scattering media, Phys. Lett. A., 147 (1990), 502-506.
doi: 10.1016/0375-9601(90)90615-U. |
[21] |
J. Garnier and K. Solna, Coherent interferometric imaging for synthetic aperture radar in the presence of noise, Inverse Problems, 24 (2008), 055001, 23 pp. |
[22] |
A. Grigis and J. Sjostrand,
Microlocal Analysis for Differential Operators: An Introduction, London Mathematical Society Lecture Note Series, 196. Cambridge University Press, Cambridge, 1994. |
[23] |
M. Gustafsson,
Multi-static Synthetic Aperture Radar and Inverse Scattering, Technical Report LUTEDX, TEAT-7123, 2004. |
[24] |
J. R. Huynen,
Phenomenological theory of radar targets, Electromagnetic Scattering, (1978), 653-712.
doi: 10.1016/B978-0-12-709650-6.50020-1. |
[25] |
J. Jackson and R. Moses,
Clutter model for VHF SAR imagery, Proc. SPIE 5427, Algorithms for Synthetic Aperture Radar Imagery Ⅺ, 271 (September 2, 2004). |
[26] |
P. Li,
An inverse random source scattering problem in inhomogeneous media, Inverse Problems, 27(2011), 035004, 22pp. |
[27] |
A. Mahalanobis, A. Forman, M. Bower, N. Day and R. Cherry,
Multi-class SAR ATR using shift-invariant correlation filters, Patter Regonition, 27 (1994), 619-626.
doi: 10.1016/0031-3203(94)90041-8. |
[28] |
L. M. Novak, G. J. Owirka and C. M. Netishen,
Radar target identification using spatial matched filters, Pattern Regonition, 27 (1994), 607-617.
doi: 10.1016/0031-3203(94)90040-X. |
[29] | |
[30] |
M. Soumekh,
Synthetic Aperture Radar Signal Processing, John Wiley and Sons Inc., New York, 1999. |
[31] |
M. E. Taylor,
Pseudodiferential Operators, Princeton University Press, Princeton, NJ, 1981. |
[32] |
L. C. Trintinalia, R. Bhalla and H. Ling,
Scattering center parametrization of wide-angle backscattered data using adaptive Gaussian representation, IEEE Trans. Ant. Prop., 45(1997), 1664-1668. |
[33] |
L. Tsang, G. Zhang and K. Pak,
Detection of a buried object under a single random rough surface with angular correlation function in EM wave scattering, Microw. Opt. Technol. Lett., 11 (1996).
|
[34] |
K. Voccola,
Synthetic aperture radar correlation imaging, SIAM J. Imaging Sci., 8 (2015), 299-330.
doi: 10.1137/14096921X. |
[35] |
K. Voccola, M. Cheney and B. Yazici,
Polarimetric synthetic-aperture inversion for extended targets in clutter, Inverse Problems, 29 (2013).
doi: 10.1088/0266-5611/29/5/054003. |
[36] |
K. Voccola,
Statistical and Analytical Techniques in Synthetic Aperture Radar Imaging, Ph. D. Thesis, Dept. Math. Sciences, Rensselaer Polytechnic Institute, Troy, NY, 2011. |
[37] |
T. Webster,
Scalar and Vector Multistatic Radar Data Models, Ph. D. Thesis, Dept. Math. Sciences, Rensselaer Polytechnic Institute, Troy, NY, 2012. |
[38] |
J. L. Wong,
A model for the radar echo from a random collection of rotating dipole scatterers, IEEE Trans. Aerosp. Electron. Syst., 3 (1967), 171-178.
doi: 10.1109/TAES.1967.5408739. |
[39] |
B. Yazici, M. Cheney and C. E. Yarman,
Synthetic-aperture inversion in the presence of noise and clutter, Inverse Problems, 22 (2006), 1705-1729.
doi: 10.1088/0266-5611/22/5/011. |
[40] |
G. Zhang, L. Tsang and Y. Kuga,
Application of angular correlation function of clutter scattering and correlation imaging in target detection, IEEE Trans. Geosci. Remote Sensing, 36 (1998), 1485-1493.
|
[41] |
G. Zhang, L. Tsang and K. Pak,
Angular correlation function and scattering coefficient of electromagnetic waves scattered by a buried object under a two-dimensional rough surface, J. Opt. Soc. Am. A, 15 (1998), 2995-3002.
doi: 10.1364/JOSAA.15.002995. |
[42] |
G. Zhang, L. Tsang and Y. Kuga,
Numerical studies of the detection of targets in clutter by using angular correlation function and angular correlation imaging, Microw. Opt. Technol. Lett., 17 (1998), 82-86.
doi: 10.1002/(SICI)1098-2760(19980205)17:2<82::AID-MOP3>3.0.CO;2-E. |
[43] |
G. Zhang, L. Tsang and Y. Kuga,
Studies of the angular correlation function of scattering by random rough surfaces with and without a buried object, IEEE Trans. Geosci. Remote Sensing, 35 (1997), 444-453.
doi: 10.1109/36.563283. |













Standard BP | 1.7158 - 0.2106i | |
Correlation BP with memory directions | 1.5112 - 0.0000i | |
Correlation BP with |
1.4772 - 0.0000i | |
Correlation BP with |
1.1470 - 0.0000i | |
Correlation BP with |
0.8461 + 0.0000i | |
Correlation BP with |
0.5869 + 0.0000i |
Standard BP | 1.7158 - 0.2106i | |
Correlation BP with memory directions | 1.5112 - 0.0000i | |
Correlation BP with |
1.4772 - 0.0000i | |
Correlation BP with |
1.1470 - 0.0000i | |
Correlation BP with |
0.8461 + 0.0000i | |
Correlation BP with |
0.5869 + 0.0000i |
Standard BP | 1.1491e-04 - 6.2788e-06i | |
Correlation BP with memory directions | 0.6668e-08 - 0.0410e-08i | |
Correlation BP with |
0.6575e-08 - 0.0410e-08i | |
Correlation BP with |
0.5030e-08 - 0.0377e-08i | |
Correlation BP with |
0.3642e-08 - 0.0290e-08i | |
Correlation BP with |
0.2490e-08 - 0.0208e-08i |
Standard BP | 1.1491e-04 - 6.2788e-06i | |
Correlation BP with memory directions | 0.6668e-08 - 0.0410e-08i | |
Correlation BP with |
0.6575e-08 - 0.0410e-08i | |
Correlation BP with |
0.5030e-08 - 0.0377e-08i | |
Correlation BP with |
0.3642e-08 - 0.0290e-08i | |
Correlation BP with |
0.2490e-08 - 0.0208e-08i |
Standard BP | 0.0090 + 0.0004i | |
Correlation BP with memory directions | 0.4206e-04 + 0.0014e-04i | |
Correlation BP with |
0.4072e-04 + 0.0014e-04i | |
Correlation BP with |
0.2535e-04 + 0.0049e-04i | |
Correlation BP with |
0.1363e-04 - 0.0087e-04i | |
Correlation BP with |
0.0592e-04 - 0.0021e-04i |
Standard BP | 0.0090 + 0.0004i | |
Correlation BP with memory directions | 0.4206e-04 + 0.0014e-04i | |
Correlation BP with |
0.4072e-04 + 0.0014e-04i | |
Correlation BP with |
0.2535e-04 + 0.0049e-04i | |
Correlation BP with |
0.1363e-04 - 0.0087e-04i | |
Correlation BP with |
0.0592e-04 - 0.0021e-04i |
Standard BP | 0.0012 - 0.0002i | |
Correlation BP with memory directions | 0.7152e-06 - 0.1448e-06i | |
Correlation BP with |
0.6983e-06 - 0.1448e-06i | |
Correlation BP with |
0.3869e-06 - 0.1183e-06i | |
Correlation BP with |
0.2159e-06 + 0.0199e-06i | |
Correlation BP with |
0.1153e-06 + 0.0139e-06i |
Standard BP | 0.0012 - 0.0002i | |
Correlation BP with memory directions | 0.7152e-06 - 0.1448e-06i | |
Correlation BP with |
0.6983e-06 - 0.1448e-06i | |
Correlation BP with |
0.3869e-06 - 0.1183e-06i | |
Correlation BP with |
0.2159e-06 + 0.0199e-06i | |
Correlation BP with |
0.1153e-06 + 0.0139e-06i |
Standard BP | 0.0010 - 0.0023i | |
Correlation BP with memory directions | 0.3106e-05 - 0.0308e-05i | |
Correlation BP with |
0.3053e-05 - 0.0308e-05i | |
Correlation BP with |
0.2214e-05 - 0.0087e-05i | |
Correlation BP with |
0.1554e-05 - 0.0159e-05i | |
Correlation BP with |
0.1115e-05 - 0.0061e-05i |
Standard BP | 0.0010 - 0.0023i | |
Correlation BP with memory directions | 0.3106e-05 - 0.0308e-05i | |
Correlation BP with |
0.3053e-05 - 0.0308e-05i | |
Correlation BP with |
0.2214e-05 - 0.0087e-05i | |
Correlation BP with |
0.1554e-05 - 0.0159e-05i | |
Correlation BP with |
0.1115e-05 - 0.0061e-05i |
Standard BP | 1.7528 + 0.2160i | |
Correlation BP with memory directions | 1.6668 - 0.3576i | |
Correlation BP with |
1.5072 - 0.3576i | |
Correlation BP with |
0.1084 - 0.1624i | |
Correlation BP with |
0.0157 - 0.0024i | |
Correlation BP with |
0.0045 - 0.0001i |
Standard BP | 1.7528 + 0.2160i | |
Correlation BP with memory directions | 1.6668 - 0.3576i | |
Correlation BP with |
1.5072 - 0.3576i | |
Correlation BP with |
0.1084 - 0.1624i | |
Correlation BP with |
0.0157 - 0.0024i | |
Correlation BP with |
0.0045 - 0.0001i |
Input SCR | Output SCR Standard BP | Output SCR Correlation BP |
Output SCR Correlation |
Output SCR Correlation |
||||
20 | 17.3087 | 51.3593 | 52.0820 | 51.9498 | ||||
10 | 7.3087 | 31.3593 | 32.0820 | 31.9498 | ||||
0 | -2.6913 | 11.3593 | 12.0820 | 11.9498 | ||||
-10 | -12.6913 | -8.6407 | -7.9180 | -8.0502 | ||||
-20 | -22.6913 | -28.6407 | -27.9180 | -28.0502 |
Input SCR | Output SCR Standard BP | Output SCR Correlation BP |
Output SCR Correlation |
Output SCR Correlation |
||||
20 | 17.3087 | 51.3593 | 52.0820 | 51.9498 | ||||
10 | 7.3087 | 31.3593 | 32.0820 | 31.9498 | ||||
0 | -2.6913 | 11.3593 | 12.0820 | 11.9498 | ||||
-10 | -12.6913 | -8.6407 | -7.9180 | -8.0502 | ||||
-20 | -22.6913 | -28.6407 | -27.9180 | -28.0502 |
Input SCR | Output SCR HH | Output SCR HV | Output SCR VV | |||
20 | 18.0264 | 18.8373 | 18.9482 | |||
10 | 8.0264 | 8.8373 | 8.9482 | |||
0 | -1.9736 | -1.1627 | -1.0518 | |||
-10 | -11.9736 | -11.1627 | -11.0518 | |||
-20 | -21.9736 | -21.1627 | -21.0518 |
Input SCR | Output SCR HH | Output SCR HV | Output SCR VV | |||
20 | 18.0264 | 18.8373 | 18.9482 | |||
10 | 8.0264 | 8.8373 | 8.9482 | |||
0 | -1.9736 | -1.1627 | -1.0518 | |||
-10 | -11.9736 | -11.1627 | -11.0518 | |||
-20 | -21.9736 | -21.1627 | -21.0518 |
Input SCR | Output SCR HH-HH | Output SCR HV-HV | Output SCR VV-VV | |||
20 | 51.1293 | 54.0229 | 53.9465 | |||
10 | 31.1293 | 34.0229 | 33.9465 | |||
0 | 11.1293 | 14.0229 | 13.9465 | |||
-10 | -8.8707 | -5.9771 | -6.0535 | |||
-20 | -28.8707 | -25.9771 | -26.0535 |
Input SCR | Output SCR HH-HH | Output SCR HV-HV | Output SCR VV-VV | |||
20 | 51.1293 | 54.0229 | 53.9465 | |||
10 | 31.1293 | 34.0229 | 33.9465 | |||
0 | 11.1293 | 14.0229 | 13.9465 | |||
-10 | -8.8707 | -5.9771 | -6.0535 | |||
-20 | -28.8707 | -25.9771 | -26.0535 |
Input SCR | Output SCR HH-HH | Output SCR HV-HV | Output SCR VV-VV | |||
20 | 51.3130 | 54.0887 | 53.9973 | |||
10 | 31.3130 | 34.0887 | 33.9973 | |||
0 | 11.3130 | 14.0887 | 13.9973 | |||
-10 | -8.6870 | -5.9113 | -6.0027 | |||
-20 | -28.6870 | -25.9113 | -26.0027 |
Input SCR | Output SCR HH-HH | Output SCR HV-HV | Output SCR VV-VV | |||
20 | 51.3130 | 54.0887 | 53.9973 | |||
10 | 31.3130 | 34.0887 | 33.9973 | |||
0 | 11.3130 | 14.0887 | 13.9973 | |||
-10 | -8.6870 | -5.9113 | -6.0027 | |||
-20 | -28.6870 | -25.9113 | -26.0027 |
Input SCR | Output SCR HH-HH | Output SCR HV-HV | Output SCR VV-VV | |||
20 | 51.4206 | 53.9605 | 53.7934 | |||
10 | 31.4206 | 33.9605 | 33.7934 | |||
0 | 11.4206 | 13.9605 | 13.7934 | |||
-10 | -8.5794 | -6.0395 | -6.2066 | |||
-20 | -28.5794 | -26.0395 | -26.2066 |
Input SCR | Output SCR HH-HH | Output SCR HV-HV | Output SCR VV-VV | |||
20 | 51.4206 | 53.9605 | 53.7934 | |||
10 | 31.4206 | 33.9605 | 33.7934 | |||
0 | 11.4206 | 13.9605 | 13.7934 | |||
-10 | -8.5794 | -6.0395 | -6.2066 | |||
-20 | -28.5794 | -26.0395 | -26.2066 |
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