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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. Google Scholar |
[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. Google Scholar |
[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. Google Scholar |
[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). Google Scholar |
[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] |
H. L. Royden, Real Analysis, Pearson, New York, 2010. Google Scholar |
[30] |
M. Soumekh, Synthetic Aperture Radar Signal Processing, John Wiley and Sons Inc., New York, 1999. Google Scholar |
[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. Google Scholar |
[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). Google Scholar |
[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. Google Scholar |
[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. Google Scholar |
[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. Google Scholar |
[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. Google Scholar |
[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). Google Scholar |
[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] |
H. L. Royden, Real Analysis, Pearson, New York, 2010. Google Scholar |
[30] |
M. Soumekh, Synthetic Aperture Radar Signal Processing, John Wiley and Sons Inc., New York, 1999. Google Scholar |
[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. Google Scholar |
[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). Google Scholar |
[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. Google Scholar |
[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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