Abstract

Using polarization measurements in remote sensing and optical studies allows for the retrieval of more information. We consider the relationship between the reflection coefficients of plane and rough surfaces for linearly polarized waves. Certain polarization properties of reflected waves and polarization invariants, in particular at the incident angle of 45°, allow finding amplitude and phase characteristics of the reflected waves. Based on this study, we introduce methods for finding dielectric permittivity, temperature, and geometric characteristics of the observed surfaces. Experimental results prove that these methods can be used for different practical purposes in technological and remote sensing applications, in a broad range of the electromagnetic spectrum.

© 2011 Optical Society of America

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References

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  1. D. K. Kalluri, Electromagnetics of Time Varying Complex Media: Frequency and Polarization Transformer, 2nd ed.(Taylor & Francis, 2010).
    [CrossRef]
  2. R. M. A. Azzam, “Direct relation between Fresnel’s interface reflection coefficients for the parallel and perpendicular polarizations,” J. Opt. Soc. Am. 69, 1007–1016 (1979).
    [CrossRef]
  3. V. V. Bogorodsky, A. I. Kozlov, and Yu. K. Shestopalov, “Determination of roughness rank and dielectric permittivity of the Earth surface by microwave measurements,” Zh. Tekh. Fiz. 54, 131–139 (1984).
  4. McGraw-Hill Dictionary of Physics, 2nd ed. (McGraw-Hill , 1996).
  5. R. M. A. Azzam, “On the reflection of light at 45° angle of incidence,” J. Mod. Opt. 26, 113 (1979).
  6. Yu. K. Shestopalov, “On the relationship of Fresnel reflection coefficients at observation angle of forty five degree,” Zh. Tekh. Fiz. 53, 144 (1983).
  7. A. N. Matveev, Optika (Optics) (Vysshaya Shkola, 1985).
  8. Yu. K. Shestopalov, “Statistical processing of passive microwave data,” IEEE Trans. Geosci. Remote Sens. 31, 1060–1065(1993).
    [CrossRef]
  9. Yu. K. Shestopalov, “Multiple incoherent wave scattering on statistically rough surface with large steep roughness,” Radiotekhnika, April 1989, pp. 67–70.
  10. P. P. Bobrov, T. A. Belyaeva, Yu. K. Shestopalov, and I. M. Shchetkin, “Peculiarities of microwave radiation from periodically uneven ground,” J. Commun. Technol. Electron. 45, 1059–1067 (2000).
  11. D. J. Daniels, Surface-Penetrating Radar—IEE Radar, Sonar, Navigation and Avionics, Series 6 (Institute of Electrical Engineers, 1996).
  12. J. L. Davis and A. P. Annan, “Ground-penetrating radar for high-resolution mapping of soil and rock stratigraphy,” Geophys. Prospect. 37, 531–551 (1989).
    [CrossRef]
  13. S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics (Springer-Verlag, 1987).
    [CrossRef]
  14. A. Jarvis, H. I. Reuter, A. Nelson, and E. Guevara, “Hole-filled seamless SRTM data, V4, International Centre for Tropical Agriculture (CIAT),” http://srtm.csi.cgiar.org (2008).
  15. “Global GIS database: digital atlas of Africa,” U.S. Geological Survey (2001).
  16. R. J. Huggett, Fundamentals of Geomorphology (Routledge, 2007).
  17. Yu. K. Shestopalov, “Microwave polarization properties of the rough surface with large steep roughness. part 2,” Izvestiya Vuzov. Radiofizika. 28, 1509–1515 (1985).

2000 (1)

P. P. Bobrov, T. A. Belyaeva, Yu. K. Shestopalov, and I. M. Shchetkin, “Peculiarities of microwave radiation from periodically uneven ground,” J. Commun. Technol. Electron. 45, 1059–1067 (2000).

1993 (1)

Yu. K. Shestopalov, “Statistical processing of passive microwave data,” IEEE Trans. Geosci. Remote Sens. 31, 1060–1065(1993).
[CrossRef]

1989 (1)

J. L. Davis and A. P. Annan, “Ground-penetrating radar for high-resolution mapping of soil and rock stratigraphy,” Geophys. Prospect. 37, 531–551 (1989).
[CrossRef]

1985 (1)

Yu. K. Shestopalov, “Microwave polarization properties of the rough surface with large steep roughness. part 2,” Izvestiya Vuzov. Radiofizika. 28, 1509–1515 (1985).

1984 (1)

V. V. Bogorodsky, A. I. Kozlov, and Yu. K. Shestopalov, “Determination of roughness rank and dielectric permittivity of the Earth surface by microwave measurements,” Zh. Tekh. Fiz. 54, 131–139 (1984).

1983 (1)

Yu. K. Shestopalov, “On the relationship of Fresnel reflection coefficients at observation angle of forty five degree,” Zh. Tekh. Fiz. 53, 144 (1983).

1979 (2)

Annan, A. P.

J. L. Davis and A. P. Annan, “Ground-penetrating radar for high-resolution mapping of soil and rock stratigraphy,” Geophys. Prospect. 37, 531–551 (1989).
[CrossRef]

Azzam, R. M. A.

Belyaeva, T. A.

P. P. Bobrov, T. A. Belyaeva, Yu. K. Shestopalov, and I. M. Shchetkin, “Peculiarities of microwave radiation from periodically uneven ground,” J. Commun. Technol. Electron. 45, 1059–1067 (2000).

Bobrov, P. P.

P. P. Bobrov, T. A. Belyaeva, Yu. K. Shestopalov, and I. M. Shchetkin, “Peculiarities of microwave radiation from periodically uneven ground,” J. Commun. Technol. Electron. 45, 1059–1067 (2000).

Bogorodsky, V. V.

V. V. Bogorodsky, A. I. Kozlov, and Yu. K. Shestopalov, “Determination of roughness rank and dielectric permittivity of the Earth surface by microwave measurements,” Zh. Tekh. Fiz. 54, 131–139 (1984).

Daniels, D. J.

D. J. Daniels, Surface-Penetrating Radar—IEE Radar, Sonar, Navigation and Avionics, Series 6 (Institute of Electrical Engineers, 1996).

Davis, J. L.

J. L. Davis and A. P. Annan, “Ground-penetrating radar for high-resolution mapping of soil and rock stratigraphy,” Geophys. Prospect. 37, 531–551 (1989).
[CrossRef]

Guevara, E.

A. Jarvis, H. I. Reuter, A. Nelson, and E. Guevara, “Hole-filled seamless SRTM data, V4, International Centre for Tropical Agriculture (CIAT),” http://srtm.csi.cgiar.org (2008).

Huggett, R. J.

R. J. Huggett, Fundamentals of Geomorphology (Routledge, 2007).

Jarvis, A.

A. Jarvis, H. I. Reuter, A. Nelson, and E. Guevara, “Hole-filled seamless SRTM data, V4, International Centre for Tropical Agriculture (CIAT),” http://srtm.csi.cgiar.org (2008).

Kalluri, D. K.

D. K. Kalluri, Electromagnetics of Time Varying Complex Media: Frequency and Polarization Transformer, 2nd ed.(Taylor & Francis, 2010).
[CrossRef]

Kozlov, A. I.

V. V. Bogorodsky, A. I. Kozlov, and Yu. K. Shestopalov, “Determination of roughness rank and dielectric permittivity of the Earth surface by microwave measurements,” Zh. Tekh. Fiz. 54, 131–139 (1984).

Kravtsov, Yu. A.

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics (Springer-Verlag, 1987).
[CrossRef]

Matveev, A. N.

A. N. Matveev, Optika (Optics) (Vysshaya Shkola, 1985).

Nelson, A.

A. Jarvis, H. I. Reuter, A. Nelson, and E. Guevara, “Hole-filled seamless SRTM data, V4, International Centre for Tropical Agriculture (CIAT),” http://srtm.csi.cgiar.org (2008).

Reuter, H. I.

A. Jarvis, H. I. Reuter, A. Nelson, and E. Guevara, “Hole-filled seamless SRTM data, V4, International Centre for Tropical Agriculture (CIAT),” http://srtm.csi.cgiar.org (2008).

Rytov, S. M.

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics (Springer-Verlag, 1987).
[CrossRef]

Shchetkin, I. M.

P. P. Bobrov, T. A. Belyaeva, Yu. K. Shestopalov, and I. M. Shchetkin, “Peculiarities of microwave radiation from periodically uneven ground,” J. Commun. Technol. Electron. 45, 1059–1067 (2000).

Shestopalov, Yu. K.

P. P. Bobrov, T. A. Belyaeva, Yu. K. Shestopalov, and I. M. Shchetkin, “Peculiarities of microwave radiation from periodically uneven ground,” J. Commun. Technol. Electron. 45, 1059–1067 (2000).

Yu. K. Shestopalov, “Statistical processing of passive microwave data,” IEEE Trans. Geosci. Remote Sens. 31, 1060–1065(1993).
[CrossRef]

Yu. K. Shestopalov, “Microwave polarization properties of the rough surface with large steep roughness. part 2,” Izvestiya Vuzov. Radiofizika. 28, 1509–1515 (1985).

V. V. Bogorodsky, A. I. Kozlov, and Yu. K. Shestopalov, “Determination of roughness rank and dielectric permittivity of the Earth surface by microwave measurements,” Zh. Tekh. Fiz. 54, 131–139 (1984).

Yu. K. Shestopalov, “On the relationship of Fresnel reflection coefficients at observation angle of forty five degree,” Zh. Tekh. Fiz. 53, 144 (1983).

Yu. K. Shestopalov, “Multiple incoherent wave scattering on statistically rough surface with large steep roughness,” Radiotekhnika, April 1989, pp. 67–70.

Tatarskii, V. I.

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics (Springer-Verlag, 1987).
[CrossRef]

Geophys. Prospect. (1)

J. L. Davis and A. P. Annan, “Ground-penetrating radar for high-resolution mapping of soil and rock stratigraphy,” Geophys. Prospect. 37, 531–551 (1989).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (1)

Yu. K. Shestopalov, “Statistical processing of passive microwave data,” IEEE Trans. Geosci. Remote Sens. 31, 1060–1065(1993).
[CrossRef]

Izvestiya Vuzov. Radiofizika. (1)

Yu. K. Shestopalov, “Microwave polarization properties of the rough surface with large steep roughness. part 2,” Izvestiya Vuzov. Radiofizika. 28, 1509–1515 (1985).

J. Commun. Technol. Electron. (1)

P. P. Bobrov, T. A. Belyaeva, Yu. K. Shestopalov, and I. M. Shchetkin, “Peculiarities of microwave radiation from periodically uneven ground,” J. Commun. Technol. Electron. 45, 1059–1067 (2000).

J. Mod. Opt. (1)

R. M. A. Azzam, “On the reflection of light at 45° angle of incidence,” J. Mod. Opt. 26, 113 (1979).

J. Opt. Soc. Am. (1)

Zh. Tekh. Fiz. (2)

V. V. Bogorodsky, A. I. Kozlov, and Yu. K. Shestopalov, “Determination of roughness rank and dielectric permittivity of the Earth surface by microwave measurements,” Zh. Tekh. Fiz. 54, 131–139 (1984).

Yu. K. Shestopalov, “On the relationship of Fresnel reflection coefficients at observation angle of forty five degree,” Zh. Tekh. Fiz. 53, 144 (1983).

Other (9)

A. N. Matveev, Optika (Optics) (Vysshaya Shkola, 1985).

McGraw-Hill Dictionary of Physics, 2nd ed. (McGraw-Hill , 1996).

D. J. Daniels, Surface-Penetrating Radar—IEE Radar, Sonar, Navigation and Avionics, Series 6 (Institute of Electrical Engineers, 1996).

Yu. K. Shestopalov, “Multiple incoherent wave scattering on statistically rough surface with large steep roughness,” Radiotekhnika, April 1989, pp. 67–70.

D. K. Kalluri, Electromagnetics of Time Varying Complex Media: Frequency and Polarization Transformer, 2nd ed.(Taylor & Francis, 2010).
[CrossRef]

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics (Springer-Verlag, 1987).
[CrossRef]

A. Jarvis, H. I. Reuter, A. Nelson, and E. Guevara, “Hole-filled seamless SRTM data, V4, International Centre for Tropical Agriculture (CIAT),” http://srtm.csi.cgiar.org (2008).

“Global GIS database: digital atlas of Africa,” U.S. Geological Survey (2001).

R. J. Huggett, Fundamentals of Geomorphology (Routledge, 2007).

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Figures (7)

Fig. 1
Fig. 1

Radiation diagrams (circles) for Brewster’s angle (left) and 45 ° angle (right).

Fig. 2
Fig. 2

Dependence of roughness coefficient on the average slope of a rough surface modeled by an assembly of cones, at an observation angle of 45 ° .

Fig. 3
Fig. 3

Roughness coefficient of the rough sand surface measured by 3.4 cm radiometer at 45 ° observation angle versus the theoretical curve. The dimensionless dielectric permittivity is 7.4; roughness is modeled by sand cones. Error bars correspond to 1 standard deviation.

Fig. 4
Fig. 4

Change of average roughness of the surface along the observed trajectory based on experimental data.

Fig. 5
Fig. 5

Elevation profile.

Fig. 6
Fig. 6

Geographic slope.

Fig. 7
Fig. 7

Change of dielectric permittivity along the observed trajectory.

Tables (1)

Tables Icon

Table 1 Accuracy of Temperature Determination (°C) Observed in Experiments

Equations (36)

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R s = ε sin 2 α cos α ε sin 2 α + cos α .
R p = ε cos α ε sin 2 α ε cos α + ε sin 2 α .
R p = R s 2 + R s cos 2 α 1 + R s cos 2 α .
| R p | sin φ p + | R s | | R p | cos 2 α sin ( φ s + φ p ) = | R s | 2 sin ( 2 φ s ) + | R s | cos 2 α sin φ s .
| R p | cos φ p + | R s | | R p | cos 2 α cos ( φ s + φ p ) = | R s | 2 cos ( 2 φ s ) + | R s | cos 2 α cos φ s .
cos φ s = | R s | 4 + | R s | 2 cos 2 2 α | R p | 2 ( 1 + | R s | 2 cos 2 2 α ) 2 | R s | cos 2 α ( | R p | 2 | R s | 2 ) .
R p = R s 2 .
φ p = 2 φ s .
ε = ( 1 + R p ) ( 1 + R s ) ( 1 R p ) ( 1 R s ) .
ε = ( 1 + 1 χ p ( cos φ p + i sin φ p ) ) ( 1 + 1 χ s ( cos φ s + i sin φ s ) ) ( 1 1 χ p ( cos φ p + i sin φ p ) ) ( 1 1 χ s ( cos φ s + i sin φ s ) ) .
R p R s 2 = 1 .
χ s 2 2 χ s χ p = 1 .
R p ( 1 + R s cos 2 α ) R s 2 + R s cos 2 α = 1 .
χ p = 2 χ s ( 1 + cos 2 α cos φ s 1 χ s ) χ s 2 1 + cos 2 2 α ( 1 χ s ) + 2 cos 2 α cos φ s 1 χ s .
χ s 2 2 χ s + 2 cos 2 α cos φ s 1 χ s ( χ s χ p ) χ p cos 2 2 α ( 1 χ s ) χ p = 1 .
T = T s 2 2 T s T p .
T s ( 1 x 2 ) 2 T s + 2 x cos 2 α cos φ s ( T s T p ) x 2 T p cos 2 2 α T p = 1 .
x 2 ( T p cos 2 2 α T s ) 2 cos 2 α cos φ s ( T p T s ) x + ( T p T s ) = 0 .
x 1 , 2 = cos 2 α ( T p T s ) ± sin 2 α ( T p T s T s 2 ) 0.5 T p cos 2 2 α T s .
S = R s 2 R p .
S χ = χ s 2 2 χ s χ p .
S χ = χ s 2 2 χ s + 2 cos 2 α cos φ s 1 χ s ( χ s χ p ) χ p cos 2 2 α ( 1 χ s ) χ p .
N = 0.5 { ( 2 T sr S χ T ) ± [ S χ 2 T 2 + 4 S χ T ( T sr T pr ) ] 1 / 2 } .
( 1 ( T s N s ) / T ) 0.5 = cos 2 α ( T p T s N p + N s ) ± sin 2 α [ ( T p N p ) ( T s N s ) ( T s N s ) 2 ] 0.5 ( T p N p ) cos 2 2 α ( T s N s ) .
δ T = 2 T s 2 δ T s + T s ( T s δ T p 2 T p δ T s ) ( 2 T s T p ) 2 .
δ T δ T bt T s ( T s 2 T p ) + 2 T s 2 ( 2 T s T p ) 2 .
δ S χ = 2 χ s 2 δ χ s + χ s ( χ s δ χ p 2 χ p δ χ s ) ( 2 χ s χ p ) 2 ,
T = T s 2 S χ ( 2 T s T p ) .
ε sin 2 α = cos α ( 1 + R s ) 1 R s .
ε = sin 2 α + cos 2 α ( 1 + R s 1 R s ) 2 = 1 + R s 2 + 2 R s cos 2 α ( 1 R s ) 2 .
R p = cos α 1 + R s 2 + 2 R s cos 2 α ( 1 R s ) 2 cos α ( 1 + R s ) 1 R s cos α 1 + R s 2 + 2 R s cos 2 α ( 1 R s ) 2 + cos α ( 1 + R s ) 1 R s = cos α ( 1 + R s 2 + 2 R s cos 2 α ) cos α ( 1 R s 2 ) cos α ( 1 + R s 2 + 2 R s cos 2 α ) + cos α ( 1 R s 2 ) = R s 2 + R s cos 2 α 1 + R s cos 2 α .
ε = 1 + R s 2 + 2 R s cos 2 α ( 1 R s ) 2 = 1 + R s 2 + 2 ( R p R s 2 ) ( 1 R p ) ( 1 R s ) 2 = ( 1 + R p ) ( 1 + R s ) ( 1 R p ) ( 1 R s ) .
R s = μ ε sin 2 α cos α μ ε sin 2 α + cos α .
R p = μ ε cos α ε sin 2 α μ ε cos α + ε sin 2 α .
R p = 1 2 ( 1 R s 2 ) s 2 μ 2 ( 1 R s ) 2 + c 2 ( 1 + R s ) 2 + 1 R s 2 .
R p = 1 4 ( 1 R s 2 ) μ 2 ( 1 R s ) 2 + ( 1 + R s ) 2 + 2 ( 1 R s 2 ) .

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