Progress on the investigation of the anisotropy of the terrain media, such as vegetation canopy and sea ice, and the study of the fluctuation-dissipation theorem in conjunction with the application of strong fluctuation theory for passive remote sensing of snowpacks is reported. The Feynman diagrammatic technique is used to derive the Dyson equation for the mean field and the Bethe-Salpeter equation for the correlation or the covariance of the field for electromagnetic wave propagation and scattering in an anisotropic random medium. With the random permittivity expressed in a general form, the bilocal and the nonlinear approximations are employed to solve the Dyson equation and the ladder approximation to the Bethe-Salpeter equation. The mean dyadic Green's function for a two layer anisotropic random medium with arbitrary three dimensional correlation function was investigated with the zeroth-order solutions to the Dyson equation under the four characteristic waves associated with the coherent vector fields propagating in an anisotropic random medium layer, which are the ordinary and extraordinary waves with upward and downward propagating vectors

Kong, J. A.

English

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REMOTE SENSING OF EARTH TERRAIN 
Na~ional Aeronautics and Space Administration 
Goddard Space Flight Center 
Contract NAG 5-270 
SEMI-ANNUAL REPORT 
covering the period 
March 1. 1985-August 31, 1985 
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August 1985 
Massachusetts Institute of Technology 
Research Laboratory of Electronics 
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REMOTE SENSING OF EARTH TERRAIN 
Principal Investigator: Jin Au Kong 
SEMI-ANNUAL Pl .. ·.-" .. RESS REPORT 
Under the sponsorship of the NASA Contract NAG5-270, we have published 14 
articles in refereed journals, 15 conference papers, and 13 technical reports and 4 student 
theses for the research on the remote sensing of earth terrain. 
We have made progress on (1) the investigation of the anisotropy of the terrain me-
dia, such a.& vegetation canopy and sea ice, and (2) the study of the fluctuation-dissipation 
theorem in conjunction with the application of strong fluctuation theory for passive remote 
sensing of snowpacks, during the period March 1, 1985 to August 31, 1985. 
The Feynman diagrammatic technique is used to derive the Dyson equation for 
the mean field and the Bethe-Salpeter equation for the correlation or the covariance of 
the field for electromagnetic wave propagation and scattering in an anisotropic random 
medium. With the random permittivity expressed in a general form, the bilocal and the 
nonlinear approximations are employed to solve the Dyson equation and the ladder ap-
proximation to the Bethe-Salpeter equation. The mean dyadic Green's function for a 
two-layer anisotropic random medium with arbitrary three-dimensional correlation func-
tions has been investigated with the zeroth-order solutions to the Dyson equation under the 
!1oalinear approximation. The effective propagation constants are calculated for the four 
characteristic waves associated with the coherent vector fields propagating in an anisotropic 
random medium layer, which are the ordinary and extraordinary waves with upward and 
downward propagating vectors. 
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The snow-covered ice field has been studied by a three-layer model, with an isotropic 
random medium layer simulating snow and an anisotropic random medium layer simulating 
sea ice. Both snow and ice exhibit volume scattering effects which are due to the granular 
ice particles and the brine inclusions, respectively. We have calculated the dyadic Green's 
functions \...f the three-layer medium and the scattered electromagnetic intensities with 
Born approximation. The backscattering cross sections are evaluated for active microwave 
remote sensing. In the model, the correlation functions are assumed to be Gaussian lat-
erally and exponential vertically for both of snow and sea ice. The average physical sizes 
and the strengths of the volume scattering of the ice particles and the brine inclusions 
are characterized by the corresponding correlation lengths and normalized variances. The 
theoretical approach can be extended to derive the bistatic scattering coefficients. After 
integrating the bistatic scattering coefficients over the upper hemisphere and substracting 
from unity, we can also compute the radiometric brightness temperatures for passive mi-
crowave remote sensing by invoking the principle of reciprocity. The theoretical results 
are illustrated for thick first-year sea ice covered by dry snow at Point Barrow and for 
artificial thin first-year sea ice coveren by wet snow at CRRFL. The radar backscattering 
cross sections art: seen to increase with snow cover for snow-covered sea ice, because vol-
ume scattering s greater from snow than from ice. The results are also used to interpret 
experimental data obtained from field measurements. 
The brightness temperature of the snowpack simulated by a bounded layer of ran-
dom discrete scatterers embedded in a homogeneous medium is obtained in the zeroth 
and first order approximation by using the fluctuation-dissipation theorem with the strong 
fluctuation approach. The functional dependence of wavelength, polarization, observation 
angle, medium depth, scaUerers' constituents (for instance, ice particles and water drops 
in dry and wet snow), and other important physical parameters are established. The the-
ory can also be extended to multi-layer media. The effects due to a thin frozen ice surface 
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over snowpack are also calculated. A thin frozen ice layer over snowpack causes compli-
cated oscillation and interferences such that the thermal radiation is shielded or re8ected. 
Therefore, less brightness temperature is observed. From data matching of brightness tem-
perature versus water equivalent for snowpack, it is shown that the scattering due to first 
order approximation is significant for larg! water equivalent which corresponds to more 
lossy scatterers. Also, it is shown that the scattering darkening effects are included in the 
use of the auxiliary permittivity, the effective permittivity, and the first order solution. 
The permittivity of the homogeneous medium is important at small observation angles, 
while the sizes and the permittivities of the scatterers are important at large observation 
angles and higher frequencies, since the contribution from the homogeneous medium or 
the randomly distributed scatterers becomes significant. The increase of scatterer size 
decreases brightness temperature, thus aged snowpacks have lower thermal radiations. 
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PUBLICATIONS SUPPORTED BY NASA CONTRACT NAG-&-270 
A. Ref~reed Journal Articles 
AI. Wave scattering and guidance by dielectric waveguides with periodic surface (S. L. 
Chuang and J. A. Kong), Journal o/the Optical Society 0/ America, vo1.73, 669-679, 
May 1983. 
A2. Dyadic Green's functions for layered anisotropic medium (J. K. Lee and J. A. Kong), 
Electromagnetics, vol.3, 111-130, 1983. 
A3. Passive and active remote sensing of atmospheric precipitation (Y. Q. Jin aI~d J. A. 
Kong), Applied Optics, vo1.22, 2535-2545, September 1983. 
A4. Scattering of electromagnetic waves from a half-!'pace of densely di!l~ributcd dielec-
tric scatterers (L. Tsang and J. A. Kong), Radio Science, vol.6, 1260-1272, Nov-Dec 
1983. 
AS. Strong fluctuation theory for electromagnetic wave scattering by a layer of random 
discrete scatterers (Y. Q. Jin and J. A. Kong), Journal 0/ Applied Physics, vo1.55, 
1364-1369, March 1984. 
A6. Radiative transfer theory for active remote sensing of a layer of nonspherical par-
ticles (L. Tsang, J. A. Kong, and R. T. Shin), Radio Science, vo1.l9, 629-642, 
March-April 1984. 
A7. Microwave thermal emission of periodic surface (J. A. Kong, S. L. Lin, and S. L. 
Chuang), IEEE Transactions on Geoscience and Remote Sensing, vol.GE-22, 377-
382, July 1984. 
A8. Scattering of electromagnetic waves from a randomly perturbed quasiperiodic sur-
face (R. T. Shin and J. A. Kong), Journal 0/ Applied Physics, vo1.56, 10-21, July 
1984. 
A9. Active microwave remote sensing of an anisotropic random medium layer (J. K. Lee 
and J. A. Kong), IEEE Trans on Geoscience and Remote Sensing, 84lO 
AlO. Passive microwave remote sensing of an anisotropic randOl.1 medium layer (J. K. 
Lee and J. A. Kong), IEEE Trans on Geoscience and Remote Sensing, 8410 
All. Wave approach to brightness temperature from a bounded layer of random discrete 
scatterers (Y. Q. Jin), ElectrQmagnetics, volA, 323-341, 1984. 
A12. Ladder and cross terms in second-order distorted Born approximation (Y. Q Jin 
and J. A. Kong), J. Mathematical Physics, vol.26(5), 994-lO11, May 1985. 
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A13. Strong fluctuation thoery for scattering, attenuation, and transmission of microwave 
through snowfall (Y. Q. Jin and J. A. Kong), IEEE Transactiions on Geoscience 
and Remote Sensing, vol.GE-23, No.5, 754-760, September 1985. 
A14. Electromagnetic wave scattering in a two-layer anisotropic random medium (J. K. 
Lee and J. A. Kong), Optical Society 0/ America, December 1985. 
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C2. 
C3. 
C4. 
C5. 
C6. 
Conference Articles 
Theoretical models for microwave reI!lote sensing of vegetation and soil moisture (J. 
A. Kong), AgRISTARS Sflmpo8ium, Houston, Texas, December 1-2, 1982. 
Thermal microwave emission from a scattering medium with rough surfaces (R. Shin 
and J. A. Kong), URSI Sflmpo8ium, Boulder, Colorado, January 5-7, 1983. 
Remote sensing of soil moisture and vegetation (J. A. Kong, S. L. Lin, S. L. Chuang, 
and R. T. Shin), URSI Sflmpo8ium, Boulder, Colorad'l, January 5-7, 1983. 
Mie scattering ot' electromagnetic waves by precipitation (Y. Q. Jin and J. A. Kong), 
Optical Socielfl 0/ America Topical Meeting on Optical Techniques/or Remote Prob-
ing 0/ the Atmosphere, Lake Tahoe, Nevada, January 10-12, 1983. 
Scattering of electromagnetic waves from a half-space of densely distributed di-
electric scatterers (L. Tsang and J. A. Kong), IEEE/AP-S Sflmposium and URSI 
Meeting, Houston, Texas, May 23-26, 1983. 
Theory of microwave remote sensing of dense medium (L. Tsang and J. A. Kong), 
URSI Symposium, San Francisco, 1983. 
C7. Wave scattering by a bounded layer of random discrete scatterers (Y. Q. Jin and 
J. A. Kong), National Radio Science Meeting, Boulder, Colorado, January 11-13, 
1984. 
C8. Scattering of electromagnetic waves by a randomly perturbed quasi-periodic sur-
face (R. T. Shin and J. A. Kong), National Radio Science Meeting, Boston, Mas-
sachusetts, June 25-28, 1984. 
C9. Modified radiative transfer equation in strong fluctuation approach (Y. Q. Jin and 
J. A. Kong), National Radio Science Meeting, Boston, Massachusetts, June 25-28, 
1984. 
C10. Active and passive microwave remote sensing of layered anisotropic random medium 
(J. K. Lee and J. A. Kong), National Radio Science Meeting, Boston, Massachusetts, 
June 25-28, 1984. 
Cll. Electromagnetic characterization of inhomogeneous media exhibiting volume scat-
tering effects (J. A. Kong), Workshop on Waves in Inhomogeneous Media, 
Schlumberger-Doll Research, Ridgefield, Connecticut, August 8-9, 1985. 
C12. Radar backscattering from snow-covered ice (F. C. Lin, J. K. Lee, J. A. Kong, and R. 
T. Shin), Proceedings Snow Symposium V, Cold Regions Research and Engineering 
Laboratory, Hanover, New Hampshire, August 13-15, 1985 
C13. Mean dyadic Green's function for a two-layer anisotropic random medium: nonlinear 
approximation to the Dyson equation, (J. K. Lee and J. A. Kong), International 
Symposium on Antennas and Propagation, Kyoto, Japan, August 20-22, 1985. 
C14. Strong fluctuation theory of random medium and applications in remote sensing 
(Y. Q. Jin and J. A. Kong). International SJlmposium on Antennas and EM Theorfl 
(ISAEj, Beijing, China, August 26-28, 1985. 
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C15. Electromagnetic wave scattering by a two-layer anisotropic random medium, (J. K. 
Lee and J. A. Kong), IGARSS 85 and URSI Meeting, Unversity of Massachusetts, 
Amherst, MA, October 7-9, 1985. 
C. Reports and Theses 
Rl. Emissivity of a two-layer random medium with anisotropic correlation function, (R. 
T. Shin and J. A. Kong), Technical Report No. EWT-RS-41-8303, MIT, 1983. 
R2. Estimation of Snow Depth with Measured Brightness Temperatures (H. Z. Wang), 
Technical Report No. EWT-RS-43-8304, MIT, 1983. 
R3. Estimation of Snow Depth from Backscattering Cross Section Obtained from Active 
Microwave Remote Sensing (H. Wang), Technical Report No. EWT-RS-45-8306, 
MIT, 1983. 
R4. Extended Boundary Condition Approach to Wave Scattering by Periodic Structures 
(S. L. Chuang and J. A. Kong), Technical Report No. EWT-RS-55-8312, MIT, 1983. 
R5. Microwave Remote Sensing of a Scattering Medium with Rough Surfaces (R. T. 
Shin and J. A. Kong), Technical Report No. EWT-RS-64-8402, MIT, 1984. 
R6. Modified Radiative Transfer Equation in Strong Fluctuation Approach (Y. Q. Jin 
and J. A. Kong), Technical Report No. EWT-RS-67-8406, MIT, 1984. 
R7. AcVve Microwave Remote sensing of an Anisotropic Random Medium Layer (J. K. 
Lp.e and J. A. Kong), Technical Report No. EWT-RS-68-8407, MIT, 1984. 
R8. Behavior of Circularly Polarized Waves in Active Remote Sensing of Two-layer 
R.andom Media (F. C. Lin), Technical Report No. EWT-RS-70-841O, MIT, 1984. 
R9. Ladder and Cross Terms in Second Order Distorted Born Approximation (Y. Q. Jin 
and J. A. Kong), Technical Report No. EWT-RS-71-8412, MIT, 1984. 
RIO. Passive Microwave Remote Sensing of an Anisotropic Random Medium Layer (J. 
K. Lee and J. A. Kong), Technical Report No. EWT-RS-72-8412, MIT, 1984. 
Rll. Wave Approach to Brightness Temperature from a Bounded Layer of Random Dis-
crete Scatterers (Y. Q. Jin), Technical Report No. EWT-RS-73-8412, MIT, 1984. 
R12. Electromagnetic Wave Scattering in a Two-layer Anisotropic Random Medium (J. 
K. Lee and J. A. Kong), Technical Report No. EWT-RS-74-8506, MIT, 1985. 
R13. Radar Backscattering from Snow-covered lee (F. C. Lin, J. K. Lee, J. A. Kong, and 
R. T. Shin), Technical Report No. EWT-RS-75-8508, MIT, 1985. 
Tl. Lin, Sching Lih, "Microwave thermal emission from a periodic surface," S.M. Thesis, 
May 1983. 
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T2. Park, Dongwook, "Passive remote sensing of layered random media with strong 
permittivity fluctuations," S. M. Thesis, May 1984. 
T3. Shin, Robert Tong-ik, "Theoretical models for microwave remote sensing of earth 
terrain," Ph.D. Thesis, September 1984. 
T4. Lee, Jay Kyoon, "Electromagnetic wave propagation and scattering in layered 
anisotropic random medium," Ph.D. Thesis, February 1985. 
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Remote sensing of earth terrain

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