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RADAR SCENE GENERATION FOR TACTICAL DECISION AIDS 

National A eron au ti cs and Space Administration 

Goddard Space Flight, Center 

Contract NAG 5-769 

FINAL REPORT 

covering the period 

April 15, 1986 - April 14, 1987 8 

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(NASA-CB-180234) EBCAB SCENE GEttEBATICB FOR S8 7-2 (34 49 11 

IACTXCAI. CECXSfCPi A1C.S 

Ayr. lost- 1455 Of Tech.) - 14 Apr- 7 E 1S€7 (Baszachusetts CSCL 171 Unclas 

Fiaal beport, 15 

63/32 45328 

, 

prepared by 

J. A. Iiong 

Principal Investigator 

Massachuset.ts Institute of Technology 

Research Laboratory of Electronics 

Cambridge, Massachusett,s 021 39 
RADAR SCENE GENERATION FOR TACTICAL DECISION AIDS 

Principal Invest'igator: Jill Au Kong 

FINAL REPORT 

Under the sponsorship of the NASA Contract NAG5-769, we have published 23 

refereed journal and conference papers and 6 technical reports for the research on the 

Radar Scene Generation For Tactical Decision Aids. 

We have studied the Mueller matrix and polarization covariance matrix for polarimetric radar systems. The clutter is modelled by a layer of random permittivity, described 

by a three-dimensional correlat,ion function, with variance, and horizontal and vertical 

correlation lengths. This model is applied, using the wave theory with Born approximations carried to the second order, to find the backscattering elements of the polarimetric 

matrices. It is found that 8 out of 16 elements of the Mueller matrix are identically zero, 

corresponding to a covariance matrix with four zero elements. Theoretical predictions are 

matched with experimental data for vegetation fields. 

A general mixing formula is derived for discret,e scatterers immersed in a host 

medium. The inclusion particles are assumed to be ellipsoidal. The electric field inside 

t.he scatterers is determined by quasistatic analysis, assuming the diameter of the inclusion 

particles to be much smaller than the wavelength. The results are applicable to general 

niultiphase mixtures, and the scat.tering ellipsoids of the different phases can have different 

sizes and arbitrary ellipticity distribution and axis orientation, i.e., the mixt.ure may be 

isotropic or anisotropic. The resulting mixing formula is nonlinear and implicit for the effective compiex dieiect,ric constant, because the approach in calculating the internal field of 

2 
. 

scatterers is self-consistent. Still. the form is especially suitable for iterative solution. The 

formula contains a quantity called the apparent permittivity. and with different choices of 

this quantity, the result leads to the generalized Loreiitz - Lorenz formula, the generalized 

Polder - van Saiiten forniula. and the generalized coherent potential - quasicrystalline approximation formula. Finally. the results are applied to calculating the complex effective 

permittivity of snow and sea ice. 

We have used the strong fluctuation theory to derive the backscattering cross sections. The study of the strong fluctuation theory for a bounded layer of random discrete 

scatterers is further extended to include higher order co-polarized and cross-polarized second moments. The backscattering cross sections per unit area are calculated by including 

the mutual coherence of the fields due to the coincidental ray paths and that due to the 

opposite ray paths which are corresponding to the ladder and cross terms in the Feynman 

diagrammatic representation. It is proved that the contributions from ladder and cross 

terms for co-polarized backscattering cross sections are the same, while the contributions 

for the cross-polarized ones are of the same order. The bistatic scattering coefficients in 

the second-order approximation for both the ladder and cross terms are also obtained. The 

enhancement in the backscattering direction can be attributed to the contributions from 

the cross terms. 

A two-layer anisotropic random medium model is developed for the active and passive microwave remote sensing of ice fields. The dyadic Green’s function for this two-layer 

anisotropic medium is derived. With a specified correlation function for the randomness 

of the dielectric constant, the backscattering cross sections are calculated with the Born 

approximation. It is shown that the depolarization effects exist in the single-scattering 

process. Treating sea ice as a tilted uiliaxia! medium, the observed strong cross-polarized 

ret,urn in the bistatic scattering coefficients is successfully predicted from the theoretical 

model. It is also shown that the backscattering cross section of horizont,al polarization can 

3 
be greater than that of vertical polarization even in the half-space case. The principle of 

reciprocity and the principle of energy conservation are invoked to calculate the brightness 

temperatures. The bistatic scattering coefficients are first calculated and then integrated 

over the upper heinisphere to be subtracted from unity. in order to obtain the einissivity 

for the random medium layer. It is shown that both the absorptive and randomly fluctuating properties of the anisotropic medium affect the behavior of the resulting brightness 

temperatures both in theory and in actual controlled field measurements. The active and 

passive results match favorably well with the experimental data obtained from the firstyear and the multiyear sea ice as well as from the corn stalks with detailed ground-truth 

information. 

A three-layer random medium model is adopt.ed to study the volume scattering 

effects for the active and passive microwave remote sensing of snow-covered ice fields. We 

simulate the snow layer by an isotropic random medium and the ice layer by an anisotropic 

random medium. In snow, the fluctuation of the permittivity and the physical sizes of the 

granular ice particles are characterized by the variance and two correlation lengths. In ice, 

the anisotropic effect is attributed to the elongated structures and the specific orientations 

of the air bubbles, the brine inclusions, and other inhomogeneities. Two variances are 

required to characterize the fluctuations of the permittivities along or perpendicular to the 

tilted optic axis. The physical sizes of those scattering elements are also described by two 

correlation lengths. 

The vegetation canopy and snow-covered ice field have been studied with a threelayer model, an isotropic random medium layer overlying an anisotropic random medium. 

We have calculated the dyadic Green’s functions of the three-layer medium and the scattered e!ectromagr;etic intensities with Borri approximation. The backscattering cross sections are evaluated for active microwave remote sensing. The theoretical approach can be 

extended to derive the bistatic scattering coefficients. 

4 
PUBLICATIONS SUPPORTED BY NASA CONTRACT NAG-5-769 

REFEREED JOURNAL AND CONFERENCE PAPERS 

Radar cross section prediction using a hybrid iiietliod (C. Lee and R. T. Shin), National 

Radio Science Meeting, Philadelphia. Pennsylvania, June 9-13, 1986. 

Radar cross section prediction for coated perfect conductors with arbitrary geometries (S. 

W. Rogers and R. T. Shin), National Radio Science Meeting, Philadelphia, Pennsylvania, 

June 9-13, 1986. 

Polarimetric microwave remote sensing of anisotropic earth terrain with strong fluctuation 

theory (M. Borgeaud, J. A. Kong, and R. T. Shin), IGARSS 87 and URSI Meeting, 

University of Michigan, Ann Arbor, MI, May 18-21, 1987. 

Theoretical models for active and passive microwave remote sensing of snow-covered sea 

ice (F. C. Lin, J. A. Kong, and R. T. Shin), IGARSS 87 and URSI Meeting, University of 

Michigan, Ann Arbor, MI, May 18-21, 1987. 

Theoretical models for polarimetric radar clutter (M. Borgeaud, R. T. Shin, and J. A. 

Kong), Journal of Electromagnetic Waves and Applications, vol. 1, no. 1, pp. 73-89, 

1987. 

Electronzagnetic Wave Theory (J. A. Kong), Wiley-Interscience, New York, 696 pages, 

1986. 

On the resonant ionospheric heating at the electron gyrofrequency (M. C. Lee, J. A. Kong, 

and S. P. Kuo), Proceedings of the International Symposium on Modification of the Ionosphere by Powerful Radio Waves,, 111, Suzdal/Moscow, U.S.S.R., September 9-12, 1986. 

Enhanced ionospheric modifications by the combined operation of HF and VLF heaters 

(M. C. Lee, J. A. Kong. and S. P. Kuo), Procecdings of the International Symposiu on 

Modification of the Ionosphere by Powerful Radio Wai~es,, 146, Suzdalfhloscow, U.S.S.R., 

Septeiiiber 9-12. 1986. 

Parametric excitation of whistler waves by HF heater (S. P. Iiuo and M. C‘. Lee). Proceedin95 of the Internatzonal Symposium on Alodificution of the Ionosphere by Pouwful Radio 

Waves, 109, Suzdal/hloscow, U.S.S.R., September 9-1 2, 1986. 

Microwave remote sensing of snow-covered sea ice (M. Borgeaud, J. A. Kong, and F. C. 

Lin), 1986 International Geoscience and Remote Sensing Symposium, Zurich, Switzerland, 

8-11, September, 1986. 

Polariinet ric radar clutter modeling with a two-layered anisotropic random medium (M. 

Borgeaud, J. A. Kong, and R. T. Shin), International Union of Radio Science Commission 

F Open Symposium, University of New Hampshire, Durham, New Hampshire, July 28- 

August 1. 1386. 

Remote sensing of snow-covered sea ice (F. C. Lin and J. A. Kong), International Union of 

Radio Science Commission F Open Symposium, University of New Hampshire, Durham, 

New Hampshire, July 28-August 1, 1986. 

5 
Nonlinear EM wave interactions with the neutral atmosphere (S. Nghiem, M. C. Lee, 

and J. A. Kong), International Union of Radio Science Commission F Open Symposium. 

University of New Hampshire, Durham, New Hampshire, July %-August 1, 1986. 

Effective perniittivity of dielectric mixtures (A. Sihvola and J. A. Kong), International 

Union of Radio Science Commission F Open Symposium, Vniversity of New Hampshire, 

Durhaiii, New Hampshire, July 28-August 1. 1986. 

. Modified radiative transfer t,heory for a two-layer anisotropic random medium (J. ki. Lee 

and J. A. Kong), National Radio Science Meeting, Philadelphia, Pennsylvania, June 9-13, 

1986. 

Theoretical modeling of polarimetric radar clutter (M. Borgeaud, R. T. Shin, and J. A. 

Kong), National Radio Science Meeting, Philadelphia, Pennsylvania, June 9-13, 1986. 

A new formula for partial fraction expansion of a transfer matrix (C. F. Chen and G. 

Freeman), Comp. 

Radar cross section prediction using a hybrid method (C. Lee and R. T. Shin), National 

Radio Science Meeting, Philadelphia, Pennsylvania, June 9-13, 1986. 

Radar cross section prediction for coated perfect conductors with arbitrary geometries (S. 

W. Rogers and R. T. Shin), NationaI Radio Science Meeting, Philadelphia, Pennsylvania, 

June 9-13, 1986. 

Maihs. with Appls., vol. 12A, no.9, 963-968, 1986. 

Stimulated backscattering of lower hybrid waves (S. P. Kuo and M. C. Lee), Physics of 

Fluids, 29(4), 1024-1028, April 1986. 

Backscattering and propagation of radar pulses in earth terrain media (F. C. Lin, J. A. 

Kong, R. T. Shin, and Y. E. Yang), IEEE IMTC'/86 Meeting, Boulder, Colorado, March 

24-27, 1986. 

Resonant. electron diffusion as a sat.uration process of the synchrotron maser instability 

(M. C. Lee and S. P. Kuo), Journal of Plasma Physics, vol. 35, part 1, 177-184, 1986. 

Theory of Microwave Remote Sensing (L. Tsang, J. A. Kong, and R. T. Shin), WileyInterscience, New York, 613 pages, 198.5. 

* 

EWT REPORTS 

Radar cross section prediction for coated perfect conductors with arbitrary geometries (S. 

W. Rogers and R. T. Shin), Technical Report No. EWT-RS-92-8606, MIT, 1986. 

Polarimetric radar clutter modeling with a two-layer anisotropic random medium (M. 

Borgeaud, J. A. Kong and R. T. Shin). Technical Report No. EWT-RS-94-8608, MIT, 

1986. 

Dielectric properties of geophysical media (A. Sihvola arid J. A. Kong), Technical Report 

NO. EWT-RS-96-8608, MIT, 1986. 

Effective pernlitt,ivity of dielectric mixtures (A. Sihvola and J. A. Kong), Technical Report 

NO. EWT-RS-97-8608, MIT, 1986. 

6 
Theoretical models for polarimetric radar clutter (hI. Borgeaud, R. T. Shin and J. A. 

Kong), Technical Report No. EWT-RS-99-8608, MIT, 1986. 

Theoretical Models for Microwave Remote Sensing of Snow-Covered Sea Ice (F. C. Lin, J. 

A. Kong, and R. T. Shin), Technical Report No. EWT-RS-102-8705, MIT, 198’7. 

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