The objectives of research over the next three years are: (1) to develop a randomly rough surface scattering model which is applicable over the entire frequency band; (2) to develop a computer simulation method and algorithm to simulate scattering from known randomly rough surfaces, Z(x,y); (3) to design and perform laboratory experiments to study geometric and physical target parameters of an inhomogeneous layer; (4) to develop scattering models for an inhomogeneous layer which accounts for near field interaction and multiple scattering in both the coherent and the incoherent scattering components; and (5) a comparison between theoretical models and measurements or numerical simulation

Blanchard, A. J.

Fung, A. K.

English

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SCATTERING MODELS AND BASIC EXPERIMENTS 
I N THE MICROWAVE REGIME 
I.Introduction 
Fung, A. K. and A. J. Blanchard 
Wave Sc attering Research Center 
Electr ica l Engineering Departmen t 
Uni versi t y o f Texas at Arlington 
Arl ington, TeRas 76019 
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The ob jec tives o f t he researc h over the next three y~ars are: 
(1 ) To develop a randomly r ough s u rface scattering model which is 
applicable ov~r the entire frequenc y band. 
(2) To development compute r simulation method and algorithm to 
s imulate scattering from known randomly roug~ surfaces,Z(x,y). 
(3) To design and perfo rm laborato ry experiments to study 
geometric and physic a l t arget pa r ameters of an inhomogeneous layer. 
(4 ) To develop s cattering models f o r an inhomogeneous layer which 
accounts for near field interaction and multiple scattering in 
bot h the coherent and the incoh~rent scattering c omponents. 
(5) Comparison between t heoretical models and measurements or 
numerical simulation. 
Al though various new approac hes in rough surface scattering 
have appeared in t he literature,they are generally restricted t o 
e i ther l ow o r high freq uency regions because- of the simplifying 
assumptions used. General theories which are not restricted by 
s uc h simplifying assumptions are so c omplex that either no 
explicit solutions are available or only the scattered field is 
available because the average scattered power is too involved to 
compute . In o rder t o ob tain a general scattering model for 
r andoml y rough surface whi c h i s explic it and simple t o use it i s 
n ec~,s,sa~y"t<? ,de,te.~m ~ l1~ ,a, :SJJf.fi<;t~l1:tly' .a,c~urate surfac:e: ~ur.r.ez:l.t, 
in~luding j ust ehough mul tipre scattering tercis t o have the 
co rrect behavio r over the entire fr~quency band but not too 
involved to deny an explicit solution. This is our goal for a 
rough surface scattering modej. I n volume scattering problems 
most theories are restricted to either a sparsely populated medium 
o r coherent scattering in a dense medium. Incoherent scattering 
which is of major inter~st in remote sensing has been investigated 
mainly by either the ~orn or the distorted Born approximation 
-i n the field approach and the radiativa transfer iormulation in the 
i ntensity approach. Other methods are needed to include mUltiple 
i n c ohere~t scattering in the field approach and techniques are 
needed t o determine the autocorrelation function in the coherent 
f ield calculRtion in dense inhomogeneous medium. Currently, the 
us::, of Percl;s Yevick approximation and the associated pair 
distribution function for hard spheres in coherent scattering 
computation leads t o nonphysical results when the volume fraction 
of the medium is around 0.6 . 
All t heoretical scattering models involve some simplifying 
assumptions. To verify these models it is best to have 
controlled experiments so that target parameters can be varied and 
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any given experiment c an be rep~ated. In the case of random surfaces it is possible to use computer simulation. This is not only cost effective compared with full scale field measurements but it is also more conven ient to change target parameters than in any controlled experiment . 
2 . Approach 
The approach to be used to develop the propospd ra,ldom surface model is to use the integral equation method. We have used this method successfully to develop a scattering monel for a perfectly conducting surface in the past year and we intend to generalize it to dielectric surfaces. To perform computer simulation for the rough surface problem we intend to investigate first the generation of a two- dimensional random surface wlth specified autocorrelation functicn. This is a major effort beca~se a lgorithms and tec hniques f o r thi s purpose have been restricted to one- dimensional s u rfaces . From the numerical o int of view this i s also a large j ob reql".i,ring l arge capac ity l 'mputer. Past experienca on a one-dimensional surfac~ indic. es that it is desirable to have at least a 10,000 point surf. :e to insure convergence of statistical parameters and it is desirable to have a 50,000 point surface to allow scattering computation at different frequencies. Once the surface is available the standard moment method will be used for scattering coefficient computati ons. Here again it is necessary to ge~erali~~ from one to two dimensions and numerically this is a pro~lem becaube we cannot allow the computation-size t o increase like a square. 
The measurement program wi ll be divir.ed into two major tasks, (1) the design and construction of a versatile volumetric target structure, and (2) the measurement of radar backsc a tter c ross sec t ion as a function of system and target parameters . The t arget is designed and constructed to simulate vegetatio,n typE.. 
,s,trl,lct14res., ' The 'target- c·an' ,be 'used , to provide a variety of ' both geometric and electrical characte ristics to include, leaf censity in three dimensions, leaf orientation and location , leaf siz0 and shape,and permittivity characteristics of the volumetric structure including relative pe rmittivity and cond~ct ivity. The target is designed to allow a number of different parameters to be evaluated while maintaining the basic t~rg et shape. r"easurements will include the effects of leaf distr iblAti on, shape, orientation a nd location on radar backscatter. Initial experiments wi).l minimize the effects of the stalk structures, however, future measurement programs could include these interaction effects as well. The measurements will be made in an indoor Radar Cross section Range. The measurements will include amplitude and phase me asurements at X band,K band, incid ent angle s from" to 513 degrees, and the four linear transmit/receive polarization states. 
In view of tte difficulties with the current theoretical approaches as stated ir. the introduction to the volume scatter ing problem, we propose to use the eikonal approximat ion for incoherent 
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scattering computation and the solution of the master equation for 
determining a more realis~ic autocorrelation function. It should 
be noted that the pair distribution func tion was derived for use 
in a dynamic medium such as a fluid . Hence, f o r a medium with 
random but rigid distributions of particles it is not appropriate 
and does lead to nonphysical results. 
3. Results to Date 
Over the past yea r we have developed a scattering model for 
an inhomogeneous layer containing needle- shaped leaves. We have 
made comparisons bet een scattering from s uch a l ayer and another 
layer containing disc-shape~ leaves . The significant difference 
between the two types o f vegetation is that the backscattering 
angular cu rve for the disc-type has a hump in the mid angular 
region while the needle-type has a dip in the same region when the 
size o f the leaves is comparable to the incident wavelength ( see 
Figures 1 and 2 ) . In addiction, study has a l so been c arried out 
, to determine the effects of Fresnel phase in the s c attering phase 
matrices on scatterers that are comparable to the inc ident 
wavelength but are much smalle r than the wavelength i n at least 
one dimension. The conclus ion is that the inclusion of the 
Fresnel phase gives a more accu r ate frequency trend dependence 
(see Lee1l984). Al s o s tudied is the effect of closer spacings 
between scatterers accounted f or in the s cattering phase matrix. 
Results indicate that a more accu rate target parameter can be 
inferred from suc h a model than is possible using a standard 
radiative transfer method (Fung and Eom1June,1984 ). The inversion 
from measurements for albedo and optical depth was studied by Fung 
and Eom (August,1984 ) with the conclusion that at least a 
first-order theo ry must be used in the radiative transfer 
formulation f or emission from an inhomogeneous layer. 
A scattering model for a perfectly conducting, randomly rough 
surface has been devel oped whic h is va l id over the entire 
frequ ency band (pan ;1984 ). It has been demonstrated analytically 
that the general s ol ution obtained, r educes correctly to the 
. geomet'dc·a·l· opti."cs' ·s·o'lu d on' in 'th·e high frequency 'liini t and · to the 
first-order small perturbation solution in the low frequency 
limi t . In the intermediate region it has a behavior which can be 
very different from either l imiting solution b~~ is liable to be 
misinterpreted as one or the other. The reason is that it could 
resemble the 10 frequency solution in polarization behavior but 
f ollow the general angu l ar trend of the Kirchhoff solution (see 
Figure 3 ) . Also developed was the scattering model for a perturbed 
sinuscidal surface ( Eom and Fung ,1984) . This was done to account 
f or 90il surfaces with row directional dependence. 
A plas t ic model f or a l ayer of leaves of either circular or 
ellipt ic shape has been designed which permits the leaf angular 
distribution, leaf size, leaf density, leaf dielectric value, and 
row direction effects to be studied under laboratory conditions. 
It is expected that measurements conducted with this target will 
be able to provide reliable data for the verification o f ex isting 
volume scattering mode ls. 
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FIG! . SIZE DEPENDENCS OF DISC- SHAPED VEGETATION ( a= radius of disc ) 
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needle) 
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Scattering Models and Basic Experiments in the Microwave Regime

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