Studies of the Angular Correlation Function of Scattering ...Guifu Zhang, Student Member, Leung T...

444 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 35, NO. 2, MARCH 1997

Studies of the Angular Correlation Functionof Scattering by Random Rough Surfaces

with and without a Buried ObjectGuifu Zhang, Student Member, Leung Tsang, Fellow, IEEE, and Yasuo Kuga, Senior Member, IEEE

Abstract—The discrimination of the scattered wave from anobject buried in shallow ground from that of the rough surfaceis a difficult task with present ground penetrating radar (GPR)systems. Recently, a new approach for this classical problem hasbeen proposed and its effectiveness has been verified. This newmethod is based on the angular correlation function (ACF) of thescattered wave observed at two or more different incident andscattered angle combinations. It has been shown that the angularmemory signatures of rough surfaces are substantially differentfrom those of typical man-made targets and by choosing theappropriate incident and scattered angles, the surface scatteringcan be minimized whereas the scattering from the target is almostunchanged. In this paper, we will present detailed numerical stud-ies of the ACF of the scattered wave from rough surfaces with andwithout a buried object. To obtain the ACF, the three averagingmethods: realization, frequency and angular averaging, are testednumerically. It is shown that a single random rough surface ofmoderate extent can exhibit memory effect by using frequencyaveraging. Frequency averaging with a wide bandwidth is alsoeffective for suppressing fluctuation in ACF and is most useful forpractical applications. Numerical simulations indicate that evenwhen the ratio of scattered intensities with and without the buriedobject is close to unity, the corresponding ratio of ACF magnitudecan be more than 10 dB. Thus, using the ACF is superior to usingthe radar cross section (RCS) in the detection of buried objects.

I. INTRODUCTION

MICROWAVE detection of buried objects such as mines,pipes, and tunnels has attracted considerable interest

in recent years [1]. Different radar systems, including wide-band pulsed radar, SAR, and polarimetric radar, have beendeveloped for ground penetrating radar (GPR) applications.Advanced data processing methods, such as wavelet transform,time-domain resonance technique, time correlation method,and tomography, have been applied for discriminating targetreturns from clutter with mixed results. An important aspect fordesigning the GPR is the ability to distinguish the scatteringof electromagnetic waves of the buried object from that ofthe random rough surface above it (Fig. 1). Because the radarreturn from the surface can be comparable to or larger thanthe target return, the GPR does not work very well for an

Manuscript received March 28, 1996; revised August 29, 1996. This workwas supported by the Office of Naval Research Grant N00014-96-1-0813) andthe National Science Foundation (ECS-9522031 and ECS-9423861).The authors are with the Electromagnetics and Remote Sensing Laboratory,

Department of Electrical Engineering, University of Washington, Seattle, WA98195 USA.Publisher Item Identifier S 0196-2892(97)02111-6.

Fig. 1. Configuration of angular correlation of wave scattering from a roughsurface with a buried object. The two incident angles are and withrespective scattered angles and . A simple arrangement can be twomono-static radars with (upper right) and and quitedifferent and .

object buried in shallow ground without using a discriminationtechnique such as a very short pulse and time-gating method.The study of scattering by random rough surfaces has

been conducted for many years [2]–[4]. The past efforts havebeen mostly restricted to the measurement and calculation ofbistatic scattering intensities and RCS. However, recent studiesrevealed that the ACF of scattered fields by rough surfaces canexhibit a strong correlation called angular memory effect [5],[6]. It has been shown that the values of the ACF are smallexcept along the memory line of the incident and scattereddirections. The angular correlation function is the correlationfunction of two scattered fields in directions andcorresponding to two incident waves in directions and ,respectively (Fig. 1). ACF is defined as

(1)

where is the scattered field in direction for incidentfield in direction , and denotes ensemble averaging overrealizations, frequency bandwidth, or angles. The simplestarrangement can consist of two monostatic radars with

and (Fig. 1). The ACF is usually a complexnumber and has a magnitude and a phase. The results shown

0196–2892/97$10.00 © 1997 IEEE

ZHANG et al.: STUDIES OF THE ANGULAR CORRELATION FUNCTION OF SCATTERING 445

(a) (b)

(c)

Fig. 2. Comparison of the ACF magnitude along the memory line. for 30% moisture, for 5% moisture,, and : (a) , (b) , and (c) comparison between SPM and numerical simulations for TE case.

in this paper are ACF magnitudes, except for that in Fig. 8,which is the phase of the ACF.The memory line obeys the angular relation of

. It is analogous to a phase matchingcondition for reflection by a flat boundary. Because a randomrough surface is not translational invariant, it has not beenapparent that the scattered fields have any phase matchingcondition. However, recent studies utilize the fact that the ran-dom rough surface can be statistically translational invariant.Thus, it exhibits a phase matching condition when ensembleaverages of the scattered fields are taken. This has been verifiedby theoretical models and experiments [7]–[11]. In all thesestudies of angular correlation functions, the memory line doesnot exhibit itself for a CW wave scattered from a singlerandom rough surface. The presense of the memory line hasonly been revealed by using many rough surfaces and takingrealization averages. Recently, we applied the ACF techniquefor the detection of a target embedded in clutter. The ACFof scattered fields by a target and that by rough surfacesare very different. The angular width of the ACF responsedue to the target is usually wide compared to that of roughsurface. Both preliminary experimental [10] and numericalresults [11] showed very promising data, but further studiesmust be conducted to use the ACF technique for the detectionof a buried object.

The crux of the problem for the detection of a buried objectunder a rough surface is how to suppress the clutter and makethe object more conspicuous. There is a fundamental differencebetween the speckle reduction in SAR or optical images andthe proposed angular correlation method. The SAR specklereduction is performed on a image which has an intensityfluctuation. Intensity is always a positive quantity. The purposeof taking average of intensity is to obtain the mean. Thisprocess will reduce the fluctuating component but the meanvalue is always nonzero. On the other hand, ACF is, in general,a complex number and is a coherent averaging technique ofproducts of complex fields. It can have a zero mean by takingaverages. We show that this ACF coherent averaging schemecan achieve a relative reduction of 15 dB.In this paper, we will present a) an analytical study of

the ACF of the scattered wave by rough surfaces based onthe small perturbation method by using realization averaging,b) a numerical study of the ACF by three average methods,and c) the application of the ACF in the detection of aburied object under a single rough surface. First, we derivethe formulas of the ACF based on the small perturbationmethod. We will show that this simple analytical expression isuseful for studying the angular range and frequency bandwidthrequired for a different averaging method. Next, we studythe ACF by using Monte Carlo simulations of exact solution


(a) (b)

(c) (d)

Fig. 3. Three-dimensional (3-D) plots of ACF magnitude by different averaging methods. Reference angles are . Dielectricconstant of region 1 is . : (a) One realization, (b) realization averaging over 100 roughsurfaces, (c) frequency averaging over a frequency band of to , and (d) angular averaging over an angular range of to .

of Maxwell’s equations. We define and test numerically thethree ensemble averaging methods: realization, frequency andangular averaging. It is shown that even with a single randomrough surface of moderate extent, the memory effect canbe exhibited by using frequency averaging. The frequencyaveraging with a wide bandwidth is effective for suppressingfluctuation in ACF and also most useful for practical appli-cations. To simulate the scattering from a buried object, asmall cylinder is placed below a rough surface and the ACF isobtained using frequency averaging. For a fair comparison,the intensity is also calculated using frequency averaging.Numerical simulations indicate that even when the ratio ofscattered intensities with and without the buried object is closeto unity, the corresponding ratio of ACF magnitudes can bemore than 10 dB. Thus, using ACF is superior to using theRCS in the detection of a buried object. Numerical results arealso illustrated for various rough surfaces and soil moistureconditions. The phase of the ACF [14] is also studied for aburied object.

II. ACF USING THE SMALL PERTURBATION METHODWhen the rms height is small and the rms

slope is less than 0.2, the small perturbation method (SPM)

is applicable and the analytical expression of ACF can beobtained [2], [3]. Consider a plane wave incident on a roughsurface.By using the first-order SPM, the scattered field is

(2)

where

(3)

, and and are the wavenumbers of the upper and lower region, respectively.In (3), is the Fourier transform of the random height

of the surface, and denotes the polarizations. Functionis described in many references and is not expressed here

[2].Substituting (3) and its conjugate into (1), we obtain the

normalized mutual correlation function of wave scattering


(a) (b)

(c) (d)

Fig. 4. Comparisons of ACF magnitude and intensity. Averaging band is to . Reference angles are . .: (a) Without the object, (b) with the object , (c) ratios of results in (a) and that in (b). In (a), (b),

and (c), the intensity is the back scattered intensity for the observation angles and a rough surface with , andis used. (d) Ratios for a rougher surface case of . Two ratios of intensities are shown. One is for the reference angles with

and one for observation angles .

from a rough surface.

(4)

where is the length of the rough surface under the antennabeam width. The subscript “ ” denotes realization averaging.For statistically homogeneous random rough surfaces, the

random spectrum has the property

(5)

where is the spectrum of the rough surface. The conditionof (5) is also known as statistically translational invariance.Using the average and difference coordinates, the integrals in

(4) can be evaluated.

(6)

with

Equation (6) is a general form of the mutual coherencefunction, which is obtained based on a plane wave incidence.The incident plane wave can be changed to a Gaussian beamwave and results are same execpt that the function in(6) will be replaced by a Gaussian function. The ACF andthe frequency correlation function can be defined from (6) byfixing parameters. For example, the ACF is obtained by setting


(a)

(b)

Fig. 5. 3-D plots of ACF magnitude with the object using frequency averag-ing. Averaging band is to . Reference angles are

. Dielectric constant of region 1 is . ,(b) .

in (6). It can be seen that the strong correlationexists when is small. In the limit of infinite, the function becomes a delta function with nonzerovalues at

(7)

For fixed and , and are linearly relatedby (7) which is called the memory line. The angular width ofthe memory line is the order of .In Fig. 2, the ACF magnitude along the memory line for

rms height , correlation length , andsurface length is shown. The reference anglesare for Fig. 2(a), and forFig. 2(b), respectively. The ACF magnitude is shown as afunction of and the corresponding is obtained from (7).The broad ACF magnitude in Fig. 2(b) is consistent with thefirst-order Kirchhoff approximation (KA), but the sharp peaksobserved for very rough surfaces are missing [8]. To showthe parameter dependence, we plotted the ACF magnitudefor different polarizations and dielectric constants in Fig. 2.The dielectric constant is obtained for the soil by using theempirical model [12] for the moisture content of 5% and30% at frequency of 1.5 GHz. They areand , respectively. In Fig. 2(c), we also

(a)

(b)

Fig. 6. ACF magnitude of different surface properties. Averaging band isto . Reference angles are .

: (a) Dependence on the roughness,for two cases: (1) and (2)

. (b) Dependence on the moisture,for 5% moisture, for

30% moisture.

compared the ACF magnitude based on SPM with exactnumerical simulations. If the rough surface parameters (rmsheight and correlation length) are within the limit stated earlier,the agreement between SPM and numerical simulations issatisfactory.The frequency correlation function can be obtained from

(6) by setting and . Because the value ofthe function is small except near the zero argument, thefrequency correlation is only appreciable whenis close to zero. Therefore, the width in the frequency domainis given by

(8)

To get independent samples, the difference of the twofrequencies must be large enough so thatcan be satisfied. In other words, the bandwidth in frequencyaveraging must be much larger than the coherent bandwidth. Although (8) is based on SPM, it is useful for estimating

a number of independent samples in frequency averaging asdescribed in the following numerical simulations.


III. ACF WITH DIFFERENT AVERAGINGMETHODS: MONTE CARLO SIMULATIONS OFEXACT SOLUTION OF MAXWELL’s EQUATIONS

In the simulation of wave scattering from rough surfaces,it is customary to use the realization average to calculate thescattering cross section. However, when the object is buriedunder a single rough surface, realization averaging may not beapplicable and other means of taking a coherent average mustbe investigated. In this section, we will define the ACF of thescattered wave based on realization, frequency, and angularaveraging methods. As shown in the previous section usingSPM, it is possible to obtain the ACF if the data are availableover a wide frequency bandwidth or angular range.Realization averaging: The ensemble average is obtained

by taking averaging over different samples (rough surfaces)with the same statistics.

(9)where denotes the realization index, and is the numberof realizations. and are total power flux of the twoincident waves, respectively. In general, many independentsamples (realizations) must be generated to get stable data.Frequency averaging: Frequency averaging takes an en-

semble average over a frequency bandwidth centeredat .

(10)where is the number of frequencies over the frequencyrange , and is the frequencyindex for .Angular averaging: The angular averaging is defined by

small changes of incident and scattering angles around thefixed angles.

(11)where is the number of the angles, and is the smallangular difference for index .Fig. 3 shows the ACF magnitude with different ensemble

averaging methods. The random rough surface is generatedby using the spectrum method [13] with a Gaussian heightdistribution and Gaussian correlation function. The test surfacewas generated with a random number and results for differentsurfaces with the same statistics are quite similar. In numericalsimulations, a tapered plane wave is used as an incident waveto eliminate the effect of edges of the rough surface. Thetapering parameter is chosen to be in the simulations.Fig. 3(a) is the result for one rough surface without anyaveraging. Fig. 3(b) is that of realization averaging taken over

100 rough surfaces. It is clear that the existence of the memoryline becomes apparent if a sufficient number of independentsamples are included. Fig. 3(c) shows the ACF magnitudeof a single rough surface based on the frequency averagingmethod with 50 equally spaced samples over the frequencybandwidth of to . The large ridges in Fig. 3(c)correspond to the measured in the forward, includingspecular, direction. Although the ACF magnitude by frequencyaveraging is noisier than that of realization averaging, a distinctmemory line is clearly visible. To suppress fluctuation inFig. 3(c), more independent samples must be included inthe averaging process. It was estimated that only about 10independent samples can be obtained with the bandwidth of

to using (8). For the frequency averaging tobe effective, a much wider bandwidth, which is available inultra-wideband radars, may be required. Fig. 3(d) shows theACF magnitude by the angular averaging method given in(11). The results are smoother than those without averaging[Fig. 3(a)], but the memory line is not as clearly visible asthat of frequency averaging. Using SPM, we estimated thatonly 3 independent samples are available within a 20 angularrange for the value of that we have chosen.

IV. SCATTERING BY A BURIEDOBJECT UNDER A ROUGH SURFACE

In this section, we will obtain the scattered field from anobject placed below a rough surface using the surface integralequation method. The equations are solved numerically givingan exact solution of Maxwell’s equations. The surface has aone-dimensional profile with the horizontally polarized (TE)wave, and we assume the buried object is a perfect conductoras shown in Fig. 1. The same technique can be applied for adielectric object with a slight modification.Let and be the fields in regions 0 and 1, respectively,

and the boundary conditions are at therough surface and on the surface of the object. Inregion 0, we have the integral equation given by

(12)

where is the incident wave field, is the Green’sfunction for region 0, and denotes the principal valueintegral over the rough surface.Similarly, in region 1, we have the integral equation given

by

(13)

where is the scattered field from the buried object, andis given by

(14)

and is the surface of the buried object.


For on the surface of the buried object, we have

(15)

where is the scattered field from the rough surface, givenby

(16)Equations (12), (13), and (15) are coupled integral equations

and can be put into a matrix form with discretization.

(17)

The matrix elements to are impedance matrices., , and denote the values of , its normal

derivative on a rough surface , and the value of the normalderivative of on an object surface , respectively.After the matrix (17) is solved, the scattered field in region

0 is calculated by

(18)The normalized scattered field is defined in (3), and the ACFbased on frequency averaging can be obtained using (10).When and , the ACF becomes thewell known scattered intensity and it can be defined based onthe frequency averaging method.

(19)

V. NUMERICAL RESULTSTo demonstrate the effectiveness of the ACF over the tra-

ditional RCS technique, we conducted numerical simulationsusing a circular cylinder as the buried object. In addition,the ACF was obtained with the frequency averaging methodbecause in a practical application, realization or angular aver-aging is difficult to perform. Also the object is buried undera single random rough surface so that taking averages overmany realizations of random rough surface is meaningless.The cylinder is placed at a depth and a surface lengthof is used (Fig. 1). Unless specified otherwise, alldistance units are based on wavelength .In Fig. 4(a) and (b), both ACF magnitude and scattered

intensity with and without the buried object are shown as afunction of the incident angle . The reference angles are

and the variable angles are set to. This configuration provides the backscattering

cross section (RCS) for intensity, but the ACF magnitudeintercepts the memory line only at at which a peakcan be observed in Fig. 4(a). In general, the RCS varies slowlyas a function of angle; whereas, the ACF becomes small awayfrom the memory line due to the destructive phase interferencein the coherent averaging process.

In a practical GPR system, the presence of a buried object isusually determined by comparison with the same measurementof clutter only (rough surface). To demonstrate the effective-ness of the ACF, therefore, we calculated the ratios of ACFwith and without the buried object. A similar definition is usedfor the intensity as defined below.

with buried objectwithout buried object

(20)

with buried objectwithout buried object

(21)

The comparisons of these two ratios are shown in Fig. 4(c).Although the ratio of ACF contains a large amount of fluctu-ation due to a limited number of independent samples, thepresence of the buried object is clearly identifiable in theACF data. For example, for , the ratioof intensity is about 1 dB while the ratio of ACF is up to15 dB. In Fig. 4(a)–(c), the intensity and its ratio are that for

at back directions .It is true that the large difference between the ratio of

ACF and that of RCS in Fig. 4(c) is partially due to thesmall scattering from the rough surface at the reference angles

. For a fair comparison, two ratiosof intensities are shown in Fig. 4(d). One is for the referenceangles with and one forobservation angles . We cansee that both the ratio of the intensity at reference angles andthat at observation angles are very small. However, the ratioof ACF can be 10 dB. It is noted that the results shown inFig. 4(d) are obtained by taking the angular averaging overthe frequency averaged results as given by

(22)

The angular averaging is taken over a 20 angular range.Parameters for Fig. 4(d) are the same as those used in Fig. 4(c)except that changes are made for the parameters of the roughsurface with and instead ofand . A rougher surface produces large clutterscattering at large angles. In this case, the ratio of intensityat both reference angles and observation angles are small, butthe ratio of ACF can be larger by 10 dB.In Table I, the ratios obtained with (20) and (21) are listed

for the reference angles of, and . In most cases, the ratio of ACF is

higher than that of the intensity.Fig. 5(a) shows the 3-D plot of the magnitude of the angular

correlation function when the object is placed atbelow the surface. The reference angles are

and the configuration is the same as the one shownin Fig. 1. The 3-D profile near the memory line is similar


(a) (b)

(c)

Fig. 7. ACF magnitude of different object positions and sizes. Averaging band is to . Reference angles are .. : (a) Depth dependence , (b) horizontal position dependence

, and (c) size dependence .

TABLE IRATIOS OF ACF MAGNITUDES AND INTENSITIES (dB)

to the ACF magnitude without an object [Fig. 3(c)] due tothe strong rough surface scattering effect. However, the ACFmagnitude away from the memory line is quite different. TheACF magnitude, on average, is higher than the ACF magnitudewithout the buried object. Fig. 5(b) is the ACF magnitude fora surface with a smaller rms height .The sharp peak corresponds to the scattering in the speculardirection.Fig. 6 shows the ACF magnitude for different rms heights

and soil moisture conditions. Results are shown for the ref-erence angles in the backscattering direction as a function ofincident angles .In Fig. 6(a), the ACF magnitudes for two surface rms heights

and are obtained with and withoutan object. The memory line is at where the valuesare at maximum. When a buried object is absent, the ACF

Fig. 8. The phase of the ACF as a function of the depth of aburied object. Reference angles are .

, ,and .

magnitude of is substantially different from thatof because the rough surface scattering dependson the surface characteristics. However, results with the buriedobject for the two different rms heights are similar because, atthese angles, the ACF is dominated by the scattering from theburied object and the contribution from the rough surface issmall. Fig. 6(b) shows results of two soil moisture conditions.


Moisture contents of 5% and 30% in soil corresponds to thedielectric constants of and

, respectively. We note that for the high moisture case(30%), the effect of the buried object becomes less because ofthe large attenuation in the soil.Fig. 7(a) shows the ACF magnitude for three different

depths of the object. Although, the ACF magnitude decreaseswith increasing depth, it is still much higher than that ofrough surface scattering only if the angles are chosen carefully.Fig. 7(b) shows the dependence of ACF magnitude on thehorizontal position of the object. When is less than [lines1 and 2 in Fig. 7(b)], the object is still within the incident beamand the scattered wave contains both rough surface and objectcontributions. This accounts for the much larger value of theACF magnitude for lines 1 and 2. For and (lines3 and 4), the object is on the edge of the incident beam, sothat the ACF magnitude becomes comparable to that of roughsurface scattering only. Fig. 7(c) shows the ACF magnitudefor three different object sizes; and .As expected, the ACF magnitude decreases as the size of theobject becomes less. However, if the incident angle is faraway from the memory line of the rough surface, a significantdifference in the ACF magnitude is apparent even with thesmallest size . Based on the data presented inFigs. 6 and 7, it is clear that the choice of the reference andvariable angles is a critical factor for the ACF technique tobe effective. Further numerical and experimental studies mustbe conducted to obtain optimum angle combinations for thegiven system parameters.In the previous section, we studied the magnitude of ACF

and applied it for the target detection. In general, the ACFis complex and the recent study of rough surface scatteringrevealed that the phase of ACF contains the information relatedto the average surface height [14]. It is shown that unlike thepresent interferometric SAR method, the technique based onACF for the retrieval of surface topography is less sensitiveto the phase wrapping problem.Here we study the phase of ACF in relation to the depth of

the buried object. We avoid the memory line in the detectionof a buried object. To demonstrate the effectiveness of thephase of ACF for the buried object detection, we present aprimary result for a object buried under an almost flat surface.We plot the phase of ACF as a function of an object depthin Fig. 8. The agreement between analytical and numericalresults is excellent. The analytical result is obtained from thefirst-order scattering of a cylinder placed under a flat surface. Ithas a simple expression for two monostatic radars, as given by

(23)

where and are transmission angles corresponding toand , respectively, and are up-and down-going

transmission coefficients, and is the scattering amplitude ofthe cylinder. For the case with a circular cylinder in this paper,

the scattering amplitude has no contribution to the phaseof the ACF and only the transmission coefficients need to beevaluated. It is well known that the phase of the scattered fieldsis sensitive to the surface characteristics and varies rapidly asthe radar foot print location changes. However, if a sufficientnumbers of independent samples are included in the averagingprocess, the phase of ACF shows a stable response whichcan be used for the determination of the depth of the buriedobject.

VI. CONCLUSIONIn this paper, we demonstrated the effectiveness of using

ACF for the detection of a buried object. The advantage ofusing ACF is that unlike tomography and the classical inversescattering problem, only a few incident and scattering anglesare needed, e.g., two incident angles and two scattered angleswith averaging over frequency. For a rough surface withmoderate rms height, we showed that the method based onthe ACF is able to reduce the rough surface scattering effectsubstantially by choosing and far from thememory line of rough surfaces. It was also shown that thefrequency and angular averaging techniques can be used forsuppressing the fluctuation in ACF and obtaining the memoryline with a single rough surface.

REFERENCES

[1] L. Peters, J. Daniels, and J. Young, “Ground penetrating radar asa subsurface environmental sensing tool,” Proc. IEEE, vol. 82, pp.1802–1822, 1994.

[2] A. Ishimaru,Wave Propagation and Scattering in Random Media. NewYork: Academic, 1978.

[3] L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave RemoteSensing. New York: Wiley Interscience, 1985.

[4] K. O’Neill, R. Lussky, and K. D. Paulsen, “Scattering from a metallicreflector embedded in a lossy dielectric beneath random rough surfaces,”IEEE Trans. Geosci. Remote Sensing, vol. 34, pp. 367–376, Mar. 1996.

[5] S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations andfluctuations of coherent wave transmission through disordered media,”Phys. Rev. Lett., vol. 61, pp. 834–837, 1988.

[6] T. R. Michel and K. A. O’Donnell, “Angular correlation functionsof amplitudes scattered from a one-dimensional, perfectly conductionrough surface,” J. Opt. Soc. Amer., vol. 9, no. 8, pp. 1374–1384, 1992.

[7] A. Ishimaru, C. Le, Y. Kuga, L. Ailes-Sengers, and T. K. Chan,“Polarimetric scattering theory for high slope rough surfaces,” Prog.Electromagnet. Res., to be published.

[8] C. T. C. Le, Y. Kuga, and A. Ishimaru, “Angular correlation functionbased on the second-order Kirchhoff approximation and comparisonwith experiments,” J. Opt. Soc. Am. A, vol. 13, no. 5, pp. 1057–1067,May 1996.

[9] M. Nieto-Vesperinas and J. A. Sanchez-Gil, “Intensity angular correla-tions of light multiply scattered from random rough surfaces,” J. Opt.Soc. Am. A, vol. 10, pp. 150–157, 1993.

[10] Y. Kuga, T.-K. Chan, and A. Ishimaru, “Detection of a target embeddedin clutter using the angular memory effect,” submitted for publication.

[11] L. Tsang, G. Zhang, and K. Pak, “Detection of a buried object undera single random rough surface with angular correlation function in EMwave scattering,” Microwave Opt. Technol. Lett., vol. 11, no. 6, pp.300–304, 1996.

[12] J. R. Wang and T. J. Schmugge, “An empirical model for the complexdielectric permittivity of soils as a function of water content,” IEEETrans. Geosci. Remote Sensing, vol. GRS-8, pp. 288–295, 1980.

[13] E. I. Thorsos, “The validity of the Kirchoff approximation for roughsurface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc.Amer., vol. 83, pp. 78–92, 1988.

[14] A. Ishimaru, C. Le, Y. Kuga, J. Yea, K. Pak, and T.-K. Chan, “Interfer-ometric technique for determining the average height profile of roughsurfaces,” in Proc. IGARSS’96, 1996, pp. 2137–2139.


Guifu Zhang (S’96) received the B.S. degree in physics from Anhui Univer-sity in 1982 and the M.S. degree in radio physics from Wuhan University,P.R. China. He is currently pursuing the Ph.D. degree in the Department ofElectrical Engineering, University of Washington, Seattle,From 1985 to 1993, he was with the Space Physics Department, Wuhan

University. In 1989, as a visiting scholar, he was working in the Communi-cation Research Laboratory, Japan. His current research interests are in wavepropagation and scattering in random media and their application in remotesensing and communication.

Leung Tsang (S’73–M’75–SM’85–F’90), for a biography, see this issue, p.223.

Yasuo Kuga (M’78–SM’90) was born in Kitakyushu, Japan. He received theB.S., M.S., and Ph.D. degrees from the University of Washington, Seattle, in1977, 1979, and 1983, respectively.From 1971 to 1975 he was an Engineer at Matsushita Electric Industrial

Corporation, Osaka, Japan, From 1979 to 1983, he was a Research Associateat the University of Washington. From 1983 to 1988, he was a ResearchAssistant Professor of Electrical Engineering at the University of Washington.From 1988 to 1991, he was an Assistant Professor of Electrical Engineeringand Computer Science at The University of Michigan. He is now an AssociateProfessor of Electrical Engineering at the University of Washington. Hisresearch interests are in the areas of microwave and millimeter-wave remotesensing and optics.Dr. Kuga is a member of the Optical Society of America and Commissions

B and F of the International Union of Radio Science. He was selectedas a 1989 Presidential Young Investigator. He is an Associate Editor ofRadio Science (1993–1996) and the IEEE TRANSACTIONS ON GEOSCIENCE ANDREMOTE SENSING (1996–present).

Studies of the Angular Correlation Function of Scattering ...Guifu Zhang, Student Member, Leung T...

Documents

Transcript of Studies of the Angular Correlation Function of Scattering ...Guifu Zhang, Student Member, Leung T...