Contains reports on four research projects.Joint Services Electronics Program (Contract DAAB07-74-C-0630)California Institute of Technology (Contract 953524

Chan, Wing-Cheung

Chu, Donald

Kong, Jin Au

Nagase, Masato

Njoki, Eni G.

Tsang, Leung

DSpace@MIT

VIII. ELECTRODYNAMICS OF MEDIAProf. Hermann A. HausProf. Jin-Au KongDonald L. LeeMonica MindenAcademic Research StaffProf. Paul L. Penfield, Jr.Graduate StudentsEni G. NjokuEdward M. SingelProf. David H. StaelinProf. Abraham Sz6keLeung TsangJohn C. UffordA. COMPARISON OF THE HORIZONTAL MAGNETIC DIPOLE JSEPWITH THE HORIZONTAL ELECTRIC DIPOLE IN GEO-PHYSICAL SUBSURFACE PROBINGJoint Services Electronics Program (Contract DAAB07-74-C-0630)Wing-Cheung Chan, Jin-Au Kong, Leung TsangThe use of a horizontal electric dipole (HED) in geophysical subsurface probing withthe electromagnetic interference fringes method has been studied extensively. 2 In thisreport similar calculations are performed for a horizontal magnetic dipole (HMD) byusing the reflection coefficient formulation 3 and the saddle-point method, and the cal-culations are compared with those obtained for a horizontal electric dipole.The radiation patterns in the broadside direction are compared in Fig. VIII-1. Theangle at which the coupling power is maximum occurs at the critical angle sin - 1 (1/n),where n is the refractive index of the half-space medium. The radiation patterns inthe end-fire direction are compared in Fig. VIII-2. It is found that the angle of maximum5 2:0HMHMD0 H 5 10 15 20 250 1.0DHEDD10 20 30 4.0 50-5 0-10 - HMD -10 HMDHED-2.0-3.0-20MMD-4.0-25MED-30Fig. VIII-1.Radiation pattern for HMD and HED at 4 =90". (Values for HED from Tsang andKong. 2 ) HMD: E1= 3.2. HED: E1 = 3.3.Fig. VIII-2.Radiation pattern for HMD and HED at =0. (Values for HED from Tsang and Kong. )HMD: E 1= 3.2. HED: E 1 = 3.5.PR No. 116JSEPDISTANCE IN FREE-SPACE WAVELENGTHSFig. VIII-3.FIRST REFLECTED TERMI.TERMDISTANCE IN FREE-SPACE WAVELENGTHS(b)(a) Interference pattern for EzE= 3. 3 d = 4X1E = 500i2 LT = 0. 005(b) Comparison of the half-space solutionwith the reflected terms.E =3.31E2 = 500id = 4XLT = 0. 005Table VIII-1. Comparison of HED and HMD.HED HMDField ComponentsTE TE TE TM TM TMBroadside H , E , H E , H , Ez P z pTM TM TM TE T E  TEEnd fire E , HTM , EH , E , Hz P z PRadiation Pattern3 2 3 2 2Upper medium [xol (0) sin2 yol (0) sin 22 2 2 2+ y C(o) c Cs2 cos + x(O) cos cos/ 3 1/2Lower medium [ xlo(a) sin 3 lo(a) sn+ yol(a)I cos ]a cosO Z+ Xo1(a)Z cos acos4]Broadside angle sin- 1 (1/n) sin-1 (1/n)1 End-fire - 1 + nEnd-fire angle sin sinPR No. 116JSEPJSEP(VIII. ELECTRODYNAMICS OF MEDIA)power coupling for the HMD occurs at sin - 1  /(l+n), while for the HED it occurs at JSEPsin-  (l+n )/2n . Thus for the HMD this angle ranges from 0 to 90 , while for theHED it only spans 0-45 .Figure VIII-3a shows an interference pattern for E z for a highly reflecting subsurfacesituated 4 free-space wavelengths below the surface. The occurrence of the high peakis illustrated by the first reflected term in Fig. VIII-3b, which evidently is due to thepower launched into medium 1 at the critical angle.In Table VIII-1, the corresponding field components in the broadside and end-firedirections are listed. The formulas used in calculating the radiation patterns are alsocompared.The implication of these results is that the HMD may be more effective in subsurfaceprobing than the HED. In the broadside direction power is more concentrated at thecritical angle; hence, there is a sharper peak in the interference pattern. Note thatthese calculations are performed for a horizontal magnetic dipole on the surface of theprobing area. In actual experiments, the HMD may have to be elevated. By using thereflection coefficient formulation and similar techniques, field components can be cal-culated in detail.References1. J. A. Kong, L. Tsang, and G. Simmons, "Geophysical Subsurface Probing withRadio-Frequency Interferometry," IEEE Trans., Vol. AP-22, No. 4, pp. 616-620,July 1974.2. L. Tsang and J. A. Kong, "Interference Patterns of a Horizontal Electric Dipoleover Layered Dielectric Media," J. Geophys. Res. 78, 3287-3300 (1973).3. J. A. Kong, "Electromagnetic Fields Due to Dipole Antennas over Stratified Aniso-tropic Media," Geophys. 37, 985-996 (1972).B. EFFECTS OF SCATTERING AND NONUNIFORM TEMPERATUREDISTRIBUTIONS ON BRIGHTNESS TEMPERATURE IN REMOTESENSINGJoint Services Electronics Program (Contract DAAB07-74-C-0630)Leung Tsang, Jin-Au KongIn passive remote sensing of the Earth with microwaves, the brightness temperaturereading of a radiometer depends on its angle of observation and on the microwave emis-sive properties of the observed area. Various theories have been developed for inter-pretation of data collected from satellites and spacecraft, with a half-space dielectricmedium used as the model. It is well understood that in snow, ice, or desert areas thesubsurface temperature profile, absorption, and scattering are dominant factors in the JSEPPR No. 116(VIII. ELECTRODYNAMICS OF MEDIA)JSEP surface-brightness temperature. 1  Assuming uniform temperature distribution, Gurvichand his co-workers derived expressions for the brightness temperatures of a half-spacerandom medium with a laminar structure. 3 Using a radiative transfer approach, England4considered a nonuniform temperature profile and assumed an isotropic scattering phasefunction. Stogryn 5 examined the brightness temperature of a vertically structured6medium with no scattering. Using a perturbation approach, he also studied scatteringby random dielectric constant fluctuations in the low-frequency limit. In this report wesolve the problem of microwave thermal emission from a half-space medium with alaminar structure and nonuniform temperature profile by using the radiative transferapproach.For a half-space medium with constant absorption and scattering coefficients, thebrightness temperature is determined by the following simple closed-form formula 72a(1-rot) aTB = T + a + y cos Th , (1)(a+Ka ) - rot(a-K a)where we assume that the temperature distribution has the profileT(z) = To + Th eYz (2)In (1) rot is the reflectivity of the medium, e the observation angle, Ka the absorptioncoefficient, anda = (Ka+K s  1 1 f Pb . (3)In (3) Ks is the scattering coefficient, Pf the forward-scattering function, Pb thebackward-scattering function, and the scattering albedo isKs (4)K +K (4)a sWe shall now examine several special cases.(a) For a medium with uniform temperature distribution and no scattering, Th = 0,K =0, and a = K . Thuss aTB = (1-rot)T .  (5)The emissivity is seen to be given by 1 - rot. This result also agrees with that obtainedby reciprocity arguments.(b) For a medium with no scattering, Ks = '= 0. ThusTB = (-rot) o K +hTa s (6)JSEP a + Y osPR No. 116(VIII. ELECTRODYNAMICS OF MEDIA)As a numerical example, we consider the subsurface temperature distribution of the JSEPAmundsen-Scott Station in Antarctica. 8 The temperature profile is first fitted with expo-0.51z 0. 66znentials. For April 1, 1958, we find that T(z) = 222 + 81 e 0 51z - 88 e . The bright-ness temperatures as a function of frequency at the nadir are shown in Fig. VIII-4 for230220 T(). 210- .000054S2001900 200 400 600FREQUENCY (GHz)Fig. VIII-4.Brightness temperature without scattering as afunction of frequency for the temperature distri-bution at the Amundsen-Scott Station in Antarctica.Em = 1.8(1 +i0. 003) Eo . It is seen that at very low frequencies TB is determined bythe temperature at greater depth, which is essentially a constant To = 222 °K, with theemissivity of ice surface approximately e = 0. 978. As the frequency increases, thesubsurface temperature becomes more important. At very high frequencies the bright-ness temperature approaches the value e(To + Th), as seen from (6).(c) For a medium with scattering and uniform temperature distribution, Th = 0. Thuswe find2Ka (l-rot)T = T . (7)(a+Ka) - rot(a-Ka)Numerical results are presented in Figs. VIII-5 and VIII-6 and compared with thoseobtained by Gurvich et al. 3 We see that for the Shelf glacier (Fig. VIII-5), higher bright-ness temperatures are predicted with our model. The reason is that Gurvich's resultsare applicable to small-scattering cases, whereas the scattering albedo for the Shelfglacier is rather large. For the Continental glacier (Fig. VIII-6) where the scatteringalbedo is quite small, both models agree quite well except at resonance where thescattering is largest.(d) For uniform temperature distribution and small scattering albedo, we expand (7)to first order in Z cast in a form to compare it with the results obtained by Gurvich et al. JSEPPR No. 116(VIII. ELECTRODYNAMICS OF MEDIA)(1-rt)k2-ot mT B = (1-rot)8k" cos (1 + 4k2 f2 cosm mThis expression differs from their result, since they have cos eo in the numerator7instead of cos e in the denominator as shown in (8). By using the wave approach, wehave an alternative derivation that confirms (8).Numerical results are given in Fig. VIII-7 to compare brightness temperature forSHELF GLACIER GURVICH NOTATION260 C * 1.8'A • 6.7 x 10-4A 0.002240T, 258*Ka 220200* 180160n, = 2.5x 10-4Zo=2mmP=2.7@w 240C 220MW~200WzS1801602 4 6 8 10WAVELENGTH (cm)Fig. VIII-5.Brightness temperature for the Shelfglacier (solid line) compared with thatobtained by Gurvich et al. (broken line).CONTINENTAL GLACIER GURVICH NOTATION1.8S5.4 x 10"  n = 2 x 10A = 0.0006- .06mm z,0.6 mmT, - 233-K P I0 2 4 6 8 10WAVELENGTH (cm)Fig. VIII-6.Brightness temperature for the Continentalglacier (solid line) compared with that ob-tained by Gurvich et al. (broken line).280 -m - v,4= 2 mmTI200 TM160U-z 120 TI80400 20 40 60VIEWING ANGLEFig. VIII-7. Brightness temperature as a function of radiometer viewingangle for TE and TM waves. (Frequency 20 GHz.)PR No. 116JSEP2 o- T(VIII. ELECTRODYNAMICS OF MEDIA)TE and TM waves as a function of radiometer viewing angle e0 , with temperature profile JSEPT(z) = 222 + 34 exp[0.81z]. Clearly, scattering lowers the brightness temperature atall viewing angles.References1. J. A. Kong, "Microwave Remote Sensing of Ice and Snow," Proc. URSI Commis-sion II Specialist Meeting on Microwave Scattering and Emission from the Earth,September 24, 1974, pp. 239-243.2. K. F. Kunzi, D. H. Staelin, and J. W. Waters, "Earth Surface Emission Measuredwith the Nimbus-5 Microwave Spectrometer," Proc. URSI Commission II SpecialistMeeting on Microwave Scattering and Emission from the Earth, September 24, 1974,p. 113.3. A. S. Gurvich, V. I. Kalinin, and D. T. Matveyev, "Influence of the Internal Struc-ture of Glaciers on Their Thermal Radio Emission," Atm. and Oceanic Phys. 9,712-717 (1973).4. A. W. England, "Thermal Microwave Emission from a Halfspace Containing Scat-terers," Radio Sci. 9, 447-454 (1974).5. A. Stogryn, "The Brightness Temperature of a Vertically Structured Medium," RadioSci. 5, 1397-1406 (1970).6. A. Stogryn, "Electromagnetic Scattering by Random Dielectric Constant Fluctuationsin a Bounded Medium," Radio Sci. 9, 509-518 (1974).7. L. Tsang and J. A. Kong, "The Brightness Temperature of a Half-Space RandomMedium with Nonuniform Temperature Profile," Electrodynamics Memo 42, ResearchLaboratory of Electronics, M.I.T., May 7, 1975.8. H. Lettau, "Antarctic Atmosphere as a Test Tube for Meteorological Theories,"in Research in the Antarctic (American Association for the Advancement of Science,Washington, D.C., 1971), pp. 443-475. JSEPPR No. 116(VIII. ELECTRODYNAMICS OF MEDIA)JSEP C. INTERPRETATION OF REMOTE SENSING DATAJoint Services Electronics Program (Contract DAAB07-74-C-0630)Masato Nagase, Donald ChuA two-layer modell has been used to match microwave emission data of fresh waterice and snow as measured by Schmugge et al. 2 The emissivity of the two-layer mediumis governed by seven parameters: d, , E, E, E', zo , and P, where 1 = E'1 + i and2 E2' + iE" are the complex dielectric constants of the top and the bottom layers, d isthe thickness of the top layer, zo is a characteristic correlation depth of the refractive1/2 2index n = n' + in" = (E' +iE1/ of the top layer, and P is related to the variance -1 1 1 noby P = (nl/no l'2Table VIII-2. Emissivity of the two-layer medium.Bear Lake0.153. Z0.04-0.04880801.1-1.60.8-1.2S. C. Glacier, P-38.43.10-0.00043.0-3.20.004-0.051.8-2. 10.75-0.9Steamboat Lake0.82.20.0460-800-801.34-1.380.37-0.4S.C. Glacier, P-I6.82.7-2.80-0.00043.1-3.20.004-0.051.9-2.00.9-0.95South Cascade Lake0.52.9-3.20.095-0.1170-800-200.35-0.450.5-0.65S. C. Glacier, P-04.92.6-2.70-0.00083.0-3.20.03-0.051.75-2.30.5-0.8PR No. 116dmZ mmodmJSEP Z mmoS1 = 3.2 + 0.04i2= 80+80izo 1.2 mmd -0.15m0.7200.6080.582x0.862 V0.90.459?1.43 2.73 5.0 10.71 19.35 37.5* 2.2 +0.04iS2= 80+ 13iP 1.36z2 - 0.4 mmd = 0.8 m0.925 x 0.914xx0.883 0.862Vx-x 0.798 0.808 x0.793 H1.0 F-JSEPS1 = 2.9+0.095 ii2=80+20iP- 0.45zo 0.6 mmd 0.5 mX0.930 x0.923 0.9411.9 -08930.656 x x0.856 Hx 0.8190.8 -0.7 I-1.43 2.73 5.0 10.71(b)I I I I I19.35 37.5 1.43 2.73 5.0 10.71 19.35 37.5(c)I =2.6+0.0041S =3.2 + 0.0002i1P =2.3Zo 0.8mmd 4.9 mx 0.952X0911x 0.889norm\ xx0.867 V0.8 Fx 0.768 H0.7560.7 I-I I I I I i1.43 2.73 5.0 10.71FREQUENCY (GHz)19.35 37.5I =2.8+0.0001i'2= 3.2 + 0.008 iP 1.9zo=0.9mmd = 6.8mX0.955-x0.9030.888 0.862 0.888x0.799 Hx0.7540.9V0.80.7I I I I1.43 2.73 5.0 10.71 19.35 37.5FREQUENCY (GHz)4 , - 3.1 + 0.0002i62- 3.2+0.004i-P=2.0zo - 0.85 mmd 8.4X 0.940x 0.877 V0.892 xx0.862x 0.8360.769 H0.7241.43 2.73 5.0 10.71 19.35 37.5FREQUENCY ( G(f)Fig. VIII-8. Results of matching microwave emission data of fresh water iceand snow. (a) Bear Lake, (b) Steamboat Spring, (c) South CascadeLake, (d) South Cascade Glacier, P-0, (e) South Cascade Glacier,P-1, (f) South Cascade Glacier, P-3.0.80.7 -0.60.9 -08 [-0.7 [-JSEPPR No. 116I I I I I I I I I I I0.9I i(VIII. ELECTRODYNAMICS OF MEDIA)JSEP1 kz ) A [ (-kz)-4 Z iA_ (k)+ - h(k z )kzik zz'eA -ik z'Z+ Bke (k ez) eA -k ikI z' ^ -ik z'C h (-kz) e z+ D h (kz) e £z 2} (1)wheree(kz) 1 2 / xk -ykx^ 1k)h (k z ) I el X k }.PR No. 116The remote sensing data are matched by inspection and by an automatic inversionscheme, implemented with the MACSYMA computer system. The results are illustratedin Fig. VIII-8 and summarized in Table VIII-2. They agree quite well with ground truthmeasurements.References1. J. A. Kong, "Microwave Remote Sensing of Ice and Snow," Proc. URSI Commis-sion II, E. Schanda (Ed.), Institute of Applied Physics, University of Bern, Switzer-land, 1974.2. T. Schmugge, T. T. Wilheit, P. Gloersen, M. F. Meier, D. Frank, and I. Dirmhirm,"Microwave Signatures of Snow and Fresh Water Ice," presented at the Interdisci-plinary Symposium on Advanced Concepts and Techniques in the Study of Snow andIce Resources (Goddard Space Flight Center, Greenbelt, Maryland, November 1973).D. CALCULATION OF THE BRIGHTNESS TEMPERATURE OFAN INHOMOGENEOUS MEDIUM WITH THE FLUCTUATION-DISSIPATION APPROACHCalifornia Institute of Technology (Contract 953524)Leung Tsang, Eni G. Njoku, Jin-Au KongWith the fluctuation-dissipation approach we calculate the brightness temperatureof a stratified medium with inhomogeneous permittivities and nonuniform temperature,using a stratified model expressed in the following form:tTB(k, ) = k3 cos 6 -E d_ 1 dz' T (z')=1 o -dJSEP(VIII. ELECTRODYNAMICS OF MEDIA)Here e is the observation angle, E is the imaginary part of the permittivity in layer 1,Tp(z') is the temperature distribution in layer f, and Ak, Bp, C , and D are wave ampli-tudes in region f that are related to those in other regions by propagation matrices.In Fig. VIII-9 the brightness temperature as observed from the nadir is plotted as afunction of frequency for the following profiles:E 1 (z) = 9.0(1+i0. ) - (5.5+i0.83) eazEt(z<-20 cm) = 9.0(1+iO. 05)T(z) = T + AT ebzTt = T(z = -20 cm)with a1 = 0. - 1Twith a =0.02cm , b =0.1 cm 1 , T = 280"K, and AT = 20OK. Note that there is anabrupt change in the permittivity profile at z = -20 cm. At low frequency there is270265260255250245240Fig. VIII-9.Brightness temperature as a functionof frequency.2 6 10 14 18FREQUENCY (GHz)270260Fig. VIII- 10.22 260.1 IFREQUENCY (GHz)Brightness temperature calculated with the stratifiedmodel and compared with the WKB result.PR No. 116IIII IIII III II(VIII. ELECTRODYNAMICS OF MEDIA)interference. In Fig. VIII-10 we illustrate the brightness temperature from the nadircalculated for the following profiles:E1 (z) = (2. 88+i0. 34) eazEt = E 1 (Z = -1 m)bzT(z) = 300 - 20 e for -oo < z < 0,with a = 2 m- and b = 3 m1 The result calculated with the stratified model is foundto agree very well with that calculated with the exact formulas for this case.When the permittivity profile is smooth enough that the WKB approach 2 is valid, thebrightness temperature can also be calculated and expressed in the following form:TE 0 1g(0) g'(z) zTh = (1-r) dz 2T(z) - g(z) exp[2 f0 ds g"(s)] (4)-h Y1g(z)I g'(0)TM 0 f(z) Jg(0)I g'(z)Tv = (l-rT ) dz 2T(z) - --- g"(z) exp[2 fOz ds g"(s)], (5)-0 f(O) Ig(z) g'(0)whereg (z) = Erk - kx - k = (g'(z) +ig"(z))g(z) + k2 + kx yf(z) =Here rT M is the reflectivity for horizontally polarized waves, rT E is the reflectivityfor vertically polarized waves, and Er(z) is the dielectric constant of the inhomogeneousmedium. To illustrate the use of (4) and (5), we plot the WKB result in Fig. VIII-10 tocompare it with that obtained from the stratified model. We note that the WKB result isquite accurate on the high-frequency side where the CPU time with WKB is also less ascompared with the stratified method.References1. J. A. Kong, "Reflection and Transmission of Electromagnetic Waves by StratifiedMoying Media," Can. J. Phys. 49, 2786-2797 (1971).2. A. Stogryn, "The Brightness Temperature of a Vertically Structured Medium,"Radio Sci. 5, 1397-1406 (1970).PR No. 116

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