RADAR REFLECTIVITY. There are many places in which a knowledge of. I. Katz. Sm.ooth Surface Scattering

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1 I. Katz RADAR REFLECTIVITY There are many places in which a knwledge f the electrical reflectivity f natural surfaces is used-radi cmmunicatins, missile guidance, and radar detectin and tracking f targets, amng thers. The new emphasis n space research brings with it a need fr additinal data n the reflectivity f planetary surfaces. There are distinct similarities between reflectin phenmena in the micrwave regin and at ptical, infrared, and the lnger radi wavelengths. In additin, certain cmmn features are exhibited in the scattering f sund and the scattering f radi waves frm irregular surfaces. While the subject f scattering frm rugh surfaces has been studied since the publicatin f Rayleigh's classical wrk n reflectins f acustic waves, l there remains much t be dne befre a cmplete understanding is available. There are current effrts t slve the prblem theretically, and with the mathematical tls develped recently in nise thery large strides can be expected sn. At the same time, in rder t answer certain practical questins, much experimental wrk n scattering is being dne. We 1 J. W. S. Rayleigh, The Thery j Sund, Vl. 2, Dver P ublicatins, New Yrk, have been invlved in research n scattering fr applicatins in radar map-matching and in missile guidance. A need is nw develping t expand ur emphasis t encmpass sme brader aspects f the prblem. It is ur intent t present a simplified treatment f many f the experimental results available t date and t suggest sme f the newer trends. T understand the scattering phenmenn mre cmpletely, ne needs reflectivity as a functin f the angle made by the field vectr with reference t sme fixed angle fr bth the transmitter and receiver ver the, entire pssible range f angles. Sm.th Surface Scattering Scattering frm a smth, partially cnducting surface has been wrked ut t a high degree f apprximatin fr linear and circular plarizatins; these derivatins may be fund in the literature. 2 Specular reflectin takes place, with the angle f incidence equal t the angle f reflectin. If the cmplex index f refractin f the surface is knwn, the amplitude reflectin cefficient p and 2 H. R. Reed and C. M. Russell, Ultra High Frequency Prpagatin, J hn Wiley and Sns, New Yrk, APL Technical Digest

2 Radar reflectivity f rugh surfaces is being studied at AP L with a view tward imprved radar and missile guidance perfrmance. This paper reviews the present state f ur experimental knwledge f the reflectivity f smth and rugh land and water surfaces. f the EAR TH'S S URFA CE the change f phase n reflectin cj> can be cmputed fr any incident wavelength and plarizatin. As an illustratin, we shw in Fig. 1 the reflectin cefficients fr hrizntal and vertical plarizatin, Pv and Ph respectively, fr C-band (5 cm) radiatin incident upn a smth sea surface. When cnsidering circular plariza tin we must take the sense f receiver plarizatin int accunt. A right-hand circularly plarized wave nrmally incident n a flat cnducting plate becmes left-hand circularly plarized n reflectin. This same wave incident n the same surface at small grazing angles retains its sense f plarizatin; the angle at which this transitin ccurs is called the Brewster angle. Thus, when we speak f the reflectivity f a circularly plarized wave we must state the sense f plarizatin; this is dne by subscript, Pcs meaning reflectin cefficient "circular, same," and Pc meaning "circular, ppsite." T detect a circularly plarized wave in free space we use identical antennas at the transmitter and receiver. If, n the ther hand, we wish t detect a circularly plarized signal reflected frm a flat cnducting surface, we use antennas plarized with ppsite sense. Fr prpagatin abve a smth surface, the signal at any pint in space can be cmputed in the fllwing way. The ttal signal strength T fr linear hrizntal r vertical plarizatin is given by T = D + Rei 0, (1 ) where D is the strength f the direct ray, that f the reflected ray is R, and D is the phase-angle difference between the direct and reflected rays because f path-length differences. The amplitudes f the reflected ray fr vertical and hrizntal plarizatin, respectively, are given by and (2) where Vr and Hr are the vltages f the incident wave btained frm the transmitter antenna pattern in the tw cases. Since a circularly plarized wave is cmpsed f a vertical and a hrizntal cmpnent, we write fr the ttal signal resulting frm circularly-plarized illuminatin, T - Vd + JHd + 1 [V. icj>" + H icj>h] i - 2 2" r pv e J r Ph e e, (3) where Vd and Hd are the vertical and hrizntal January - February

3 I r------_ _, ir t---t---±:::::::;;:;;;;;;;;+----_t-=::t===:::::=-..,--., I Z ill EE 0.6 z Q I I-.'----I f_--- t---- r Li ill LI NEAR POLARIZATION: VERTICAL - p, HORIZONTAL - Ph CIRCULAR POLARIZATION: OPPOSITE - p c SAME- p cs 0.2 -l---j r t t L L L GRAZING ANGLE (d egrees) Fig. I-SJDth sea reflectin cefficient fr linear and circular plarizatins. signal vltages that wuld be received if the surface were absent, Vr and Hr are again the crrespnding vltages incident n the surface, and j and i are the space and time quadrature vectrs, respectively. One functin f the circularly plarized antenna is t remve the space quadrature relatinship between the vertical and hrizntal cmpnents. In Eq. (3) the transmitting and receiving antennas have the same sense f circular plarizatin. Since, fr circular plarizatin, Vr = H r, and since the space vectr disappears frm the utput, we have where (4a) PCB = UPv 2 + Ph 2 + 2P vph cs ((j>h - (j> v)] 1/2, (4b) and </>" Sin-l{: (Sin</>. + Sin</>k)}. (4c) If the receivmg antenna is plarized t receive plarizatin f ppsite sense t that transmitted, and where D = 0, T=R![VrP vei v - jllrphe i h] v:.pceic, (5a) Pe = UPv 2 + Ph 2-2PvPh cs ((j>h - (j> v) ]1/2, (5b) and. - 1 {pv (. Ph.)} (j>c = sm 2 PCB sm(j>v - Pv Sm(j>h (5c) Values f Pes and Pe are pltted in Fig. 1. The reflectivity f a circularly plarized wave is unity fr lw grazing angles and is zer fr nrmal incidence when the receiver is plarized in the same sense as the transmitter. Fr a receiver plarized ppsite t the transmitter, the reverse is true; i.e., at small depressin angles the reflectin cefficient is zer and it increases t 0.8 at if; = 90. Thus, the prblem f frward scattering fr radi waves frm smth surfaces may be cnsidered slved. If we knw the surface electrical prperties, we can predict the" signal strength at any pint in space t the degree f precisin required fr ur purpses. Frward Scattering Over Rugh Water Surfaces Real surfaces are, in general, nt smth. Of curse, hw a given surface appears t the radi wave depends n the relatinship f the size f the surface irregularities t the electrmagnetic wavelength. Rayleigh prpsed a quantitative criterin f rughness, suggesting that if the phase difference between tw adjacent rays is small, then the surface seems smth. Quantitatively, the surface is 12 APL Technical Digest

4 cnsidered t be smth if h sin1f < }./ 8, where h is a measure f the peak-t-trugh irregularity height, 1f is the grazing angle, and}. is the wavelength. Mre recently a mdel was r sed 3 that predicts certain features f frward scattering ver water. The si nal is cnsidered t cnsist f a cnstant direct si nal, a cherentl reflected signal (in the sense f the smth surface discussed a ve w se am litude and p'hase are determined b gemetry and sea cnditins, and a fluctuating reflected signal, randm in amplitude and hase. The amplitudes f the cherent and incherent cm nents de end n the rughness parameter h1f/ }., where h is nw the rt-tneansquare wave height. In Fig. 2 are shwn values f t e c erent an incherent parts f the reflected signal as fund by experiments at the Glden Gate and verified later in the Gulf f Mexic;4 in this figure 1f is in milliradians. Bth C and (1, the cerent and incherent terms respectively, are nrmalized t the direct ray D and the smthsea reflectin cefficient p. Ntice that the cherent term drps gradually frm unity t near zer in the range f rughness values between zer and abut 300, while the incherent term rises much mre sharply t a value f abut 0.3, then flattens and tends t drp smewhat at states f higher rughness. Whether the drp in (11 Dp is real and cntinues fr increasing rughness abve that shwn in the graph is a subject fr future experiment. By using the abve with curves f smth sea reflectin cefficient, we can predict signal strength and its fluctuatin (variance) at pints in space abve the surface if the sea state is knwn. 1.0 c5 0.8 U :2 S5 0.6 f f- 0.4 S5 I U LL-L--L-±;--30 :2 0.3 S5 f- t Z w 0.2 S5 I U ROUGHNESS PARAM ETER hl/;/ >" (mils) Fig. 2.- Cherent and incherent reflectin cmpnents fr rugh cean surfaces. 3 C. 1. Beard,!. Katz, and L. M. Spetner, " P henmenlgical Mdel f Micrwave Reflectins frm the Ocean," Trans. I RE, AP-4, April 1956, C. 1. Beard, "Cherent and Incherent Scattering f Micrwaves frm t he Ocean," Trans. IRE, AP-9, Sept. 1961, s: "'----r------,------, Q).E n:: w O.4 Ll _ _1 > i= :s \ L FREQU ENCY (cps) Fig.3- Spectra f radi waves, shwing bradening with increasing surface rughness. In additin t the mean signal value and its variance, we can predict the time spectrum f the amplitude variatin f the received signal in pintt-pint transmissin in the fllwing way. It was fund in experiments invlving small grazing angles 5 that the signal received at a fixed pint in space frm a fixed transmitter varied in its frequency cntent as a functin f the vertical mtin f the surface and the surface rughness. As illustratin, Fig. 3 shws hw the frequency spectrum f the amplitude variatin f the received radi signal bradens with increased rughnes. The signal at an hi/; I}. = 25 has mst f its energy in frequencies well belw 0.5 cps, whereas fr h1f/ }. = 590, there is still cnsiderable energy abve 2 cps. Curves are available that shw a quantitative relatinship between signal-strength spectra, the frequency (in cps) f the maximum f the heightversus-time spectrum f the cean waves, and cean rughness. If we frm the rati f the frequency at which the radi spectrum has drpped t, say, Yt 0 pwer t the frequency f the peak in the cean spectrum prevailing at the same time, and plt it against cean rughness, we fid a linear relatinship. That is t say, the rati f d ' If d increases linearly with h1f I }. If this is f;;esther pwer-rati pints in the signal spectrum, we btain a set f curves, typical nes being shwn in Fig. 4 fr pwer pints frm 0.1 t 0.9. Frm these curves, if ne knws the cean spectrum and wave height, the spectral cntent f the radi signal can nw be predicted. Frward Scattering Over Land As is true with frward scattering ver water, there is a strng dependence f field strength n the character f the land surface. Quantitatively, 5 C. 1. Beard and 1. Katz, " T he Dependence f Micrwave R adi Signa l Spectra n Ocean R ughness and Wave Spect ra," Trans. IRE, AP-5, April 1957, January - February

5 r-----, r-----' r J----, ""-I OL- L RO UGHN ESS hfr/ ).. (mils) Fig.4-Variatin f the rati f the radi signal spectral width t the frequency f the maximum f the wave spectrum, with cean rughness. hwever, we are in a much less favrable psitin regarding frward scatter ver terrain as cmpared with prpagatin ver water. If the earth is smth, the reflectin cefficient can be cmputed just frm a knwledge f the electrical prperties f the surface. Measurements made ver rugh surfaces indicate that reflectin cefficients are abut 0.2 t 0.4. Hwever, small differences in receiver psitin can cause significant changes in signal strength; hence, signal strength predictin is difficult. Measurements almst always fall belw predicted values, smetimes as much as 30 db. Mst research ver land has been dne with bradcast frequencies. The deviatin frm plane-earth predicted values varies inversely with frequency in the range f frequency between 40 and 1000 me; at 40 me measured and predicted median values are in agreement, while at 1000 me the discrepancy is abut 27 db; the variatin is linear n a semi-lg plt f db belw plane-earth value versus frequency. In natural terrain the irregularities can be large and receivers may be situated in shadw regins. In such lcatins we are cncerned with multipath prpagatin; reflectins frm hills r large bjects give rise t strng signals frm directins ther than the transmitter directin, these reflectins being independent f frequency r plarizatin. "Ghsts" in televisin receptin and crss-talk in cmmunicatins systems are gd examples f multipath cnditins. Prpagatin ver grund is als highly dependent n the seasn f the year because f changes in the dielectric cnstant f the sil. Signal strength changes f as much as 14 d b have been fund ver smth grund when sil misture cntent varied. Trees, shrubs, and buildings have a decided effect n transmissin f radi waves. A frest may be either paque r transparent depending n the tree density. Attenuatins thrugh wded areas have been measured, varying between 0.02 and 0.35 db per meter 6 depending n the density, plarizatin, seasn, and frequency. By cmparing the freging with the earlier treatment f ver-water prpagatin, ne can see easily that the ver-water case is better understd. Clear-cut quantitative statements can be made cncerning the ver-water situatin, and as a result we may expect dependable predictins fr given sea-state cnditins. In the ver-land case, n-site tests must be made t determine the prpagatin expected t prevail at any distance frm a transmitter. Backsca tter Over Water We nw turn ur attentin t the backscatter r "clutter" prblem. A smth cnducting surface backscatters nly at nrmal incidence. Fr all angles ther than 90 there is n backscattered energy. A rugh surface, hwever, scatters energy in ther than the specular directin. Radars abard ships and aircraft are frequently limited in their peratin because f such clutter. If the clutter is larger than the return frm a target, the target will be bscured. While the physical nature f the backscattering prblem is nt yet well understd, there are certain features f the prblem which are gradually becming clear. Sea clutter is generally described in terms f the radar crss sectin per unit area f the sea surface, 0'0. This is a dimensinless measure f the reflectivity f the surface, and it depends n the grazing angle, plarizatin, sea rughness, and rientatin. 6 M. P. Bachynski, "Micrwave Prpagatin ver R ugh Surfaces," RCA Review, 20. June 1959, APL Technical Digest

6 20 «ID 1- ::0- z =>. '-.. b Zu.i OU f= «- IO Vl Vl O - 20 Vl ULL :(0-30 « DEPR ESS ION ANGLE (degrees) Fig. 5-Qualitative variatin f radar crss sectin f the sea with depressin angle fr smth, intermediate, and rugh surface cnditins. Flying ver sea surfaces varying frm "smth" t "rugh" t determine the cean crss sectin versus grazing angle, we wuld find the fllwing. Under calm water cnditins, measurements wuld indicate a peak in CTO at 90, with rapidly decreasing values at angles ff the vertical as illustrated in Fig. 5. If the wind waves and/ r swell increased, the measured curve wuld have less f a peak at 90, but the magnitude f CTO wuld increase at the smaller angles and wuld perhaps fllw the curve marked "intermediate." Fr a very rugh sea, the CT-versus-grazing-angle curve wuld be quite flat. 20 As yet we d nt have quantitative measures f rughness fr backscattering. If the rughness measured fr frward scattering hlds fr clutter, then at 10 and fr X-band (3 cm), fr example, it wuld take ripples f abut 2 in. rt-me ansquare t make the sea effectively rugh. Thus, ne wuld expect t pass frm the "smth" curve t the "rugh" curve with nly the slightest wind blwing ver the sea. "Smth" cnditins fr micrwaves wuld indeed be rare. A better understanding f the clutter prblem is btained by studying results f experiments perfrmed expressly t determine CTO. Curves f CT shwn in Fig. 6 were btained by the Naval Research Labratry. The clutter is greater fr vertical plarizatin than f<;>r hrizntal at the smaller angles, but the difference tends t disappear at higher angles. Nte als that the curves seem cmpsed f tw curves, ne rather sharply peaked arund the vertical, and a secnd, much flatter curve. One interpretatin f such cmpsite curves states that the peak arund vertical incidence results frm scattering frm large facets n the surface, while the less steep prtin is caused by mre istrpic scattering frm smaller facets.7 Fr high sea states, there wuld be n difference in return n the tw plarizatins. 7 L. M. Spetner and I. Katz, " Tw Stat istical Mdels fr Radar Terrain Return," Trans. IRE, AP-8, May 1960, :0 < I- Z => '- 10 X BAN D = HORIZ. POLARI ZATION I:J. = VERT. POLARIZATION (frm Naval Research Labratry data) -- z NEW JERSEY WOODS f= Vl 0 c U < 0 « r--.",""'"..,"'".",., DEPR ESSION ANGLE (d egrees) Fig. 6-Variatin f the radar crss sectin f a rugh surface with depressin angle, in water- cvered and frest-cvered surfaces. 90 Jan uary - February

7 There is a clear dependence f clutter n wind directin; the upwind directin gives greater return than the dwnwind. Again, as with tw plarizatins, the difference tends t disappear at the larger depressin angles. Many curves have been btained experimentally that illustrate the change f crss sectin with radar frequency and with sea rughness. These data bear ut the qualitative statements made earlier that clutter increases with increasing rughness and with increasing frequency. Fr a given wave-height cnditin, as ne increases the radar frequency (decreases wavelength), the apparent rughness increases. Of prime imprtance fr search radar functins is the shape f the clutter curve at very lw angles. Generally, clutter n vertical plarizatin is greater than n hrizntal; hwever, there is sme indicatin that, at angles belw perhaps 3, n hrizntal plarizatin the clutter is greater than n vertical. Backscatter Over Land A smewhat typical curve fr CT-versus-grazingangle ver land is shwn in Fig. 6. This ne was btained in flights ver a frested area. Unquestinably, trees 60 ft high present a "rugh" surface t 3-cm radiatin. As a result, it can be expected that the curve wuld be quite flat. Actually, curves similar t the ne shwn are flat even fr grassy areas with vertical irregularities just a few inches high, i.e., even grass is rugh at = 3 cm. Nt until we apprach smething like a cncrete rad des the radiatin apprach the smth-earth value. Literally hundreds f curves f terrain clutter nw exist fr different terrains, plarizatins, and frequencies. 8 The results btained are surprisingly repeatable- better than ± I db. N unified thery has yet been advanced that can be used t predict backscatter fr any given surface, ver land r ver water. Sme limited success has been achieved by Peake 9 using the methd f Rice. l His success has been limited t surfaces with rughness and electrical prperties like thse f asphalt and cncrete rads. Fr mre irregular grassy surfaces, the present theretical apprach seems t fail. 8 R. L. Csgriff, W. H. Peake, and R. C. T aylr, "Terrain Scattering Prpert ies fr Sensr System Design," Terrain Handbk, Ohi State University, May W. H. Peake, " T he Interactin f Elect rmagnetic Radiatin wi t h Sme Natural Surfaces," Ohi State Universit y Reprt N , May 30, S. O. Rice, "Refl ectin f Electrmagnetic Waves by Slightly R ugh Surfaces," The Thery f E lectrmagnetic Waves, Interscience P ublishing C., New Yrk, In the paper discussing the thery f radar terrain return/ a mdel was frmulated that applies t bth land and water surfaces and deals with the wavelength dependence f varius types f surfaces. That apprach cnsidered tw types f surface, a distributin f randm scatterers and a surface cnsisting f specular reflectrs. The nrmalized radar crss sectin f the surfaces was cmputed as a functin f depressin angle and f wavelength. The islated scatterer mdel led t n dependence n depressin angle but t a wavelength dependence which varied frm - 6 t -2, depending n density f scatterers and n the relatinship between and the gemetrical areas f the scatterers. On the ther hand, the specular reflectin surface shwed a depressin-angle dependence f exp { -cot(/ 2CT 82) } r exp { -ct2(/ 2CT 82)}, where is the depressin angle and CT 8 is the variance f the slpe f the reflecting facets. The wavelength dependence was -2 fr this surface. It appears that bth mdels represent true surfaces. But whatever the mdel, it seems certain that there is a fairly strng wavelength dependence. It has been prpsed ll that this prperty be used in a radar t distinguish varius types f surfaces. A "plychrmatic" (multifrequency) radar culd be used in mapping the grund fr autmatic navigatin. Whether such a radar is feasible depends n further research in terrain reflectivity. If varius natural surfaces turn ut t have predictable and different wavelength dependencies, then a plychrmatic radar is a real pssibility. Future Research Frm the preceding discussin n frward- and backscattering, ne may reasnably cnclude that, althugh prgress is being made in ur understanding f the ttal reflectivity prcess, many gaps are still present. Under certain gemetries and surface cnditins we can predict the field strength.in space. In general, hwever, this is nt true; the exact causal mechanisms are as yet nt firm. Tw majr prblem areas are clear. First, a cmplete slutin f the rugh-surface reflectivity prblem will likely cme nly with the bistatic * apprach since frward- and backscattering are special cases f the general scattering phenmenn Kat z and L. M. Spetner, " A Plychrmatic Ra dar," The J hns H pkins University, Applied Physics Labratry, C F 2898, Oct. 24, * Where t he transmitter and receiver are in t he same place we designate the m easured reflectivity as "mnstatic"; if t hey are separated, t he scattering is called " bistatic." 16 APL T echnical Digest

8 Secndly, an adequate descriptin f the surface is usually lacking. New research is being cnducted in bth f these areas; sme cncepts and trends f this research are discussed belw. Bistatic Reflectivity The bistatic gemetry is pictured in Fig. 7. Here we see tw aircraft, ne cntaining the transmitter and the ther the receiver. Ideally, these aircraft are equipped with narrw-beam antennas in rder t illuminate r receive frm a narrw angular regin. The indicated depressin angles Y;T and Y;R are nt usually the same. Fr a given surface cnditin, all pssible cmbinatins f angular values are scanned. In practice, fr practical reasns, it is likely that a wide-beam antenna mdel wuld be used with the transmitter and a narrw-beam with the receiver. Experiments using this prcedure are visualized fr the future., Fig.7-Gemetry f bistatic reflectivity prblem; V;T = transmitter depressin angle, and V;R = receiver depressin angle. A prgram is nw being cnducted t btain data frm missile flights by using the dpplershifted frequency f the returned signal. With the transmitter abard ship and the receiver n an aircraft r missile, the bistatic reflectivity fr a smewhat limited, but useful, range f transmitter depressin angles can be btained. The ship transmits a cntinuus-wave signal that illuminates a target airplane and the sea surface. Signals reflected frm the target and the sea cntain dppler frequencies that depend n aircraft speeds and gemetry. The receiver airplane r missile shuld have a wide-beam antenna, and its pattern must be accurately knwn ver a wide angular regin. Areas n the surface at different depressin angles Y;R cntribute different dppler cmpnents t the received signal. If the reflectivity f the target airplane r calibratr is knwn and the received signal spectrum is measured, the reflectivity f each f the areas n the sea may be determined. A prgram t btain bistatic reflectivity is cntinuing at APL, and it is hped that a dependable set f bistatic curves may be btained. Clearly, with the transmitter munted n shipbard, the maximum Y;T will be restricted t less than several degrees. Sea Surface Measurelllents It was mentined earlier that befre a cmplete slutin f rugh-surface scattering is btained, we must find an adequate descriptin f the surface. Present methds fr measuring cean waves are nt applicable t the present prblem. We can, at any pint in water and t any desired sensitivity, determine the height f water as a functin f time. Althugh frm height-time recrdings a spectrum can be cmputed, this spectrum is nt the ne required. The spectrum btained frm a measurement f height versus distance alng the surface is the ne needed. If all waves mved with cnstant speed and directin, we culd transfrm the time spectrum int the desired space spectrum. Unfrtunately, waves f different lengths mve with different speeds and nt necessarily in the same directin; thus, the transfrmatin frm the time t the space spectrum cannt be made. T btain the descriptin f the surface, a jint prgram spnsred by the Office f Naval Research and APL is in prgress t develp a sterephtgrammetric methd t measure surface structure. A special pair f stere cameras is being munted abard a ship t determine the feasibility f making wave measurements with the desired sensitivity. The present gal is t measure wave heights with a sensitivity f ±O.l in. Frm these phtgraphs, three-dimensinal space spectra are t be btained fr times during which radar reflectivity measurements are made. Cnclusins Prgress is being made in ur understanding f reflectivity f electrmagnetic waves frm rugh surfaces. Ultimately, we hpe, radar bservatin f surfaces will permit cmputatins f satisfactry descriptins f the surface states. Over land it will prvide an all-weather navigatin system. Over water we will be able t measure wave height with a remte prbe, and ur ability t detect targets amid sea clutter will be imprved. January - February 196) 17