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JOURNAL OF RESEARCH of the National Bureau of Sta ndards-D. Radio Propagation Vol. 67D, No. 2, March-April 1963
Radar Reflections From the Moon at 425 Mc/s1 George H. Millman and Fred L. Rose
Contribution from General Electric Company, Syracuse, N.Y.
(Received September 26, 1962)
The characteri stics of the lunar surface deduced from radar-lunar measurements con ducted at the U.S. Air Force Trinidad T est Site during 1960 are discussed. Evidence is presente~ which tends to con firm t hat, at 425 megacycles per second, thc front portion of the moon IS a comparatIvely smooth reflector while t he back portion behaves as a rough scatterer. The pulse decay of t he average envelope of lunar echo es is found to follow t he slope of the Lomrncl-Seeli ger scattering la w. From the cumulative probabili t.v dist ributions of thc total cross section of t he moon meas ured on t ,,·o different d ay~, it is indicated t hat 50 percent of t he total cross section measurcments we re less than 5.0 to 8.5 X IO ll square meters 01' 117.0 to 119.3 decibels abovc one square meter. Sta t istical data, such as the probability density fun ctions of t he total lunar echo ampli tude a nd t he autocorrelation func tion, a re also presented. . The power density spectrum co mputcd fr om t he autocorrelation function is co mpart'cl Wit h the theoretICal Doppler spread resul t ing fr om the moon's libration. 1. Introduction sis Led of many rfl,ndom scnLLerers in relative moLion, brought about by Lbe moon's lib ration . This T he firsL radio rcIJectimoonrise nnd moonset bv length of the (l -mscc) Lransmitted pulse, showed the U .S. Army Sig ll al Corps [Webb, 1946J. A mor:c Lhat the moon wa s fL "roug ll" reflec lor at lhe fre compleLe descripLion of t lte SignfLl Corps resulLs is quency used. described by DeWiLt and Stodola [1949]. 111 order T he first successful transmissioll S at UTIF usin g 'l to obLain Llte required sCllsiLivi ty, a receiver b and Lhe moon as a relay staLioll were fLccomplis hed by width of fLbouL 50 cis, a transmiLLer pulse length of ulzer, Montgomery, and Gc ries [1952J. ConLinu 0.25 sec, and a Ln1,llSlnitter peak powcr of 3 kw were ous waves (CW) mdio signnls fl,t a frequency of 418 used. The experimen tal results showed that the Mc/s wc]'e relayed from Cedn,!' Rapids, 10wfl" to returned ecbo amplitude was often less t hfl,n the SLerlillg, Va. It was found that the signal was sub theoretically computcd one, and, on occ fl,sions, could jecL to severe fading, iLs amplitude varying from not be deLecLed. In addition, the siO'nal amplitude t il(' rcceiver noise level to occasioll ill peaks as high as underwen t unexpected fluctuations, 11aving periods 10 db fl,bove the noise. of sevcral minutes, whicll were attributed to anoma M efl,SUTements of radar-lunar echoes by Evans lous io nospheric refraction. [1957] at 120 Mc/s, by Trexler [1958J at 19 Nic/s, At approximately the SfLme tim.e fl,S the Signal and by Yaplee, Bruton, Craig, and Roman [1958] at Corps observations, Bay [1946] also reported that 2860 Mc/s revealed that radar reflection takes place radm' con tact had been made with the moon at fL within a small area at the cen ter of the moon's sur frequency of 120 Mc/s. These measurements indi facp, the radius of which is fl,ppro ximately one-third cfl,ted a power reflection coefficient for the moon's the radius of the moon. These results confirmed that surface on the order of 0.1. the moon appeared to be a quasi-smooth refle ctor at Kerr, Shain, and Higgins [1949J of Australia per radio wave frequencies. formed the moon reflection experiment at 21.5 The characteristics of lunar echoes, such as libra Mc/s, during moonrise and moonset, mfLinly to tion fading of the order of 2 to 3 cis and pulse study the cbaracteristics of low angle propagation lengthening to approximately one lunar r adius, have through the ionosphere. Their records [Kerr and recently been noted by investigator operating in the Shain, 1951] indicfLted fL rather slow fLmplitude 400 to 440 Mc/s frequency range [Pettengill, 1960; fiuctuaLion ril.te which also was attributed to iono Leadabl'and, D yce, Fredricksen, Presn ell, and spheric refraction phenomena. The rapid amplitUde Schlobo hm, 1960J. The latter phenomenon in flu ctufLtion s, having pel'iods of a few seconds were dicated the possibility that the rear portion of the explained by assuming that the moon's s urfac~ con- moon behaved as a rough scatterer. In this paper, the analyses of the reflectivity • 'rbis paper was presented at the joint meeting of the International Scien ti fi c characteristics of the lunar surface, as determined Racli<:> Union .(U R SI) and of the Institute of R adio Engin eers, llelcl on April 30. from radfl,l' measurements made at 425 :Mc/s, are 1962, m Washlllgton, D.C. Th.s work was sponsored by tho Rome Ail' D evelop ment Contol' under Contract AF 30(602)- 2244. discussed.
666696- 63-- 2 107 2 . Experimental Measurements positioned, in 3-min intervals, an 84-ft diam steerable antenna so as to follow the theoretical path of the The experimental observations discussed in this moon. paper were conducted at Trinidad, B.W.I., between The radar data pertaining to the lunar echo return January and July 1960, with a high-powered pulsed were recorded in digital form on magnetic tape in radar. Linear (horizontal) polarization was em order to facilitate data processing and analysis. In ' ployed on transmission, while the reflected radar addition, photographic recordings were made of the signals were simultaneously received on both the various combinations of the amplitude, range, and transmitted and the orthogonal (vertical) polariza time coordinates. tion. The transmitted pulse was 2.0 msec in dura A tracing of a typical A-scope photograph of a tion, while the pulse repetition frequency was radar-lunar echo recorded at Trinidad is shown in approximately 30 pulses/sec. figure 1. The upper trace is the horizontally polar Automatic tracking of the moon was accomplished ized signal while the lower is the vertical. It is by means of an orbit programer which continuously noted that the pulse return is stretched out to ap-
- f- f- I I I 1 - HORIZONTAL POLARIZATION f- 126 .3 ,- -l- a: I-- w >- 116 ,3 w 113 .2 ::I; ,\ w 110 a: 1062 101 .I '" I \. A I §'" l""Y "1 w " z - o -l- w I > 122 .3 fil f- VERTICAL POLARIZATION 116. 1 .
o 3 6 9 12 15 RELATIVE TIME. msec
FIGURE 1. A typical luna?' echo recorded at Trinidad at 425 Mc/s, showing p1dse lengthening.
I r T I - HORIZONTA L POLARIZATION
a: ~ 116 .2 ~ 113 I\, w 110 .0 I", .2 ~ ~ 106 ,II v \. '\. V is 101 .1 rf ~I
o 3 6 9 12 15 RELATIVE TIME . msec
FIGU RE 2. A typical 11lna?' echo recorded at Trinidad at 425 NIc/s, showing pulse distort·ion.
108 ~~.------~~~--
proximately 12 msec in length and that the echo on It is also seen in figure 1 that the maximum radar both polarizations is similar in shape. cross section of 126.3 db above 1 m2 is obtained on If the moon were a perfectly smooth body, an horizontal polarization. This value compares reason electromagnetic pulse incident on iLs surface would ably well with the geometrically projected lunar disk not be extended in range by reflection from the real' area of 129 .8 db above 1 m 2 (radius of moon= 1740 portions of its surface. This is basically due to the lun). Assuming a smooth moon with a power re fact that, according to Fresnel diffraction theory, flection coefficient of 0.15, the theoretical echoing only a small region of the moon's surface would area should be on the order of 121.6 db above 1 1112. contribute to the received reflected energy, i.e., at At times, the lunar echo was found to undergo 425 Mc/s, the radius of the first Fresnel zone is both pulse lengthening and distortion. A represent approximately 11.6 km. ative example illustrating these characteristics is With regard to the effect of scattering from a rough contained in figure 2, the signal amplitude in this ~ surface on the pulse shape, since all portions of a case being only 114 db above 1 m2• rough body contribute to the total reflected signal, A selected sample of an amplitude versus time the returned echo would be extended in length, i.e., fading record, displaying the ionospheric effect of the pulse lengthening would be equal to the time it Faraday rotation and the presence of lunar libration, > takes the wave to travel from the nearest surface to is shown in figure 3. The Faraday phenomenon is the limb and then back again to the surface. Since the radio-depth of the moon is 11.6 msec, a pulse recognizable by the appearance of lunar signals of width of 2 msec, incident on a rough moon, would approximately equal amplitude in both the ortho be elongated to a length of 13.6 msec after reflection. gonal receiver channels during the period when hori As indicated in figure 1, the lun ar echo do es undergo zontal polarization was employed on transmission. pulse stretching, the elongation being approximately The lunar libration is indicated by the rapid fading , equal to the theoretical predictions. of the envelope of the amplitude-time function, the
HORIZONTAL POLARIZATION LOGARITHM OF AMPLITUDE
VERTICAL POLAR I ZATION LOGAR ITHM OF AMPLITU DE
FIGURE 3. Amplitude verS1iS time fi lm rec01'd of lunar echoes recorded at Trinidad al 425 Mc/s displaying Faraday rotation and lunar lib ration, 12 January 1960, 161 7 EST.
10 -
0- HOR IZ ONTAL POLAR I ZATION RELATIVE RANGE IN MILLISECONDS
10-
0 - VERT I CAL POLARIZATION
FIGU RE 4. A typical mnge versus time photograph of mdar-lunar echoes recorded at Trinidad at 425 Mc/s, 12 January 1960, 1638 ES'I'.
109 back portion of the pulse returns exhibiting a much from a diffuse surface having irregularities on the higher fading rate than the front portion. order of a wavelength, stittes that the scattered It is interesting to note tlu'Lt the fading patterns energy in any direction is proportional to the cosine of the main echo pulse (the large signal amplitude) of the angle between the incident ray and the normal observed on both polarizations are identical. The to the surface itnd to the cosine of the itngle between significance of this is that the polarization of the the scattered ray and the norlllaL incidcn t pulses on reflection from the front part of ' iVhen the relative echo power is plotted itS a the moon is maintained, which implies that this function of the cosine oJ the angle of incidence, as region of the moon's surface appears reasonably depicted in figure 6, it is found that the Lommel smooth at a frequency of 425 Mc/s. Depolarization Seelinger 1m\' and the Lallibert law reduce to straighL of a signal which should occur on reflection from a lines and that the pulse decay riLte follows the slope rough surface would result in the amplitude fading of the Lomillel-Scllinger scattering law displaced patterns observed on orthogonal polarizations to be by a factor of approximately one-eighth. somewhat different. It should be mell tioned that Pettengill [1 960] has A typical range-versus-time photograph of lunar reported that, following the decay of the initiitl echoes, also revealing pulse lengthening, is shown specular component, the angular distribution of in figure 4. The signal fading indicated by the power in the moon echo obeyed the Lambert-type reduction of the echo intensity in the back portion law except for a small alilount of Jill1b brighten of the range scale is basically due to the moon's ing at the extreme ranges. Since the Trin icl ad and librfttion. Millstone Hill investigations were conducted at approxililately the same frequency, i.e., the trans 3 . Data Analysis mission frertuency at YIillstone Hill WitS 440 Mc/s c0 l11pared to 425 Mc/s itt Trilllclad, the discrepancy 3.1. Lunar Reflection Laws in the resultsillay be attributed to the fact that the lunar echo analyzed by Pettengill was a composite The supposition that the moon is a rough body of 24,000 pulses, integrated at each 500-,usec range at radar frequencies has led to the speculation of increment. various scattering laws and functions to describe the manner in which radio waves would scatter 0 from the moon's surface. A method of investigating 1 1 1 r an applicable scattering law is to characterize the x • A,'''. '9/'9" ~ 0" "ZCOSB(LO MM EL-SEELIGER L AW] decay rate of the trailin g edge of a lunar echo. 0,. ",COS 2 8 [I..A,MBERT LAW] In order to reduce the effect of short-term fluctua 6 = !I+~8 +yB2+&B3 tions in the envelope of a lunar echo, 130 A-scope photographs, consisting of 65 different pulse returns received on the two orthogonal polarizations, were avemged to obtain a representative sample for analysis purposes. The resultant lunar echo, shown in figure 5, was obtained by dividing each pulse into 0.25-msec intervals. At each interval along the pulse, an average amplitude was calculated from the 130 different data points. It is seen that the trailing edge of the pulse can be described in terms of the third degree polynominal, 0 3 ~• 1.0 \ a + J30 + ,,02 + 80 , where the constants a = 39 .06, ~O . 9 1\ 13 = 74.33, ,, = 39.09, and 8= -3.38. The variable, ~o . e 0, is the angle of incidence with respect to the normal \6 a: 0 .1 "Vr\ to the surface of the Inoo,?-. It is obvious, however, 0.6 AVERAGED LUNAR ECHO that the angular scattenng law, as suggested by 0.' r\1\ Leadabrand [19601, A l (sin 20/20) 20, where A I =163, f\ does not seem to apply to this example. 0.< 0 The trigonometric functions, A2 cosO and Al cos 2 0, where A2 = 11.2 and A 3= 13.65, also shown m figure 5, 1 are representative of the Lommel-Seelinger and \ the Lambert scattering law, respectively.
The Lommel-Seelinger law refers to scattering 0.' X taking place from a rough surface having irregulari ties that are large compared with wavelength. The energy scattered from all regions of the surface is the same. Thus, when considering radio wave , reflection from such a surface, the received power 10 £0 30 4 0 ~o 60 70 60 90 is only proportional to the cosine of the angle be A NGLE OF INC IOENeE - 8 (DEGREES 1 tween the incident ray and the normal to the surface. FIGURE 5. Scattering laws applied to lunar ech9 as a function i The Lambert law, which applies to the scitttering of the angle vf incidence. lID '0 angle val'?ing from 5 to 344 deg a nd d ev~tt i on ~lI1g1 e 6 . 1a +,8 8 "'!8~ 18 8 , 20 of about 82 deg. , )[ • • ,(SIN U/lfll 7 fL is seen th at, for th e low angle meHsurem ents, 50 --;;; l)ercent or tb e Lotfll cross sections were equ al Lo or , 1\ less th a n 5.0 X 101l m 2, while, a t tr ansit, the value "- 2 . 1\ in cI"Cased to 7.5 X 10ll m . "- LUlHU' observations o n ] 2 J anuary 1960 disclosed \ lO .... El-SEE L IG EA LA ... , th a~ 50 percent of tllC Lobll c ross sectio , ~~ n ~ar t?-e hOI'lzon were eq u ~tl Lo or less t h~tn 8.5 X 10 m -, wlu le "- a t tmnsit thcy reduced to 6.0 X 10 11 m 2. . \ Assumino' tJla t th e m oo n is ~t perfect conductmg 2 "- , sphere its ~'adH r cross section is then the projected \ LA M BER T L AW "'- , geometric H r C ~ t 0(' lhe wllOle disk or 9.5 X 10 1 2 m 2. It
\, AV ERA GED follows th at, for 50 percc nt 0(' Lh e o b se r v~tti o n s , th e LUN A R ECHO \ , power r eflection coefficienL of th e moon's surface a , ~ \ .0 1\ peared to lie beLween 0.05 and 0.085. ft IS est l o. , ~ m ated tha t th e ex])erimcntnl crror incurred in this . 8 ~ a nalysis shouJd be less U I ~m :3 d b . 7 \ .. '\k. \ Me ~l s ur e m e n ls madc by F ri cker , Tngalls, 1Llson, and SwirL [1 960], at It fr eq uency 0 (' 412 11c/s uSll1 g ~L ., \'r 1\ GVV systrm inciic,lLed ~ t lunar power refl ectIO n co ~ .' 1\ efficir 'lt of 0.074. According to Blevis However, Browne, Evans, Hargreaves, and 1i[ur 3 .3. Statistical Distribution of Luna! Echo Amplitudes ray [1956J, h ave fo und Lhat a n analysis of lunar echo data observed at a frequency of' 120 11c/s, gives best The rapicl fluctuations of radar pulse reflected agre~l1l e nt wi Lh the LOlllm cl-Seelinger scattering frol11 th e Ill oon's sUlJace are usually aL t ributed to ~he model. libl'aLion which is defined as the oscillaLory motiOn of the moon about an axis which iLself' changes with 3 .2 . Cross Sec tion and Refle ction Coefficient of the time. Moon The e:fIect of the moon's libmLioll on Lhe reflecled siO' nal Cfln be explained by ~lssuming that Lhe moel1's In analyzing the cross sectional area of t~le moon s ~'f ace co nsists · of a randolll number of sC HLt erers. and the statistical distribution of the amplitudes of T he alllplitude of the r efl ecLed pulse, as observed on lunar siO' nals which is discussed in the next section, the earth's surface, is the resultan t o[ the signals r e the nUl.o~litude of the amplitude of the received echoes flected from each of tbe scattering elements. Since was m~ asured at a constant position within the the m oon underO"o es an apparent rocking 1ll0Lion, or pulse, i.e., at 1 msec after the beginning of the pulse libmtion, the s i ~.lflls scattered ('rom vm~o u s pn,rLs of which corresponds in range to a lunar depth of its surface are continuously u ndergolllg nwdolll 150 km. changes in phase and a mpliLude \rhich, in turn , pro Th e cumulative probability distributions of the duce fluctuations in the resultant signHl. Lotal cross section of the moon obscrved on 8 Feb For surface in'eO'ular ities which SCfl llel' inciden t r uary 1960, during two 1O-min pe ri~d s, .are shown in mdiation with ran~l olll p hases an d amplitudes, Lhe fi gure 7. 'rhe total lunar cross sectIOn 1S m erely the probability of occurrence of a ny res ul~ a nt sig nal .a~ll addition of cross sections obtained on the orthogonal plitude is therefore given by Lhe RayleIgh probablh ty polflriza tion r cceiver channels. Each cumulative d istribution curve was calculfLted from approximately disLribuLion hw. The co ncept of the R ayleigh d is 18 000 individual data points. The interval betwecn tribution is maintained, provided thllt the number of 14 :3 0 an d ]440 EST corresponds to th e time when the scattering nreas is large, i.e., at least on the order of moon was oriented at an azimuth angle of about 72 .6 1001' greater. deg a Ll d elevation anglrs of .6.0 to 8.0 deg,. while The probfl bility, P (R)dR, of finding au a mplitude b etween 2025 and 2035 EST It was at an aZll1ll1th between Rand (R+ dR) is therefore given by 111 PO WER REFLECTI ON CO EFFICIENT 0001 00. I 0.1 I 0 I I r TTT II I I I I I I II V-,- TIME AZ I MUTH ELEVATI ON V o . 9 /' 1430 EST 7 2 . 6° 6.0 0 / / I--- 144 0 73 .0° 8 .0 0 1/ o.e- / ./ - ,/ ,/ 2025 EST 5.2° 82 . 4 0 o .7 - 2035 344.3° 82.20 - 1/ / o. 6 V / 1/ 2025-2035 EST 1430 1440 ES;/ o.5 / / 0 .4 V / / 0 .3 7 v o.2 / /" ./ .,.- V ./ o.I .....r::::- 10 10 4 10 II TOTAL CROSS SECTION ,m2 FIGU RE 7. CUlnulative probability distrib1tlion of the total cross sectl:on of the moon, 8 February 1960. R2 where B is the amplitude of the steady signal, V is P(R)dR =~ e - U dR, (1) the envelope. of the resultant amplitude comprised of ~he steady SIgnal (B) and the random signal (R), 1/; IS a. constant defined. by (2), and I o(VB/-.f;) is the where R is the amplitude of the resultant scattered modified Bessel functIOn of the first kind of zero signal at any instant of time, and 1/; is a constant order. related to the mean value of R by In determining the statistical distribution of the signal amplitudes, the lunar echoes recorded in two 10-min intervals between 1430 and 1440 EST and (2) 2025 and 2035 EST, on 8 February 1960 we;e se lected. It should be noted that the amplitude data The condition in which a steady signal is super from these tinle periods are identical with the lunar imposed on a signal which is the resultant of ele cross section data discussed in figure 7. The statis mentary contributions originating from random ~ical analysis was made on the total signal amplitude m or~er to reduce the effect of ionospheric Faraday scatter~ng areas is of considerable interest since it may rotatIOn. approXImate a possible situation prevailing in the The probability density function of the total lunar lunar reflection of radio waves. The steady signal corresponds to a specularly re amplitude, recorded during moonrise when the libra flected wave coming from the first Fresnel zone or tion fading rate was normally low, is illustrated in from a relatively srnall number of smooth surface figure 8. The theoretical curves were calculated areas in the region of the first Fresnel zone. The utilizing (3) with 1/; ~ 28.0, this constant being eval random signal is caused by the lunar libration or by uated from the experImental data. random surface irregularities. If the number of The presence of a strong steady signal would be smooth surface areas becomes very large it is pos indicated by a probability density function which sible for the signals reflected by these area~ to under wO';lld be of the form of the b= 2 curve where b= B I-.,fif;. go cancellation and reinforcement. Thus instead of It IS seen that the experimental points coincide, specular reflection taking place, a random~type noise to. so~e degree, with the theoretical Rayleigh dis could resul t. tnbutIOn (b = O) for low amplitude values but com The probability density distribution function that mence to diverge for a normalized amplitude of 12 describes the envelope of such a resultant signal can or greater. be written, according to Rice's theory of random T~e expe~imental and theoretical probability noise [1945], as denSIty functlOns of the total amplitude of the lunar echoes observed for 10 min near transit are shown in fig.Ul'e. 9. Af.ter normalization, the parameter 1/;, for (3) thiS tune perIOd, was found to be 40.0. It is interest ing to note that the experimental data appear to tend 112 , 0.12 , r I I I I I I / 0 o E . PERI .... E NTAL DA TA o ()(PERIWENTAl OATA. THE O RETI C AL THEORETICAL 0 \ RAYL EIGH ~ ~,R A YLEIGH 0 DIS TR IBUTION DISTRIBUT ION CO .. 0 b < 0 W 9 to / 00 00' I< II . 1 / 0'Y\ 1\ OU II'" II o o~ 10 k 0 ri' , 0 ~ '0 ' / I'\" , 0/ o 0 , II' \ 1\ I / \ \ If 0 V , /0/ o J X / 1\ 0 .0:'1 ~ I . I FI \ > ~ 1\ I / V ~ I '\ L , f} 1)/ ...:J 0 .0 / \ V \' \ II l\ J I) 0.0 ,Ii 1\ 1\ f\ / 1\ I ~~ rf \ 0 \ , / 1\ '\ ~ If / "- 01' ~ 0 0 "'" 0 V 0 OJ 0 "" "-- Y " 10 12 ""1 4 '0 NOR MA LI ZED AM PLlTUOE NO"MA LIHO AM PLI TUDE FIGURE 8. The probability density function of the total FIGURE 9. The probability density function of the total ampli amplitude of the lunar echo, 8 Febmary 1960, 1430 to 144-0 tude of the lunar echo, 8 February 1960, 2025 to 2035 EST. EST. 3 .4. Doppler Frequency Shift toward the b= l probability density curve except for the slight di~p l ace~llent at th.e maximuf!1. 0 Because of the relative motion of the moon with A companson of the experimental pomts m figures respect to the earth, radio waves reflected from the 8 and 9 indicates that, at high elevation angles where moon are shifted in frequency. libration fading is a maximum [Fricker, Ingalls, The Doppler frequency shifts measured dming Mason Swift, 1960], the amplitude signals were ob the partial lunar orbits of 12 January 1960 and 8 served 'more often having greater magnitudes than F ebruary 1960 are shown in figure 10. It is quite those detected near moonrise. evident that the experimental observations are in An amplitude record of 1 min in duration (2026:20 agreement with the theoretical predictions. The to 2027 :20 EST), taken from the same statistical theoretical cmves were computed according to the population, was also analyzed to determine the effect method proposed by Fricker et al. [1960]. The of a shortened sample size on the experimental dis Doppler shift is a maximum of approximately + 1130 tribution. In general, it was found that the ampli cis at moonrise and a minimum at the moon's tudes of the I-min sample were distributed in a some transit. what similar fashion to those of the 10-min sample. The Doppler frequency shift at 120 Mcls, as The results of this analysis reveal evidence of the reported by Browne et al. [1956], was on the order presence of a slight specul~r compo?-ent reflected of ± 50 cis for observations taken when the hour from the lunar smface durmg the tIme when the angle of the moon was less than 30 min of time. moon was near transit. This was not the case, Doppler shifts as large as ± 1000 cis at 412 Mc/s however, for observations conducted at moonrise. It is possible that, instead of one large smooth have been recorded by Fricker, Ingalls, Mason, reo ion on the smface of the moon, there are many Stone, and Swift [1958]. s~ooth areas which give rise to specular reflection. Thus this would have the effect of impo ing a ran 3 .5 . Doppler Frequency Spread dom phase and random amplitude fluctuation of the Radio waves, when reiiected from the moon, I resultant specular component. It would fo llow that the steady signal, which would be normally experience a Doppler spread in frequency in addition expected if the moon consisted of only one large to undergoing a Doppler shift. The former phenom smooth reflecting area, would, in essence, be washed enon is predominantly the result of the moon's out or smeared. libration. 113 + 1400 + 1200 f--- ..... ~ ...... 1 + 1000 "- "- ~ "- (, + 800 r-.... ',,- "\ -1~52:yE1~~~~6o ~ + 600 t '\'\ ~ THEORETiCAL >- FEBRUARY 8, 1960---+l~ \, ~ +400 o ...~ J 200 1\ ~ + o o \ _ EXPER IMENIL OATA o - 200 \ - 400 - 600 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 240i:! TIME (E S T ) FlGClm 10. Doppler j1'equency shift of lunar echoes recorded at T rin idad at 425 NIcls. \ ! J Fricker et a1. [1960], have shown that the fre The power density spectrum derived from the \ quency spread at transit is always a maximum, autocorrelation function is given in figure 12. It is while at moonrise it could have any value, depending seen that the principal frequencies are all less than upon the moon's effective total libration rate in 1 cis, i.e. , 0.27,0.53,0.69, and 0.94, with the dominant latitude and longitude. frequency b eing 0.27 cis. In an attempt to determine the existence of the The theoretical maximum Doppler spread for this Doppler frequency spread, the power spectrum particular time was found to be 2.21 cis for the for one lunar observation was calculated and com fractional radius of 0.404. This calculation was pared with the theoretical prediction. based on the lunar libration rate constants presented The power density spectrunl is the Fourier trans m tn,ble 1 and applied to the theoretical relationships form of the autocorrelation function which is com of Fricker et a1. [1960]. \ puted from an amplitude-versus-time function. In Since the Doppler frequency spread is directly \ this analysis, the autocorrelation function was cal proportional to the fractionitl radius of the m0011 culated from the t otal lunar cross section which is (Fricker , Ingalls, Mason, and Swift 1960], and since proportional to the square of the signal amplitude. t.he experimental dominant frequency of 0.27 cis The power density spectrum, as discussed in this is 0.12 times smaller thitn the theoretical estimate section, defines, in essence, the frequency-power of 2.21 cis, it fo llows that the fractional radius content of the time variation of the total echoing 'within which the observed amplitude variation is area of the moon. ~ con tained is about 0.049. The autocorrelation function of the total cross At it frequen cy of 425 1!fc/s, the first Fresnel section of the moon, calculated from radar data zone on the moon has a fractional radius of approxi recorded during a I-min interval on 8 February mately 0.007 . It appears, therefore, that while the 1960, is presented in figure 11. The total signal effective radius responsible for most of the amplitude power for each pulse, i.e., sum of the power received variation is smaller than 71 3 km, the radius of the ' on the two orthogonal polarizations, was measured 1 msec after the rise of the pulse. This corresponds spherical cap corresponding to a fractional radius 1 to the coverage of a spherical cap on the moon of 0.404, it is larger than the radius of the first with a fractional radius of 0.404, t he fractional Fresnel zone, 11.7 km, by approximately 7 times. radius being defined as the ratio of radius of the As shown in the photograph of the front portion bllse of the ~sphe ri cal cap to the radius of the moon. of the moon's face, figure 13, there is a comparatively 114 1.00 0.78 ~ O.!IO \ AZIMUTH = 7 1.5 0 ELEVATION: 0 .7 0 14 0 0 : 0 1 TO 1401: 01 EST 0 .215 \ V ./ \ / 1\ ~ ~V "\ - 0 .25 1\ / '--V - 0 .&0 CORRELATION TIME 1 sec F1GU R E 11 . A utoconelation junction oj the total cross section oj the m oon, 8 Fe&1'1wry 1960. smoo t h area in the ce n.ter of the moon , Sinus Medii, O.lO large enough to encompass at least 7 Fresnel zones. This region is sllrrounded by a number of mountain 0 .2:' peaks that rise 5,000 to 8,000 feet [N eiso n, 1876]. AZI MutH I 7 "~o ELEVATION ' 0 .1° It could be possible that the librational motion of . 4 00 : 01 TO '4 0 1 :01 EST these peaks account for the higher frequency terms obtained in the power density sp ectrum. For example, the mountain range, Rhaetieus with a ~ 0 .1:' I fractional r adius of approximately 0.08 to 0.09, could have impar ted at its lo cation a fading rate of about 0.84 to 0.95 cIs on 8 F ebl'llary 1960. It is I in terestin g to note that the fading rate, possibly due to Rhaeticus, compares favorably with one of ~/ 1'\ the frequencies, 0.94 cis, present in the power V v ~ density spectrum of that date. o '--- The feasibility of m apping the surface of the o 0.' 2.0 moon by means of Doppler shift power spectrum FREOUEN CY , cis measurements has been demonstrated by Petten FIGURE 12. Power density spectnun of the total cross section of gill [1960]. the ?noon, 8 February 1.960. T A BLE l. L ibl'ation rate constants for the evaluation oj Doppe?' Jreqnency spread 8 February 1960, 1401 EST Azimuth Elevation Total libraLion 'l'otalli bration i\1aximum I ,, = tan-1 [ -IT' ] angle angle rate in latitude rate in longitude o ITL Doppler ITS ITL I spread Degrees Degrees Radians/sec Radians/sec Del/rees cis -5. 14733 X 10- 7 69.1 5.450 K * 71.5 0.7 - 1. 34796XlO.... I *K=Fraetional radius of the moon. 11 5 , j FIGURE 13. Fresnel zones on the face of the moon. 4 . Conclusions 2. The probability density function of the total amplitude of the 1~ll1ar echoes, for one 10-min sample, An analysis of radar pulses reflected from the reveals the possIble presence of a steady siO"nal moon has revealed pertinent data regarding the which may be indicative of a specular refle~ted characteristics of its surface. signal. The analysis is based on Rice's [1945J It appears that, at a frequency of 425 Mc/s, the theory of random noise. front portion of the moon is comparatively smooth 3. The envelope or fading pattern of the amplitude and is the region where specular reflection takes versus-time photographs of the main lunar echo place. The following experimental evidence is the received on two linear orthogonal polarizations are basis of this conclusion. always identical. This implies that the polarizations 1. Radar-pulse measurements of the cross section of the incident pulses are not altered on reflection and the power reflection coefficient of the moon are from the front portion of the moon's surface. approximately the same as those determined by CW 4. The rotation of the plane of polarization of the systems operating at a frequency of 412 Mc/s radar-lunar echoes is found to be entirely due to the Faraday effect of the ionosphere. The polari [Fricker, Ingalls, Mason, and Swift, 1960J and 488 zation of the received signal often attains an acute Mc/s [Blevis and Chapman, 1960]. This indicates angle of zero degrees and 90 deg, whereas, according that a pulsed radar system covering a sufficient to Senior and Siegel [1959; 1960], a rough body can number of Fresnel zones measures the same echoing be expected to yield a minimum signal, containing area as a GW system covering the entire sUTface of at least 30 percent of the total received energy. In the moon. other words, the polarization angle of signals reflected 116 from a rough body should vary between 18 and 73 D. W. Swift (Dec. 1958), Characteristics of moon-reflected deg and not between zero and 90 deg. UHF signals, Mass. Inst. Technol., Lincoln Laboratory, Tech. Rept. No. 187. 5. The pulse shape of thernain reflected echo l' ricker, S. J ., R. P . Ingalls, W. C. Mason, and D . W. Swift most often resembles the transmitted pulse. (Sept.-Oct. 1960), Computation and measurement of the The experimental evidence, indicating that the fading rate of moon-reflected UHF signals, J . Research back portion of the moon behaves as rough scatter, NBS, 64D (Radio Prop.) 455- 465. I(err, F . J., C. A. Shain, and C. S. I-Iiggins (Feb. 1949), Moon :/ is based on the following. echo es and p enetration of the ionosphere, Nature 163, 310- 1. A-scope photographs of lunar echoes show that 313. the pulses are stretched out in length to approxi Kerr, F. J., and C. A. Shain (Mar. 1951), Moon echoes and transmission through the ionosphere, PI·OC . IRE 39, 230- mately the radio-depth of the moon, i.e., 11.6 lIlsec. 242. 2. It is found that the decay of the trailing edge Leadabrand, R. L., R. B. Dyce, A. Fredricksen, R. 1. Presnell, of a composite lunar echo, which is the average of and J . C. Schlobohm (Oct. 1960), Evidence that t he moon 130 echoes, obeys the Lommel-Seeliger scattering is a rough scatterer at radio frequencies, J. Geophys. law displaced by a factor of approximately one Research 65 , 3071- 3078. Neison, E. (1876), The moon and the condition and confi gura eighth. tion of its surface (Longmans Green, London). Pettengill, G. H . (May 1960), Measurements of lunar reflec tivity using the Millstone radar, Proc. IRE 48, 933- 934. The assistance of R . Wolfe in analyzing the radar Rice, S. O. (July 1944), Mathematical analysis of random amplitude data in the study of the scattering laws noise, Bell System Tech. J . 23, 282- 332. Rice, S. O. (Jan. 1945), Mathematical analysis of random applicable to the lunar surface is greatly appreciated. noise, Bell System Tech. J . 24, 46- 156. Scnior, T . n. A., and K . M. Siegel (1959), Radar re fl ection 5. References characteristics of the moon, Paris Symp. Radio Astron., edited by R . N. Brace\\'ell, (Stanford University Press, Bay, Z. (Apr. 1946), Refl ections of microwaves from the moon, Stanford, Calif.) 29- 45. Hungarian Acta Physica 1., 1- 22. Senior, T . B . A., and K. M. Siegcl (May- June 1960), A theory Blevis, B. C., and J. E . Chapman (July-Aug. 1960), Charac of radar scattering by the moon, J . Research NBS, 64D teristics of 488 megacycles per second radio signals refl ected (Radio Prop.) 217- 229. from the moon, J . Research NBS, 64D (Radio Prop.) Sulzer, P. G., G . F. MontgomcrY, and 1. II. Gerks (Mar. 331-334. 1952), An UHF moon relay, Proc. IRE 40, 361. .1 Browne,!. C., J. V. Evans, J. K. Hargreaves, and W. A. S . Trexler, J . H . (J an. 1958), Lunar radio echoes, Proc. IRE 46, Murray, (Sept. 1956), Radio echoes from the moon, Proc. 286- 292. I Phys. Soc. (London) B69, 901- 920. Webb, II. D. (Apr. 1946), Project Diana- Army radar con DeWitt, J . H., and B. K. Stodola (Mar . 1949), Detcction of tacts the moon, Sky and Telcscope 5 3- 6. radio signals reflected from the moon, Proc. IRE 37, Yaplee, B. S., R . II. Bruton, K . J . Craig, and N. G. Roman 229- 242. (Jan. 1958), Radar echoes from the moon at a wavelength Evans, J . V. (1957), The scattering of radio waves by the of 10 cm, Proc. IRE 46, 293- 297. moon, Proe. Phys. Soc. (London) B70 , 1105. Fricker, S. J., R . P. Ingalls, W. C. Mason, M. JJ . Stone, and (Paper 67D2- 248) 117