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Tor Hagfors* It Is Shown L 0 (CODE) IPAEES) 2- 30 (CATEGORY) RADAR fS(0PERTES OF THE MOON Tor Hagfors* A brief review is given of radar methods as applied to lunar studies and their interpretation. It is shown tht the radas data are consistenf; with a porous, un- dulating surface strewn vith rocklike objects, and argued that rqml craters are both rougher and denser than their su-roundirqs . DITR031JCTION Radar observations of the moon have in the past contributed to our know- ledge about the hmas surface in a number of ways. The low radar scat- teriR3 cross section has led to - or confirmed - the view that the lunm surface in general comists of material which is in a rather looselj. con- >acted state, at least to a de;Tth of many centimeters. Varintion in the amount of backscattering with angle of incidence has siim that the sur- i face on a scale of a few centfieters is fairly sn~okhand gently uncicrlat- ing with typical average slopes of the order of 10-13'. Observations of the degree of depolarization qFear to indicate that a small scale struc- ture, probably rock-like, must be scattered over most of the surface. Finally, it has been found that young and rayed craters are much more efficient backscatterers than their surroundings. In what folluws we shall introduce the various observation techniques used in lunar rad= studies, describe obser-fational results and. their in- teqretation. Finally, a brief discussion is given of what possible use- ful infornation cm be gleaned f'rm further radar studies of the moon, 8 particularly in view of the spectacular photographs obtained in the Ranger, b Surveyor and Luna programs. ------------- * Lincoln Laboratory, Massachusetts Institute of Technology, operated with support from the U. S. National Aeronautics and Space Administration under Contract NSR 22-009-106. 1 CROSS SECTION OBSERVATIONS The radar cross section of the moon as a whole has been measured by a nucber of workers mer a wavelength interval from 8 mm to 20 meters. Table 1 lists some of the results obtained. The error estimates me sub- stantial in most cases. This is due to difficulties with absolute Cali- bration in the data taking process. The low uncertainty at 23 cm was obtained by calibrating the radar system against a well known calibration sphere in satellite orbit around the earth. Figure 1 shows a plot of the cross section against wavelength. Due to the Large experimntal uncer- tainties it is difficult to assign a definite frequency law to the re- flectivity. It does appaz, however, as if the cross section increases somewhat with wavelength. Fig. 1 Lunu Radar Cross Section Versus Wavelength. On the basis of assuming the surface material to behave like a perfect dielectric, homogeneous with depth, one concludes that the dielectric constant must be somewhat less than three (Rea et- -'a1 1965). This low value of the dielectric constant indicates that the surface cannot con- sist of compacted rock material, but must be porous. Radiometric obser- vations of the thermal emission from the moon (Troitskii, 1$5), however, seems to indicate an even lower value of the dielectric constant. A 2 Table 1 VALUES FOR TIlE HhlNR CROSS SECTION OF TEE KOOM AS A FUNCTION OF WAVEI;ENGTH REFORTED BY VARIW WORKERS Wavelength 2 Estimated Author Year cm 0/7B Error, db Lynn --et a1 O.% 0.07 i 1. Kabrin 3.0 0.07 5 1. 3.6 0.07 i 1.5 Evzns and Pettengill 3 06 0.04 i 3. Eughes 10.0 0.05 f 3. Victor- --et a1 12.5 0.022 * 3. Evans adHagfors 230. 0.065 4 0.5 Blevis and Chapman 61.0 0.05. * 3. Fricker et-- a1 73 00 0.074 i 1. Trexler 100.0 0.07 zk 4. EVTJlS 250.0 0.10 I, 3. Evens --et a1 300.0 0.19 3. Evms 2nd Ingalls 784.0 0.06 f 5. Davis and Rohlfs 1130.0 0.19 + 3. - 2. Davis and Rohlfs 1964 1560. o 0.13 + 3. - 2. Davis and Rohlfs 1964 190.0 0.16 1- 3. * Revised value (privately comrmrnicated to Evans and Pettengill [l963c 1 ) . 3 c- reconciliation of the radar and the radiometric determinations of the dielectric constant can be brought about by models involving a gradual transition with depth rather than am abmpt change. This change may either be in the form of a homogeneous tenuous boundary layer or in the form of a continuously changing transition layer (Hagfors, 1967). In- homogeneity with depth can also easily explain an increase in cross section with wavelength as ap>ascntly is observed. A!’?GlJTAR VARIATION OF THE BACSCATTEIIED POWER The cqability of a rad= system to resolve very finely in range can be used to measure the angular variation of the scattering. Figure 2 shows the one-to-one relation between delay and angle of incidence on the moon. ~IJ-JO-SIIS] INCIDENT AND REFLECTED RAY &.A , 4NNULUS ILLUMINATED BY A PULSE 4T A TlMF I AFTER FIRST STRIKING THE SURFACE o :RADIUS OF THE MOON c =VELOCITV OF LIGHT Fig. 2 Relation Between Delay and Angle of Incidence nus, by resolving the power returned from the moon in range it is possi- ble to axrive at the angular scattering law. Figure 3 shows the reflected ,power plotted against range for several different wavelengths. A wave- length dependence is clearly seen in the data. Before discussing what the physical significance of these results might be it should be mentioned that the angular scattering law can also be de- rived by a different technique. 9ue to relative rotation of the earth and the aoon different portions of the lunar disk will scatter back with different Doppler shifts relative to the center of the moon. By frequency I 4 c - I- -o w(T. x 20- w 2- a _I y 24- DELAY Imwcl Fig. 3 Backscattered Power Versus Delay for Several Wavelengths analysis it is possible to wive at a strip-distribution of power acrosz the disk. This strip distribution can be converted to a parerdelay re- lationship and hence provides the same type of information as the direct 2over-delay masurements . This technique has found more frequency apI2li- cation in planetazy observa,tions than in lunar studies. Analysis of the curves in Sigure 3 shows that the scattering near normal incidence decreases markedly with vavelength whereas the scattering at nore oblique angles increases somewhat with decreasing wavelength. The backscattering new normal incidence caa be thought of as arising frDm flat facets tilted with respect to the mean lunar surface so as to be favorably oriented for reflection. On this basis the power versus angle relationship can be translated to a distribution of surface slopes. The r.m.s. slopes found in this way typically carrespond to the range of angles 10-15'. At the shorter wavelengths the slopes observed tend to apFear steeper. This may be understood if it is realized that the shorter wavelength observations are sensitive to structure of smaller lateral ..I- * extent than the longer wavelength ones. For the scattering at oblique incidence, i.e., at angles of incidence in excess of 250 , the returns nay iio longer be thought of as reflections from flat facets, but rather as scattering from a collection of relatively small individual objects. The increase in the amount of oblique angle scattering with decreasing wavelength may be understood if it is realized that the shorter wavelength experiments are sensitive to a wider range I of rock sizes than the longer wavelength ones. Calculations of the strength of the backscattering expected from rocks such as the ones seen in the vicinity of Luna 9 or Surveyor I seem to show that the number of rocks &prunit surface area may be adequate to account for the scatter- ing at oblique angles of incidence. For angles of incidence in excess of 25' the backscattering per unit surface mea goes as coshg . There are indications that this law chenges to a cos @ dependence near pazing incidence. In radar illumination the lunar disk therefore looks nearly uniformly brigh% with a brilliant spot corresponding to quasispeculm return in the center. POIARIZATION OBSERVATIONS 3adm astronorqy allows the observer to control the polarization of the illumination of his target. At a wavelength of 23 cm this capability has been exploited filly in order to improve our understanding of the nature of the surface. The surface has been illuminated with circularly polar- ized waves and the amount of depolarization has been studied as a function of angle of incidence. Figure 4 shows the ratio of the polarized and the depolarized backscattered components as a function of angle of incidence for circular illumination. Figure 5 shows this ratio when the illumina- tion is linearly polarized. In both of these cases the interpretation is consistent with the interpretation derived f'ram the angular variation of the backscattered per (Hagfors, 1967). MAPPING TECHNBUES Resolution in delay and in relative Doppler offset has already been men- tioned as alternative techniques for obtaining information on angular parer variation. Combination of the two techniques provides us with a 6 &OIfi E c- H $4 10 a6 01 02 01 (106 0.04 002 cos 0 Fig. 4 ExLio of Polarized and Depolarized achsccttered Power versus cos @ for Circularly Polarized Illwnina- tion I'I ' I I'II I I I LINEAR ILLUMINATION FEK~,%~ozoo-oeooesf 1 W N 6- 2 4: 0 2- '3 a. 0: oslrl ' ' ' I 111, I 1 I I Fig. 5 iiatio oi' i'olarized 2nd Depola5zed 3xkscaTtered Power versus cos 6 Tor Linewly Polcrized Illuninction coordincte system of ci:-cles centered on the sub-rzda point and stmight 3t-rcliel eQuidistcnt lines Ecross the 6isk 02 the moos.
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