Quarterly Progress Report Radar Studies of the Moon Prepared for the U.S. National Aeronautics and Space Administration under Contract NSR 22-009-106 by Lincoln Laboratorv d MASSACHUSETTS INSTITUTE OF TECHNOLOGY Lexington, Massachusetts 2 15 May 1966 Issued 2 June 1966 https://ntrs.nasa.gov/search.jsp?R=19660020448 2020-03-16T20:57:31+00:00Z I FOREWORD This is the second Quarterly Progress Report required under Contract NSR 22-009-106 between the National Aeronautics and Space Administration and Lincoln Laboratory, M. I .T. In addition to covering the first four months' work under the contract, the first progress re- port reviewed in considerable detail the work performed and the methods used to study the lunar surface by radar up to the time of the start of the contract period. In the present and subsequent progress reports frequent reference will be made to this review material and the plans described in the first report [referred to as QPR (1966:l)J. Section I of the present report covers the more important aspects of the research completed under the contract during the period 1 February through 30 April 1966.. It also briefly ex- plains certain additional experiments which were carried out during the period;. some of the results will be reported in detail in the next quarterly report. This section contains some theoretical material pertaining to the effect of shadowing on the backscattering from a rough surface. Section 11 contains some information on the plans and the present status of the 8-mm radar work. A survey is also presented of the considerable progress in the development of both the hardware and software necessary for mapping at 3.8 cm:' Section whereby the depth of the surface layer may be measured. contains a discussion of possible future experiments, not previously planned, -\\ iii Foreword CONTENTS iii I. RESEARCH RESULTS A. Scattering Properties at 23 cm 1. Introduction 2. Observational Procedure 3. Power vs Range, Polarized Component 4. 5. 6. Discussion of Results 7. Conclusions B. Other Observations Power vs Range, Depolarized Component Observations of Total Radar Cross Section 1. 2. Polarization Observations at 23-cm Wavelength Observations at a Wavelength of 3.8 cm C. Theoretical Results 1. The Effect of Shadowing on the Backscattering of Waves from a Random Rough Surface 11. PLANS AND PREPARATIONS A. Preparations for 3.8-cm Mapping 1. Computer Program Development 2. Equipment Development B. Preparations for 8-mm Observations 111. NOTES ON FUTURE WORK A. Experiments to Determine the Depth of a Lunar Surface Layer 1. Introduction 2. 3 . Other Observations 4. 5. A Very Deep Layer 6. Conclusion Polarization Experiments at Longer Wavelengths Other Models of the Surface 1 1 1 1 4 7 i o 11 19 19 20 20 21 21 35 35 35 38 38 41 41 41 41 43 46 47 49 References 50 iv I . RESEARCH R E S U L T S A. SCATTERING PROPERTIES AT 23 cm 1. Introduction Short pulse studies of the lunar surface have been made at a number of wavelengths. These measurements are , in our view, usually to be preferred to other types such as power spectrum measurements, discussed by Evans and Pettengill (1963a), for the following reasons: (a) better resolution can be obtained by examining the distribution of echo power with respect to delay rather than frequency owing to the small angular rotation rate of the moon (an exception is the a rea near the subradar point), (b) there is a direct correspondence between the echo power at a given range delay t and the angle of incidence and reflection cp of the radio waves, and (c) for practical reasons it is often possible to explore the echo power over a larger dynamic range when separating the echoes with respect to range, than when resolving them in frequency. The scattering properties of the lunar surface were previously explored over almost the full range of angles 0 < cp < 90" at 3.6- and 68-cm and 6-m wavelengths. tions made thus far, together with those reported here. ments and also the intervals at which the echo power was sampled (Table I ) differed considerably. It can be seen that prior to the present measurements the behavior in the region 10 to 90" had been observed only at wavelengths of 3.6, 68 and 600cm. prevented a useful examination of the region cp < 10" at all but two wavelengths, namely 10 and 68 cm. to match the resolution achieved at 3.6- and 68-cm wavelength, and the scattering behavior has been explored over all cp for both the expected and depolarized components of the echo. Table I l is ts the observa- The pulse lengths used in these measure- In addition, the pulse lengths employed During the observations at 23-cm wavelength reported here, experiments were conducted 2. Observational Procedure The observations reported herein a t 2 k m wavelength were made using the Lincoln Labora- tory, Millstone Hill Radar (42.6"N, 71.5"W). The system parameters employed are listed in Table 11. means of a Univac 490 digital computer or by automatic readings of a prepared punched paper tape which gave pointing instructions a t 10sec intervals. Checks could be made by means of a television camera aligned along the axis of the beam to confirm that the pointing was accurate. The receiver w a s tuned to within 0.i cps of expected frequency of the echo by means of a special linearly varying frequency generator, the slope of the linear frequency variation being reset at 5-minute intervals. Doppler shift, the variation of the position of the echo on the time-base due to the continuously changing range was compensated to within a small fraction of the pulse length. samples of the echo intensity could be taken at fixed delays with respect to the echo position, and these could be averaged to obtain the mean echo power at that delay. these range and frequency compensations are provided has been described elsewhere (Evans, gal., 1965). The antenna was directed to point continuously at the center of the moon's disk by In addition to guiding the receiver tuning in frequency to match the expected In this way The manner in which i Section I $ I 2 i Section I TABLE II MILLSTONE L-BAND RADAR PARAMETERS Frequency Antenna Antenna Gain Polarization Beamwidth Transmitter Power Pulse Length Receiver Bandwidth System Noise Temperature Overall feed-line and other losses 1295.0 Mcps 84-ft parabola with Cassegrain feed arrangement 47.3 db right circular transmitted 0.6" between half power points variable, 5-MW peak maximum (continuously right and ieft circuiar separateiy received monitored) were employed in these xervotions variable, pulses 10 to 200 100- or 50-kcps predetector. Postdetector filter ec long matched to 10-pec pulses for 10-psec pulse transmissions, matched to 207aec pulses for all other transmissions. .c 150°K (continuously monitored) 2.1 db Following the last frequency conversion in the multiple superheterodyne receiver the signal is applied to a pair of phase detectors, which a r e driven at the same reference frequency but shifted in phase by 90". of the signal. identical digital voltmeters. of delay. were conducted with sampling frequencies of 50 or 100kcps. The outputs of these detectors a r e thus the sine and cosine components These components a r e separately filtered by low-pass fi l ters and sampled by The voltmeters a r e commanded to take samples at equal intervals A choice of several sampling frequencies is available. Most of the measurements The time required for the voltmeter to make a determination is 0.25 w e c . Each voltmeter determines the sign of the signal and assigns it one of 32 possible levels. range of the receiver system is therefore limited by these voltmeters to 30db. intensity could be explored over a wider range than this, however, by raising the transmitter power and repeating the measurements at different signal-to-noise levels. in this fashion were recorded digitally on magnetic tape for la ter computer processing. The total dynamic The echo The samples obtained In the simplest form of processing the pair of samples corresponding to a given range delay This sum is then added to all other a r e squared and added to yield the echo power at that delay. sums for that delay to yield an average for the echo power at that delay. The 23-cm system contains two complete channels like the above, making it possible to receive and record the two orthogonally polarized components of the signals simultaneously. En this way the polarization of the reflected signals could be explored. 3 Section I 3. Power vs Range, Polarized Component In this measurement a circularly polarized wave of one sense was transmitted and the opposite (i.e., the expected sense) was received. the complete radar depth of the moon (11.6msec) observations conducted with a variety of pulse lengths were carried out. In order to explore the echo power P ( t ) over The echo power was established for the region of delays 0 to 700 psec using a pulse 1 0 psec long and a sampling interval of 10 psec. with a 20-p.sec sample interval were used. was lowered to ensure that the echo power did not exceed the maximum sampling level of the digital voltmeters. These measurements were then repeated a t a somewhat higher power to establish the dependence in the region 0 to 2.4msec, yielding finally the results plotted in Fig. 1 Observations made with 30-, 100- and 200-psec pulses and corresponding sample intervals Observations were also made in which 3epsec pulses For both se t s of observations the t ransmit ter power of 20, 100 and 200 psec were then used to establish the curve in the region 2.4 to 11.6 msec. These observations a re plotted in Fig. 2. Since the antenna beam of the Millstone radar has a half power beam-width comparable to the angular extent of the moon it was necessary to correct the observations for the non-uniform 0 -4 -8 - 12 - a 0 LL W ? -16 W - 2 5 2 -20 LL -24 -28 * AVERAGE OF IO MINUTES DATA TAKEN ON I 2 MARCH 1965. IOusec PULSE AND IOusec SAMPLE INTERVALS. i * AVERAGE OF 2 0 MINUTES DATATAKEN ON 26 FEB. 1965.30usec PULSE AND 2Opssec SAMPLE INTERVALS. I 400 800 1200 1600 2000 2400 DELAY (used Fig. 1. Observations of moon echoes over range of delays t to t ~ 2 . 4 msec a t 23-cm wavelength. 0 4 Section t 0 -8 I ," - 4 6 t w a 0 1 - 2 4 0 w c) s - 32 - 4 0 -40 'ANTENNA PATTERN - 20 MIN. DATA 30usec PULSE 26 FEE. 1965 - 20MIN. DATA COusec PULSE 26FEB. 1965 - 20MlN. DATA 200usec PULSE 26FEB. 1965 - 2OMIN.DATA 200usec PULSE 2MAR.1965 . ,CORRECTED CURVE %_ CO RECTED OBSERVED CURVE 2 4 6 E l 0 4 2 ,_1.-- 2 4 6 E l 0 4 2 DELAY (msec l Fig. 2. Observations of moon echoes over full range of delays 0 to 11.6 msec using pulses of 30, 100, and 200 pet. Dashed curve was obtained by correcting obserw- tions for effect of non-uniform illumination introduced by antenna bean, and has been taken to give variation of echo power of range of delays 2.4 to 11.6 msec. illumination of the moon's surface. radio s t a r s and a distant beacon transmitter as sources. presents a pattern obtained by averaging plots obtained for the azimuth and elevation planes. Since the moon has a diameter of 0.5" the antenna pattern correction required is not large, amounting to only 4db at the limbs. tion equally so that the effect must be included twice.) The antenna radiation pattern (Fig. 3 ) was established using Both methods agreed well and Fig. 3 (Note that the antenna weights the transmission and recep- In Figs. I and 2 we have shown the corrected curve of echo power vs delay P ( t ) obtained when the effect of the antenna has been removed. The corrected curves were next replotted as func- tions of the logarithm of the echo delay, t, and overlaid to obtain a single smooth curve. this way we remove the effect of the saturation of the receiver encountered at the leading edge when attempting to observe the limbs. In Figure 4 shows the results obtained. The values plotted in Fig. 4, together with the values observed at 3.6- and 68-cm wavelengths by Evans and Pettengill (i963b), were included in Radar Studies of the Moon Quarterly Progress Report ( i966: i ) as Table 111. Figure 5 shows the results obtained at the three wavelengths 5 Section I -28 } I I I O a75 a 5 0.25 o 0.25 a 5 0.75 LO DEGREES Fig. 4. Plot of combined results of all measurements at 23-cm wavelength to obtain complete dependence of echo power with delay. Fig. 3. Antenna pattern for Millstone Hi l l 1295 Mcps radar obtained by scanning radio stars and a distant beacon transmitter. Pattern shown imposes a weight- ing of results both on transmission and reception. Effect of this weighting i s indicated in Figs. 1 and 2. W 5 a -J Y I 2 0 . D 10 AND 30 psec PULSE OBSERVATIONS 0 - 7 0 0 p r e c PLOT 10 AND 3Opsec PULSE OBSERVATIONS 0 - 2.4mrec PLOT 30 AND 20Opsec PULSE OBSERVATIONS 0 - 11.6rnsec PLOT 28 - 0 100 1000 10,ooo DELAY (vsecl 6 Section 1 3ouuc PULSE LENGTH 20- RESOLUTON IN =LAY \ 2 4 6 OELAY (msec) 8 Fig. 5. Comparisbn of 23-cm results shown ..I Fig.2 with results reported by Evans and Pettengill (196%) at 3.6- and 68-an wavelengths. when pulses of 30psec a r e used to resolve the leading edge. normalized at the origin and are the only results at different wavelengths in which exactly the same resolution was employed. These three curves have been 4. By receiving the same sense of circular polarization a s was transmitted it is possible to Power vs Range, Depolarized Component determine the amount of power that has been converted into the orthogonal circularly polarized mode. Evans and Pettengill (1 96313) called this component the "depolarized" component, though additional measurements using linearly polarized waves are required if the complete scattering matrix f o r the surface is to be established. With the Millstone system, measurements of the depolarized and polarized components could be made simultaneously, o r alternately at will. depolarized component. Up to a delay of 4msec, 160ysec pulses, 50-kcps predetection fi l ters and a sample interval of 160 psec were used, while 1-msec pulses, 2-kcps predetection fi l ters and a sample interval of 480 (Isec were used for delays beyond 4msec. echo can be established by injecting into the receiver ir?put terminals (via a directional coupler) a pulse of noise corresponding to a known increase in system temperature on each sweep of the time-base. Figure 6 shows the distribution of depolarized echo power, D(t), v s delay, obtained for the The absolufe level of the This pulse served to determine the relationship between D(t) and the polarized 7 Section I -20 -j 10 12 T I M E DELAY FROM LEADING EDGE OF LUNAR ECHO (msec) Fig. 6. wavelength on 3 Feb. 1966. Depolarized or opposite sense circularly polarized mode observed at 23 cm 0 - 8 - n n - - i 6 Fig. 7. Comparison of Fig.6 results with a determination of the expected component of echo power (3 Feb. 1966). g 0 s - 2 4 -32 0 CIRCULAR POLARIZATION TRANSMITTED ORTHOGONAL CIRCULARS RECEIVED 0 B 0 0 00 0, 00 EXPECTED SENSE 8 .'* Y O O *. %. . 0 ..-. 0 .. . COMPONENT 0 0 . o . o . o 0 I 0 I L I I 4 8 DELAY (msec l L 42 8 Section I power, P(t). In order to remove the effects of pulse length, P ( t ) was redetermined using a i60-psec pulse a d 2 5 N c p s receiver bandwidth. Figlire 7 compares the curves obtained for the two polarizations. The percentage polarization p(t) which can be defined as is then plotted in Fig. 8 . Also shown is the curve for p(t) obtained previously at 68 cm by Evans and Pettengill (1963b). It can be seen that the amount of depolarization has increased with fre- quency. DELAY (msec) Fig. 8. Percentage polarization observed for circularly polarized components (Fig.7) compared with previous results for 68 an. Two independent sets of measurements a r e included in deriving Fig. 8. indicate the uncertainty associated with the points shown as closed circles. establishing the exact relative position of the two curves in Fig. 7 is the major source of uncer- tainty in deriving percent polarization. it w a s necessary, in addition to including a calibration pulse in each measurement, to establish the waveguide and other losses between the horn feed and the receiver input terminals for the two senses of polarization. on a tower in the near-field of the antenna. the amount of power radiated by the beacon transmitter. mission and reception could be checked. lends some confidence in the method and suggests that the uncertainty estimate that has been assigned is too large. The e r r o r bars The difficulty of To establish these curve positions as well as possible, This w a s done using a beacon transmitter coupled to a dipole mounted The dipole could be rotated at w i l l without influencing In this way the circularity of the trans- The agreement between the two sets of points in Fig. 8 9 Section I 5. Observations of Total Radar Cross Section Previous efforts to obtain reliable total cross section measurements for the moon have been reviewed by Evans and Pettengill ( 1 9 6 3 ~ ) . the uncertainty in the antenna gain (typically 1 db) enters twice, and uncertainties associated with the determination of the absolute power transmitted and the absolute calibration of the receiver a r e usually of comparable order. The e r r o r s encountered a r e usually large, because A very precise determination of the moon's radar cross section is now possible by comparing the lunar echoes with those from a carefully machined metal sphere placed in earth orbit. sphere, the Lincoln Calibration Sphere (LCS) has a c ros s section of exactly 1 m2 at a wavelength of 23 cm (Prosser , 1965). Unfortunately, despite its close range the calibration sphere is a weaker target than the moon by approximately 40db. Accordingly, the full sensitivity of the Millstone Hill radar is required in order to observe it accurately. The procedure adopted in these measurements was as follows: A time w a s chosen when the This moon's elevation and that of the sphere were comparable. the normal closed-loop tracking afforded by the multiple beam system of the Millstone Hill radar . The automatic tracking system requires the transmission of 2-msec radar pulses. receiver with a bandwidth of 8 kcps was used in order to determine the echo amplitude. output of this receiver w a s rectified using a square-law detector and sampled at 200-psec inter- vals. computer for consecutive 30-second intervals. normal calibration noise pulse. and each of these w a s used to determine the overall sensitivity of the radar using an appropriate value determined for the mean range of the satellite during that 30-second period. vations yielded the following relation: The sphere w a s then tracked using A separate The The integration over the time-base w a s achieved by summing the digital samples in a Included in the integration process w a s the About forty successive 30-second integrations were obtained These obser- = 18.071 * 0.038 - 4 loglO R logl 0 Techo where T and R is its range. pendent calibrations (Table 11) we should expect is the equivalent increase in the system temperature caused by the satellite echo echo Based upon the parameters of the r ada r system as determined from inde- = 18.066 = 4 loglo R . l og lo Techo In this instance i t seems that the radar sensitivity could, in fact, have been quite accurately predicted without this overall calibration. The agreement between ( 2 ) and (3), however, lends considerable confidence to the result reported here. the values of individual equipment parameters to better than *I o r 2db. There is still no way of being certain of Following the observations of the LCS sphere, the ratlar was employed to observe the moon in precisely the same way, except that the antenna pointing information w a s derived from the punched paper tape reader. satellite, it was also necessary to reduce the system sensitivity by about 30db to prevent the receiver from saturating. This w a s accomplished by reducing the transmitter power by an amount which was measured using a carefully calibrated power meter. achieve the same effect by placing attenuators at the receiver input terminals, but this w a s Since the moon echoes a r e very much stronger than those from the It is also possible to 10 Section I considered undesirable a s it could disturb the matching of the receiver to the line. of ar? 8-kcps receiver baxhridth w a s m-ade iii order to reinove any amp?;tiide fPictuationa t h i might arise from small e r r o r s in the automatic compensation of the Doppler shift during the observations of the calibration sphere. Observations of moon echoes were made for periods of 30 seconds and a mean of 14 such periods was then taken. the ful l depth of the moon (11.6 rnsec), at no t ime was tine whole lunar hemisphere illuminated and therefore contributing to the echo power. That i s , the c ross section u(T) observed with a pulse length of T milliseconds, is simply The choice Since a 2-msec pulse is less than where u is the total cross section. observed with 2-msec pulses is scaled up to the value for the whole moon we obtain This function is plotted in Fig. 9. When the c ross section 0 (5) 2 u = 0.065 f 0.008 r a . 0 where a is the moon radius. The uncertainty given is the rms e r r o r resulting from the spread of the values obtained in the 40 observations of the satellite (*0.38 db) and the 14 observations of the moon (also *0.38db). We believe that the only source of systematic e r r o r remaining is that associated with reading the power meter monitoring the transmitter power and the linearity of its scale. These e r ro r s are thought to be substantially smaller than the uncertainty quoted. 6. Discussion of Results The wavelength dependence in the scattering behavior reported initially by Evans and Pettengill (1963b) and supported by Davis and Rohlfs (1964) and Klemperer (1965) is strengthened - O B - z - P v - bl Fig. 9. Variation of total cross section of moon io=- at 23 an wavelength as a function of pulse length. Curve was derived fran results presented in Fig.4 - and has been employed in obtaining an accurate E (H 1 - determination of rodar cross section of moon (Sec. ; - I-A-5). - - - - L’ 3 Section I Fig. 10. Summary of radar observations of moon using pulse length of 100 psec or less. I , I , I . I . I . 2 4 6 8 40" it appears that the echo is entirely reflected from within the lunar surface and thus the echo power from any small region depends upon the square of the local transmission coefficient. normal to the local plane of incidence a re different, and any one range ring includes al l possible local planes of incidence, this will serve to cause some depolarization. that the magnitude of an effect of this type is inadequate to account for the large amount of depolarization observed a s shown in Fig. 7. demonstrably present in lunar reflection, the original explanation (a) proposed by Evans and Since the transmission coefficients for waves polarized in and However, it appears Stated otherwise, although an effect of type (b) is 15 ' . I l l 1 I 1 I I 1 Section I I I p:! a U 0 - 2 - n - 4 L U w 0 L - 6 3 - 8 32 t P Fig. 15. with new result added. Cross section of moon vs wavelength W A V E L E N G T H (cml 16 Section I Pettengill (1963b) appears correct. attempting to account for the polarization of radar echoes from the sea at grazing incidence. We note that Long (1965) invokes a s imilar explanation in The echoes from the quasi-specular region are not depolarized much and this is to be ex- pected for reflections from a largely smooth undulating surface (Hagfors, 1964). however, a marked transition at about 3-msec delay (Fig. 8) beyond which the amount of depolar- ization is roughly constant. not depolarize and a random collection of linear dipoles which do. Randomly arranged dipoles would completely depolarize an incident circularly polarized wave, since they would destroy the h/4 phase relationship between the two linears into which a circular wave may be resolved. Thus in order to account for the amount of polarization (about 40 pe'rcent) observed at t = 8 m s e c (Fig. 8) we require that roughly 40 percent of the energy be returned from the facets and 60 per- cent from the dipoles. In this case the dipoles will split their reflections equally between the two components to give 30 percent in the depolarized component and 70 percent will appear in the expected sense - a s is observed. reflect in the incident and orthogonal planes in the ratio 3:i (Mack and Reiffen, 1964). It follows that of the 60 percent of the power reflected by the dipoles, only 1/4, i .e., 15 percent, w i l l be in a sense orthogonal to the expected mode. prediction in the next quarterly progress report. There is, W e may model the scat terers in this region a s flat facets which do When linearly polarized waves a r e employed the dipoles We should be ready to report a comparison of tnis Some support for the model proposed here is given in Fig. 14 where w e have plotted the echo power observed in the opposite sense circular mode to the expected sense [i.e., D ( t ) shown in Fig. 61 as a function of cos q. which is similar to the law observed for the diffuse component of the expected signal in the extreme limb region. 1963b). We find that the echo power conforms to the law D(q) a cos cp, A law D ( q ) a cos 40 was also observed at 68 cm (Evans and Pettengill, It should be understood that this modeling of the surface a s a collection of facets and dipoles is merely a convenient fiction which approximately serves to describe the electrical performance of the surface. that there a r e elements having small radii of curvature and a s such force the induced currents to flow in preferred directions different from those of the field exciting them. support the view advanced ear l ier that the scattering in the diffuse region is dissimilar to that of the center of the disk. We do not suppose that the lunar surface is covered with dipoles, but merely These results Let us now turn to the significance of the new and accurate determination of total cross section reported above. in te rms of fractions of physical cross section. report which is reproduced here, with the new, accurate 23-cm value added, as Fig. 15. increase in cross section with increasing wavelength suggested depends largely on the three long wave measurements reported by Davis and Rohlfs (1964). been subject to systematic e r r o r s introduced by ionospheric effects. ignored, the remainder show no clear wavelength dependence. values where these have been given, or *3 db where no uncertainty was published. Previously obtained data were presented in QPR (1966:l) as Table I1 The data were also presented a s Fig. 3 of that The These measurements may have If these three points a r e The e r r o r s given a r e the reported The e r r o r s associated with these measurements a r e generally large for reasons we have already enumerated. would require that each radar be calibrated in the manner described in Sec. A-5. It seems that a reliable determination of the cross section vs wavelength Section I The scattering c ros s section expected fo r a large dielectric sphere may be written (Evans and Pettengill, 1963b) 7 where p the directivity of the target, i.e., the ability to scatter preferentially toward the radar . case of a perfect sphere g = 1 and for the case where the surface has large scale irregularities (but is locally smooth on the scale of at least a wavelength) g = 1 t cy2, where a 2 is the mean square surface slope (Hagfors, 1964). a range of structure having scales down to and smaller than the wavelength in size, g has not been evaluated quantitatively. If the surface is completely covered with structure comparable with the wavelength and as a result behaves as a Lambert scatterer, then g = 8 /3 (Grieg, 1948). jects comparable in size to the wavelength, g increases from unity toward a value of about 3 o r possibly higher. is the Fresnel reflection coefficient fo r normal incidence and g a t e r m which denotes 0 In the For the general case in which the sphere is covered with G., It is thought, therefore, that a s the surface is covered to an increasing extent with ob- F o r the long wave measurements (A >, 1 m ) shown in Fig. 3 of QPR (1966:1) we conclude that g = 1.0 but that g increases for h < 1 m. indicates that po is decreasing with wavelength, and hence suggests that the reflection a r i ses in an inhomo- geneous surface. the longest waves w i l l penetrate deepest and the effective reflection coefficient will increase accordingly. The absence of a corresponding increase in u 0 If the density of the material on the lunar surface increases with depth then F rom the 68-cm results Evans and Pettengill (1963b) derived a reflection coefficient po = 0.064 By assuming after attempting to subtract out the echo power attributable to the diffuse component. that the electrical conductivity of the lunar surface is zero and hence the dielectric constant k = (1 t &o)2/(f the same experimental results, but employed a somewhat more rigorous method of removing the echo power attributable to the rough structure (for which the value of g i s not known) and obtained k = 2.6. for t e r r e s t r i a l rocks (Brunschwig, 5 G., 1960) a r e in fact considerably higher than values obtained in passive radiometric observations. in such studies is to determine the degree of polarization exhibited by the thermal radio emission, since this depends directly upon the transmission coefficient of the surface (1 - p ) (Troitsky, 1954). 1962; Heiles and Drake, 1963; Mezger, 1965; Davies and Gardner, 1965) and yield values chiefly in the range k = 1.7 to k = 2.1. Other values obtained by studying the thermal history of the moon over a lunation a r e less direct but also yield values in the range 1.5 to 2.0 (e.g., Troitsky, 1962; Salomonovich and Losovsky, 1962; Krotikov and Troitsky, 1962). The dis- crepancy between the radar and passive results has long remained a puzzle. (Hagfors and Morriello, 1965) of the effect of surface roughness on the interpretation of the passive observations have indicated that, though this does tend t o ra i se the value of k that is derived, the effect is not large enough to account for the discrepancy. The difficulty seems resolved as a result of recent radar observations reported by Hagfors, et al. (1965) which Evans and Pettengill derived a value k = 2.8. Rea, et e. (1964) used These radar values, although very low when compared with the values observed Perhaps the most reliable method of deriving k 0 Measurements of this kind have been performed by a number of observers (e.g., Soboleva, Calculations -- 18 L Section I indicate that the radar echoes at normal incidence a r e partially reflected from within the lunar surface, and that the upper layer has a dielectric constant of only about 1.8. s e e QF'R (1966:i) Sec.1-J.) It seems, therefore, that the passive measurements refer to the uppermost material (extending in depth perhaps some tens of centimeters) and that the radar reflections yield an average value related somehow to the way in which the density increases as a functicn of depth. (For further details Giraud (1965) has examined the way in which the reflection coefficient would vary in the case of a surface in which the density increases from zero linearly with depth over a distance of d to a density corresponding to a dielectric constant ki. O n the basis of this model, it is only when A > 20 d that the reflection coefficient is the same as that which wnuld be attributed to the subsurface layer in the absence of an inhomogeneous covering. If the measurements listed in QPR (1966:i) Table I1 could be repeated with an accuracy equal to that reported in this paper, it seems that the depth of the layer of light material overlying the lunar surface might be estab- lished. moon a r e given in Sec. 111-A. Further discussions of possibilities for determining the depth of a surface layer on the 7. Conclusions On the basis of the experimental results presented in this section it is possible to draw a number of conclusions about the behavior of the lunar surface as a whole as a scat terer of radio waves. measurements. the depolarizing properties have been explored. ing from the center of the disk is largely from regions that are locally smooth on the scale of the wavelength, whereas for an angle of incidence rp > 40". scattering from rough structure appears to predominate. In the central region the theory of the scattering apparently is in satisfactory shape, and the surface can be described a s having an exponential autocorrelation function and a mean slope of about 10" when measured over an interval of a few meters . limb region where scattering from rough structure predominates the theory is less satisfactory. The scat terers may be modeled as collections of dipoles and flat facets, and at 23-cm wavelength 60 percent of the power is reflected by the dipoles. to l ie largely within the surface according to separate experiments reported by Hagfors. (1965). inferred if very precise radar cross section measurements could be made at many wavelengths. Section A-5 outlines one method of accomplishing this using a precisely machined calibration sphere in Earth orbit as a radar reference standard. . The wavelength dependence observed by ear l ier workers has been supported by these By employing different polarizations for transmission and reception, some of These results support the view that the scatter- In the This irregular structure appears, however, &. The depth and perhaps some other properties of the uppermost tenuous layer might be B. OTHER OBSERVATIONS In this section a brief review is given of some additional observations made during this reporting period, most of which a r e still being analyzed. a s tentative. Results must, therefore, be regarded 19 Section I 1. Some additional polarization experiments have been carried out at 23-cm in order to obtain Polarization Observations at 23-cm Wavelength further information on the nature of the scattering mechanism involved, particularly in the limb regions of the surface. The moon was illuminated by linearly polarized waves and the behavior of the polarized and the depolarized linear components w a s studied f o r returns from complete range rings. behavior of the polarized component appears to be the same as that of the polarized component when the illumination is circularly polarized. somewhat differently from the one observed when the illumination is circularly polarized. angular scattering l a w appears to follow a COS3" cp law rather than a cos cp l a w as in the circular polarization case, for reasons not fully understood at present. The ratio of polarized to depolarized components in th i s case appears to remain approximately constant at 6 to 7 db from a delay of 3 msec on out to the lunar limb. The The depolarized component, however, behaves The Further studies were conducted with linearly polarized illumination with small a r eas resolved by means of the range-Doppler technique. wave polarized with the E-field in the plane of incidence, the ratio of depolarized to polarized received components increases out to 3-msec delay, then remains constant to about 8msec a s for the return from a complete range ring. again toward the limb a t 11.6msec where it is only approximately 50 percent of its value when a range ring is considered a s a whole. polarization experiments conducted by Hagfors, g. (1965). Results show that with the illuminating Beyond 8 msec, however, the ratio s ta r t s decreasing This behavior appears to confirm the results of previous 2. Work on the se r i e s beam-switch regulator (SBSR) and other hardware was completed at Observations at a Wavelength of 3.8 cm Haystack during the quarter, so that short pulse radar observations became possible. capability was used to make two different types of observation, namely measurement of the mean scattering l a w of the moon at a wavelength of 3.8 cm and measurement of the ratio of the back- scattering coefficients for the two orthogonal linearly polarized components, one aligned with the plane of incidence, the other orthogonal t o this plane. This new The determination of the mean scattering law w a s carried out by measuring the power a s a function of range for a number of different offsets of the center of the antenna beam from the sub-radar point. The experiment w a s performed by offsetting the antenna beam in steps along several radii across the lunar disk. diagram makes it possible to determine the angular scattering law within certain angular inter- vals for each antenna offset. The results thus obtained may be joined together to make a complete power vs angle plot for the entire range of angles from normal incidence to grazing incidence. The information contained in these data should provide a mean scattering law against which the lunar maps to be obtained somewhat la te r in this program may be compared. the large amount of data obtained has not yet been completed, but the mean lunar scattering law a t this wavelength should be available f o r the next Quarterly Progress Report. Accurate knowledge of the effect of the antenna polar The analysis of The polarization experiment w a s carried out in a way similar to the 23-cm experiment r e - ported in QPR (1966:1). The illumination was circularly polarized. Two receiver channels w e r e 20 Section I used to receive orthogonal l inear polarizations. The direction of linear polarization of one of the two channels was always adjusted to be aligned with the radius connecting the beam center and the center of the lunar disc. its E-field aligned with the plane of incidence. out the limited a reas necessary was achieved by range gating and by the limited angular extent of the polar diagram of the antenna beam. Preliminary analysis of the data has shown that the scattering is stronger f o r the component that is polarized (E-field) in the local plane of incidence, which was also the case at L-band (Hagfors, et g., 1965). coefficients at 3.8 cm is, however, Significantly closer t o unity than at 23 cm. tion of this result is not yet clear. It may be related to a gradual increase in dielectric constant with depth, with the assumption that the backscattering takes place from irregularit ies embedded in the surface layer. on top of the surface to cause appreciable scattering at 3.8 cm but negligible scattering at 23 cm. Further study of the results is required. In this way one channel would always correspond to one having The angular discrimination required to single The ratio of the two backscattering The interpreta- It may also be that small scale irregularit ies - small pebbles - are present C. THEORETICAL RESULTS 1. The Effect of Shadowing on the Backscattering of Waves from a Random Rough Surface As was explained in QPR (1966:l) the scattering from the lunar surface can be described in te rms of an exponential correlation function relating neighboring height-deviations on the surface. dominant out to an angle of incidence of 30 to 40", depending on wavelength. This description holds only for the so-called quasi-specular component which is Beckmann (1965a) recently advanced a theory to account for the shadowing effect and was able to predict quite accurately the scattering law of the moon on the basis of his theory (Beckmann, 1965b). Because it was felt that some of the physical principles underlying Beckmann's approach w e r e invalid, some work was started to check the theory of the shadowing. In Beckmann's shadowing theory as applied to lunar and planetary radar returns the scat- tered power is first determined without respect to shadowing, and then the shadowing is taken into account by multiplying this result by a function S(e ) which is basically the fraction of the total surface st i l l illuminated, and which varies from unity at normal incidence (e = 0) to zero a t grazing incidence (e = 90"). For the case of a random rough surface which introduces "deep" phase modulation in the scattered wave, it is well known (Hagfors, 1964) that the scattering in this type of approach takes place mainly from areas which are oriented so a s to provide specular reflection in the direction of the observer. Thus, in the backscattering case, only surface elements which a r e perpendicular to the line of sight of the observer will contribute significantly. shadowing, it seems, should therefore not be a question of the fraction of illuminated area, but ra ther a question of the fraction of illuminated, favorably oriented surface elements. Intuitively, in backscattering, it seems that a potential reflection point is much less likely to be in the shadow than an arbi t rary point on the surface. would overestimate the effect of shadowing by a considerable amount. The effect of I t was therefore felt that the "shadowing theory" In order to justify that the number of favorably oriented reflection points per unit surface a rea (per unit length in a convenient one-dimensional surface model) is indeed proportional to 21 Section I the backscattered power, we have to show first that this leads to the correct result in the geo- metric optics limit. portional to the radius of curvature at that point. In this l imit the amount of power returned from a specular point is pro- Let the surface height deviations from a plane mean surface be described by the function f(x), where x is the distance along the mean plane in the plane of incidence. extent of the surface and let Is be the extent of the total surface which is in the geometric shadow. Beckmann's shadowing function is then defined as: Let I be the total s (e ) = (1 - I ~ ) / L . ( 9 ) Let the number of points on the surface which have a normal along the line-of-sight to the ob- se rve r be NR and let the number of these which a r e in the geometric shadow be N shadowing function which w e believe is correct is defined by: The RS' = (NR - N R s ) / ~ R . In order to show that R ( 8 ) is the s t r ic t ly correct solution in the limiting case of geometric optics it is only necessary to show that the mean backscattered power is exclusively determined by the probability distribution of surface slopes. method of Kac (1943) . This can be shown quite readily following the Introduce the following variables: Let the joint probability density of 5 and 17 at a point x = xi be denoted by p(5, TJ ; xi) . probability that { crosses the level 5 = t a n 8 (i.e., condition for reflection point) with 7 TJ < TJ The < 1 t dv is: 1 2 When reflection occurs at an angle of incidence 8 f rom a point where d f/dx2 = T J ~ , the contri- bution to the power in the limit of geometric optics is proportional to 8 . I TJ I -I, i .e. , to the inverse of the magnitude of the radius of curvature at that point. The mean contribution to the backscattered power at an angle of incidence 0 f rom the interval xl , x1 t dx i s , therefore: The backscattered power per unit a rea (length) is therefore seen to be purely a matter of su r - face slope. for the cases when x In other words we determine: In the numerical analysis presented below w e essentially determine p(tan 8; x ) 1 is an arbi t rary point on the surface and when x1 is a point in the shadow. 1 NR p(tan 8; arbi t rary) = -I NRS p( tan8; shadow) = - . IS 22 Section I Our shadowing function R ( 8 ) as defined in (10) can be rewritten as: R ( 8 ) = ( N R - N RS )/N R = [ 1 r:) - --I S ( % ) ] b . (2) = (1 . p(tan8; arbi t rary)- -Is - p(tan8; shadow))/f . p(tan 0; arbi t rary) It can be seen that our R ( 8 ) is identical to S ( 0 ) only under the condition that p(tan Ff; sh.dnw) = p( tan8; arbitrary) . (16) Several vain attempts were made to obtain an analytical evaluation of the fraction of reflec- tion points in shadow. experiment was devised to compare Beckmann's shadowing function with the relative number of illuminated reflection points. This approach was finally abandoned and instead a digital computer Random uncorrelated noise samples were obtained by sampling receiver noise by means of The center frequency of the IF noise output was 200 kcps and the an analog-to-digital converter. bandwidth was I00 kcps. sample was about 50nanosec. peak range of the analog to digital converter was 3 volts. into 64 levels corresponding to s ix bit numbers. were stored on a magnetic tape for further analysis. The rate of sampling was 25 kcps and the t ime taken to estimate each The r m s value of the noise was about 0.25 volt, and the peak to This three-volt range was quantized The resulting uncorrelated noise samples F rom these noise samples a sequence of correlated noise samples can be generated by filtering in a computer. tN This filtering process can be expressed by the following sum f i = w . n . . 1 where w . a r e weight factors determined by the type of autocorrelation function desired for f . and where n . is one of the uncorrelated noise samples. function of the w . must be made identical to the one desired for fi. w e consider here only the case of a gaussian autocorrelation function for the surface. weight factors must then also be gaussian with a "width" which is I/& of that of the desired autocorrelation function. 3 1' It can be shown that the autocorrelation J For the sake of illustration J The The sum in (17) which should be carried between infinite limits was truncated by putting N = 50. exp-x ) . Z / G (Gautschi. 1964) as follows: The weight factors w. were chosen from tables of the function 2 J 2 2 w. =- expi- (j/20) ] , J G The autocorrelation function of f . should hence fall to e-' for a shift of 20 X f i = 28 points. magnetic tape was produced by means of the formula (17) with the weight factors (18). number of 1,290,600 correlated noise samples w a s produced and stored. correlated noise tape the autocorrelation function was computed for different sections of the A A total As a check on the 23 Section I 0 IO 20 30 40 50 6 0 SHIFT (points) 70 Fig. 16. for surface model. Comparison of computed and desired autocorrelation functions noise tape to test for stationarity. samples is shown in Fig. 1 6 and is compared with the expected autocorrelation function exp[-(1/2) ( i / 2 0 ) 1 . pected value. the expected one obviously stems from the truncation in the sum ( 1 7 ) . The autocorrelation function found for the f i rs t 648,885 2 A s can be seen, the autocorrelation estimated very closely fits the ex- The fact that the computed autocorrelation function is slightly narrower than The actual computational procedure used to a r r ive a t the relative a r e a shaded, the number of reflection points and the number of reflection points lost in the shadowed regions is best ex- plained with reference to Fig. 17. The beginning of a region of shadow between sampling points i and i - 1 is characterized by the condition: 1 1 I I I I 1 I I I ! 1 1 1 1 1 1 1 1 1 1 1 1 1 I l I I 1 I I I I I I I I l I ~ l 1 ' I X 1 + 1 Fig. 17. of shadowed regions. Surface model, definition of angle of incidence, representation 24 I t i Section I where 8 is the angle of incidence and where f(x) is the noise-waveform from which the correlated sai-iiples a r e derived. The derivatives int-olved were acttially computed f rom the samples hj-: dfi (20 - - dx - (fi+l - fi-f)/2 Ax where Ax is the spacing corresponding t o subsequent samples. When condition (19) is satisfied for i = k and f k is not already in the shadow a sequence of points is computed from the straight line formula: C = f k - (i - k) Ax . cotan8 (21 and a tes t is made to determine whether the points following point k lie above o r below this straight line. number be denoted by NS. is reinitiated. number of samples in the sequence an estimate of the fraction of the surface in the shadow is obtained. This should correspond to the shadowing function of Beckmann (1965a). Whenever f i < C the count of points in shadow is increased by one. Let this As soon as f . > C, the search for a starting point for another tangent By counting the total number of points in the shadow and dividing by the total At the same time a test is carried out to determine reflection points. These a r e charac- terized by the condition: and corresponds to the incident ray being perpendicular to the surface somewhere in the interval between (i - I ) Ax and i Ax. the number of such points which a r e also in the shadow is counted separately and denoted by NRS. fined by: The total number of such points is counted and denoted by NR and If the total number of samples analyzed is N, the required shadowing functions a r e de- S ( e ) = (N - NS)/N corresponding to Beckmann's theory and: R ( e ) = (NR - NRs)/NR corresponding to what we believe to be the more appropriate shadowing function. The r m s value h of all the f i on the correlated noise tape was found to be 0.1296247 and the The 0 numerical value for Ax was chosen so that the ratio L/h quantity L is the scale length in the gaussian autocorrelation function: assumed the values 1, 2 , 4 and 1 0 . 0 p(6x) = e x p [ - ( s x / ~ ) ~ l . (24) In view of the discussion in the previous section, we see that L = 28 Ax and hence that: L 28 ax - = ho 0.1296247 ' The numerical results of the computations are given in Tables IV, V , VI and VII. on the computational results, N As a check was normalized and plotted a s a function of angle of incidence 8. R 25 Section I 8 " 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 TABLE IV RESULTS OF NUMERICAL COMPUTATIONS FOR Ax = 0.004630 AND L/h = 1.0 NS 0 0 850 1 52333 130993 22441 1 320853 415797 506752 594407 6804 16 763548 84726 1 930256 101 3496 109871 1 1 190228 NRS 0 0 3 2 02 923 2194 359 1 4860 5802 6391 6608 6079 4735 2567 599 7 0 NR 35544 35286 34952 34427 3381 7 32815 31566 29968 27890 24872 2 1390 16784 11 140 5366 1 056 10 0 S(8 1 1.000 1.000 0.993 0.959 0.899 0.826 0.751 0.678 0.607 0.539 0.473 0.408 0.344 0.279 0.215 0.149 0.078 ~ R(9 ) 1.000 1.000 1 . 000 0.994 0.973 0.933 0.886 0.838 0.792 0.743 0.691 0.638 0.575 0.522 0.433 0.300 - Section I I ' I e o z J 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 TABLE V RESULTS OF NUMERICAL COMPUTATIONS FOR Ax = 0.009259 AND L/ho = 2.0 NS I NRS 0 0 0 22 1 748 10614 31040 66380 113992 170538 235080 305285 382209 466631 558407 659741 771208 0 0 0 0 0 2 19 70 144 191 189 114 213 4 0 0 0 NR 2478 1 241 89 23331 21936 20202 17888 15396 12350 9078 6046 3354 1 300 234 16 0 0 0 s(e 1 1.090 1.0oO 1.OOO 1.OOO 0.998 0.988 0.966 0.927 0.874 0.81 1 0.740 0.662 0.577 0.483 0.382 0.270 0.146 1 ~ 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.994 0.984 0.968 0.944 0.912 0.880 0.750 - - - 27 Section I e o 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 TABLE VI RESULTS OF NUMERICAL COMPUTATIONS FOR Ax=0.018519 AND L/ho=4.0 NS 0 0 0 0 0 0 0 682 472 9 17827 47818 103513 189903 31 1074 471 181 677 1 02 9421 16 NRS 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 NR 34569 31506 26798 20942 14710 9206 4988 2076 616 112 10 0 0 0 0 0 0 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.994 0.996 0.986 0.963 0.920 0.853 0.759 0.634 0.475 0.270 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 - - - - - - 28 Section i 8" 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 TABLE VI1 RESULTS OF NUMERICAL COMPUTATIONS FOR Ax = 0.0462% AND L/ho= 10.0 NS 0 0 0 0 0 0 0 0 0 0 0 0 638 7392 41 806 15371 0 40452 1 NRS 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 NR 20712 1 1522 4244 962 96 8 0 0 0 0 0 0 0 0 0 0 0 1.OOO 1.OOO 1.ooO 1.OOO 1.OOO 1.OOO 1.OOO 1.OOO 1.OOO 1.000 1.000 1.000 0.999 0.991 0.954 0.830 0.552 Section I ANGLE OF INCIDENCE 0 (degl Fig. 18. as obtained from noise theory and from computer program. Relative number of reflection points plotted against angle of incidence ANGLE OF INCIDENCE 8 (deg) Fig. 19. Comparison of shadowing functions S(0) and S,(e). 30 Section I The relationship between NR and 0 can be determined directly f rom noise theory (Kac, 1943). It is lmown that for a zero mean gaussian variable f with variance J, the probability of f passing through a level F is proportional to: 0 (26) 2 P ( F ) - exp[-F /WO1 . In our example the slope df/dx is a zero mean random variable with variance df d dx = 5 (a sin a x ) = aa cos ax = -cotan 8 - Hence, the probability of the perpendicularity condition being fulfilled for df/dx = tan 0 should be: (28 1 2 2 2 P ( t a n 0 ) - exp[-L tan 0/4h0] . This function is shown fully drawn in Fig. 18. waveform for specular points a r e shown on the same plot and for the same parameters. agreement between the direct analysis of the noise waveform and the predictions from noise theory is seen to be exceedingly good. The values determined by analyzing the noise The As a further check on the results w e compare the derived function S ( 0 ) a s defined in Eq. (9) with the expression for this function given by Beckmann (1965a) for the fraction of the surface in the shadow, viz: 1 S (0) = exp [- 3 t a n 0 erfc (L/2ho . t a n e l ] . B for the same values of L/ho for which w e carried out the analysis of the noise waveform. can be seen from Fig. 19 where both S ( 0 ) and S , ( 0 ) a r e plotted for comparison, the two functions can at best be said to be in qualitative agreement in that they approach unity at 0 = 0 and zero at 8 = 90". That is, the expression given by Beckmann (1965a), Le., Eq. (29) does not agree with our numerical analysis even when we assume Beckmann's definition [Eq. ( 9 ) ] for the role played by shadowing is correct. The violent and unexpected discrepancy between the two functions led us to suspect that section of our program which evaluates the fractional part of the surface which is in the shadow. of correlated noise samples by a sequence of samples taken on a sinusoidal waveform. For this type of waveform it is possible to estimate the fractional part of the surface which is in the shadow as a function of angle of incidence a s follows. into the shadow is determined by: As In order to put this section of the program to a test we replaced the sequence The point xi where the surface enters and xi = a r c cos (-cotan 8/aa ) . The point x where the surface emerges from the shadow is determined from the equation 2 31 Section I a . s i n a x l (x - x i ) cotan0 = a s i n a x The shadowing function S ( 0 ) therefore becomes (32) Figure 2 0 compares the results obtained from ( 3 3 ) with the results obtained from the computer program applied to sinusoidally varying samples - approximately 101 samples pe r cycle. The actual sinewave used in the comparison was of the form: f ( x ) = 0.183 . s in (x . 13.45) . (34) The noise samples were picked from the formula: f . = 0.183 . s in(0 . 0623 . i ) ( 3 5 ) and Ax = 0.00463. obtained by the two methods. We a r e therefore forced to the conclusion that the function S ( 0 ) found from the analysis of the noise samples is the correct shadowing function in Beckmann's sense in the particular case under consideration. We are , furthermore, led to believe that the expression given b y Heckmann [Eq. ( 2 9 ) ] is either misinterpreted by us or is incorrect. The comparison shows that there is very good agreement between the results _ _ _ DERIVED FROM COMPUTER PROGRAM (, - DERIVED BY DIRECT ANALYSIS 1 1 I I I 1 I I 0 8 - - 0 6 - 0.4 - 0 2 - I I 0 10 20 30 40 50 60 70 80 90 I I I 1 I I I Y ANGLE OF INCIDENCE 8 (deg) Fig. 20. Test of computer program for sinusoidally varying surface. The discrepancy between S ( 0 ) that Beckmann (1965a) should have arrived at, and SB(0) that he actually reached, possibly due to mathematical e r ro r s , makes it difficult to prove the point made in the introduction. then an examination of Tables IV and V clearly indicates that the simple shadowing theory over- estimates the effect of shadowing with respect to the theory which considers the fraction of re- flection points which a r e in the shadow represented by R ( 0 ) as purported in the introduction. When L/ho = 4.0 and 10.0 a s in Tables VI and VI1 a comparison between S ( 0 ) and R ( 0 ) is no longer possible because of the extremely small number of reflection points obtained at angles 0 If we take S ( 0 ) a s representative of the correct shadowing theory, 32 Section I large enough for shadowing to be of importance. Eq. (29) (which we do not believe to be the correct shadowing fnnction en thc basis of Beckmann's premises) it turns out that SB(8) appears to underestimate shadowing when L/ho = 1.0 and over- estimate i t when L/h Beckmann (1965a) may have arrived at an erroneous expression [Eq. ( 2 9 ) ] for S ( 0 ) as a If, on the other hand, R ( O ) is compared with = 2.0. 0 result of mathematical e r r o r a s pointed ou? by Shax (1966). We are, therefore, forced to conclude in general that recently advanced theories which attempt to explain the scattering from the lunar surface in te rms of Kirckhoff theory and with shadowing included a r e erroneous and tend to overestimate the effect of shadowing. lent agreement obtained between theor?. and experim-ental results, %e think, is Iurtuitous and certainly cannot be claimed a s a proof that Kirckhoff theory with locally plane boundary condi- tions can be validly applied to lunar returns for all angles of incidence. We are still of the opinion that the return at oblique angles of incidence must be explained in terms of discrete small scale scat terers having a radius of curvature comparable with the wavelength of the ex- ploring wave and thus violating the basic assumptions made in Kirckhoff theory. The excel- 3 3 II. P L A N S A N D P R E P A R A T I O N S I At the commencement of the contract period the Lincoln Laboratory Millstone Hill Radar was ready for use for lunar radar stiidies. As indicated Ir, QPR (1905: 1) 23-crn measurements have, therefore, been able to go forward without delay. operable for lunar studies during the first four months of the contract, and only became so during this reporting period. this instrument a t the present time. to make fine resolution radar maps of the moon's reflectivity. The work which must be performed before this can be accomplished is outlined in Sec. 11-A below. A s can be seen, this additional capability wi l l be brought about by the completion of a number of computer programs (outlined in Sec. 11-A-1) and the construction of some additional items of equipment (Sec. 11-A-2). Work in all these a reas has commenced but may not be completed for a further 2 to 3 months. The Haystack 3.8-cm radar was not However, there remain restrictions upon what can be accomplished with In partiriilar it is not preseotly possible ts cmplcjr the radar In order to gain some operating experience, and test those parts of the equipment and the computer programs that a r e complete (or nearly so), we intend to continue to operate the Haystack radar in conjunction with the Millstone data recording facilities. these recording facilities (which a re inferior to those being provided but not yet completed for Haystack) preclude the possibility of making maps containing the fu l l resolution that is both possible and planned. overall procedure to be employed later when the work of readying Haystack is complete. interim scheme can be put into effect with the addition of only one computer program for the Millstone SDS 9300 computer, which will perform the function of transcribing data samples into a magnetic tape record having the proper format. Instrumental limitations in Accordingly, this interim arrangement wi l l serve mainly to establish the The Whereas the Haystack radar has begun some of its program of observations and should be ready to embark on the mapping program some time this summer, the Lincoln Laboratory 8-mm radar requires a considerable amount of engineering design development and construction before it wi l l be ready. The nature of the work is outlined briefly in See. 11-B. A. PREPARATIONS FOR 3.8-cm MAPPING 1. Computer Program Development The computer programs required for the Haystack CDC 3200 t o provide radar maps of the lunar surface fall into four main categories: (a) Pre-run calculations and planning (b) Real-time tracking of a point on the lunar surface (c) Real-time data processing of radar returns (d) Post-run mapping of data onto lunar surface. The programs that wi l l accomplish these tasks a r e outlined in this report and a block diagram of their relationship is shown in Fig. 21. 35 Section II b - l TRACKING PRINT-OUT SPECTRA I RAW I MAPPING _ _ _ PRINT-OUT 35mm FILM POLAROID DATA I DISPLAY L 35mm FILM POLAROID CRAIG- FLECK MACHINE CONVERSION RAW DATA A H S Fig. 21. Block diagram of computer programs required for lunar mapping a t 3.8 crn. a. Pre-run Calculations The Moon Libration Program, MLIB, performs all non-real time calculations required for lunar work at Millstone and Haystack. elevation, range, Doppler, and related quantities for the sub-radar point. Four options a r e available. The basic output of this program is a printout of azimuth, (1) ( 2 ) ( 3 ) ( 4 ) Millstone Mode - Provides basic output, setting for Millstone range tracker, and a pointing tape. Offset Mode - Provides basic output and similar printouts for specified points on the lunar surface. Haystack Mode - Provides basic output and a libration tape for input to the mapping program (see Sec. 11-A-1-d). Planning Mode - Provides printout of observation periods for standard LAC quadrants, including resolution statistics. MLIB can be run for any ground station. It requires a binary moon ephemeris tape a s input, punched cards) once each year. This tape is prepared from Naval Observatory data (most of which is supplied to us on b. Real-Time Tracking The Haystack antenna is pointed by digital commands from a Univac 490 computer. The original pointing programs provided for real-time tracking of the lunar sub-radar point only. An addition has been made to allow for tracking in azimuth, elevation, range, and Doppler of a specified point on the lunar surface. The point may be designated in four ways: (1) Selenographic latitude and longitude ( 2 ) Direction cosines in selenographic coordinate system 36 I I - Section l l I ( 3 ) (4) Delay and angle. c. Real-time Data Processing Direction cosines in observer coordinate system A real-time data processing program, MOONRTS, has been written for the CDC 3200. This program wi l l accept the raw radar data, record it on magnetic tape, reformat and edit the data, and compute the echo power spectrum f o r each range interval over a specified integration period. The spectra a r e then recorded on magnetic tape for input to the mapping program (see Sec. 11-A-I-d). There a r e three modes of inputting the radar data: (1) NORMAL: Data are stored directly Lrts the CDC 3209 computzr cere via the Direct Data Interface (DDI). ( 2 ) TAPE: The raw data tape, recorded on a previous run, replaces the DDI. ( 3 ) SIMULATION: In this mode a signal of known frequencies is generated by the program, formatted to look like raw data from the DDI and stored on the d isk file for input. This allows us to "replay" a run if desired. The program utilizes a Tukey-Cooley subroutine to perform the Fourier analysis and a package of d isk file routines for data storage and retrieval. t o be implemented. time. A planned display portion remains This wil l allow simple monitoring of the data reduction process in rea l Because of the unavailability of certain hardware at Haystack, the f i r s t cut a t actual data processing will use the range-tracking machine at Millstone. sampled and digitally recorded on magnetic tape. tape recorded at Millstone to the same format a s the raw data tape created by MOONRTS. tape wi l l then become input under the existing TAPE Mode. Haystack radar data w i l l be A program is being written t o convert the This d. Post-Run Mapping The mapping program uses tapes from MLIB and MOONRTS as input. The latter tape provides power vs frequency for each range gate a s a function of time. represent samples of noise and others of noise plus a calibration pulse. in normalizing the signal plus noise data. power from the radar coordinate system involving delay and frequency to a coordinate system of selenographic latitude and longitude. are incoherently integrated until the mutually sliding coordinate systems demand a new trans- formation. The data are corrected for the effect of the beam pattern and scattering law, and are normalized to remove variations of the radar parameters. on a disk or on tape which wi l l be the input to a display routine. played on a monitor scope and/or photographed. Certain range gates These will be used The purpose of this program is to transform the The data from consecutive coherent integration periods The MLIB tape provides the information necessary to determine these intervals. Final output w i l l consist of a data file either There the maps wi l l be dis- The program, a s presently planned, does not include calibration or display capability. In conclusion, some portions of the lunar mapping software system a r e entering the test stage, but considerable programming effort remains. Appropriate contract help is being sought. 37 Section II 2. Equipment Development As mentioned earlier, a short pulse ranging capability became available in the Haystack system during this quarter. only by making use of the Millstone Hill data processing and timing equipment and the intersite coupling. remains some vital construction to be accomplished at Haystack, particularly in the data processing and timing areas, before fully self-contained operations can be undertaken. status of various important components is as follows: The lunar pulse measurements outlined in Sec. I-B-2 were possible It is not feasible to do the full lunar studies measurements task in this way. There The The transmitter is operational. I t must, however, still be used at slightly reduced power (75 kw) because of limitations in the series-beam switch regulator . The analog-to-digital converter and multiplexer system to be used to introduce signal data into the CDC 3200 real-time data processing computer is virtually complete. The computer interface has been checked out. There remains only the connecting of real-time clock data to the computer and the interfacing of the radar timing system to the analog-to-digital converter controls. A low frequency amplifier, filter, and phase detector system is currently under development. This sub-system accepts 2-Mcps data from the radar receiver and converts it t o a zero frequency signal (through phase detectors), producing quadrature components of the signal. and converted to digital data for processing by the computer. The radar receivers a r e operational. to provide an improved signal calibration system and easier conversion between various experimental arrangements such a s changing from linear t o circular polarization. The receivers have been operated with- out the benefit of cooled parametric amplifiers for lunar work during this quarter. With cryogenic cooling, a system temperature of 200°K is possible. Radar system timing required for the lunar mapping is the largest piece of equipment remaining to be constructed. control the transmitter modulation and receiver TR gating. It also must control the analog-to-digital converter and reference calibration timing with an offset r a t e so that the motion of the moon is tracked automatically in range. The equipment required to control the receiver Doppler frequency timing from the U490 pointing computer is complete but has not been checked. These video signals a r e then passed through matched fi l ters Work is currently in progress The timing equipment must B. PREPARATIONS FOR 8-mm OBSERVATIONS A 28-foot parabolic antenna system operating at the shortest wavelength (8.6 mm) that we plan to employ f o r lunar studies, is mounted on the roof of the main Laboratory building. being the smallest of the three antennas, the 28-foot parabola has the highest gain by virtue of its short operating wavelength. a $-inch layer of polymer was made to take up the proper parabolic shape by spinning the metal and fiberglas support structure. polymer and this in turn was given a thin coating of plastic t o protect it f rom the weather. method of constructing large precision parabolas has been described by Dawson (1 962) . Despite This parabola was formed by a spincasting process in which A thin reflecting layer of zinc was flame-sprayed over the This In order to feed an antenna of this s ize at millimeter wavelengths a special. " r e a r feed" w a s devised. This consists of an open-ended circular waveguide operating in its dominant mode 38 Section I I (TEI1) with a circular reflecting d i s k positioned approximately 3.5 wavelengths in front of the open guide. also provides weather protection. ment in which the feed point has been chosen s o close t o the prime focus that a plane secondary reflector is required in place of the hyperbolic subreflector normally encountered. This novel feed arrangement has an advantage over most other types in thzt EC l i r g e supportLq-g s t ruts are required, which would introduce aperture blockage and increase the sidelobe levels. The feed design has been described by Keeping (1960) and the electrical performance of the antenna has been reported by Fitzgerald, A small hemispherical radome serves to hold the reflecting disk in position and The system may be likened to a Cassegrain feed arrange- &. (1 963). The antenna was installed on the roof of one of the main T.ahoratm-y buildings in Lexir?gton b. 1962, and employed to make radar studies of the moon in April and May 1963. The performance of the antenna can rapidly be checked at any time using permanently installed pattern measure- ment equipment. To permit focusing of the antenna without the use of flexible waveguide o r movable joints, all the microwave components of the radar and pattern receiver a re mounted on a single large plate in the equipment housing. the entire plate and feed. azimuth-elevation drive system, which, unfortunately, is inadequate to permit the use of position- servo drives. loops with reference to a boresighted-television system. gearing and flexibility of the mount base, the 6-inch lens system and television camera are installed directly on the reflector backup structure. The rate-servo controls and television monitor a r e located in a nearby building along with the other non-microwave portions of the multiplier. Adjustment is accomplished by movement of The antenna is mounted on an Horizontal polarization is employed. The prime method of directing the beam is manual control of rate-feedback-servo To avoid e r r o r s due to inaccurate The 1 0-watt transmitter consisted basically of a floating-drift-tube klystron oscillator phase- locked to the required frequency which w a s generated by a crystal-controlled frequency-multiplier chain. a multiple superheterodyne which converted the incoming signals to a nominal IF of 2.5 kcps where it was examined in a bank of ten filters 170 cps wide and spaced 100 cps apart. bank at the output was used because of uncertainty as to the stability of the multipliers; it also guarded against signal loss in case of incorrect Doppler compensation. receiver was a crystal mixer. et al. (1963). The spectral width of the radiated signal was not more than 100 cps. The receiver was A filter The first stage in the Further details of this radar system have been given by Lynn, _ - Since its use as a moon radar in 1963, the 28-foot parabola has been employed largely for For this purpose a larger feed line has been radiometric observations at 1.5-cm wavelength. installed which may, if used at 8 mm, yield a 2-db improvement in the performance of the radar. However, it is possible that when coupled t o the diameter-reducing taper (required to illuminate the dish properly at 8-mm wavelength) this large feed line may develop high loss due to the trapping of unwanted modes. reveal any evidence of high loss. on the bench. procure. A set of experiments using the antenna range has s o f a r failed to Further tests on the loss in the line with taper will be made These tests require special waveguide connections which wi l l take two months to As a first step in reactivating the radar it is proposed to reinstall the 10-w equipment employed by Lynn, et al. (1963). Some components of this system have been rebuilt. These -- 39 Section II modifications have provided an improvement in the overall frequency stability (now 5 cps) and the reliability. The transmitter power will still, however, be only 10 w, which is quite inadequate for the work planned. Lunar reflection measurements made with this radar will serve to famil- iarize the engineers with the equipment and operating procedure, but a r e unlikely to add signifi- cantly to the results reported by Lynn, 5 &. (1963). A higher power transmitter is of the utmost importance. A modest increase (to 50w) is expected in June when two 50-w tubes (originally scheduled for delivery on 1 5 February) should arr ive. than the existing 10-w tube. It is not c lear at present whether it wi l l be more difficult to phase-lock these tubes For measurements in which any degree of detailed resolution (either in delay or frequency) is required, a much larger increase in transmitter power is vital. conducted for the construction of a 1-kw tube, and a purchase order will be placed. approvals fo r the procurement of the 1-kw tube seem likely to delay the s t a r t of the lunar observa- tions with the high power transmitter. Also required for the high power transmitter is a new frequency multiplier chain having a higher level output and better frequency stability than the existing one. a lso in getting a source (at 5 Mcps) with a spectrum pure enough to withstand multiplication to 35 Gcps. oscillators and multiplier chains that promise to be satisfactory. Negotiations have been Delays in There has been considerable difficulty in getting bids on this multiplier chain and These troubles now appear to have been overcome; orders have been placed for Extensive investigations have been made of the possibility of obtaining a two-channel para- metr ic amplifier that would yield an appreciable increase in sensitivity. prospect that this can be accomplished in the t ime available, and for the duration of the present program balanced mixers wi l l be employed as f i r s t stages in the receivers . There seems little The high-power radar will have the capability of (1) transmitting circular polarization and receiving circular polarization in the same sense and in the opposite sense; ( 2 ) transmitting circular and receiving two orthogonal linear polarizations, oriented at wil l ; ( 3 ) transmitting linear polarization, oriented at wil l , and receiving that linear polarization and the orthogonal one. for electroforming them a r e now being made. Waveguide elements for performing these functions have been designed, and the mandrels Operation at low power (either 10 or 50 w ) is expected this summer. Full high power opera- tion is hoped for during the f i r s t quarter of 1967. 40 111. N O T E S ON F U T U R E WORK A. EXPERIMENTS TO DETERMINE THE DEPTH OF ALUNAR SURFACE LAYER 1. Introduction The purpose of this section is to consider how it might be possible to determine the depth of the upper layer of light material on the lunar surface by radio methods. One of the most di- rec t approaches to placing some limit to the depth would be to repeat the experiment performed by Hagfors, 9 &, a s described in Q P R (1966:1), at increasing wavelengths. Thus, in the next section we discuss the way the experiment could be conducted at longer wavelengths where diffi- culties will be encountered due to ionospheric effects. In Sec. 111-A-3 we discuss another approach which depends for success on the layer being of roughly constant thickness over moderately large regions of the lunar surface. The experiment would, however, reveal the presence of a continu- ous gradation in density with depth (should this be the case). suitable for determining the layer depth if this is substantially greater than 4 to 5 m. depth is very great (e.g., 100 m), then it appears that it could be determined, at least i n princi- ple, from short pulse experiments that a r e discussed in Sec. 111-A-5. These schemes a re probably un- If the 2. The depth of the layer of light material is presumed to be i r regular but must be greater than Polarization Experiments at Longer Wavelengths about one wavelength for pronounced polarization effects to be observed. A straightforward way to attempt to place an upper limit on the depth of the layer would be to repeat the experiment de- scribed in Sec. I-J of QPR (1966: i ) at increasing wavelengths, until the polarization effects dis- appear. Unfortunately this is more difficult than i s at f irst obvious for the following reasons. (a) Ionospheric Faraday rotation of a linearly polarized wave increases with wavelength a s hz. wave in the ear th 's ionosphere i s usually not larger than about I O " and hence can be compensated o r even neglected. For a wavelength of 3 m the one way Faraday rotation may be a s large a s 1 0 o r so complete rotations. Variations occur over short periods of time due to both the changing ge- ometry of the r ay path through the ionosphere (as the moon's motion is followed), and the diurnal variations of the electron density in the iono- sphere. At midlatitudes the rate at which the total rotation may change has been found on occasion to be a s high a s 4"/minute at a wavelength of 3 m. In the observations performed at Millstone Hil l an adequate resolution in the frequency domain could be obtained using 2-cps fi l ters. However, the overall bandwidth of the reflected signals var ies a s $/A and thus to obtain the same resolution at 3 m one would require fi l ters - 0.16 cps wide. At a wavelength of 23 cm the Faraday rotation of a plane (b) Faraday rotation may be expected to be sufficiently serious at all wavelengths longer than In order to remove the effects of Faraday rotation about 30 cm so that it could not be ignored. it would be necessary in fact to determine continuously the total amount of rotation Q . could be accomplished by transmitting a linearly polarized wave (in place of a circular one) and receiving both orthogonal components. This 4 1 Section I l l By comparing the intensity of the two components one would obtain the ambiguous fractional rota- tion A n where fi = nr f A 0 f r / 2 . (36) However, by repeating the observations at another frequency separated from the f i rs t by df, R can be determined from the observed change dR from where f i s the radar frequency. In practice one might transmit alternate pulses at the two fre- quencies and hence continuously determine dR. F rom these measurements it would be possible la te r to determine D a s a function of time. One could then select f rom the observations those periods where the transmitted linear signal lay parallel to or perpendicular to the axis of the moon's libration. for the center Doppler s t r ip only, one would be able to obtain the rat io of the two transmission coefficients. By processing these periods to obtain the echo power a s a function of delay Whereas in principle it should always be possible to compensate for Faraday rotati.on (effect a), it will not always be possible to maintain the frequency resolution of the radar necessary to resolve a central s t r ip of the disk a s the wavelength i s increased (effect b). We have seen that for h = 3 m we require a filter width of the order 0.16 cps. l e s s than the frequency stability imposed by phase fluctuations in the ionosphere. width that can be achieved ultimately depends upon (a) the overall stability of the radar system (which probably improves with increasing wavelength), and (b) the stability of the propagation med iu m. This might be comparable with or The fi l ter The Millstone Hill radar operating at 23 cm has been shown to have an overall frequency stability, i.e., (a) , above, on the order of 0.1 cps (Evans, d., 1965), and it is expected tha t at longer wavelengths even better stability should be realized, since fewer multiplications of the basic frequency standard a r e required. better than 0.05 cps should be obtainable at 3-m wavelength. It seems safe to assume that an overall stability of The influence of the ionosphere on the frequency stability of radar transmissions, Le., (a), above, has not been the subject of much experimental investigation. Irregular density fluctua- tions a r e known to be present for much of the time and these give r i s e to scintillations of radio s ta rs . The density fluctuations may be seen on ionospheric sounders as Spread F echoes. The world-wide occurrence of Spread F i s shown in Fig. 22 . currence rate is least between 30" and 50" geomagnetic latitudes. 7.84-m wavelength have been conducted from within this range of latitudes (Evans and Ingalls, 1 9 6 2 ) and the echoes were found to be spread by ionospheric scintillations according to For the northern hemisphere the oc- Observations of the moon at P ( f ) df a exp [- l(ai)'] 2 A f m df where P(f) is the power spectrum of the fluctuations and Afm had a value of 0.2 cps. ticipated that the mean intensity of these fluctuations var ies a s the secant of the zenith angle It i s an- 42 Section 111 90N 60N 3011 0 305 6 0 5 905 GEOMAGNETIC LATITUDE (degf Fig. 22. Percentage Occurrence of Spread F as observed by the topside sounder Alouette. Spread F i s associated with ionospheric scintillations of mdio sources. and inversely a s the square of the wavelength. servations a r e conducted with the moon in the zenith at say 30"N geomagnetic latitude, we might anticipate that the spectral broadening introduced by the moon and the ionosphere will on the average be roughly comparable at a wavelength of about 6 m. may be considerably better but this would not be known a priori . In the most favorable circumstances, when ob- On occasion the effective "seeing" -- In conclusion then, it i s considered that the Millstone Hill experiment could be repeated without ser ious difficulty a t wavelengths up to 3 m, and under favorable circumstances perhaps to 6 m, but not at longer wavelengths due to the phase instability imposed by the ionosphere. 3. Other Observations A second type of measurement which would yield the depth of the layer of light material i s Let u s suppose that a small a r ea on the lunar sur - based upon observing interference effects. face may be isolated in which the layer depth d i s comparatively uniform. the reflection coefficient will be At normal incidence Rl + R2 + 2 , / v i ( I - 2 s in 2 27rd/A R(0) = I + RiR2 + 24% (I - 2 sin2 2nd/A (39) where Ri i s the reflection coefficient of the upper interface and R that of the second interface. It can be seen that the reflection coefficient is greatest for d = h / 2 , A, 3h/2 and least for d = A / 4 , 3 A / 4 , 5 A / 4 . if Rl = R will cause the reflection coefficient to change l e s s with wavelength than predicted by (39). the actual depth departs f rom the mean in a random fashion we may expect the depth of the f i r s t minimum in the reflection coefficient to be decreased. d = 3 A / 4 , 5 h / 4 w i l l be more seriously affected and may be totally obscured. fore, that only the first minimum can be recognized. 2 When d has a value of m A / 4 the reflection coefficient may fall to a very low value In practice the variation of the depth d over the surface corresponding to cl =&. 2 If Successive minima corresponding to It may be there- Table VI11 gives the operating frequencies 43 Section Ill Mi nirnum v 4 3 v 4 7 v 4 5 x/4 9x/4 TABLE V l l l FREQUENCIES AT WHICH THERE WILL BE A MINIMUM IN THE REFLECTION COEFFICIENT FOR DIFFERENT VALUES OF THE LAYER THICKNESS d Frequency W P d d = l m d = 5 m d = 2% 75 15 3 225 45 9 375 75 15 525 1 05 21 675 135 27 a t which m i n i m a might b e e x p e c t e d f o r v a l u e s of d = 1, 5 and 2 5 m e t e r s . m i n i m a a r e evenly s p a c e d in f r e q u e n c y , and b e c a u s e r e l i a b l e m e a s u r e m e n t s cannot b e m a d e f rom the e a r t h a t f r e q u e n c i e s of less t h a n about 2 0 IL'Icps (owing t o i o n o s p h e r i c e f f e c t s ) the f i r s t m i n i - m u m m a y not be o b s e r v a b l e if d > 5 m e t e r s . It c a n b e s e e n t h a t t h e L e t u s suppose that a s e a r c h i s t o b e conducted f o r a m i n i m u m i n t h e r a d a r cross s e c t i o n u s i n g the 1000-ft a n t e n n a a t t h e A r e c i b o I o n o s p h e r i c O b s e r v a t o r y . In o r d e r t o i s o l a t e a r e g i o n in which the waves a re n e a r - n o r m a l l y incident on t h e l u n a r s u r f a c e , a p u l s e length of 100 p s e c might b e employed , and the e c h o f r o m the leading e d g e only e x a m i n e d . Such a p u l s e would i l - l u m i n a t e a reg ion a t the c e n t e r of t h e v i s i b l e d i s c having a r a d i u s of about one tenth ihe l u n a r r a d i u s . T a b l e I X l i s t s the a s s u m p t i o n s m a d e in the c a l c u l a t i o n s in o r d e r t o a r r i v e a t a l i s t of the p a r a m - e t e r s of t h e r a d a r s y s t e m tha t might b e r e q u i r e d . T h e s e p a r a m e t e r s a r e then l i s t e d in T a b l e X. It h a s b e e n a s s u m e d that a s i g n a l - t o - n o i s e r a t i o of 1 0 d b i s r e q u i r e d , and that a r e c e i v e r band- width of 1 0 k c p s i s e m p l o y e d in o r d e r t o m a t c h the s p e c t r a l width of the t r a n s m i t t e r p u l s e . s y s t e m t e m p e r a t u r e s a s s u m e d a r e t h o s e of the s k y background in dirctct ions away f rom t h e p l a n e of t h e g a l a x y o r t h e sun . T h e i n c r e a s e in t e m p e r a t u r e with wavelength, t o g e t h e r with t h e re- duced a n t e n n a gain, a r e joint ly r e s p o n s i b l e f o r the h i g h e r t r a n s m i t t e r p o w e r s r e q u i r e d a t t h e l o n g e r wavelengths . t o b e employed , t h e t r a n s m i t t e r p o w e r s r e q u i r e d would b e some 250 t i m e s t h o s e l i s t e d in T a b l e X. T h u s the r a n g e of v a l u e s of a n g l e s of i n c i d e n c e e n c o u n t e r e d would b e f r o m 0 to 7 " . T h e If a n a n t e n n a t h e s i z e of the J o d r e l l Bank Mk I i .e . , 250-ft d i a m e t e r , w e r e Ionospher ic s c i n t i l l a t i o n s should not h a m p e r a n e x p e r i m e n t of t h i s kind a s we r e q u i r e p h a s e However , s t a b i l i t y o n l y o v e r a n i n t e r v a l e q u a l t o the length of t h e t r a m s m i t t e r p u l s e (100 p s e c ) . F a r a d a y ro ta t ion would need t o b e c o m p e n s a t e d e i t h e r by t r a n s m i t t i n g a n d r e c e i v i n g c i r c u l a r l y p o l a r i z e d waves or by t r a n s m i t t i n g one l i n e a r a n d r e c e i v i n g both o r t h o g o n a l c o m p o n e n t s . S e v e r a l d i f f icu l t ies e x i s t in a n e x p e r i m e n t of t h i s type which should b e touched upon. I h e t o the l i b r a t i o n of t h e moon, t h e s u b r a d a r point wil l b e d i f f e r e n t f r o m day- to-day , and c o n s e - quent ly t h e value of d m a y v a r y with t h e t i m e of o b s e r v a t i o n . It would, therefor t , , be p r e f e r - a b l e t o m a k e o b s e r v a t i o n s o v e r t h e e n t i r e f r e q u e n c y r a n g e of i n t o r e s t i n a s s h o r t a n i n t e r v a l of 44 Section 111 x (m) 3.3 5 7.5 10 15 TABLE IX ASSUMPTIONS MADE IN COMPUTING THE TRANSMITTER POWER REQUIRED FOR LONG WAVE OBSERVATIONS OF THE MOON AT THE ARECIBO IONOSPHERIC OBSERVATORY f (Mcps) 100 60 40 30 20 Total radar cross section Fraction of toto1 cross section observed using a 100-pc pulse Pulse length Receiver bandwidth System temperature Antenna employed System Temperature (OK) 1 03. O I 03e5 1 04- O 1 04- 1 04- 1o5eo Antenna efficiency Required signal-to-noise ratio System (w) T r a m itter Power 1.5 13 90 300 2000 5000 2 0. Oha 40 percent 100 p=c 10 kcps Set by sky background (see Table IV) 1000-ft spherical reflector at Arecibo, Puerto Rico 40 percent +10 db TABLE X PARAMETERS OF LONG WAVE RADARS EMPLOYING THE 1000-FT ANTENNA AT ARECIBO 20 1 15 Antenna Gain (db over isotropic) 46 42 39 36 32.5 30 Observing Time (min) 70 120 210 240 350 480 45 Section I l l t ime a s possible. cycles must be taken in o rde r to reduce the uncertainty in the value for the mean echo power. For the leading edge echo observed at 100 Mcps the fading period would typically be 1 0 seconds, and will increase l inearly with wavelength. Thus, if we a r e to reduce the result ing uncertainty in the measurements to say *5 percent, we require the observing t imes listed in the las t column of Table X. may be viewed from the Arecibo instrument in a single day. is made, it is clear that a swept frequency r ada r s y s t e m cannot be employed at the longest wave- lengths. A separate r ada r sys t em i s required fo r each frequency that i s to be examined. The problems of operating so many r a d a r systems simultaneously a r e not insuperable, but c lear ly the experiment constitutes a major undertaking. Radio echoes f r o m the moon fade, however, and an average over many fading At 15 Mcps the t ime required (8 hours) i s longer than the t ime for which the moon Even if a sacr i f ice in the accuracy Let u s suppose that a system has been devised which will measu re the lunar r a d a r c r o s s section at intervals of s ay 5 Mcps over the range 1 5 to 1 0 0 Mcps. of accurately calibrating these r a d a r systems. known c r o s s section, f o r example, a metal sphere placed in ea r th orbit . A l - m sphere placed in a synchronous orbit would be a poorer target than the moon by 100db. sphere must be placed in a lower altitude orbit . ame te r (e.g. , 5 m ) so that i t s c r o s s section will r ema in appreciable when observed at the longest wavelength. longer be possible to calibrate the r a d a r systems at will - e.g., during the course of the measu re - ments. pa rame te r s of each of the sys t ems . ally be determined adequately, but there i s no simple method by which the antenna gains could be established in the case of the Arecibo antenna, where the gain i s a function of the zenith angle. There r ema ins the problem 2 Ideally one would do this against a target of It follows that the Fur the r , the sphere must have a l a rge di- An altitude of about 1000 to 2000 km might be adequate, but unfortunately it would no The alternative to using some form of test target i s to determine separately the r a d a r The t ransmit ter powers and sys t em t empera tu res can u s u - Many of the problems encountered in this experiment (in par t icular the ionospheric effects) However, a new could be obviated by placing the r a d a r ( s ) in a satell i te in orbit about the moon. set of problems then a r i s e s owing to the motion of the satellite causing it to sample different a r e a s of the surface beneath. 4. Other Models of the Surface Giraud (1965) has considered a model of the surface in which the dielectric constant E in- c r e a s e s f rom unity l inearly with depth over some finite distance d and then becomes constant a t some value c2 . c2 = 5 f o r a number of values of d. tion would provide a tes t of this model. k in the reflection coefficient but simply a wavelength dependence, a wider spacing of the f r e - quencies might be employed. layer alone when the wavelength h = 3 0 d . h if the layer depth d exceeds about 1 meter . then be recognized. Here a satell i te experiment, i .e. , a lunar orbiting vehicle, may provide the F igu re 2 3 shows the variation of reflection coefficient to be expected for the case The same type of experiment described in the previous sec - Because one would not now be searching for a minimum The reflection coefficient r eaches that attributable to the base Since the observations would be limited to wavelengths 20 m by ionospheric effects, the full range of reflection coefficients will not be encountered The fact that this model may be co r rec t would not 46 . Section Ill t 1 1 10 100 A l C r n ) c2 = 5 Fig. 23. Variation of reflection coefficient of surfoce in which uppermost layer hos o dielectric constont that increases lineorly with depth over a distome d and then becanes constont a t e = 5.0. solution, but an accurate calibration of the multifrequency radar system employed would be ex- tremely difficult. 5. A Very Deep Layer None of the methods discussed so far would be capable of determining from ear th the depth of a very deep layer of material, i.e., d > 5m. The most direct method to be employed in such a case would be to use an extremely short pulse radar and search for echoes separated in delay arising from reflections at each interface. In order to remove the dispersion of the echo due to the variation of surface height it would be desirable to localize a region a t the center of the lunar disc using extremely high angular resolution afforded by a large antenna. of the moon's surface will cause the mean height h to vary by an amount The curvature Ah = t'/a (40) where f is the radius of the illuminated region and a the radius of the moon. that the depth of the layer d i s 100 meters. Ah = 15 m. This could be isolated with an antenna having a diameter of 5 X l o 4 wavelengths. antennas in existence having diameters as large a s l o 3 wavelengths, and hence this scheme is impracticable at present. Let u s suppose Since we require that d >>Ah let u s take a value The region illuminated would be required to have a radius t = 4 km. Unfortunately there are f e w The remaining possibility open to u s is that of performing an aperture synthesis. In this experiment the autocorrelation function of the echoes from the center of the disc is obtained repeatedly throughout a day when the direction of the axis of libration changes by 180". then possible to construct the two dimensional autocorrelation function of the complex echo It is 47 Section I l l amplitude whose double F o u r i e r t r a n s f o r m is the br ightness distribution. operation at successive range intervals w e should encounter a point where the echo f r o m the second interface l i e s in the center of the br ightness plot, and that f r o m the upper interface at the s a m e range l i e s in a halo around it. In o r d e r to achieve an adequate range resolution to r e c - ognize a layer of 100 m e t e r s depth we would r equ i r e a pulse length in the range 10 to 30 nanosec. The duration over which the autocorrelation functions a r e formed would define the s i ze of the synthesized aperture and hence the resolved region on the lunar disc . By performing this Because ionospheric scinti l lat ion e f f ec t s vary a s A 2 and the coherence t ime of the ref lec- 3 . tions as A , there is a l a rge penalty (A ) in attempting this experiment a t a long wavelength. suggested system would be to employ the Haystack antenna sys t em at a wavelength of 3.8 cm. The r a d a r would b e required to be completely coherent for a period of m o r e than 10 seconds in o r d e r t o resolve regions of the surface having a r ad ius of 2 km. Table XI l i s t s the p a r a m e t e r s of the r a d a r system required. bution of echo power with delay has never been determined using pulses a s short as this. How- ever , by extrapolating f r o m e a r l i e r measurements a t this wavelength Safran (1 964) h a s obtained a value fo r the c r o s s section of the lunar surface at n o r m a l incidence of Odb per square me te r . It follows that a region some 2 km in radius will have a c r o s s section of -2 X 1 0 the path l o s s wi l l be -300db. A reduction could be achieved by degrading the depth resolution f r o m 1 . 5 m (a value obtained by matching the pulse length to the depth of the curvature of a region 2 k m in r ad ius ) to, say, ten t imes as much. be smoother than - * I O m over a region some 2 km in diameter . t r ansmi t t e r power to 6MW which might perhaps be achieved using a 0.5-MW C W t r ansmi t t e r to- gether with a 12:i pulse compression scheme. A * The path l o s s a s sumed i s somewhat uncertain since the d i s t r i - 7 mz and that The t r ansmi t t e r power required i s r a t h e r l a rge . This would hardly be a se r ious lo s s since it is unlikely that the surface anywhere will This would reduce the required TABLE XI PARAMETERS OF A VERY SHORT PULSE RADAR USING THE HAYSTACK ANTENNA Assumed path loss Frequency Antenna gain Pulse length Receiver bandwidth System temperature Peak transmitter power required for unity signal-to-noise ratio 300 db 8000 Mcps 66 db 10 nanosecs (corresponding to 100 Mcps a resolution in depth of 1.5 rn) . 10JoK 6 X 107W 48 Section 111 6. Conclusion We have mtlined in QPE%(?366:?) the radar evidence for the existence of a layer of light m- ter ia l on the lunar surface, and here we considered several ways in which the depth of this ma- ter ia l might be established. the presence of this material was recognized, at longer wavelengths. cedure might be satisfactory for a depth of less than 3 meters. ity of the ear th ' s ionosphere, problems would be encountered in making observations at longer wavelengths. surface by spectral analysis of the echoes. lengths of up to about 15 meters as it depends oniy on observing the reflection coefficient vs fre- quency. the lunar surface density at a depth of up to 4 meters. a continuous gradation of density over a depth of 1 meter or less. The f i rs t of these would simply be to repeat the experiment in which It seems that this pro- Due to the limited phase stabil- This would make it difficult or impossible to isolate separate regions of the lunar The second method discussed can be applied at wave- This method is exceedingly difficult to implement, but could detect a discontinuity in This same technique would also reveal If the depth of the material is very large, e.g., 100 m, then it seems it might be inferred f rom observations in which extremely short pulses seconds) a re used, to resolve the re- flections from the two boundaries. In order to isolate a small portion of the lunar surface at the center of the disc that is normal to t h e ray path, a scheme of aperture synthesis would be necessary. negligible and the coherence time required of the radar hopefully can be achieved. This might best be accomplished at short wavelengths where ionospheric effects a r e ACKNOWLEDGMENTS The work of most of the technical personnel of Group 3 1, Surveillance Techniques, which operates the facilities of the Field Station, in pre- paring and conducting the work reported to date is gratefully acknowl- edged, as is the work of members of Group 46, Microwave Compo- nents, in cooperating with D r . McCue on the 8.6-mm radar. The use of the facilities of the Lincoln Laboratory Millstone-Haystack complex, provided by the U.S. A i r Force, is also gratefully acknowledged. 49 Beckmann, P., "Shadowing of Random (1965a). , "Radar Backscattering Res. 70, 2345-2350 (196533). - REF ER ENC ES Rough Surfaces," IEEE T r a n s . AP 13, 384-388 from the Surface of the Moon," J . Geophys. - Brunschwig, M., 4. (10 authors), "Estimation of the Physical Constants of the Lunar Surface," The University of Michigan Rep. 3544- 1-F (1960). Daniels, F. B., "Radar Determination of the Root Mean Square Slope of the Lunar Surface," J . Geophys. Res. 68, 449-453 (1963a). , "Radar Determination of Lunar Slopes: Correctiqn for the Diffuse Component," J . Geophys. Res. 68, 2864-2865 (196313). Davies, R.D., and Gardner, F. F., "Linear Polarization of Lunar Emission," J . Res , Natl. Bur. Standards E D , 1613 (1965). Davies, J . R., and Rohlfs, D. C., "Lunar Radio-Reflection Properties a t Decameter Wavelengths," J. Geophys. Res. 69, 3257-3262 (1964). Dawson, J . W., "28 f t . Liquid-Spun Radio Reflector for Millimeter Wavelengths," Proc. IRE - 50, 1541 (1962). Evans, J .V. , Brockelman, R.A., Henry, J .C . , Hyde, G.M., Kraft, L.G. , Reid, W.A., and Smith, W.W., "Radio Echo Observations of Venus and Mercury a t 23 cm Wavelength," Astron. J . 3, 486-501 (1965). Evans, J .V. , and Hagfors, T., "On the Interpretation of Radar Reflections from the Moon," Icarus 2, 151- 160 (1964). 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Shaw, L., "Comments on 'Shadowing of Random Surfaces'," IEEE Trans. AP 14, 253 (1966). Soboleva, N . S . , "Measurement of the Polarization of Lunar Radio Emission on a Wave- length of 3.2cm," Astron. J. USSR 39, 1124-1126 (1962). Troitsky, V.S., "Theory of Lunar Radio Emission," Astron. J. USSR 3-l. 511-528 (1954). 533- 542 (1964). 34-41 (1964). - 5 1

Radar studies of the moon Quarterly progress report no. 2, 1 Feb. - 30 Apr. 1966

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