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We compute the linear parametric convective amplification of electron plasma waves by an O mode pump propagating vertically into a vertically stratified ionosphere. The upshifted plasma line compares favorably with Arecibo observations, center frequency, spectral width, and possibly amplitude when the radar is aimed in a northerly direction. The dependence of the computed enhanced plasma line shape upon density scale length, electron-to-ion temperature ratio, pump power, density gradient scale length, and backscatter radar incidence angle is investigated.

A 32-element HF-phased array has been used to study the angular spectrum of spread F returns from an ionosphere modified by the powerful radio frequency heater transmitter at Platteville, Colorado. The diagnostic radar is a coherent pulse system that provides an angular resolution of 2.7° at the midband frequency of 7.5 MHz, a range resolution of 30 km, and a Doppler resolution of 0.08 Hz. The results are presented in the form of sky maps (brightness versus azimuth and elevation) of the returns as a function of group delay, Doppler shift, polarization, and sounding frequency. The principal result is that the returns that suffer the greatest group delay at a given sounding frequency come from a direction looking up the earth's magnetic field and exhibit negative Doppler shift. Ray-tracing simulation of the observed dependence of the range and the Doppler on the angle of arrival of the returns supports the view that the heater-generated spread F is caused by field-aligned ducts produced within the heated volume. A simulation run for Arecibo, Puerto Rico, in comparison with that for Platteville, reveals that the group delay spread is about the same and the angular spread is approximately in the same ratio as the heater beam widths at the two locations.

A coordinated program between satellite, VHF radar, and optical auroral observations was carried out in Alaska during the spring of 1972. On 18 days in February, March, and April the positions of the >130-keV isotropic and cutoff trapping boundaries in the evening sector of the oval were determined on satellite 1971-89a. On 9 of these days, simultaneous VHF 50-MHz auroral radar backscatter echoes were observed to lie equatorward of the cutoff trapping boundary regardless of the phase of the auroral substorm. The analysis of these data with respect to substorm phase, Dst, and position of the aurora shows that the motion of the trapping boundary is a dynamic feature of the substorm that can be monitored and approximately located by the VHF radar echoes.

Rocket borne Langmuir probe measurements of electron temperature in the E-region are examined in relation to recent laboratory investigations of surface drift effects which can lead to erroneously high and time-dependent electron temperature measurements. The rocket data is consistent with the laboratory expectations thus supporting the suggested importance of surface effects in rocket measurements and in relation to the E-region discrepancy with simultaneous incoherent radar scatter measurements.

Auroral zone E-region neutral winds have been derived from simultaneous measurements of ion drift velocities in different altitudes by the incoherent radar facility at Chatanika, Alaska, on a quiet day before and during the great magnetospheric storm of Aug. 3-9, 1972. The neutral wind expected for a day-night pressure asymmetry appears to be strongly opposed by ion drag and local pressure gradients in the auroral oval.

Previous work on the second-order contributions of radar sea echo by Hasselmann and Barrick is generalized to include the effect of capillarity (i.e., surface tension) in the hydrodynamic part of the transfer coefficient, the lossy dielectric properties of the sea, and the angle of incidence and the polarization of the electromagnetic radiation. The present theoretical results apply to the backscattering of electromagnetic radiation from water waves that are gravity or gravity capillary waves. The introduction of surface tension in the analysis allows for second-order resonant interactions of the gravity capillary wave components. To include resonant interactions of gravity waves, the analysis must be extended to higher order. In general, resonant interactions produce higher-order contributions in the Doppler spectrum at the frequency of the first-order Bragg line that represent the nonstationary and non-Gaussian properties of the water surface. Furthermore, because of the different dispersion relation of gravity capillary water waves, the secondary lines of the second-order Doppler spectrum now are shifted toward the Bragg frequency and 2½ times the Bragg frequency. Numerical results are presented from our generalized theory for various radar and sea (water surface) parameters.

Expressions for the interplanetary radar time delay in the one-body problem of an arbitrary gravitational theory are deduced. The structure of the theory enters the result through two functions of one variable,f(r) andq(r), always connected by an identity.

The plasma fluid equations used by Sudan and his co-workers to explain the small-scale secondary irregularities observed in the equatorial electrojet are applied to the diffuse radar aurora. It is shown that the increased magnitude of the ambient magnetic field in the auroral zone and the decreased ion-neutral collision frequency, due to the higher altitude at which diffuse radar aurora occurs, combine to stabilize secondary two-stream irregularities over the expected range of electron drift velocities and primary irregularity amplitudes. It is also shown that secondary gradient drift irregularities are unstable for electron drift velocities in the vicinity of the ion acoustic velocity and that in addition to primary two-stream irregularities, primary gradient drift irregularities may be generated in the auroral E layer density gradients. These results are used to explain some of the spectral observations of the diffuse radar aurora.

Observations of the behavior of the auroral zone ionosphere were made with the incoherent scatter radar at Chatanika, Alaska, during the total solar eclipse of July 10, 1972. The radar beam intersected the approximate center of the eclipse shadow at a height of 400 km. The electron temperature decreased by more than 1200°K, and the ion temperature decreased by approximately 100°K near eclipse totality. Electron concentrations in the E and lower F regions decreased by 50%. Concentrations above the F layer peak decreased slightly, but there was no net change in ionization at the F layer maximum. Apparently, downward diffusion of upper F region ionization was just adequate to balance the loss processes at the layer maximum. An estimate of the heat input to the electron gas at 340 km showed that this quantity fell to about 25% of its background value during totality. Control radar data for the eclipse observations were obtained on July 9, 11, and 12, 1972, along with supporting vertical incidence ionosonde and magnetometer data acquired near College, Alaska.

During the transit of Mercury on 9 May 1970, the photoelectric Hertzsprung method was used to measure the diameter of the planet. Although the weather conditions were poor, a careful examination of the various causes of errors, in combination with previous measurements, leads to a value ⩾4920km, about 1% larger than the radar value, and corresponding to a mean density of 5.30 g cm −3 . Sources of systematic errors in a variety of optical methods are discussed..

Continuum observations of Mars at 21 cm with the NRAO interferometer during the 1971 opposition give an integrated brightness temperature of 179±11K, a value for the surface dielectric constant in agreement with those determined by radar, and lead to a flat microwave spectrum.

The formal relationship is established between the geometric optic approach and the autocorrelation approach to the analysis of lunar and planetary radar echoes for a Gaussian autocorrelation function when the surface has Gaussian height statistics and introduces deep phase modulation on the incident wave. Similarly it is inferred that such an analogy also holds whenever the surface undulations contain structure no smaller than the wavelength of observation divided by the rms slope of the surface. If an appreciable amount of small-scale structure is present, it is shown that (1) the range of scales responsible for the scattering will include an increasing amount of small-scale structure with increasing angle of incidence and (2) no ample relationship appears to exist between the distribution of apparent surface slopes and the power backscattered as a function of angle of incidence.

One of the puzzling, and hitherto unexplained, properties of VHF backscatter from the auroral electrojet is the occurrence of a thin, horizontal and remarkably uniform backscattering layer during the afternoon period. If the backscattering regions are in fact twostream plasma instabilities, it is shown that the properties of the afternoon backscatter can be explained by invoking an electric field perpendicular to the magnetic field.

Forward-oblique ionograms made on the path from Thule, Greenland, to College, Alaska in 1963–1964 were studied to determine whether HF signals propagating through the auroral curtain were adversely affected by scattering or blanketing effects. The location of the aurora was determined by an HF radar at College. Neither scatter from the auroral curtain nor blanketing by the auroral-E layer was found to significantly affect the 1F forward-oblique propagation mode on the Thule-College path. Higher-order modes and spread signals diminished appreciably at the onset of an auroral disturbance and reappeared with the decay of the disturbance. The disappearance or marked attenuation of the 1F mode on the Thule-College path was almost always found to be caused by an increase in auroral absorption and not by blanketing or scattering effects. Although auroral-E critical frequencies near 65° magnetic latitude were frequently above 5 MHz, they were rarely above 2 MHz between 70° and 72°, indicating the presence of a strong southward gradient in the electron concentration of the auroral-E layer between 65° and 72°. In an earlier paper it was concluded that auroral sporadic E caused the observed cutoff of the ground scatter echo at the range of the auroral curtain. This suggestion is discussed in light of the results presented in this paper.

A technique to measure the direction of the geomagnetic field by using incoherent scatter techniques is described. The technique has been used to measure the inclination of the magnetic field at the Jicamarca Radar Observatory with an accuracy of the order of 1 minute of arc in the height range from 200 to 800 km. The corresponding inclinations obtained from the Goddard Space Flight Center (12/66) and the International Geomagnetic Reference Field (10/68) models are found to be about 1° in error.

During the period from December 1963 to April 1964, a large number of combined Faraday polarization and Doppler frequency measurements were made on lunar radar echoes at Stanford, California. The results of the measurements taken while the moon was in the antisolar quadrant show a large spatial variation of the electron content beyond the ionosphere. A first-order model of the earth's magnetospheric wake is deduced, having the following characteristics: (1) the electron density inside the wake is about 200 cm−3 greater than the solar wind electron density; (2) the wave extends at least to the orbit of the moon; and (3) the wake intersects the lunar orbit at about 120° from the earth-sun line.

Measurements related to the nature of field-aligned irregularities in the ionosphere E region are presented. The measurements were performed near the magnetic equator, and the irregularities are attributed to the equatorial electrojet. It is shown that the irregularities are most likely to consist of plane acoustic waves generated by an instability resulting from the flow of current in the electrojet. Reference is made to a recent theory in which the existence of such waves is predicted. The characteristics of auroral radar echoes are shown to be similar to those of the equatorial echoes. It is inferred that the auroral field-aligned irregularities are also caused by the flow of electrojets. (auth)

Langmuir probe and retarding potential analyzer (RPA) data on the electron and ion temperatures Te and Ti obtained from Ogo 6 are compared with Te and Ti values obtained from the incoherent scatter network. The satellite to radar temperature ratio TeS/TeR is 1.15 on the average for these comparisons. This discrepancy is larger than the uncertainties usually placed on the probe and radar Te values. The ion temperature ratio TiS/TiR approximately 1.0, independent of the particular radar examined. This comparison serves as an intercalibration of the incoherent scatter network.

The Faraday rotation of 425-Mc/s radar signals reflected from the moon's surface has been analyzed to yield data on the ionization in the ionosphere. The experimental measurements were taken at Trinidad, West Indies, between January and July 1960. A method is presented which permits resolving the ambiguity of the number of rotations of the plane of polarization when one frequency is employed in radar-lunar studies. The total integrated electron density in a vertical column through the ionosphere inferred from the radar Faraday data is found to undergo a diurnal variation, having a maximum value during the late afternoon. An analysis of other ionospheric parameters, such as the equivalent slab thickness, the scale height, and the ratio of the electron content above the peak of the F layer to that below, is also presented.

Satellite data on precipitating auroral particle fluxes were acquired simultaneously with ground-based observations of auroral radar echoes. Measurements on the auroral particle fluxes were in the energy range from about 0.5 to 50 kev, and the auroral radar observations were made at 23 cm with frequency spectra analysis to investigate the motion of the scattering region. The results for an afternoon event show that strong radar echoes occurred in the absence of observable electron precipitation but were in close time and spatial coincidence with proton precipitation, although the proton contribution to the ionization at the scattering height at 112 km was computed to be negligible compared with the solar ionization. The frequency spectra of the auroral radar echoes were not of the character expected from a two-stream instability.

Backscatter and forward-scatter reflection properties of chemically created electron clouds were measured throughout the HF spectrum. The measurements included radar cross sections, signal fading characteristics, and frequency-time-dependence. These quantities led to certain conclusions regarding the cloud model which describes in general the chemical releases. The model so presented appears to be a limited coherent type of reflector; i.e., it is composed of an assembly of reflectors of coherent nature in a random motion which in turn give rise to a partially incoherent radar scatter signal. This simple model adequately describes most of the cesium releases, but it fails often enough to show that further experimentation is required.

Incoherent ionospherically backscattered radar returns have been observed at 440 Mc/s over an approximate height range of 100 to 800 km. The results of experiments designed to determine the variation with height of both the intensity and the frequency spectrum of backscattered returns are presented. Backscatter signal-intensity measurements at radio frequencies much greater than the F2 critical frequency provide an independent means of estimating electron densities. Height profiles of electron densities obtained from experimental data are discussed. Experimentally determined values of the scattering cross section are approximately equal to the square of the classical electron radius. A typical result of the frequency spectrum measurements at 440 Mc/s indicates a half-power spectrum width of about 11 kc/s at a height of about 300 km during midafternoon of a March day. Spectrum widths observed at several heights and at various times of day and night are discussed.

The phenomenon of incoherent scattering of electromagnetic waves by the free electrons in the ionosphere, initially hypothesized by Gordon [1958], has been experimentally validated as a possible technique for studying the characteristics of the ionosphere [Bowles, 1958, 1961; Pineo et al., 1960a, b; Pineo and Hynek, 1962; Millman et al., 1961; Greenhow et al., 1962; Evans, 1962]. In this note the detection of apparent ionospheric movements by the incoherent backscatter technique is described. The experimental observations were conducted in January and February 1961 at the U.S. Air Force Trinidad Test Site, West Indies (10.7° N, 61.6° W), with a high-powered pulsed radar operating at a frequency of 425 Mc/s.

The ionized medium between the earth and the moon is being studied at Stanford by means of lunar radar echoes. Of prime interest is the electron density beyond the earth's ionosphere, in regions (at distances of several to 60 earth radii) where the interplanetary gas may be dominant. Six related techniques for measuring the total integrated electron density are discussed. In practice the ionospheric part could be determined separately and subtracted from the total. These same techniques could be used to measure by radar the electron density between the earth and various planets, and to measure by one-way propagation the integrated electron density between a space probe and the earth. The moon's radar range exceeds the true range, especially at low frequencies, because of group retardation, which is a measure of integrated electron density. Density measurements based on absolute measures of radar range would require very high peak power (for pulse ranging) or very high equipment stability (for CW ranging); futhermore, the true lunar range is not known accurately. In two of the methods described here, the full average power capability of the transmitter can be used without need for high stability or precise knowledge of the lunar range. In effect, a reference is sent with the measuring quantities and only relative radar range is measured. Doppler frequency shifts and the earth's magnetic field cause only slight difficulties. However, path splitting, electron ‘blobs’ and lunar surface irregularities possibly could affect the waves more than the electrons do. The measurements might then yield information about the lunar surface or about the temporal and spatial variations of the cislunar medium.

A six-frequency radar was operated at Homer, Alaska, to determine the wavelength dependence and aspect sensitivity of radar auroral echoes at 50, 139, 398, 850, 1210, and 3000 Mhz. The lack of dependence of aspect sensitivity on frequency and the nature of the wavelength dependence indicates that the formulation for field-aligned scattering described by Booker is not adequate. It is believed that a more plausible model for the generation of field-aligned ionization is described by Farley. However, the nature of these results and the status of Farley's theory make quantitative comparisons beyond the scope of this paper.

The results of a series of radar studies of the sun at 38.2 MHz are presented. The echoes imply ever-present compressional waves in the corona, and these waves are likely associated with coronal heating. Some echoes are refracted by plasma clouds high in the corona. Other echoes are reflected by dense plasma irregularities moving outward very slowly at 0 to 20 km/sec. These are sometimes found as far out as three solar radii from the sun's center. Suggestions for future solar radar experiments and the need for them are outlined.

By means of a relatively sensitive 400-Mc radar located at College, Alaska, the variation of Doppler shift of auroral echoes has been determined as a function of the following parameters: (1) azimuth angle of the radar ray; (2) off-perpendicular intersection angle of the radar ray and the earth's magnetic field; (3) elevation angle of the radar ray; (4 ) range of the echoes; (5) altitude of the reflection centers; (6) time of day; (7) number of occurrences; (8) strength of the echoes. These data have been further delineated in terms of the type of echo seen (discrete or diffuse) and whether the data were taken before or after magnetic midnight. An estimate of the spectrum spread of auroral echoes has also been determined by pulse and by CW techniques. A consistent trend in these data has been found which would indicate an east-west motion of the ionospheric irregularities. There is no appreciable variation in the direction of motion with time of day or with respect to magnetic midnight. The mean velocity of the east-west motion appears to be 500 meters per second. These conclusions agree with those of Kim and Currie [1958] but disagree with those of Lyon and Kavadas [1958], Nichols [1957], and Bullough et al. [1957].

The return of an ionospherically propagated radar pulse may be a combination of both specular reflection and diffuse scattering from the earth, and it is of some interest to estimate the structure of the return pulse due to this combination. In particular, it appears that specular reflections may occur between the transmitter and its co-located receiver as a result of pulse reflection from suitably disposed geological and man-made facets and that scanning over these specular areas may give some structure in the backscattered pulse.

The possibility of utilizing irregularities produced in the ionospheric D layer by radio-frequency heating or by intense optical radiation from lasers to scatter radio waves is considered. Intense beams passing through the D region can produce large horizontal gradients in electron density where the beam intensity is falling off rapidly. The mechanism in the case of radio frequency is enhancement of electron attachment rate due to electron heating and in the case of lasers is photodetachment. In these regions radio waves may be scattered from blobs produced by turbulent mixing. A recently discovered anomalous relationship between electron energy and electromagnetic field intensity gives rise to the additional possibility of producing sharp vertical gradients in the propagation characteristics of an intense high-frequency wave in a plasma. Some interesting applications to f orward scatter propagation links and to ionospheric research with the Arecibo radar are suggested.

Power spectra of VHF radar auroral echoes were obtained near Anchorage, Alaska, during October 15–23, 1970. These spectra were obtained concurrently with standard range-time-intensity (RTI) film strips of the echoing region using the same radar system. In this paper, these spectra and the RTI film strips are examined and are compared with previously defined radar auroral classifications. The results indicate that there are at least two, and possibly three, separate types of spectra that correspond to identifiable echo configurations on the RTI film strips. Identification of the two-stream instability as an irregularity-producing mechanism for one of these spectral types is possible but not definitive. Another type of spectrum is similar to the type II spectra seen in the equatorial electrojet. The third spectral type bears no similarity to any results obtained at the equator.

Recent interest in the use of a multifrequency radar as a remote sensor for exploration of the earth and the moon has stimulated this study of the variation of radar backscattering with change in electromagnetic wavelength. The analysis of data has shown that radar cross sections of land and sea surfaces decrease with increasing wavelength and, on the average, follow approximately a λ−1 behavior, although the exponent may vary from +2 to −6 in individual cases. Snow-covered surfaces at all depression angles and sea surfaces at angles above 73° are the ones with positive values for the exponent. The wavelength dependence of the moon and the average values found on the earth in this study are quite similar. The combination of polarization and wavelength dependence versus depression angle may be characteristic features for distinguishing various terrain types by a multifrequency radar.

Meteor rate data tabulated from controlled parameter radar survey of Southern Hemisphere activity, noting diurnal and annual variations

Long-range, fast-fade radar echoes at 14 Mc/s observed looking north from Ithaca, N.Y., are described. They are explained in terms of backscatter from field-aligned irregularities located in a region where straight ray paths come within 10° of perpendicularity to the earth's magnetic field. A typical echo was spread in range from about 1000 to 2000 km, had a fading rate comparable to auroral fading at the same frequency, and seemed to correlate on an hour-by-hour basis with the occurrence of spread F. The minimum echo range was observed to be dependent on the penetration frequency of the F layer. This would not be predicted by geometry with straight ray paths, whereas bending of the ray paths into strict perpendicularity as a result of refractive effects does account for the observed echoes.

A ‘layered’ exponential model for the vertical distribution of refractivity in the form N = N6 exp [−c4 (z −z4)] is investigated. Here N6 and z4 are the refractivity and height, respectively, at a mandatory pressure level. The parameter c4 is the ‘best fit’ when N = N6+1 is the value at the next level where z = Z6+1. A formula for c4 is derived and is found to give good agreement, layer by layer, with the above model. This model appears to have particular merits for the case of air-to-air radar tracking.

Geomagnetic equatorial ionospheric ion temperature, comparing incoherent scatter radar and OGO-D retarding potential analyzer values

A coherent radar was used to measure the ‘sea clutter’ or backscattering of X-band electromagnetic energy from the sea surface. More than 200 recorded samples of clutter were analyzed to give power spectra of the clutter. Each spectrum was displayed as a function of frequency and of position on the water surface and was also averaged to give the mean spectrum of patches 3750 feet long. Five of the samples showed an anomalous downwind displacement of the clutter by as much as 7 knots. The displays indicate again, as in earlier Control Systems Laboratory measurements, that the upwind edge of the clutter spectrum is smooth for all wind speeds observed, but that the downwind edge, for sea state 3 or above, is broadened in an irregular fashion as a function of range. This irregular broadening implies a considerable variability, from patch to patch, in the downwind side of the probability distribution of velocity of scatterers on the sea surface. The width at half-power of a mean spectrum is proportional, for reasonable assumptions, to the width at half-maximum of the probability distribution of scatterer velocities. The variation of the latter width, Δ0, with sea state can be represented by the equation (expressed in consistent units) Δ0=11H1/3/Tm where the numerical factor is dimensionless, H1/3 is the significant wave height, and Tm is the period corresponding to the maximum of the energy spectrum for the water waves themselves when this spectrum is plotted as a function of frequency. This equation fits the experimental data within about 10 per cent for bandwidths in the range of 2 to 5 knots (64 to 160 cps) and wind speeds in the range of 8 to 19 knots. The bandwidth of the clutter is found to be approximately proportional to the wind speed. The relationships of clutter bandwidths to wave and whitecap velocities, radar depression angle, and wind direction are also discussed.

A series of cesium-seeded explosive bursts in the 90- to 110-km altitude region have been observed with meter and decameter wave radar. Detailed measurements of contact surface expansion, undulation, and stabilization have been used to acquire estimates of the altitude dependence of atmospheric pressure and density in the lower ionosphere. It has been found that events in the development of the contact surface are retarded relative to those predicted by Brode’s blast wave model, and this retardation is interpreted as evidence of magnetohydrodynamic effects upon the blast wave. Comparison of the results of these observations with previous results of Rosenberg (1964, 1965) suggests that a suitable combination of optical and radio-frequency instrumentation can be utilized to study in detail both the neutral gas and the magnetofluid characteristics of the lower ionosphere simultaneously.

Recent probes of the planet Venus reveal a probable surface temperature exceeding 700K and a pressure exceeding 100 atm. A very dusty lower atmosphere may exist which is composed of micron-sized particles kept airborne by mild turbulence and a gentle circulation of deep adiabatic currents. A study of surface conditions responsible for generation and persistence of surface dust clouds is of fundamental importance in the radiative and dynamic properties of the atmosphere. Also spurious radar echoes may be caused by suspended particulate matter, thus explaining the high relief reported by radar altimeters.

The effect of ion-neutral atom (or molecule) collisions on the excitation of ion-acoustic instabilities in the auroral ionosphere is considered. These collisions may play an important role in selecting the wavelength of the perturbations that are most likely to grow at any given height. The results of the calculations are compared with observational evidence obtained from radio star scintillations and radar aurora echoes.

Doubly scattered radiation magnitude as function of heights and aerosol concentrations for bistatic laser radar

Radar ranging experiment onboard Jupiter orbiter, concerning perturbations, gravitational harmonics and short arc orbit determination

The brightness temperature of an element of a planetary disk is dependent both on the direction of linear polarization to which the observing antenna is sensitive and the inclination of the element to the line-of-sight. Instruments of high resolution can be used to measure this dependence, providing values for the dielectric constant and emissivity of the planet's surface. The behavior of theoretical models, to which observations may be compared, is given. Observations of the Moon and Venus are presented as examples of application of this theory. The dielectric constant of the Moon at 21 cm is found to be 2.1, in good agreement with the radar results. This implies the emissivity at the center of the disk is 0.97, yielding 241 ± 26°K as the actual surface temperature at the center of the disk. The radiometric data for Venus show the expected behavior but the dielectric constant obtained is inconsistent with the value obtained from radar experiments.

Field-strength correlation can provide a means for velocity sensing which is particularly well suited to lunar landing missions. An earth-based transmitter directed toward the moon can set up an irregular field-strength distribution which is the sum of the direct wave and of many waves reflected from the lunar surface. This irregular pattern can be sensed by simple receivers with appropriately spaced antennas on a spacecraft. Because the field-strength pattern will be essentially stationary with respect to the lunar surface, the speed that is measured by cross correlating the features of the,pattern will be that of the vehicle with respect to the moon itself. Since this technique is based on tracking the peak of the correlation function, the nature of this function has been investigated both analytically and experimentally by simulation. In general, the results indicate that the correlation functions which would be obtained in the vicinity of the moon are suitable for tracking. A spaceborne velocity sensor employing this principle should be operable anywhere within a region defined by radial extension of the visible half of the moon out to an altitude of about 1000 miles.

The experimentally measured dependence of the mean radar power backscattered from the lunar surface on the angle of incidence (delay time) is compared with the theoretical formula based on a lunar surface consisting of a superposition of several normal random processes of different structures. The theoretically derived curve accounts for shadowing and matches the experimental data over almost the entire range of angles of incidence to within ±1 db. The wavelength dependence is also consistent with the observed data as far as they are available. The analysis yields a value of 11° for the rms slope of the lunar surface.