196 



ECHOES AND TARGETS 



ytli one. Then the relumed t^jgnal from this pailieiilar 



target is 



P ^' ^' ^' 



where oj is the radar cross section of the y'lh seattercr, 

 P( the power transmitted, G the gain, A the wave- 

 length, and 1! the i-ange. uj dillers from the customary 

 cross section in that it incorporates the propagation 

 factor and hence nuiy depend on the height of target 

 and the glancing angle of the incident ray. In consid- 

 ering the time average of the total power received by 

 the radar we can take the scattering to be incoherent. 

 Heuce the average radar signal is the sum of Frj over 

 all the ;■ scatterers lying within the area illuminated 

 by the beam width and pulse length : 



Pr 



p, cr- X- 



{iwyii' 



1^' 



It is assumed that the illuminated area is sufficiently 

 large that the sum contains many scatterers and is 

 proportional to the size of the area. In that case this 

 formula can lie written 



_ P.Cr-y- TC 



Pt = <t>-'^, 



{iwy 2 



where </> is the azimuthal beam width, t the pulse 

 length in seconds, c the speed of light, and cr is defined 

 as the radar cross section of sea echo per unit area of 

 the sea surface and hence is dimensionless. This quan- 

 tity <T is a function of many parameters: the state 

 of the sea, the glancing angle of the incident beam 

 (and therefore the range), the polarization, and the 

 wavelength. A comprehensive program is under way 

 in the Eadiation Laboratory to cheek the assumptions 

 underlying this formula and to determine the cross 

 section o- as a function of these parameters. 



Uhlenbeck has pointed out that the dependence of 

 o- on wavelength should be an especially sensitive 

 function of the scattering mechanism assumed. For 

 drops whose circumference is small compared to the 

 wavelength, the scattering should be of the Eayleigh 

 type, i.e., varying as 1/X^ If one takes into account 

 the lobe pattern of the incident field due to reflection 

 on the water surface, the dependence is even faster, 

 possibly as l/A^ On the other hand, if we are dealing 

 with reflection or diffraction from large curved sur- 

 faces, then cr should be substantially independent of 

 wavelength or even increase with A. By measuring a 

 simultaneously on two or more frequencies, it should 

 be possiljle to decide between these mechanisms. 



iVccordingly, such measurements were made in the 

 sunnner of r.i4f at Bar Ilarlior, using the calibrated 

 S- and X-band mobile radars belonging to the Wave 

 Propagation Group of the Eadiation Laboratory. The 

 site elevation was 1,500 ft, and the ranges about 

 10,000 yd, so that the incident angles were quite small. 

 The constants in the formula for Pr were determined 

 as accurately as possible. In addition, the power, pulse 

 length, and Ijeam width were made comparable in 

 both systems. For relatively stormy sea conditions the 

 ratio of a on the two wavelengths was found to be : 



— = -f5±4db 



for both polarizations. If the Eayleigh l/A"* law holds, 

 the ratio should be -|-18.o db, which would seem to 

 exclude spray drops as the scatterers. 



One of the difficulties of this type of measurement 

 is to determine the average level of a signal that 

 fluctuates as rapidly as does sea echo. To remove this 

 source of trouble, a device has been developed that 

 reads the average power directly. It might be de- 

 scribed as a gated noise meter. With the aid of this 

 instrument we have again begun making measui'e- 

 ments of a on S and X bands, this time from Deer 

 Island in Boston Harbor. The elevation is only 120 

 ft, and the ranges are correspondingly small. 



The results obtained so far do not agree in all re- 

 spects with the j)revious data obtained at Bar Harbor. 

 When the sea is fairly calm (Beaufort 3 or less), the 

 ratio of ax to o-g is reproducibly given by : 



— = -M2 ± 2db horizontal 



(7.S 



on horizontal polarization. The scatter is much greater 

 on vertical polarization, and the ratio is much smaller: 



-^ '~ -hi: db vertical. 



0"S 



One set of worth-while measurements has been made 

 with a sea that was considerably rougher (Beaufort 

 4-5). The ratio was significantly smaller for both 

 l>olarizations : 



— = +5 ± 2db horizontal 



O'S 



-f2db vertical. 



At the time these data were obtained the first 

 measuicments were made with a calibrated experi- 

 mental K-band set recently constructed. Only hori- 



