192 



ECHOES AND TARGETS 



was measured over a period of 4 days. The amount of 

 fluctuation was estimated visually every half hour. 

 These results showed a definite correlation with the 

 speed of the wind. Large fluctuations occurred only 

 with high winds. It was calculated that if the fluctua- 

 tion had indeed been independent of wind speed the 

 odds against getting the set of readings obtained by 

 these measurements would l)e 10,000.000 to 1. 



12.1.2 Assemblies of Random Scatterers 



In a more common type of radar target the entire 

 illuminated area contains a large number of independ- 

 ent targets with random phases. If we represent the 

 signal from each target by a vector showing amplitudes 

 and phase, then the total signal is found by adding 

 up all these vectors. If the phase of the individual 

 vector is changed slightly (for instance, by relative 

 motion) this vector diagram would be rearranged and 

 the total signal changed. Some practical examples are 

 jirecipitation echoes, where the individual targets are 

 the drops : window, where the echo arises from many 

 strips of tin foil ; and sea echo, where the individual 

 targets are probably areas of reflection from the sur- 

 face of the sea. 



The theory of tliis type of target has been extensively 

 worked out.^"^ One of the questions that can be an- 

 swered by the theory is to determine the probability 

 /'(/) that a given signal from the target will be of 

 intensity I in range (//. Or equivalently, one can find 

 the fraction of returned pulses having intensity / in 

 range (//. [/^(/) has liecn called tlie first ])rol)atiility 

 disiributiiiJi.] 'I'lie result is simply 



P (J) dl 



-ilh . 





where If, is the average intensity of the echo. The con- 

 tinuous curve in Figure 1 is a plot of this experi- 

 mental formula. 



The equation for P{I) is independent of the dis- 

 tribution of the individual amplitudes, nor is it re- 

 quired that the individual amplitudes be constant 

 with time, only that the distribution shall be station- 

 ary with time. The only other conditions that must be 

 satisfied are that there shall be a large number of scat- 

 terers and that they shall be independent of each other 

 with phase random both in space and time. It will be 

 seen from the formula that the most probable signal is 

 always zero. Furthermore the distriljution is inde]:)en- 

 dent of the number of targets. The rapidity of the fluc- 

 tuati(nis is determined essenfiallv liv the echo chantres 



and the relative velocity of the scatterers. The detailed 

 relation has been worked out between the frequency 

 spectrum of the fluctuations and the velocity distribu- 

 tion of the particles.''' The frequency of fluctuations 

 should increase linearly with r-f frequency. 



In order to investigate experimentally this type of 

 radar signal, it is necessary to get some method of 

 measuring the intensity of the individual pulses. In 

 our case this was obtained by photography of the single 

 sweeps on the A scope. For this purpose a special A 

 scope was used with a Idue screen tube operated at 6 

 kv. Commercial Ki-mm movie cameras were used in 

 which the shutter and claw had been removed and to 

 which a high-speed motor drive had been added. 



By photographing a calibrated r-f signal generator 

 pulse at the same receiver gain but at different r-f 

 levels, one can obtain a curve for the deflection in 

 centimeters against r-f intensity. By means of this 

 curve the measured deflections from the pulse-to-pulse 

 films can be converted into measurements of r-f in- 

 tensity. From these expea'imental data it is possible 

 to comjiute an experimental first probability distribu- 

 tion. 



Figure 1 is an example of such an experimental dis- 

 trilnition obtained by measuring a thousand pulses of 



Figure 1. The first probability distribution, P (/) of 

 the intensity of cloud echoes. Curve: P(I) =e~"'o 

 Histogram: experimental results. Film 90, S band, 

 1,000 pulses. 



precipitation echo on S band. The continuous curve in 

 that figure shows the theoretical formula given above. 

 The agreement is good. 



By what is essentially a Fourier analysis of these 

 data, one can also determine the frequency spectrum 

 of the video signal. Figure 3 shows such an experi- 

 mentally determined frequency spectrum for sea echo 

 on both S and X bands. The spectrum extends to 

 1'20 c o]i X band and about oO c on S. The ratio be- 



