ECHOES AND TARGETS 307 
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 
precipitation 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 this 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 
P(Z) that a given signal from the target will be of 
intensity Z in range dJ. Or equivalently, one can find 
the fraction of returned pulses having intensity J in 
range dJ. [P(J) has been called the first probability 
distribution.] The result is simply 
dl 
P (D1) dI =e —, 
Io 
where J, 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(Z) 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 distribution is indepen- 
dent of the number of targets. The rapidity of the fluc- 
tuations is determined essentially by the echo changes 
and the relative velocity of the scatterers. The detailed 
Telation 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 blue screen tube operated at 6 
kv. Commercial 16-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 experimental data it is possible 
to compute an experimental first probability distribu- 
tion. 
Figure 1 is an example of such an experimental dis- 
tribution obtained by measuring a thousand pulses of 
FiaureE 1. The first probability distribution, P (I) of 
the intensity of cloud echoes. Curve: P(I) =e7/0 
Histogram: experimental results. Film 90, S band, 
1,000 pulses. 
precipitation echo on S band. The continuous curve in 
that figure shows the thcoretical 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 2 shows such an experi- 
mentally determined frequency spectrum for sea echo 
yn both S and X bands. The spectrum extends to 
120 c on X band and about 50 c on S. The ratio be- 
VIDEO FREQUENCY SPECTRUM 
FOR SEA ECHO 
mice ——S BAND FILM 106 
Y -—--—X BAND FILM 107 
PRF 333 1/3 PER SECOND 
eA NGS ee ae 
OE SS GE eS 
120 
VY IN CYCLES PER SEGOND 
Figure 2. Experimentally determined frequency spec- 
trum for sea echo. 
tween the width of the spectra is 2.4 compared to 
2.88 for the ratio of wavelengths. This discrepancy is 
probably due to the crudity of the measurements on 
X band. 
