Radar System Engineering

48 THE RADAR EQUATION [SEC.212
other words, under free-space conditions. It is this ratio, which we shall
call F, that we want now to compute.
The difference in length between the paths All and AMB, if the angle
o is small, is given quite closely by
Xim-m=y. (24)
This is responsible for a difference in electrical phase of 4rhlh,/RA radians
bet ween the two waves arriving at B, to which we must add any phase
klG. 29.-Pr0pagati0n
over a flat reflecting surface
shift ~ resulting from the reflection of the one wave at M. The total
phase difference b is then
If the reflection at M is total, both waves arriving at 1? will have substantially
the same intensity, namely, that corresponding to free-space
propagation. 1 Taking the phase difference into account, then
(25)
F’ = 2(1 + COS~). (26)
The angle #, contained in O, depends upon the nature of the reflecting
medium, upon the angle 0 between the surface and the direction of wave
travel, and upon the polarization. If the surface were a perfect conductor,
# would be r radians for horizontal polarization (electric vector
parallel to surface) and zero for vertical polarization (magnetic vector
parallel to surface). We shall be chiefly concerned, however, with the
surface of the sea, and to a lesser extent with land, and these mediums
behave more like dielectrics than conductors at microwave frequencies.
For horizontal polarization it is still true that ~ = r, but for vertical
polarization the situation is more complicated. If O is considerably
1The fact that the waves arriveat B from slightlydifferentdirections,as well as
the effectof the slightlyunequalpath lengthsupon the relativeintensity,neednot be
takeninto account so long as R >>h, >>A.
‘ This use of the terms “horizontal” and “vertical” polarization, though not
meticulous,is common radarpractice,and causes no confusionwhenthe directionsof
propagation make small angles with the horizontal, Gf course the electric vector
of a verticallypolarizedwave travelingfrom A to M is not preciselyvertical.