Radar System Engineering

52 THE RADAR EQUATION [SEC. 2.12
The maxima and minima which one might have expected in the
nearer region are not conspicuous in Fig. 2.12. The reason for this is
that the target was not a point with a unique height hz but a complicated
object extending from the surface up to some maximum height. In this
“near zone” some parts of the ship lie on maxima and some lie in the
nulls, and the net result at any instant is some sort of average, in
the fluctuations of which one could hardly expect to discern traces of the
regular interference pattern predicted by Eq. (29). The absence of a
sharply defined break in the curve between the two regions is readily
justified on the same grounds. The location of the break, ill-defined as
it is, can however be used to compute some “effective height” hz.
Although the relation in Eq. (30) fixes roughly the inner boundary of
the “ R–a region, ” were we to cling to our flat-earth hypothesis there
would be no outer limit. Actually, of course, the region is ultimately
FIG. 2, 13.—Reflection from an irregularsurface.
bounded by the radar horizon, where a new and even more drastic fallingoff
in signal strength sets in. In many instances, especially at microwave
frequencies, this limit occurs so soon after the beginning of the eighthpower
region as to reduce the latter to rather inconsequential size.
Before we discuss the effect of the earth’s curvature, we should
comment on certain other, less important, shortcomings of the preceding
simplified argument. For one thing, we have ignored the fact that the
reflecting suface is not smooth; even in the case of the sea, the irregularities
(waves) are both wide and deep compared to a microwavelength; in
the case of a land surface, we may be confronted with any imaginable
irregularity. Nevertheless, at least for reflection on the sea at nearly
grazing incidence, the observed reflection coefficient is rather close to
what a glassily smooth sea would give. 1 This is, perhaps, no more
surprising than the fact that an ordinary piece of paper displays, at
nearly grazing incidence, specular reflection of light, and it can be made
plausible by some argument such as this: In Fig. 2.13, two parallel rays,
AB and DE, strike a “rough” surface, the roughness consisting of a
single bump of height h. The reader will find with little trouble that the
net path difference between the two rays ~F — AB is just 2h sin O. If
I The reflectioncoefficientwould have to be substantiallylessthan 1 to changethe
resultsignificantly,so far as the radarproblem is concerned.