332 PROPAGATION THROUGH THE STANDARD ATMOSPHERE 
in the siting of very high frequency [VHF] com- 
munication sets. ~ 
5. Diffraction. The mechanism by which radio 
waves curve around edges and penetrate into the 
shadow region behind an opaque obstacle is called 
diffraction. The explanation usually given is based 
on Huyghens’ principle. This, in effect, states that 
every elementary area on a wavefront (see P in 
Figure 6) is a center which radiates in all directions 
S< Shadow zone 
oo 
Figure 6: Diffraction around an obstacle. 
on the forward side of the wavefront; the intensity 
of radiation is a maximum in the direction per- 
pendicular to the wavefront and depends on angle 
6 according to the function (1 + cos @). The field at 
any point, either inside or outside the shadow zone, is 
obtained by summing the contributions from all the 
elementary areas comprising the wavefront. 
As a result of these calculations, the field along the 
line AA’ in Figure 6 varies approximately as indi- 
cated in the curve. Unity represents the field value 
if the obstacle were removed. It is seen that the 
field strength rises from a minimum at point A to 0.5 
at the edge of the shadow zone and thereafter oscil- 
lates about unity. The field outside the shadow zone, 
therefore, at certain points is stronger and at other 
points is weaker than it would be if there were no 
obstacle. The curve, of course, varies with the 
position of the line AA’, the size and shape of the 
obstacle, the wavelength of the radiation, and the 
type of polarization. The diffraction of radiant 
energy into the shadow zone increases with increas- 
ing wavelength. 
Of prime importance for propagation of radio 
waves is the diffraction of these waves into the 
diffraction region below the line of sight (see Figure 
5). But it should be noted that the influence of 
diffraction is not confined to this region but extends 
well above the line of sight. [In general, the influ- 
ence extends upward far enough to affect the shape 
of the lower part of the first lobe in a coverage 
diagram (see Figures 25 and 26 of Chapter 5). In 
this region the diffraction contribution must be 
added to the contributions of the direct and reflected 
rays to give the correct value of the field strength 
at R in Figure 5.] 
Of importance in communication problems is 
diffraction of waves around obstacles such as hills, 
trees, houses, etc. This is illustrated in Figure 6. 
Again diffraction is important in problems involving 
propagation above two different earth conditions. 
An especially important case is that of a radar set 
well inland and searching far out over the sea. Here 
the shore line is treated as a diffracting edge for the 
radiation from the image antenna. 
6. Absorption and scattering. No account is taken 
in this book of the absorption and scattering of radio 
waves by the various constituents of the atmos- 
phere. Oxygen, water vapor, water droplets, and 
rain all contribute to absorption. Their influence, 
however, is important only in the microwave range 
and in general tends to increase with frequency. 
General Nature 
of the Radiation Field 
In the last section , reference was made to the 
role of reflection by the earth. The resultant of the 
direct and indirect rays at points in the region above 
the line of sight gives rise to the lobes of an inter- 
ference pattern (see Figures 9 to 12). The maximum 
number of lobes is the largest integral number of 
times that the quarter wavelength is contained in the 
transmitter height. 
In the case of horizontal polarization over a 
smooth surface, e.g., a calm sea, the reflected and 
direct rays are comparable in strength, so that at 
certain points (on lines for which the points corre- 
spond to a path difference of a half wavelength) 
where the reinforcement is a maximum, the field 
may be as much as twice the free-space field. More 
exactly, the free-space field is multiplied at points of 
maxima by (1 + FD), where D is the value of the . 
divergence factor for the point and F gives the rela- - 
tive strength of the reflected and direct rays attribut- 
able to the antenna beam pattern. At points of 
minima (the nulls) the field is (1 — FD) times the 
free-space field. 
In general the magnitude of the reflected wave is 
reduced both by the increased divergence resulting 
from reflection from the convex surface of the earth 
but also because the electrical properties of the 
earth are such that only part of the incident energy 
is reflected. The magnitude of the reflection coeffi- 
cient is then pD instead of the D used in the preced- 
ing paragraph, where p is the magnitude of the 
reflection coefficient for plane waves impinging on 
a plane surface. The field strength, then, lies be- 
tween (1 + pFD) and (1 — pFD). As a result of 
the smaller value of pFD for vertical polarization 
the maxima of the interference pattern are reduced 
and the nulls strengthened. 
At low heights (see Figure 3 of Chapter 5) the 
effect of diffraction is important, so that when refer- 
ence is made to the optical interference region, it 
