PROPAGATION OF RADIO WAVES 465 
DIGRESSION ON FRESNEL’S THEORY 
Fresnel Zones 
The concept of the Fresnel zone has played an 
important role in the development of diffraction 
theory. As it is frequently referred to in papers on 
the subject, it may be useful to digress briefly on it. 
Fresnel’s original construction is based on the con- 
ception that any small element of space in the path 
of a wave may be considered as the source of a 
secondary wavelet, and that the radiation field can 
Ficure 6. Relations of Fresnel zones and diffracting 
slots. 
be built up by the superposition of all these wave- 
lets (Huyghens’ principle). In particular, consider 
the field produced by the transmitter in the open 
part of the plane containing the diffracting screen 
(EAPBF in Figure 1) and let each element of this 
plane be the source of a secondary wavelet. This 
may be achieved by distributing a suitable ficti- 
tious system of oscillating currents (or a system of 
elemertary doublets of proper strength) over the 
surface of the plane. The field at the receiver is then 
the superposition of all the fields produced by the 
wavelets. 
Now let (Figure 6) S be a plane perpendicular to 
the line TR and let M be the point in which the line 
TR intersects the plane S. Let Q be a point on the 
plane S such that the difference in path between 
TQR and TMR is just 4/2. The locus of these 
points is a circle about M. Similarly we can con- 
struct other circles so that the corresponding path 
differences are integral multiples of 4/2. The area 
within the first circle is called the first Fresnel zone, 
the subsequent ring-shaped areas are called the 
second, third, etc., Fresnel zones. The secondary 
wavelets originating in the first, third, fifth, etc., 
Fresnel zones are in phase with each other and rein- 
force each other by constructive interference at R, 
while the secondary wavelets originating in the 
second, fourth, etc., zones are in phase with each 
other but out of phase with the former group and 
tend to cancel the field produced by this group. 
Hence if the plane S is opaque except for a round 
hole centered on M, the intensity of the radiation 
field at R will depend on the number of Fresnel 
zones that fall inside the hole. If we start out with a 
very small hole and progressively increase its size, 
there will be a maximum of intensity at R (nearly 
twice the free-space field Ho) when the hole just 
comprises the first Fresnel zone. If the size of the 
hole is further increased, the destructive interference 
of the second zone comes into play, decreasing the 
intensity, and a minimum (very nearly zero) is 
reached when the hole contains just the first two 
zones. On continued increase of the hole size, 
further maxima and minima appear. The amplitude 
of these oscillations decreases very gradually until 
eventually the field at R approaches the free-space 
value. 
Diffraction by a Slot 
The preceding considerations indicate that only a 
comparatively small area of an opening, of the order 
of one Fresnel zone, is required to produce an 
illumination that is comparable in order of magni- 
tude to the free-space field. It is also seen that the 
simple geometrical construction of the Fresnel zones 
is more suitable when dealing with the diffraction 
by round openings than with screens bounded by 
straightedges.- Qualitatively, however, the conditions 
are similar. 
As an example, consider the case of a slot bounded 
by parallel edges at distances ho and ho’ from the 
point of intersection M between the plane of the 
slot and the direction from the observer to the 
distant light source (see Figure 6). The diffracted 
field H will obviously be equal to the free-space 
field Ep if the slot is infinitely wide on both sides of 
M, which corresponds to a vector joining the two 
foci of the Cornu spiral. However, there is an infinite 
number of other finite openings of the slot which 
also will give the free-space field. Suppose, for 
instance, that ho = ho’ in Figure 6 and that the slot 
width is gradually increased from zero. A glance 
at the Cornu spiral (Figure 3) shows that when 
v = 0.75 and v’ = —0.75, the vector representing 
the diffraction field is approximately equal to the 
free-space field. This width represents, for a slot, 
the analogue of the first Fresnel zone for a circular 
opening. 
DIFFRACTION BY HILLS 
Introduction 
The formula for diffraction by a straight edge may 
be applied in radio practice to determine the diffrac- 
tion field behind a ridge. The ridge need not be 
perpendicular to the transmission path, but the 
condition given in equation (1) must be approx- 
imately fulfilled. The distance from transmitter 
and receiver to the ridge should be large compared 
