80 TECHNICAL SURVEY 
RESULTANT 
A B 
Figure 12. Phase of a zone. 
that the electric intensity of the wave at the point P 
is doubled (m: = 2S) and the power intensity is four 
times as great as for the unobstructed wave. If the 
aperture is increased to include the second zone, the 
intensity at P will be reduced nearly to zero. The 
disturbances from the second zone are out of phase 
with those of the first zone and equal in magnitude 
and therefore cause cancellation. 
Ficure 13. Polarity of zones. 
Reflection from Rough Surfaces— 
Rayleigh’s Criterion 
A rough surface may destroy all phase relations 
between the elements on the wavefront. The second- 
ary wavelets start from the elevated portions of the 
surface first, since these portions are struck first by 
the incident wave, and the lower portions send out 
secondary disturbances at various other times in 
random phase. It is impossible to arrange any zone 
system on such a surface for there are all possible 
phase differences irregularly distributed over the 
reflected wavefront and each point on the surface 
acts as an independent source radiating in all 
directions. 
In Figure 14 is shown a plane surface zy with 
incident rays SB and SA falling on a raised portion 
and a crevice respectively and being reflected to P. 
The path difference is SA + AP — (SB + BP). 
Since BP and AP are practically parallel, the path 
difference may be taken as BA — BK.’ 
H 
oe ~ sin Ww’ 
BK = BA - cos2wv. 
TO DISTANT POINT P 
Ficure 14. Reflection from rough surface. 
The path difference 
gee 
sin Vv 
= 2H sinv. (13) 
KN = (1 — cos 2) 
The corresponding difference in phase is 
=> F ay see (14) 
Since the path difference increases as the grazing 
angle increases, the diffusion is greatest when the 
rays are perpendicular. When the angle is small, 
near zero, regular reflection may be obtained. It was 
suggested by Rayleigh to take as an upper limit for 
the grazing angle, giving regular reflection, the value 
corresponding to a phase difference of 7/4. By 
equation (14) this angle is given by 
a  4nrH . 
4 = = ae: 
or ¢ ON 
sin¥ = 7 - (15) 
For a given wavelength and lobe angle the terrain 
at the reflection point may be examined to determine 
the limiting height of the roughness for regular 
reflections. Equation (15) may also be given in a 
more convenient form using the approximation 
sin YW = W radians for small values of V: 
3,520 
i ca 
H= (16) 
