OPTICAL PROPERTIES OF THE EARTH'S SURFACE AND ATMOSPHERE 



:S7 



nth interference maximum of the direct and ground- 

 reflected rays, namely, 



4M 



(20) 



where /ii is the height of the transmitter above the 

 ground, the criterion can be written in the form 



// 



4n 



(21) 



Although admittedly rough, the criterion indicates 

 the order of magnitude of the angle above which 

 specular reflection will be greatly reduced in favor 

 of diffuse scattering of the type which, in ordinary 

 optics, is produced by a dull, white surface. It is 

 reasonably safe to assume that for angles exceeding 

 the critical angle the amount of specular reflection 

 will be reduced to a small fraction, perhaps to the 

 order of one-fifth, of the value of the reflection under 

 ideal conditions. 



Diffraction by Terrain 



A number of the influences of the earth's surface 

 upon wave propagation -have the common charac- 

 teristic that they represent deviations of the actual 

 earth from the idealized model of a smooth sphere 

 endowed with homogeneous electrical constants. 

 Diffraction by the earth's average curvature is not 

 included among the effects considered here since it 

 is dealt with extensively in Vilume 3. 



There are two main classes of phenomena that fall 

 under the general heading of diffraction. One is the 

 diffraction by obstacles, such as hills, trees or houses, 

 and the other is the diffraction by the structure of 

 an otherwise fairly level ground, in particular, rough- 

 ness and horizontal variations of dielectric constant. 



The diffraction by hills and similar obstacles of the 

 terrain is commonly treated theoretically by means 

 of the Fresnel-Kirchhoff diffraction theory as found 

 in textbooks on optics. The only problem which is 

 sufficiently simple to admit of a direct application to 

 short wave transmission is that of diffraction by a 

 straight edge. It is not necessary that the edge be 

 perpendicular to the line connecting the transmitter 

 and receiver but for the validity of the theory it is 

 necessary to suppose that the distances from the 

 diffracting obstacle to the transmitter and receiver 

 are large compared to the height of the obstacle, 

 which means that the angles of diffraction are small. 



"• 25 



45 



0.15 0.2 0.3 0.4 



7U" 



Figure 7. Field in shadow behind a diffracting ridge. 



Figure 7 shows a nomogram from which the field 

 strength in the shadow of a diffracting edge can be 

 read in decibels below that of free space. The geo- 

 metrical significance of the quantities used is illus- 

 trated on the figure. 



Such experiments as have been made show a gen- 

 eral agreement with theory, but it is difficult in prac- 

 tice to realize conditions of transmission that ap- 

 proach ideal ones, to which the Fresnel-Kirchhoff 

 theory refers. When appropriate values are taken 

 for the reflection coefficient of the ground and the 

 four components of the resulting field are added 

 vectorially, good agreement has been found between 

 experiment and theory for selected terrain. (See 

 Chapter 15 of this volume.) Sometimes the terrain 

 conditions are often so complicated that they do 

 not readily lend themselves to idealization by simple 

 geometrical models. For these reasons the Fresnel- 

 Kirchhoff diffraction theory has been of only limited 

 value in short wave radio propagation. 



A case which quite often can be described ade- 



