178 



DIFFRACTION BY TEKKAIN 



method of images on assuming that the radiation 

 reflected on the transmitter side of the obstacle 

 issues from an image transmitter and that the radia- 

 tion reflected on the receiver side is incident upon 



FiGTJRE 11. Diffraction of both direct and refiected 



rays. 



an image receiver (Figure 11). The total field at the 

 receiver may be written 



E = El — E2 — E3 -{- Ei, 



where each term on the right-hand side is of the 

 form of equation (6), Ei corresponding to the direct 

 radiation, E^ to the radiation from the image trans- 

 mitter to the receiver, Es to the radiation from the 

 transmitter to the image receiver, and Ei to the 

 radiation from one image to the other. These four 

 terms differ in the value of v assigned to each of 

 them; the effective height ho computed by equation 

 (12) and the path lengths being different in each case. 



8.3.6 



Example 



Assume that from a topographic map the profile 

 shown in Figure 12 has been drawn. The horizontal 

 scale is in kilometers and the vertical scale in meters 

 above sea level. From this profile, combined with 

 inspection of the terrain, it has been found that the 

 ground is so rough that the reflected rays may be 



FiGLTHE 12. Assumed profile. 



disregarded. The heights above sea level of trans- 

 mitter, receiver, and obstacle, are respectively 

 hi = 24 meters, hz = 33 meters, h = 69 meters. 

 Since di = 9,000 meters, ^2 = 5,400 meters, d = 

 14,400 meters, we find from equation (12) that 

 ho = — 39 meters. Assume a wavelength of 1 meter : 



— ho , d, 



x= -= = 0.325 with - = 0.6. 

 ^l\d di 



From Figure 9, the diffracted field is found to be 

 14 db below the free-space field at the same distance. 



84 DIFFRACTION BY COASTS 



*•* ' Introduction 



Diffraction occurring at coast lines is significant 

 for coverage problems of coastal radars. It becomes 

 particularly important when the sets are used for 

 height-finding purposes where an accurate knowledge 

 of the lobe angle and possible deformation of the 

 lobes is required. ' 



The diffraction might be due either to the fact 

 that the radar is sited on a cliff or to the sudden 

 change in surface properties. Reflection from rough 

 ground is diffuse, so that there is no interference 

 between direct and reflected rays when the reflection 

 point lies on this type of terrain, but interference 

 does occur when the reflection point lies on the sea 

 surface from which I'egular reflection is obtained. A 

 situation commonly occurring is that of a search 

 radar sited on rough terrain a few miles inland from 

 the coast. Here coastal diffraction maj'' result in an 

 appreciable deformation (shortening or lengthening) 

 of the lobes. 



More generally, diffraction occurs with level 

 ground whenever there is a change, especiallj'' a 

 sudden change, of ground properties along the trans- 

 mission path. The formulas developed for coast- 

 line diffraction may equally be applied to the case 

 where rough ground suddenly changes into smooth, 

 reflecting ground. Similarly, the effect of patches 

 of smooth ground in rough surroundings, such as a 

 lake in wooded country and, vice versa, rough 

 patches in smooth terrain, may be treated by means 

 of the Fresnel-Kirchhoff theory. Here, attention 

 will be confined to the case of a straight boundary, 

 apph'ing the diffraction theory developed in Sec- 

 tion 8.1. 



t.4.2 



Level Site Near Coast 



Assume a transmitter sited on rough ground near 

 a coast. If diffraction were disregarded, the coverage 

 pattern would appear as follows. AVhen the reflec- 

 tion point is on the land, the reflected ray is diffusely 

 scattered and its field at the receiver is negligible. 

 Again, if the reflection point falls on the sea, the 

 reflected ray will be present and will interfere mth 



