OU'lLINE OF THEORY 



171 



tions will then be written down at once (Sections 

 8.1.4 to 8.1.6). 



8.1.4 



The Straight Edge Formula 



8.1.3 



Mechanism of Diffraction 



The physical idea underlying the Fresnel-Kirch- 

 hoff diffraction theory may be presented as folloA^-s. 

 At points visible from T the field, to a first approx- 

 imation, is equal to the free-space field E^. This 

 applies in particular to all points of the plane ECDF 

 containing the screen. The receiver R recei^'es 

 radiation from the open part EAPBF of the plane, 

 while there is no radiation incident upon R from the 

 opaque surface CAPBD. In order to compute the 

 field at R, it is assumed that in the open part of the 

 plane the field is Eq while on the opaque screen the 

 field vanishes. Such a field distribution may be 

 realized physically by assuming that there is a con- 

 ducting sheet in the open region EAPBF with 

 suitably chosen oscillating charges or cun'ents such 

 that the field Eo is produced on the side of the sheet 

 facing the receiver. The total radiation received 

 at R from such a current-sheet will be equivalent 

 to the radiation from T bent around the diffracting 

 screen. The fictitious sheet EAPBF forms a system 

 of secondary sources of radiation whose effect is 

 equivalent to that of the primary source for all 

 points on the far side of the plane ECDF (side of the 

 receiver), but not on the near side (side of the 

 transmitter). 



It is evident that most of the radiation received 

 at R comes from the area near the point P above the 

 line APB. The relative importance of contributions 

 of areas more or less removed from P is discussed in 

 Section 8.2. 



When the primary source at T is replaced by a 

 distribution of secondary sources in the plane of the 

 screen, an essential approximation is made. It is 

 assumed that there are no secondary sources in the 

 opaque region CAPBD. In reality, the screen is a 

 physical body and, whether it is a conductor or a 

 dielectric, there is an electromagnetic field in its 

 surface layers, especially near the edge APB, and 

 this field makes a contribution to the radiation 

 received at R. In the approximate theory, it is 

 assumed that the field on the surface of the opaque 

 screen is negligible. In the terminology of optics, 

 this implies that the screen is black; in radio termi- 

 nology, it means that the surface of the screen is 

 rough (Section 8.3.2). 



The physical picture just described can be put 

 into mathematical language. When the rather 

 intricate derivations are carried through, a rela- 

 tively simple formula results. 



The symbols and designations used are illustrated 

 in Figure 2. In accordance with practice it is 

 assumed that the line TR is nearly horizontal. The 

 trace of the opaque screen on a vertical plane through 

 T and R is assumed perpendicular to the line TR 



ELEVATION 



Figure 2. Diffraction around straight edge. 



(upper part of Figure 2). The trace of the screen 

 on a horizontal plane may, however, make an 

 angle (j) Avith the line TR (lower part of Figure 2). 



In view of the approximate nature of the theory 

 explained in the ijreceding paragraph, the foUomng 

 conditions must be fulfilled in order to obtain 

 reUable results: 



Ch,ck > >/2o > >X. 



(1) 



That is, the distances from the transmitter and 

 receiver to the obstacle must be large compared to 

 the height of the latter above the line TR, and this 

 height must be large compared to the wavelength. 

 The second of these conditions is likely to be ful- 

 filled in the short-wave and microwave bands, and 

 the first will be fulfilled when the angles of elevation 

 ai and ao of the rays, drawn from the transmitter 

 and receiver to the edge, are small. 



A second condition for the vahdity of the diffrac- 

 tion formula refera to the horizontal extension of the 

 screen. The formulas are derived for a screen of 

 infinite horizontal extent, but in practice it will 

 usually suffice if the horizontal extension of the 

 screen is large compared to the height ho. 



