CALCULATIONS FOR OPTICAL-INTERFERENCE REGION 



79 



5 1 4 Di99 



Figure 22. Contours of constant divergence factor D and path difference variable R. (Radiation Laboratory.) 



'* ILLUSTRATIVE CALCULATIONS FOR 

 THE OPTICAL-INTERFERENCE REGION 



5.6.1 



Introduction 



The general expression for the gain factor A in the 

 interference region is obtained by combining equa- 

 tions (44) and (7). Then 



A = AoF_ 



i\|(l- 







(108) 



Ky+iK sin'- 2 



The vahie of the radio gain is then given by equa- 

 tion (3) and the value of radar gain is given by equa- 

 tion (5). The value of the radical which defines the 

 interference pattern has a range of values between 

 and 2. The extreme values can occur only when 

 K = 1 (p = 1, D = 1, F2/F1 = 1); the value 

 (nulls) is then given by sin- (fi/2) = and the value 

 2 (maxima) is given by sitf (fi/2) = 1. 



In general, the value of A lies between the two 

 extremes 



A = AoFi (1 ± K), 



the positive sign giving a maximum and the negative 

 giving a minimum. At any other point, the value 

 lies between these two extremes. For range calcula- 

 tions (which involve maxima), the variation in A 

 is from 1 to 2 times the free-space value, according 

 to the value of K, so that in practice a quick rule of 

 thumb for range may be devised. Assume (1 -|- K) 

 equal to 1.9 for favorable conditions (sea water, 

 horizontal polarization, or, in the case of vertical 

 polarization, small grazing angles) down to (1 -|- K) 

 = 1 or iv = for propagation over rough terrain. 

 The problem of finding the range is thus reduced 

 to a problem for free space. In range calculations, 

 Po/Pi is given by the ratio of minimum detectable 

 power to power output. ^4 is then determined by 

 equations (3) or (5), and the range is given by find- 

 ing d from the relation (writing Aq = 3X/87rrf) 



KSTTdJ 



(1 + K). 



(109) 



More detailed calculations are presented in this 



