4-2] REFLECTION OF RADAR WAVES 177 



metallic sheet perpendicular to the direction of the incoming wave. If we 

 neglect edge effects, the current density is of constant amplitude and phase 

 throughout the sheet. Accordingly, the sheet reradiates like an antenna of 

 aperture A' with a uniform amplitude and phase distribution. Since the 

 gain of such an antenna is 



G' - 47r A'l\^ (4-7) 



(which is large \i A' l\'^ is large) we obtain from Equation 4-6 



(7 = 4x(/f 7X^)2, for A'/\ » 1 (4-8) 



One of the conditions assumed in 

 deriving Equation 4-1 is that the x\i- ^^-^ 



variation in range R over the target \P-^^- "" 



results in a negligible variation of ^^-^^ 



the phase of the incident field. In ^^"^ xT 



order to obtain a numerical estimate \" 



of the significance of this limitation, 



we may consider, as an example, an 



airborne search radar viewing, in 



free space, a rectilinear target of 



length 2L at a range R, as illustrated pic. 4.1 Geometry for Limitations of 



in Fig. 4-1. The difference in range Plane-Wave Conditions. 



between a point at x on the target 



and the nearest point of the target is 



Ai? = (i?2 + ;,2)l/2 _ ^ ^ y,2i2R. (4-9) 



Assuming that the antenna may be treated as a point source, the round-trip 

 phase difference between the fields reflected back to the source from these 

 two points is 



A0 = IkLR = l-KX-'IXR. (4-10) 



From Equation 4-3 the contribution of a differential length of the target 

 to the received signal in free space is 



^£. = 1^ ^-^2^(«+^«> --i/ ' (4-11) 



R~ 



where dl = differential radar length of the differential target element dx 

 located at a distance x from the center of the target. 



If we denote the plane-wave radar length of the target by / and assume for 

 simplicity that the radar length per unit length of the target is constant. 



