170 THE CALCULATION OF RADAR DETECTION PROBABILITY 



Pattern of a Uniformly 



Illuminated Circular Aperture 



2Ji(x) 



-29 -30/2 -9 -0/2 0/2 30/2 20 



Fig. 3-15 Two-Way Voltage Envelope Generated by a Scan over a Single Target. 



aperture than at the edge, the sidelobe level can be minimized, but at the 

 expense of a wider beamwidth. In actual practice it is customary to taper 

 the illumination so that the effective beamwidth is about 20 per cent greater 

 than indicated by Equation 3-64; i.e., the multiplying factor becomes 70 

 rather than 58. 



Resolution Criteria. When two targets are separated sufficiently, 

 they can be identified as two distinct targets. When they are brought 

 together, their returns merge into a single unresolved return. There are a 

 number of criteria for deciding just when there are two returns and when 

 there is only one. Fundamentally, resolution should be defined relative to 

 the discrimination abilities of the human operator in the particular system 

 involved. In general, though, this is much too complex an approach because 

 of the many factors aflecting human performance, and it is more convenient 

 to adopt an arbitrary definition of resolution. In some cases, this will lead 

 to a situation where targets which are defined to be unresolved can actually 

 be observed as separate entities. Most of the definitions which have been 

 suggested for angular resolution lead approximately to the same result: 

 targets separated by about 1 beamwidth can be resolved. A beamwidth is 

 normally defined as the width between half-power points of the main lobe. 

 We shall adopt a very similar definition of resolution which has the con- 

 venient virtue of yielding a resolution of 1 beamwidth for a uniformly 

 illuminated circular aperture. We shall say that two point targets are 

 resolved when the average minimum of the received power envelope in a scan 

 over thejn is less than half the power from the maxiynum of the smaller of the two. 



This definition is illustrated in Fig. 3-16, the two-way voltage envelope 

 received from two point targets which are just resolved. As indicated in the 

 figure, the voltage pattern fluctuates markedly depending upon whether 

 the returns are in phase or out of phase. When the received reflections are 



