784 AIRBORNE NAVIGATION AND GROUND SURVEILLANCE 



14-20 RESOLUTION LIMITS IN GROUND MAPPING 

 SYSTEMSi^ 



The systems factors which determine the resolution of ground mapping 

 systems can be grouped roughly into two categories; those that determine 

 pulse packet size and those that deal with the receiver and display. 



Pulse packet size, as defined by the half-power beamwidth and pulse 

 length, is used frequently to describe the resolution capability of a mapping 

 system. It is a useful concept for obtaining a relative comparison of the 

 capabilities of two systems equal in other respects. However, care must be 

 exercised since the values assigned to the packet dimensions can be very 

 misleading if they are used to determine randomly observed resolubility. 

 One of the major problems in applying the packet concept results from the 

 wide range of amplitudes of signal returns. In general the resolution of 

 targets from which the return is very weak approaches the limits defined by 

 the half power packet. However, for targets from which the return is much 

 stronger the effective beamwidth and pulselength are increased. In effect, 

 strong targets are mapped with a packet size proportional to their ampli- 

 tudes as well as their relative positions and ranges from the airplane. 

 Experience with ground mapping systems indicates that the packet size 

 which should be used to determine resolution is somewhat undefinable 

 unless strictly qualified. However, a qualitative estimate of the validity of 

 the concept can be obtained by examining the form of the signal return as 

 the antenna scans by two closely spaced point targets. 



Freedman has used this approach to study the azimuth resolution of two 

 closely spaced point targets. ^^ His results, expressed in terms of the ratio of 

 power midway between the targets and the power at one of the targets as a 

 function of target separation in beamwidths, indicate that resolution will 

 occur for a target separation slightly greater than 1 beamwidth. The exact 

 separation required depends on the criterion used to define resolution. 

 Using Rayleigh's familiar rule for resolution, the required separation is 

 about 1.1 beamwidths; using a half-power criterion, the required separation 

 is about 1.2 beamwidths. It should be noted, however, that in the vector 

 addition of the integrated signals from the two targets an average phase 

 difference of 90° has been assumed. In most practical cases the number of 

 pulse returns from each target will not be sufficient for the statistical 

 average to apply. As Freedman notes, the average phase difference will 

 vary between the extremes of "in phase" and "out of phase" so that in 

 some instances targets would be resolved and in other instances the same 

 targets would not be resolved. This phenomenon is observed in the opera- 

 tion of mapping systems. 



i'*See Chapter 3 for a more detailed discussion of resolution. 



15J. Freedman, "Resolution in Radar Systems," Proc. IRE 39 (July 1951). 



