3-6] FACTORS AFFECTING ANGULAR RESOLUTION 169 



Antenna Pattern Characteristics. Angular resolution is provided 

 by the directive properties of the radar antenna. The greater the direc- 

 tivity, the better the resolution. 



There is an enormous variety of types of microwave antennas in use 

 today. The most widely used in airborne radar systems are those employing 

 parabolic reflectors. The discussion will center about this type of antenna 

 although many of the observations are applicable to a much wider class. 



Parabolic reflectors can be constructed whose characteristics closely 

 approximate those of a uniformly illuminated aperture. The relative 

 voltage pattern radiated (or received) by a uniformly illuminated circular 

 aperture will have the following form^^ at long ranges. 



r^ , • , 2Ji[(7rD/X) sin^] ,^ ,^, 



Une-way voltage pattern, circular aperture = , ^ .^ , . — - — (3-63) 



(tt/J/a) sm p 



where D = aperture diameter 



X = wavelength 



d = angle relative to aperture normal 



Ji( ) = first-order Bessel function. 



For convenience, we represent the argument of this expression by x so that 

 the one-way relative voltage pattern is 2Ji(;c) /x. 



The received voltage reflected from a point target to a uniformly illumi- 

 nated circular aperture used both for transmission and reception will be 

 given by the square of the function in Equation 3-63 or (2Ji{x) jxY. This is 

 also equal to the one-way relative power pattern of such an antenna. This 

 pattern is illustrated in Fig. 3-15 where it is referred to as the two-way 

 voltage envelope generated by a scan over a single target. 



The antenna beamwidth is normally defined as the width between the 

 half-power points of the one-way antenna pattern. This is indicated in 

 Fig. 3-15. For a uniformly illuminated circular aperture the beamwidth is 

 related to the diameter and wa.elength by 



Beamwidth, circular aperture = 58X/Z) degrees. (3-64) 



The envelope of the received power on the two-way power pattern is 

 probably most significant for defining resolution. This is given by the 

 square of the envelope plotted in Fig. 3-15 or {2]i{x) IxY. 



The antenna pattern and the beamwidth can be modified by illuminating 

 the aperture in a nonuniform manner. A uniform illumination yields one 

 of the narrowest beams, but the sidelobe level is relatively high. The 

 sidelobes of the one-way power pattern in Fig. 3-15 are down 17.6 db from 

 the peak. When the illumination is tapered or stronger in the center of the 



i«J. D. Kraus, Antennas, p. 344, McGraw-Hill Book Co., Inc., New York, 1950. 



