RA DA R A NT EN N A S 2 83 



beam antenna field for there we find optical instruments in abundance, 

 parabolic reflectors and even lenses. 



It is not a very big step to proceed from an examination of optical systems 

 to the suggestion that a scanning antenna can be provided by moving a 

 feed over the focal plane of a reflector. Nevertheless experience shows 

 that this will not be especially profitable unless done with due caution. 

 The first efl'ect of moving the feed away from the focus in the focal plane of 

 a paraboloid is indeed a beam shift but before this process has gone far a 

 third order curvature of the phase front is produced and is accompanied 

 by a serious deterioration in the pattern and reduction in gain. This 

 difficulty or aberration is well known in classical optical theory and is called 

 coma. Coma is typified by patterns such as the one shown in Fig. 16. 

 It is the first obstacle in the path of the engineer who wishes to design a 

 good moving feed scanning antenna. 



Coma is not an insuperable obstacle however. Its removal can be 

 accomplished by the application of a very simple geometrical principle. 

 This principle can be stated as follows: "The condition for the absence of 

 coma is that each part of the focussing reflector or lens should be located on 

 a circle with center at the focus." 



This condition can be regarded as a statement of the spacial relation- 

 ship required between the feed and all parts of the focussing element. It 

 is a condition which insures that the phase front will remain nearly linear 

 when the feed is moved in the focal plane. It can be applied approximately 

 whether the focussing element is a reflector or a lens and to optical systems 

 which scan in both directions as well as those which scan in one direction. 



Coma is usually the most serious aberration to be reckoned with in a 

 scanning optical system, but it is by no means the only one. Any defect 

 in the phase and amplitude characteristic which arises when the feed is 

 moved can cause trouble and must be eliminated or reduced until it is toler- 

 able. Another defect in phase which arises is 'defocussing'. Defocussing 

 is a square law curvature of phase and arises when the feed is placed at an 

 improper distance from the reflector or lens. Its effect may be as shown 

 in Fig. 14. It can in principle always be corrected by moving the feed in a 

 correctly chosen arc, but this is not always consistent with other require- 

 ments on the system. In addition to troubles in phase an improper ampli- 

 tude across the aperture of the antenna will arise when the feed is trans- 

 lated unless proper rotation accompanies this motion. 



To combat the imperfections in an optical scanning system we can 

 choose over-all dimensions in such a way that they will be lessened. Thus 

 it is generally true that an increase in focal length or a decrease in aperture 

 will increase the scanning capabilities of an optical system. This alone 

 is usually not enough, however, we must also employ the degrees of free- 



