244 BELL S YS TEM TECH NIC A L JOURNA L 



(2) The defocussing of a reflector or lens due to improper placing of the 

 primary feed. 



(3) The defocussing of a zoned reflector or lens due to operation at a fre- 

 quency off mid-band. 



In addition to providing distant patterns of apertures with curved wave 

 fronts (44) provides theoretical 'close in' patterns of antennas with plane 

 wave fronts. This arises from the simple fact that a plane aperture appears 

 as a curved aperture to close in points. The degree of curvature depends 

 on the distance and can be evaluated by extremely simple geometrical con- 

 siderations. When this has been done we find that Fig. 14 represents the 

 so-called Fresnel diffraction field. 



With this interpretation of square law variation of the aperture we can 

 examine several additional useful problems. We can for instance justify 

 the commonly used relation 



for the minimum permissible distance of the field source from an experi- 

 mental antenna test site. This distance produces an effective phase curva- 

 ture of X/16. We can examine optical antenna systems employing large 

 primary feeds, in particular those employing parabolic cylinders illuminated 

 by line sources. 



3.10 Ejffed on Pattern of Cubic Phase Variation 



If we assume a constant amplitude and a cubic phase variation <l>'{x) = 

 — kzx over the aperture from — a/2 < x < a/2 then equation (36) becomes 



F{a) = f"'e-"^'.e''^''''>"'°".(ix (46) 



J- a/2 



If ksx < ~ then it is a fairly good approximation to write 



e-^'l^' = I - ikW - ^Af -^ ... (47) 



from which it follows that (46) can be integrated since it reduces to a sum of 

 three terms each of which can be integrated. 



Typical computed patterns for apertures with cubic phase variation are 

 plotted in Figs. 15 and 16. Cubic phase distortions are found in practice 

 when reflectors or lenses are illuminated by primary feeds which are off axis 

 either because of inaccurate alignment or because beam lobing or scanning 

 through feed motion is desired. The beam distortion due to cubic phase 

 variation is known in optics as 'coma' and the increased unsymmetrical lobe 

 which is particularly evident in Fig. 16 is commonly called a 'coma lobe'. 



