A THEORY OF SCANNING 



481 



when it reproduces all the image components represented by a given 

 signal component, it suitably suppresses all those but the dominant one 

 desired. 



Effect of a Finite Aperture at the Transmitting Station 



In the preceding pages the scanning aperture has been assumed as 

 infinitesimal in size, or merely a point. In any actual scanning system 

 the necessary finite size of the aperture introduces effects which will 

 now be considered for the transmitting end. 



Let us first review briefly the usual theory of this effect when the 

 picture is analyzed simply as a one-dimensional Fourier series. Ac- 

 cording to equation (3) above, this series is 



+ 00 



Ei(x) = J^ AnexpiT{nx/L). 



Let ^ be a coordinate fixed with respect to the scanning aperture as 

 shown in Fig. 11 and let the optical transmission of the aperture for 



E (x)ORIGINAL PICTURE 



Fig. 11 — Analysis of one-dimensional scanning operation. * 



any value of ^ be T{^).^ Then if x is taken as a coordinate of the 

 origin of ^ the illumination at any point ^ of the aperture is 



-foo 



■Ei(» + ?) = L Anexpiirinlx + ^2/1), 



(15) 



3 This optical transmission may represent either the transparency of an aperture 

 of constant width or the width of an aperture which is a shaped hole in an opaque 

 screen. 



