PRODUCTION OF TELEVISION SIGNALS 603 



In the case of the circular aperture we can divide the aperture up 

 into narrow elements parallel to the direction of motion, as shown 

 in Fig. 30. Elements at a distance h from the middle line of the 

 strip have lengths 



2h = 2 VrV4 - K\ (5) 



Each element considered as an independent rectangular aperture has 

 the frequency characteristic 



sin t\oo sin w^T'^jA — h'^ 



CO 0) 



The mean of all of these elementary frequency characteristics is 



^ - sin [w VrV4 - h^2dh =7^ sin [co VrV4 - n'^dh 



i J-T12 ^ ^ ^Jg 



1 r" ■ r Til I 4F1 2dh 



= — I sin [To)l2->l\. — x^~\dx 



= ^AiTcol2), 



Z.03 



where J\ indicates a Bessel function of the first order. In place of 



1 1-1 . . . . sin {To)l2) ^ . 

 the amplitude variation function tor the square aperture, 



w 



we have — as such a factor. From the very nature of the 



CO 



physical processes under consideration it follows that this average 

 value of the elementary frequency characteristics is effectively the 

 frequency characteristic of the aperture as a whole. 



