A THEORY OF SCANNING 475 



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I{t) = KY. L O'mn COS 

 m=Q n= — oo 



I mu , nv\ ^ , 1 ,^^. 



Thus if u and v are constants, each wave of the image field gives rise 

 to a corresponding Fourier component of the signal. The frequencies 

 of the signal components are 



^ 2a^2b ^^^^ 



The frequency spectrum of the signal is thus made up of a series of 

 possible discrete lines, the position of which in that spectrum is deter- 

 mined by u and v, that is, by the particular scanning motion employed. 

 We shall designate these lines by the indices m, -\-n and m, —n, as 

 they are correlated with the particular components of the image field 

 that generated them. 



A different choice of values for u and v (so long as these, once having 

 been chosen, remain constant) changes the location of the lines in the 

 frequency spectrum, but their amplitudes, depending only on the 

 corresponding components of the image field, remain unchanged. In 

 other words, the lines in the frequency spectrum of the signal are 

 characteristic of the image field, and the scanning motion merely deter- 

 mines where they will appear in the frequency spectrum. Thus, if for 

 a given subject the distribution of energy over the frequency scale is 

 known for one method of scanning, it can be predicted for a great many 

 other methods. 



To scan a field in lines approximately parallel to the x axis, the 

 velocity v must be made small compared to ii. Under such conditions, 

 u/{2a) of equation (11) is the line scanning frequency and v/{2b) is the 

 frequency of image repetitions (or "frame frequency"). The fre- 

 quency spectrum of the signal for a "still" picture thus consists of 

 certain fundamental components at multiples of the line scanning 

 frequency u/{2a), each of which is accompanied by a series of lines 

 spaced at equal successive intervals to either side of it. The spacing 

 between these satellites is the image repetition or frame frequency 

 v/(2b). 



If the picture changes with time the amplitudes of these fundamental 

 lines and their satellites are modulated, also with respect to time. In 

 other words they each develop sidebands or become diffuse. The 

 diffuseness will not overlap from satellite to satellite unless the fre- 

 quency of modulation becomes as great as half the frame frequency. 



