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BELL SYSTEM TECHNICAL JOURNAL 



The equivalent of scanning a single field in parallel lines is obtained 

 by assuming that the scanning point moves across the repeated fields 

 along a sloping path as indicated. Let u be the velocity parallel to 



Fig. 6 — Array of periodically recurring scanned fields. 



the X axis and v the velocity parallel to the y axis. Then the picture 

 illumination at the scanning point at any instant, and consequently 

 the signal current, may be obtained by substituting 



J\i Jo't'y 



Vt 



in the double Fourier series representing the image field, equation (8). 

 Of course the entire expression must be multiplied by a factor K which 

 is the constant ratio between the signal current and the picture 

 illumination. This gives for the real signal as a function of time "^ 



2 It will be noted that this process does not explore the picture completely, inas- 

 much as, no matter how fine the scanning, there will always be unexplored regions 

 between scanning lines. In this respect the process is quite analogous to that 

 followed in analyzing a function of a single variable into a simple Fourier series 

 when the values of the function are given only at discrete (even though closely spaced) 

 values of the variable. The complete exact theory, which necessarily depends upon 

 the size and shape of the finite scanning spot or aperture, will be given further below. 



