A THEORY OF SCANNING 



473 



The Frequency Spectrum of the Signal 



When an image field is scanned by a point aperture tracing across it, 

 each portion of the picture traversed causes variations in the light 

 reaching the light sensitive cell and is thus translated into a corre- 



<^ 0.6 



2 0.4 



< 



UJ 



> 



<,0.2 



0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 



WAVE LENGTH IN TERMS OF DIAMETER OF CIRCLE A. 



Fig. 5 — Amplitudes of field components for a circular area of brightness. 



spending signal. Further, each Fourier component in the field is trans- 

 lated into a corresponding Fourier component in the signal. An equiv- 

 alent translation occurs when a pencil of light traces over a photo- 

 graphic film in telephotography, or when a subject is scanned by a beam 

 of light in television, whether or not a simple flat two-dimensional image 

 is ever physically formed at the transmitting station. For clarity and 

 simplicity, the discussion will be confined to the case in which a point 

 aperture traces across a plane image field. 



In most systems the aperture traces a line across the field and then 

 there is a sudden jump back to the beginning of the next succeeding 

 line. This discontinuous motion is naturally not easily subjected to 

 mathematical treatment. It is much simpler to deal with the equival- 

 ent result that would be obtained if the scanning point, instead of trac- 

 ing successive parallel paths across the same field, moved continuously 

 across a series of identical fields. Such an equivalent scanning motion 

 can fortunately easily be used because a double Fourier series represents 

 not only a single field, but a whole succession of identical image fields 

 covering the entire xy plane, and repeated periodically in both the x 

 and y direction as illustrated in Fig. 6. 



