A THEORY OF SCANNING 493 



The quantity Fa it will be noted is almost the same, for the receiving 

 aperture, as the Yi is in equation (20') for the sending aperture. 

 Thus, on the normally reproduced component the receiving aperture 

 merely adds whatever filtering action it has to that which has already 

 been caused by the sending aperture. 



As noted, in addition to this normal component, the integral (35) 

 exists in general for other values of m' and n' and thus gives rise to 

 extraneous components in the reproduced image. If equation (36) is 

 applied particularly to the usual system of scanning in N lines in 

 which as in equation (12), v = uh/{Na), it becomes 



m+^=m'+^. (39) 



For values of m' and n' satisfying equation (39), the reproduced com- 

 ponent has the complex amplitude (neglecting constant real factors) 



Bm'r.' = AmnYrim, u) Yi{m' , n'). (40) 



Looking back at equation (14) and comparing it with equation (39) 

 it may be seen that these components correspond in indices to the 

 original image components that are confused in the signal to give only 

 one signal component. The result is, therefore, after all quite reason- 

 able from a physical point of view. For when a signal of a certain 

 frequency is transmitted over the line the receiving apparatus has no 

 information by which to judge which component in the original picture 

 it is supposed to represent. So, as shown by equation (40) it impar- 

 tially reproduces every one of the components it could possibly repre- 

 sent, each component with the intensity and phase it would have if it 

 were really the one intended to be represented by the signal. The 

 components are then all superimposed in the picture. 



From this development it is clear that the process of scanning an 

 image field in strips and reproducing it in a similar manner not only 

 reproduces the components of the original image but also introduces 

 extraneous components. The reproduced field thus consists of two 

 superposed fields: a normal image built up from the normally repro- 

 duced components, and an additional field of extraneous components. 

 Although not really independent, it is convenient to consider these 

 two fields as existing separately, and thus to think of the normal image 

 field as having an extraneous field superposed on it. 



Considering the normal field alone, we may term the reproduction of 

 its detail as the reproduction of normal detail. There is a loss in such 

 reproduction, for both the transmitting and receiving apertures intro- 



