A THEORY OF SCANNING 489 



complete function shows, by the very small transfer admittance in the 

 regions half-way between the fundamental lines, an additional reason 

 why the signal currents in these regions will be weak and relatively in- 

 capable of transmitting appreciable image detail. 



Examination of the other apertures for which computations are given 

 in Appendix I will show that, in general, for all ordinary apertures the 

 same broad phenomena are observed as for the rectangular aperture, 

 although it is not always possible to express the complete function in 

 the simple product form above, in which case the curves for the suc- 

 cessive values of m will vary gradually in shape. 



The final signal current is proportional to the light flux through the 

 aperture, given in equation (20). Neglecting constant factors it may, 

 therefore, be written as 



m = L E Fi(m,nM.„expiVf— +^)/. (24) 



Reconstruction of the Image at the Receiving Station 



At the receiving station the signal current is translated back into 

 light to illuminate an aperture moving in synchronism with the one 

 at the sending end. Neglecting constant factors the flow of light F^it) 

 to the receiving aperture is 



^2(0 = m- (25) 



Let Ez(x, y) be the resulting apparent illumination (integrated with 

 respect to time) at a point x, y of the reproduced image, or, in tele- 

 photography, the integrated exposure of the recording film at this point. 

 This illumination may be expressed as a double Fourier series, similar 

 to equation (7) (but primed subscripts will be used to distinguish them 

 from those of that equation). 



where 



Mx, y) = L L 5».'.' exp iV ( — + ^ y (26) 



Bm'n' =^^ j'^" £^E,(x,y)exp -i^ (^H^ ^I^yxdy. (27) 



Reproduction of detail in the image may be studied by comparing 

 these components with the corresponding ones of the original image. 



The apparent illumination is the same as if the aperture traced a 

 single strip across repeated fields in the xy plane as illustrated in Fig. 

 14, and all of the repeated fields included between y = — b and 



