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BELL SYSTEM TECHNICAL JOURNAL 



y = -^ h were cut out and superposed to form the image. Let 

 Ez{x, y) be the illumination of this strip. Then, since the exponential 



Fig. 14 — -Analysis of received picture. 



factor of the integrand in equation (27) is periodic in x and identically 

 reproduced in each of the fields, the integral is equal to 



Bm'n' = -T—u I I ^ii^^ y) exp -«V ( — - + —r-] dxdy. (28) 



The limits —b to -\-b in y and the infinite limits in x may be used be- 

 cause the illumination is zero everywhere outside of the strip. 



Again taking a coordinate system ^-q fixed with respect to the aper- 

 ture, such that 



x = ^ + ut, y = 7] + vt (29) 



the instantaneous illumination of any point covered by the aperture is, 

 neglecting constant factors, 



T2{^, v)I{t) = T^ix - ut,y - vt)I(t). (30) 



The total illumination of any point xy in the image strip is thus 



Esix, y) = I T2(x — ut,y — vt)I{t)dt. 



Substitution in integral (28) and a change in the order of integration 



