602 



BELL SYSTEM TECHNICAL JOURNAL 



Let T = time required for the aperture to pass a given point, 

 Fig. 29. 



Let 9?(/i) be height of aperture at distance /i from its center. 



Fig. 29 Fig. 30 



Analysis of the aperture 



The instantaneous amount of hght passing through the aperture is 



n+Tl2 



F{t) = f ^{h)mdt 



>t+Ti2 



(piti)dti I A{i>)) cos [/iW + $(w)]</co 



t- Tl2 ^0 



(2) 



->t+Tl2 



= 1 A{ix!)dw I (^(/i) cos [/loj + ^{oi)~\dti. 



In the case of the rectangular aperture 



ip{ti) — a constant 

 and, except for a neghgible constant factor, 



/»oo r*t-\-Tl2 



F{t) = I A(u)do} I cos [/ico + $(co)]rf/i 



'Jo 'h- TI2 



(3) 



sin \{t - r/2)co + cJ'(co)] 



/»oo 



(4) 



sin 7"co/2 



cos [/co + $(w)]](/co. 



The transformation from f{t) to F{t) amounts merely to changing the 



relative amplitude of the Fourier components of f{t) by a factor 



sin Twll 

 proportional to . 



