A THEORY OF SCANNING 



469 



Along any other line in the x direction a similar series holds with 

 different coefficients, that is, the ^'s are functions of y. They may 



Fig. 2 — Scanned field and Image, 

 therefore each be written as a Fourier series along y 



Am = 12 AmnexpiTr(ny/b). (6) 



n=— OT 



Substitution in equation (5) gives the double Fourier series, 



E{x, y) = E E Amnexpiir I— +^)- (7) 



For purposes of physical interpretation, as in the case of the simple 

 Fourier series, it is desirable to combine the -\-m, -\-n term with the 

 — m, —n term (giving the single (m, +w)th component) and similarly 



