A THEORY OF SCANNING 485 



In the two-dimensional case T(^, 77) is defined, for a hole in an 

 opaque screen, as unity throughout the area of the hole, and zero for 

 the screen. Where the aperture is covered with a non-uniform screen 

 T may take on intermediate values. 



The transfer admittances have been calculated for a variety of 

 shapes of aperture in Appendix I. It will be noted that for those types 

 of aperture for which T can be separated into two factors, one a func- 

 tion of ^ only and the other a function of 77 only, namely, for which 



TiU, 77) = rj(^) • T,(r,), (21) 



then equation (20') becomes 



Yi{-m, n) = I T^(^) exp {iTrm^/a)d^ 1 ^,,(17) exp (iirnr]/a)dr] 



»^aperture •-'aperture 



= Y^im) . Y,(n) (22) 



and Fj and F, are each one-dimensional integrals of the type illustrated 

 in Fig. 12. 



The rectangular aperture is a simple case of this type. Assume 

 the field to be scanned in N lines and take the dimensions of the aper- 

 ture, 2c and 2d parallel to the x and y axes, respectively, as 



Then 



,, / s sin Trmc/a 

 Y^{m) = 



and 



wmc/a 



sin TTfid/b 

 ■wnd/h 



and the frequency corresponding to a given signal component mn is, 

 from equation (11) 



Thus, Yi{m, n) considered as a function of the signaling frequency 

 corresponding to each component of indices mn, consists of a succes- 

 sion of similar curves u/2a cycles apart, corresponding to the successive 

 integral values of m (these curves are themselves really not continuous 

 but consist of a succession of points u/{2aN) cycles apart. For con- 

 venience, however, the drawings will always show the curves as con- 



