498 BELL SYSTEM TECHNICAL JOURNAL 



eous pattern," for /x equal to 2 and — 2, respectively, for m = 0. (The 

 shift from m' = to m' = ±1 and ± 2 has been ignored since if N is 

 at all large this has a negligible effect on Yim', n'), as may be noted from 

 Fig. 13.) An examination of Fig. 17 and a consideration of the nature 

 of Y(m, n) and Y{m' , n') shows that the principal interference effect 

 will come from the pattern for which |m| = 1, and that the relative 

 amplitudes become very small as /i increases in absolute magnitude. 

 In general, therefore, only the first extraneous pattern may be con- 

 sidered as of really serious importance. Considering this pattern in 

 Fig. 17 it will be seen that the amplitude F(0, n) F(0, n') increases as 

 \n'\ increases from zero, the extraneous components becoming more 

 and more comparable to the normal components. At N/2, both com- 

 ponents are of the same amplitude, and the extraneous components are 

 therefore masking the normal components. It will be noted that the 

 index region at N /2 corresponds to the centers of the relatively empty 

 regions in the frequency spectrum of the signal. The large masking 

 effect caused by the extraneous components explains why such small 

 signal energy as exists in these regions is almost completely incapable 

 of transmitting any useful image detail. 



It will be noted that the components with values of \n'\ in the 

 neighborhood of N/2 and greater are in general almost parallel to the 

 direction of scanning. The masking loss will therefore be greatest 

 across the direction of scanning and practically negligible along the 

 direction of scanning. This is quite reasonable because the extraneous 

 components constitute the line structure of the reproduced image, and 

 should therefore cause the greatest loss of detail across the direction of 

 scanning. 



For clarity in the explanation up to this point, masking loss has been 

 discussed as if an extraneous component could only mask the normal 

 component with which its indices happened to coincide. In reality the 

 masking is of a more serious nature. An extraneous component un- 

 doubtedly obscures any normal component that has about the same 

 wave length and the same slope across the field even though it does not 

 exactly coincide in these characteristics. 



More detailed curves than Fig. 17, showing the amplitudes of the 

 extraneous components have been prepared in Appendix II. These 

 also show the results for other index values of m than zero, and for 

 other than the simple rectangular aperture. The results indicate that 

 the extraneous patterns diminish in intensity progressively as more 

 overlap is tolerated between adjacent scanning lines, at the expense, of 

 course, of increased aperture loss for the normal components. This 

 point will be taken up again below. 



