A THEORY OF SCANNING 497 



an imperfect optical system. Specifically the effect of a sending or 

 receiving circular aperture alone, or Y{ni, n), is the same as that caused 

 by an optical system which reproduces a mathematical point in the 

 original as a circle of uniform illumination (circle of confusion) in the 

 image of the same size (with respect to the image) as the scanning 

 aperture. The effect of the two apertures in tandem, or [F(w, w)3^, 

 may be very closely simulated by a circle of confusion of about twice 

 the area of either aperture, as can be judged from the discussion which 

 has been given above regarding the curves in Fig. 12. 



The Extraneous Components 



It will be clearly understood that the discussion immediately pre- 

 ceding has been confined entirely to the normal image components, 

 that is, to the image that would be seen if no extraneous components 

 were present. In particular, it should be clear that the reproduction 

 of normal detail equally well in the direction of scanning and across the 

 direction of scanning does not mean that the details of the total result- 

 ant image will be seen equally well in the two directions, for the 

 extraneous components will to a certain extent mask the normal 

 image. 



In the same manner as for the normally reproduced components, the 

 amplitudes of the extraneous components, according to the preceding 

 theory, are given by equation (40) above, where 



m' = m + ju, 

 n' = n — txN, 

 where 



M = an integer = m' — m = (\/N){n — n'). (41) 



The composite transfer admittance F(w, n) • Y{m', n') may therefore 

 be taken as a measure of the extent to which the extraneous components 

 are introduced. If a picture be assumed in which all the original com- 

 ponents have the same amplitude then Y{m, n) • Y{ni', n') is the 

 amplitude of the extraneous components. 



A given original component of indices m, n gives rise to a whole 

 series of extraneous components, ni' , n' , as ^l ranges from 1 up through 

 the positive integers and — 1 down through the negative integers. 

 As an illustration we have plotted the case of a rectangular aperture 

 of a width just equal to the scanning pitch, in Fig. 17, which has just 

 been referred to in considering the normal components. The two 

 lines marked "first extraneous pattern" show the relative amplitudes 

 for /i equal to 1 and — 1, respectively, and those marked "second extran- 



