406 



Lord Rayleigh's Investigations in Optici 



tral tangent plane. The third column relates to an aperture 

 about a fourth part larger, for which the extreme aberration 

 is (1*26) 3 quarter-periods or nearly half a period, and the 

 fourth column relates to an aperture such that extreme aber- 

 ration amounts to about three quarters of a period. 



From columns 2 and 3 we see that an increase of aperture 

 up to that corresponding to an extreme aberration of half a 

 period has no ill effect upon the central band, but it increases 

 unduly the intensity of the first lateral band at ?n= +3*2. 

 Indeed the principal objection to much greater apertures is 

 this augmented importance of the lateral band. The practical 

 conclusion is that the best results will be obtained with an 

 aperture giving an extreme aberration of from a quarter to 

 half a period, and that with an increased aperture aberration 

 is not so much a direct cause of deterioration as an obstacle to 

 the attainment of that improved definition which should accom- 

 pany the increase of aperture. 



We will now suppose the aperture given, and examine the 

 effect of increasing aberration. In applying the tabular results 

 we must have regard to the factor (Ac)~~ s , which occurs in (4), 

 and we must take account of the variation of the relative scale 

 of m and f in passing from one curve to another (£ oc?n \/4c). 

 The results for three cases are expressed graphically by the 

 curves in fig. 6. The first, which rises highest, represents 



Fig. 6. 



the intensity at the various points of the focal plane when 

 there is no aberration — the same as in fig. 1. The second and 

 third curves represent the intensities when the extreme aber- 

 rations are a quarter period and half a period respectively. 

 The total areas of these curves are the same, since the whole 



