Possibilities of Future Development 107 



h 



where A. := is the de BroeHe wavelength. The diameter of the 



mv 



confusion disk becomes, if we express r by the aperture angle a 



d — a\/2CXj (35) 



This shows that diffraction has not entirely destroyed Kompf- 

 ner's correction of the spherical aberration. The error diameter d 

 increases only with the first power of the aperture instead of 

 with the third. But a cannot be decreased below any limit, 

 because, as remarked above, Ar cannot be larger than the physi- 

 cal aperture 2a/. Substituting r = 2af into equation (34) we 

 obtain for the smallest, i.e., optimum size of the aperture 



Oopt 



- {scf} 



(36) 



For 60 kev electrons, / =z 0.5 cm and C =^ 2, this is 4.7 X 10"^ 

 radian. The optimum error diameter becomes 



do^t = O.SS(Ci)k^ (37) 



This, apart from the numerical factor, is the same formula as 

 equation (24) which we obtained for the uncorrected microscope. 

 If the relation between A and V is taken into account, the numeri- 

 cal coefificient of equation (37) is found to be 0.73 of the factor 

 of equation (24). But in the derivation of equation (24) we 

 have allowed a factor of 0.67 for the ratio of resolution limit to 

 confusion diameter. Making the same allowance in equation (37) 

 we see that the maximum gain by Kompfner's suggestion is 

 about 0.73 X 0.67 = 0.5. Though this appears an appreciable 

 improvement, it would be almost certainly more than outweighed 

 by the technical difiBculties arising from the complication of the 

 scheme. , 



2. Space charge corrected objectives 



Equation (37), hke equation (24), reveals the principal diffi- 

 culty in improving the electron microscope. Not only are C and 



