258 



THE DIFFRACTION THEORY OF MICROSCOPY 



by the presence of the object specimen. Equation 8.1 is most readily 

 applied to object specimens which can be subdi\'ided into areas of 

 practically constant optical path. Equation 8.1 is not the most con- 

 venient way of formulating the function x in the case of spherical 

 particles (more generally, lens-like particles). 



We shall now derive Eq. 8.1 on the supposition that the virtual image 

 of the source of light as formed by the combined lamp and substage 

 condensers behaves as a self-luminous source. Because the condenser 

 diaphragm is located at or slightly inside the first focal plane of the 



iX„y|,(plane of the virtual image of the source) 



\j:i, = Ms Xs 



Fig. VII. 6. Relative locations of the object plane A'oFo and tlie plane X„Yv which 

 is occupied by the virtual image of the source of Ught. The distance Z„ will be great. 



substage condenser, the plane X^Yy of the virtual image is located far 

 to the left of the object plane XqYq of Fig. VII. 0. The luminous portion 

 of the X^F-t, plane is limited to the image formed in this plane of the 

 opening in the condenser diaphragm. 



Wavelets from a point P^ within the luminous portion of the distant 

 XvYv plane expand according to the law e^"'""^''/-^- For points belonging 

 to the object plane 



wherein 



= [R^^ + xq^ + ijQ- - 2(xox„ + yoVv)]^; 



Rxi = {Xy" -\- l/v" + Zu")^. 



(8.2) 



(8.3) 



When Zv is large enough, R^^ » xq + Vq . Then with excellent 



