272 



THE DIFFRACTION THEORY OF MICROSCOPY 



in which 



1 VT 



f, = /_, = — sm— (1 - e 

 irv Z 



iA^ 



(10.1.2) 



Then from Eqs. 10.15-10.18 



A2TrilM)(pox+goy) 



Fo{x,y,po, qo) = — 



AI^ 



X 



°° / 



Po _v_ go 



M 2Ml' M 



\j^^i.(.xlMl)^ (10.1.3) 



For simphcity, let us consider the special case of narrow-coned, axial 

 illumination. The opening in the condenser diaphragm is a small hole 

 centered on the optical axis, and, correspondingly, the conjugate area 

 of the diffraction plate is a small spot centered on the optical axis. The 

 hole in the condenser diaphragm shall be made so small that one is 

 willing to accept the approximation 



From Eqs. 10.1.3 and 10.1.4 



M'Foix, y, Po, qo) = e(2xz7M)(pox+.o.) ^ p (^^^f^^i^i^xiMi)^ (10 15) 



Since Pip, g) = when p^ -|- g^ > pr,^, the largest value of v for which 

 P F^ is given by 



A^ N.A. 



2MI 



2\M\l 



^ Pm 



M\ 



(10.1.6) 



With the integer N determined by Eq. 10.1.6, v ranges from v = —N 

 to V = +A^inEq. 10.1.5. 



As in Eq. 7.6, the total energy density G{x, y) over the image plane 

 in the case of narrow-coned axial illumination obeys the law 



Gix, y) = K\Fq{x, y, po, go)|" == 



K 





^2ML 



\f.e 



iTvivxIMl) 



^ G{x). 

 (10.1.7) 



The constant K is proportional to the intensity of the source and to the 

 area of the opening in the condenser diaphragm. Whereas the amplitude 



