262 



THE DIFFRACTION THEORY OF MICROSCOPY 



through the object specimen in the manner iUustrated by Fig. VII. 7. 

 The rays that pass through the surround continue uninterrupted except 

 at the cover glass or other discontinuities which are of secondary interest 

 and which need not be considered here. The rays that pass through the 

 interior of the particle suffer a lateral displacement but emerge parallel 

 to their original course. Rays that pass through the edge e of the 

 particle suffer both displacement and deviation. The magnitude of the 

 displacement and deviation depends on the physical properties at the 



Xq,Yq (object plane) 



Po' 9o' 



Particle; fix^, y^, p^, q^) = f^ 



Surround; f(x^, y^. p^. q^) = f^ 



Fig. VII. 7. Passage of rays through plate-like particles. 



edge of the particle. As a result, the rays that emerge from the edge of a 

 relatively thick particle may form a brush of rays po', qo'- If the particle 

 becomes very thin, this brush effect becomes weak and, finally, negligible. 

 Herein lies an important difference between thick and thin plate-like 

 particles. 



Suppose first that the particle is so thin that the brush effect may be 

 neglected. For points Xq, yo in the surround we may set 



f(xo, yo, Po, qo) = fiipo, go) = |/i(7>o, go)| e'^'''^'^^'''^'\ 



For points Xo, yo in the particle, we may set 



fixo, yo, Po, qo) = foiPo, qo) = |/o(po, 9o)| e' ^^^^"^^«'^°\ 



(9.1) 



(9.2) 



The amplitude transmissions \fo(po, qo)\ and \f\ipo, qo)\ are to be 

 determined along the direction in which the rays pass through the 



