PLATE-LIKE OBJECT PARTICLES 263 



particle and the surround for equal thicknesses of particle and surround. 

 However, arg/o(po, 9o) and arg/i(po, Qo), the phase transmissions, are 

 to be determined from the optical path along the normal to the particle 

 and for equal thicknesses of particle and surround. It is assumed that 

 the plane of the particle is practically normal to the optical axis. The 

 phase transmissions arg foipo, qo) and arg fiipn, cjq) do not depend on 

 po, Qo because phase variations due to po, Qo are automatically included 

 except for secondary effects due to the object specimen in the spherical 

 aberration function Wo(p, q). 

 If the surround is opaque, 



Jx(po,qo) =0. (9.3) 



If the surround is not opaque, as is usual in microscopy, one may set 



/i(Po,9o) = l (9.4) 



and write 



/o(po, qo) = gipo, qo)e'^ (9.5) 



in which A is the optical path difference between the particle and an 

 equal thickness of the surround with A considered positive when the 

 optical path of the particle exceeds that of the surround. g{po, Qo) is the 

 ratio of the amplitude transmission of the particle to the amplitude 

 transmission of an equal thickness of the surround. Now in systems- 

 of phase microscopy the conjugate area of the diffraction plate is ordi- 

 narily narrow. Conseciuently the range of po, qo is limited. Since 

 amplitude transmissions are slowly varying functions of po, qo, it 

 suffices to take 



g = giPom, qom) (9.6) 



where {pom, qom) are the median values of (po, qo)- Hence 



foiPo,qo) =ge'^; (9.7) 



h{Vo,qo) = l (9.8) 



express the object function /(.ro, ijo, Po, qo) for thin plate-like particles 

 in a transmitting surround. The amplitude transmission ratio g is to 

 be computed for the median value of po, qo of the bundle of rays incident 

 upon the object plane. If, for example, the opening in the condenser 

 diaphragm is a small hole centered upon the optical axis, the median 

 values of po, qo are po = 9o = 0- Q is then the amplitude transmission 

 ratio between particle and surround for rays that pass through the 

 object plane along the normal to the object plane. 



Suppose next that the particle is so thick that the brush effect at its 

 edge cannot be neglected. Equations 9.7 and 9.8 still hold for points 

 ^0, Vo which are located within the edge and beyond the edge of the 



