82 



INSTRUMENTATION 



with the fixed values 5 = —90°, y = ^, and hi = 1 also follow from 

 Eqs. 1 1. 8. 7 and 1 1. 8. 8 and are given by the relations 



Gs = h?; (1.4) 



Gp = /i2 + 2 - 2 cos A - 2/i sin A. (1.5) 



Consequently when A approaches zero, Gp approaches Gg, so that finally 

 the particle cannot be distinguished from its surround. When A = 0, 

 Gp = Gg = /r. The curves of Fig. III.l have been computed from 

 Eqs. 1.4 and 1.5 for the special case, h = 0.5. They show Gg and Gp as 

 functions of the optical path difference A. As A increases from zero, 

 the light intensity in the image of the particle first decreases until 



1.4 

 1.3 

 1.2 

 1.1 

 1.0 

 0.9 

 0.8 

 0.7 

 0.6 

 0.5 

 0.4 

 0.3 

 0.2 

 0.1 

 







10 20 30 40 50 



60 



70 80 



90 



Fig. III.l. The en<'rgv densities G., and Gp as a function of the value of A for par- 

 ticles for which g = I and which are observed with a phase objective described by 



6 = -90° and h = 0.5. 



{Gp)nnn Js reachcd, and then increases. For values of A greater than 

 53.13° the image of the particle becomes brighter than the image of 

 the surround. A reversal of contrast may therefore be expected at the 

 point A = 53.13° when 5 = —90° and h = 0.5. If, as a criterion of 

 good dark contrast, the value of K is taken between the limits 

 — 1 ^ /v ^ —"H, i.e., if the light intensity in the image of the particle 

 shall not exceed }4 the intensity in the image of the surrotmd, there will 

 exist for every value of /i a pair of values Aj and A2 such that the diffrac- 



