PHASE-CONTRAST MICROSCOPY 67 



value of the ordinate). Both sinusoids Kj and K, are identical as the 

 bacterium is invisible throughout the field, viz., the light-intensity is 

 constant over the whole field. Now, intensity being proportional 

 to the square a^ of amplitude a, all vibrations passing through the 

 specimen have the same amplitude and, more particularly, the vibra- 

 tions Vi and K, which, hence, are identical. 



These two vibrations, although but slightly shifted in relation to 

 one another, do exhibit either the path difference 1 or the phase 

 difference fp = InAjX. Assuming the J/A ratio and, therefore, (p to be 

 small, the square (p^ of the phase difference fp can be disregarded. 

 Let us consider the sinusoid V^ denoting the vibration traversing the 

 bacterium. It can be assumed that this sinusoid is the sum of 2 sinusoids : 



(a) Sinusoid K,, 



(b) Sinusoid V^ (shifted) by A/4 {njl in phase difference) in relation 

 to the former and of low amplitude OM. A glance at Fig 2.3 reveals 

 that the summed ordinates of these two curves {V^, and V^) do evince 

 sinusoid V^ at once. The equation: y = a^mlnxjl readily yields the 

 amplitude OM: all that is required is to substitute x for A since xjX, 

 i.e. Ajl, being small, sin2j7: 1/-^ can be substituted for InAfX. Under 

 these conditions, then: 



27iA 

 OM ^a -y ^a<p. (2.1) 



A 



Let us write a -^ I and, hence, the amplitude OM of the vibration 

 F3 is denoted merely by 7. Let us now give a physical meaning to 

 vibrations V^, V^ and Kg by going into Figs. 2.1 and 2.3. The si- 

 nusoid F3 matches the bacterium-diffracted vibrations; its amplitude 

 OM is proportional to 7 and is the lower as the n — n' difference is 

 smaller. IfA7 _= n' the phase difference between K, and V-2 i. e. the 

 phase jifference between ravs 1 and 2, F ig. 2.2 . is zero. The v ibration 

 Kg vgnkhes and theie_is_jT o diffracted light any longer. As to the 

 vibration V^, it denotes the direct fight passing at S[ in F ig 2.1, which 

 is spread over the image P' . 



To sum up, the vibration K^, passing through the bacterium can 

 be divided in two: (a) the vibration K2, which is the same as in the 

 remainder of the field where there is no bacterium; (b) the vibration Kg, 

 diffracted by the bacterium and the ampfitude of which, proportional 

 to fp, is all the smaUer as // is closer to n . 



The direct and the diffracted vibrations, V.^ and F3, respectively, 

 are shifted by XjA (phase difference: njl) regardless of the 7 value, 



