24 AN ELEMENTARY THEORY OF PHASE AHCROSCOPY 



mer's theorem. These additional violations consist in altering the 

 relative amplitude and phase of the deviated and undeviated waves 

 originating bj^ diffraction at the object specimen. This alteration is 

 accomplished by taking advantage of the facts that the undeviated 

 wave passes through the conjugate area of the diffraction plate and that 

 most of the de^'iated wave passes through the complementary area of 

 the diffraction plate. Because the characteristics of the image are 

 determined by the interference phenomena that take place between the 

 undeviated and deviated waves as they reach the plane of the image, 

 and because the amplitude and phase of the resultant wave formed by 

 the interference of the undeviated and the de^'iated waves depend on 

 the relative amplitude and phase of the undeviated and deviated waves, 

 it is possible to choose a diffraction plate that produces optimum contrast 

 in the sharply focused image plane. The manner in which optimum 

 contrast can be obtained in the sharply focused image plane will now be 

 discussed in detail for the particle differing from its surround only by a 

 small amount in optical path. 



If the opening in the condenser diaphragm is chosen in the usual 

 manner as a narrow annulus, as in Fig. II. 5, the conjugate area of the 

 diffraction plate formed by the image of the opening in the condenser 

 diaphragm will also be a relatively narrow annulus. The complemen- 

 tary area is then the remaining area of the diffraction plate within the 

 clear aperture of the second focal plane of the ol)jecti\'e. 



As we have seen in Section 3.1, the light radiated from a point C in 

 the condenser diaphragm is incident as a substantially plane wave upon 

 the object plane. The incident wave is split by diffraction at the object 

 specimen into an undeviated *S wave, which emerges from all elements 

 of area in the object plane, and into a deviated D wave, which emerges 

 from elements of area that are confined almost entirely to the particle. 

 The undeviated wave passes through the. conjugate area and is subse- 

 quently spread over the entire image plane, whereas the deviated wave 

 is spread mainly over the complementary area of the diffraction plate 

 and is then reconcentrated upon the neighborhood of the geometrical 

 image of the particle. These phenomena are illustrated in Fig. II. 5. 

 The amplitude and phase distribution over the image of the surround is 

 determined by the undeviated wave alone, whereas the amplitude and 

 phase distribution of the light over the geometrical image of the particle 

 is determined by the resultant wave produced by the interference of the 

 undeviated and deviated waves as they pass through the geometrical 

 image of the particle. 



The ordinary microscope is one whose diffraction plate is uncoated 

 so that the amplitude and phase transmissions of the conjugate and 



