66 AN ELEMENTARY THEORY OF PHASE MICROSCOPY 



There will now be a different P wave and hence a different D wave for 

 each particle, but the imdeviated wave remains the same as for the single 

 particle. The undeviated wave passes through the conjugate area and 

 is subsequently spread over the entire plane of the image. The un- 

 deviated waves diverge from the particles at which they originate, are 

 spread over the complementary area, and are reconcentrated upon the 

 geometrical images of the respective particles from which they originate. 

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

 again determined by the undeviated wave alone, whereas the amplitude 

 and phase distribvition over the geometrical images of the various 

 particles is determined by the resultant wave produced by the inter- 

 ference of the undeviated wave with the deviated waves over the 

 geometrical image of each of the particles. Within the scope of the 

 elementary theory, the deviated waves from the various particles act 

 independently in the sense that they do not disturb one another. 

 Consequently the amplitude and phase distribution may be computed 

 for each particle from the law^s already described for the single particle. 

 It is to be expected, as can be verified from the more complete theory, 

 that the amplitude and phase distributions computed from the elemen- 

 tary theory will depart further from the truth as the particles are 

 crowded together. 



If the object specimen is a grating, the elevations of the grating may be 

 regarded as the surround and the troughs may be regarded as constitut- 

 ing the various particles or, indeed, a single particle. The generaliza- 

 tion of the quantitative elementary theory to complex object specimens 

 is therefore similar to the generalization of the more qualitative theory 

 as described in Sections 3.3 and 3.4. 



The following theorems follow from the statements of this section and 

 are valid within the scope of the elementary theory. 



Theorem 6: Those particles which appear with similar contrast, no 

 matter which diffraction plate is selected, have similar amplitude trans- 

 missions and optical paths. 



Theorem 7: Those particles which appear with dissimilar contrast 

 have dissimilar amplitude transmissions and. optical paths. 



These theorems are of practical value in making comparisons among 

 the object particles and can be expected to hold with at least fair degree 

 of reliability when the particles are separated by distances greater than 

 four times the limit of resolution of the objective. On the basis of the 

 general theory also, the size, shape, and separations of the particles are 

 found to influence contrast in the images of the particles. Consequently, 

 Theorems 6 and 7 cannot be applied without reservation. 



