OBJECT SPECIMENS HAVING PERIODIC STRUCTURE 33 



are far enough apart with relation to the resolving power of the objective, 

 a negligible amount of overlapping will take place in the image plane of 

 the deviated waves that belong to different particles. Under these 

 circumstances, the images of the various particles will be formed inde- 

 pendently of one another. The above-described principles which apply 

 to the image formation of a single particle apply, therefore, to the 

 imagery of each particle in a field consisting of several well-separated 

 particles. When the separation of two or more particles becomes so 

 small that the overlapping of their diffraction images is no longer 

 negligible, more general considerations are required in order to under- 

 stand the resulting image formation. 



3.4. Extension of the elementary theory to object specimens 

 having periodic structure 



If a simple diffraction grating is employed as the object specimen, the 

 troughs of the grating can be regarded as a complex particle and the 

 elevations of the grating can be regarded as the surround, or vice versa. 

 Provided that the light transmission of the troughs and elevations are 

 alike, and provided that the optical path difference between the eleva- 

 tions and troughs is a small fraction of a wavelength, the state of contrast 

 between the geometrical images of the troughs and of the elevations can 

 be predicted from the very same rules that have been explained in the 

 above subsections for an object field consisting of a single particle in a 

 uniform surround. Suppose, for example, that the optical path through 

 the elevations of the grating exceeds the optical path through the 

 troughs. Let us regard the elevations as the "particle." The particle, 

 and hence the elevations, should appear brighter or darker than the 

 troughs according as the optical path of the conjugate area is increased 

 or decreased with respect to the optical path of the complementary 

 area by 3^ wavelength. Contrast in the image should be optimum 

 when the amplitudes of the undeviated and deviated waves have been 

 equalized by placing the absorbing material upon the conjugate area of 

 the diffraction plate. These predictions are in good qualitative agree- 

 ment with experiment so long as the optical path difference between the 

 elevations and troughs is small. 



The crossed or double periodic structure of many object specimens is 

 due to a lattice arrangement of particles. If the optical path of these 

 particles exceeds that of their surround by a small amount, the conclu- 

 sions of the elementary theory may be applied to predict that the 

 particles will appear brighter or darker than the surround according 

 as the optical path through the conjugate area of the selected diffraction 

 plate has l)een increased or decreased by approximately 3^ wavelength 



