36 AN ELEMENTARY THEORY OF PHASE MICROSCOPY 



only a portion of the deviated wave succeeds in reaching the plane of the 

 image. One assumption made in the elementary theory of phase 

 microscopy is that the entire deviated bundle reaches the plane of the 

 image. 



The separations C^„', C increase with decreasing spacing of the lines 

 of the object grating, and conversely. If, therefore, the lines of the 

 grating are suitably spaced, points C+i' and C_i' will fall in the comple- 

 mentary area. But with relatively coarse gratings it is possible that 

 one or both of points C+i' and C_i' may fall within the conjugate area. 

 With an unfortunately spaced fine grating it is possible that point C_-/ 

 may escape the portion of the conjugate area which is adjacent to C, 

 only to fall into another portion of the conjugate area near point B. In 

 such special cases another diffraction plate whose conjugate area is 

 located elsewhere must be selected in order to meet the physical require- 

 ments for obtaining phase microscopy. In Fig. II. 9 the secondary 

 spectral image C_2' is illustrated as falling within the conjugate area. 

 Although such an occurrence can be expected to impair contrast in the 

 image, its effect is not likely to be serious. If the conjugate area is made 

 very narrow, the likelihood that any point Cj.,/ will fall within the 

 conjugate area becomes so small that the first or higher spectral orders 

 may be said to pass through the complementary area. A second assump- 

 tion of the elementary theory is then fulfilled. In fact, the method of 

 phase microscopy hinges upon the physical possibility of complete or 

 partial separation of the undeviated and deviated spectral orders at the 

 conjugate and complementary areas of the diffraction plate, whether 

 these orders are determined by diffraction at an object grating or at some 

 other object specimen. 



It will be noted that the undeviated and deviated rays which leave a 

 particular point in the object grating, for example point a, are refocused 

 about the corresponding image point a'. It is seen how the undeviated 

 rays pass through the conjugate area, how the deviated rays spread over 

 the complementary area, and how these rays (and hence the undeviated 

 and deviated waves) overlap in the plane of the image to form the 

 image a' of a. 



If the object grating is remo\'ed, there will be no deviated rays. 

 Conseciuently, the light incident upon the object plane obeys the laws of 

 geometrical optics and passes only through the conjugate area. For 

 this reason, it is preferable to remove the object specimen in aligning the 

 phase microscope. If the object specinlen is allowed to remain on the 

 stage, specimens such as gratings, diatoms, and paramecia are likely 

 to deviate so much light into the complementary area that accurate 

 alignment of the instrument becomes difficult or impossible. 



