294 THE DIFFRACTION THEORY OF MICROSCOPY 



pi = 0.0033, pm = 0.033, and \M\p„, = N.A. = 0.14. Despite the fact 

 that the value pi = 0.0033 was much larger than the conservative 

 theoretical values re([uired by Eqs. 15.11 and 15.18, the observed 

 A region extended throughout large portions of relatively large particles. 

 Moreover for the A region, the h and 8 values producing extreme 

 contrast between the A region and the surround were in substantial 

 accord with the elementary theory. 



When the method of this section is applied to diffraction plates having 

 annular conjugate areas, as in the usual practice of phase microscopy, 

 an A region is found to exist. This region is increased b}^ increasing the 

 numerical aperture of the objective and by decreasing the width of the 

 conjugate area. It is, however, difficult to form an estimate of the 

 size of the A region. Whereas the function Hr{x, y) is of character 

 permitting an extended A region, the function Hs{x, y) is not readily 

 amenable to the purpose of relating the size of the A region to the 

 properties of the particle and of the optical system. Experiments 

 performed by Dr. H. Jupnik and described briefly by her in Section 5 

 of Chapter III are at least consistent with the conclusion that the 

 A region increases with decreasing width of the annular conjugate area. 



In summary, the geometrical image of the particle can exhibit three 

 distinctly different regions of contrast. In the .4 region the contrast 

 with respect to the image of the surround obeys the laws of the elemen- 

 tary theory of phase microscopy. The .4 region is usually surrounded 

 by the B region which may extend 5 or more Airy units beyond the 

 boundary of the geometrical image of the particle. The energy density 

 may change rapidly in the B region. The halo near the edge of the 

 geometrical image belongs, for example, to the B region. The C region 

 occurs only in the far interior of relatively large particles. The energy 

 density of the C region is equal to that of the surround when the ampli- 

 tude transmission of the particle is equal to that of the surround. The 

 C region is brighter or darker than the surround according as the 

 particle has higher or lower light transmission than its surround. Except 

 for the fact that the energy density of the C region is proportional to the 

 energy transmission of the conjugate area of the diffraction plate, the 

 C region is unaffected by a Zernike system of phase microscopy. All 

 three regions are predicted by the general theory, but only the A region 

 together with the region of the surround is predicted by the elementary 

 theory of phase microscopy. Experiment indicates the existence of all 

 three regions in the image of relatively large particles. The system of 

 microscopy described by Dyson (1949) is a method for avoiding the 

 C region. 



