RESOLVING POWER OF PHASE MICROSCOPES 71 



This does not prove that the position of the first minimum is unaffected 

 by the choice of diffraction plate l)ut demonstrates that it is possible to 

 choose the zonal aperture ratios pi/pm and P2I Pm and the h and 5 values 

 of the diffraction plate in such a manner that the first minimum of the 

 primary diff'raction curve falls practically at the Airy limit. In some 

 cases the constants of the diffraction plate can be chosen so that the first 

 minimum in the energy density occurs at a position slightly inside the 

 Airy limit, as in Fig. 11.215. On the basis of Airy's criterion for 

 resolution, the resolving power of an objective for two particles is 

 determined by the distance r from the diffraction head to the first 

 minimum in the energy density of the primary diffraction curve. Since 

 it is possible to choose diffraction plates so that the first minimum in 

 the energy density falls practically at the Airy limit, no significant gain 

 or loss in resolution is to be expected on this account from a well-chosen 

 diffraction plate. 



The diff'raction plates of Fig. 11.22.4 and B differ only in ring width. 

 Thus po — pi is greater in B than in .4. It will be noted that the first 

 minimum in the energy density occurs at a greater distance from the 

 diffraction head with the diffraction plate which has the narrower ring 

 width. One can expect that with the /r and 5 values of Fig. 11.22 

 the diffraction plate having the wider ring width should give the better 

 resolution. In general, higher contrasts can be produced by diffraction 

 plates having the narrower annuli. This can be expected from the fact 

 that the undeviated and deviated waves are separated more completely 

 at diffraction plates with the smaller conjugate area. In practice, the 

 difficulties of designing a diffraction plate so as to attain the most 

 favorable compromise between contrast and definition are augmented by 

 the spherical aberration which is always present in objectives of high 

 numerical aperture and by the curvature of field in the image of the 

 opening in the condenser diaphragm. 



It will be seen that the energy densities at the diffraction head are 

 decidedly lower for all illustrated diffraction plates than with the Airy- 

 type objective. A particularly marked loss of energy density at the 

 diffraction head occurs with the 2.50BdzX/4 diffraction plate. A 

 portion of the lost energ}^ is due to absorption at the conjugate or 

 complementary area. Since the complementary area bears the absorb- 

 ing material in a B-type diffraction plate and since the complementary 

 area is large compared to the conjugate area, most of the reduction in 

 the energy density at the diffraction head with the 2.50B±X/4 diffrac- 

 tion plate can be attributed to absorption at the diffraction plate. 

 Losses due to such widespread absorption at the diffraction plate serve 

 mainly to lower the energy content of the entire diffraction image and 



