RESOLVING POWER OF PHASE MICROSCOPES 67 



18. EFFECT OF THE DIFFRACTION PLATE ON RESOLVING POWER 



The ciiiestion of whether or not the resolving power of the microscope 

 is impaired by the diffraction plate is a proper concern of the critical 

 microscopist. Whereas it is true that the zonal spherical aberrations of 

 the microscope objective are purposely increased in order to achieve 

 phase microscopy, both theory and experiment have shown that phase 

 microscopy is not necessarily obtained at the expense of resolving power. 

 The phase microscope was intended originally to improve contrast in 

 the image of unstained particles whose optical path differs so little from 

 that of the surround that the particle is practically invisible in the 

 ordinary microscope. In resolving two such particles a properly con- 

 structed phase microscope possesses greater resolving power than is 

 inherent in the ordinary microscope. This unpublished conclusion is 

 derivable from the more general theory of phase microscopy and is based 

 on more fundamental considerations than the obvious criterion that two 

 particles must be seen before they can be resolved. 



Unfortunately, a presentation of the more ad\'anced theories of 

 resolution is beyond the scope of this book. These theories have shown 

 that both the ordinary and the phase microscopes are capable of greater 

 resolution than is indicated by the Airy limit of resolution, that the 

 resolution of two particles depends to a marked extent on their absolute 

 and relative dimensions and on their amplitude and phase transmissions, 

 and that the less general classical theory of resolution is at best qualita- 

 tive. The following qualitative considerations based on the usual 

 classical concepts indicate that the resolving power of a phase microscope 

 need not differ appreciably from the resolving power of the ordinary 

 microscope. 



One effect of introducing a diffraction plate is to modify the diffraction 

 image which the objective forms of an object consisting of a pinhole in a 

 silvered slide. The plot of the energy density in this diffraction image 

 as a function of the radial distance from the center of the image will be 

 called the primary diffraction curve of the objective. The center of the 

 diffraction image will be called the diffraction head. An Airy-type 

 objective is defined as one whose diffraction curve obeys the usual law 



in which G{r) is the energy density in the diffraction image as a function 

 of the radial distance r in wavelengths from the diffraction head, J\ is a 

 Bessel function of the first kind and first order, and 



p,n = sin drr,, (18.2) 



