288 H. K. SCHACHMAN AND R. C. WILLIAMS 



through the field unscattered. As a consequence, the degree of structural 

 detail that can be discerned in the final image (or interference pattern) is 

 dependent upon the wavelength of the radiation employed and upon the 

 angular aperture of the imaging system. It has been established for many 

 years, both from theoretical considerations and from experimental tests, 

 that a simple formula can be written to represent the minimal distance 

 by which two opaque points can be separated in the object plane and 

 still be separably imaged (the "minimum resolvable distance"). The 

 formula is based upon diffraction theory and assumes that the effects of 

 spherical aberration are negligible. It may be written: 



where A is the wavelength of the radiation in air, 6 is the half-angle sub- 

 tended by the imaging lens at the object point, and n is the refractive index 

 of the medium between the object space and the lens. 



It is evident from Equation 37 that d^^^g cannot be less than about one- 

 half the wavelength employed, since n sin 6 cannot be made much greater 

 than 1.25. Consequently it cannot be expected, when visible hght (A = O.S/x) 

 is employed in ordinary microscopy, that any but the largest viruses can be 

 resolved one from the other nor can a single virus particle be discerned 

 against its background. Under dark-field conditions, where only scattered 

 light is used for image formation, and where a particle-free nonscattering 

 background wiU appear dark, the image of a particle can be discerned no 

 matter how small it is. Resolution is not improved in dark-field microscopy, 

 of course, but the visibility of single, small particles is distinctly enhanced. 



ii. Resolving Power of an Electron Microscope. In an electron image 

 Equation 37 is still valid in setting a lower limit upon the minimum resolvable 

 distance, but unfortunately it does not represent the only consideration. 

 If only Equation 37 were the relevant one (and if n sin could be made as 

 large as unity) the d^^ff would be about 0.02A, corresponding to an electron 

 wavelength of 0.04A. In the derivation of Equation 37 it is assumed that the 

 lens systems are perfect, i.e., that the geometrical aberrations of the lens 

 system are negligible. In the case of electron imagery there is a severe 

 restriction upon the degree to which aberrations can be reduced. Focusing 

 of the electrons is accomplished by means of either magnetic or electric 

 fields which universally act as positive lenses, thus preventing the correction 

 of aberrations by combinations of positive and negative lenses, a universal 

 procedure in ordinary microscope lens systems. The only aberration of mag- 

 netic lenses (or electrostatic ones) that is important for paraxial electrons, 

 but which has so far proven uncorrectable, is spherical aberration. Owing to 



