32 AN ELEMENTARY THEORY OF PHASE MICROSCOPY 



conjugate area as A approaches zero. Finally, both the iindeviated and 

 deviated waves become so weak with diminishing A that the entire 

 image appears dark and the particle becomes invisible. The value of A 

 at which the particle is invisible will depend on the intensity of the 

 available sources of light and on the amount of scattering of the optical 

 system. With present-day phase microscopes the particle can be 

 rendered visible when the optical path difference A is well below 3-ioo 

 wavelength. It is advantageous to use light of short wavelength as the 

 optical path differences become small. 



It will be apparent from the previous paragraph that, even with the 

 restricted class of particles that differ from their surround only by small 

 amounts in optical path, more than one diffraction plate is required in 

 order to obtain optimum contrast with particles of different optical path. 

 The series of diffraction plates will have conjugate and complementary 

 areas differing by the fixed amount of 3^ wavelength in optical path. 

 However, the plates will vary appreciably as regards the amount of 

 absorbing material added to the conjugate area. Fortunately, a single 

 diffraction plate serves moderately well for the entire practical range of 

 small optical path differences A, provided that sufficient absorption has 

 been added to its conjugate area. It is to be expected that with parti- 

 cles whose optical path difference with respect to the surround is not 

 small or with particles that absorb selectively with respect to their 

 surround the relation between the undeviated and deviated waves that 

 arise by diffraction at the object specimen will vary greatly from one 

 particle to another. Correspondingly, the conjugate and complementary 

 areas of the diffraction plate must be coated differently for use with the 

 various particles in order to obtain optimum contrast in the image. In 

 fact, particles exist for which the deviated wave is stronger than the 

 undeviated wave so that the absorbing material has to be applied to 

 the complementary area of the diffraction plate in order to equalize 

 the amplitudes of the undeviated and deviated waves for optimum 

 contrast in the image. The need for a series of diffraction plates can 

 therefore be seen even from this simplified discussion of phase microscopy. 



3.3. Extension of the elementary theory to object fields contain- 

 ing more than one particle 



The elementary theory of phase microscopy is easily extended to 

 include object fields consisting of more than one particle. Each particle 

 gives rise to a deviated wave that, after passage through the objective, 

 is reconcentrated upon the neighborhood of the image of the particle 

 from which it originated. The undeviated »S' wave remains substantially 

 the same as when the field contains but a single particle. If the particles 



