CHAPTER II 



AN ELEMENTARY THEORY 

 OF PHASE IVIICROSCOPY 



1. INTRODUCTORY REMARKS 



Image formation in the phase microscope depends so intimatel}^ upon 

 the phenomena of diffraction that even a qualitative explanation of phase 

 mJcroscopy must inx'oh^e some of the principles of diffraction. The main 

 purpose of the elementary theory is to provide insight into the physical 

 action of a phase microscope without resorting to the more complicated 

 and rigorous theory based upon Kirchhoff's or Luneberg's diffraction 

 formula. A second purpose of the elementary theory is to obtain a set 

 of quantitative relations which have proved of assistance in the applica- 

 tion of phase microscopy. Whereas these relations are admittedly but 

 the first approximation to the truth, they may be used in a surprisingly 

 large number of cases to predict the character of the contrast which will 

 be produced in the image of a gi^'en particle by a proposed diffraction 

 plate. Conversely, these relations often enable the observer to deduce 

 significant information about the relative optical properties of the parti- 

 cle and its surround from the properties of the diffraction plate which is 

 required for prodvicing darkest contrast in the image of the particle. 



The minimum essentials of a qualitative explanation of phase mi- 

 croscopy have been included in Section 3, Chapter I. The qualitative 

 explanation of phase microscopy will be presented in greater detail in 

 Sections 2 and 3 of this chapter. The remaining sections deal with the 

 quantitative aspects of the elementary theory. These quantitative 

 relations will be derived with the aid of complex numbers rather than in 

 terms of the equivalent but cumbersome pseudo-vectors. In this way 

 the laws of phase microscopy can be presented with greater simplicity 

 and clarity. Only the simplest rules of operation with complex numbers 

 are required, and these will be described as they are needed. The final 

 laws of phase microscopy do not involve complex numbers. These 

 laws are stated in sufficient detail so that the microscopist will be able 

 to apply them without referring to the methods of derivation. 



The reader who is interested in the fundamentals of the more general 



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