CHAPTER VH 



APPENDIX: THE DIFFRACTION THEORY 



OF PHASE MICROSCOPY WITH 



KOHLER ILLUMINATION 



1. INTRODUCTION 



The following diffraction theory of image formation in the microscope 

 will be derived under the suppositions that the illuminating beam is 

 unpolarized and that the microscope has been adjusted as in Kohler 

 illumination. The phenomena of phase microscopy are different with 

 Kohler and with critical illumination but can become highly similar 

 under conditions that are well satisfied in the normal usage of the 

 typical microscope. Even the theory for Kohler illumination becomes 

 cumbersome when the integrations for the total energy density in the 

 image are referred to the radiating atoms in the source of light. Sim- 

 plicity of argument will be obtained by supposing that the virtual image 

 of the source as imaged by the combined lamp and substage condensers 

 acts for the purposes of microscopy as a self-luminous source. This 

 supposition can be justified with at least fair approximation when the 

 speeds of the lamp and substage condensers are high and when the 

 opening in the diaphragm of the substage condenser is not too narrow. 

 The effect of closing down the field stop in Kohler illumination is to 

 decrease the speed of the lamp condenser and thus to spread the diffrac- 

 tion image of a point in the source over a greater area at the condenser 

 diaphragm. If the supposition as to the self-luminous character of the 

 virtual image of the source is to be valid, the field stop should be opened 

 far enough so that the diffraction image of a point in the source is small 

 compared with the width of the opening in the diaphragm of the sub- 

 stage condenser. We note that simplifications occur also when the 

 field stop is closed to point dimensions, but a discussion of this specialized 

 case will not be included. 



In integrating over the virtual image of the source, we shall obtain 

 additional simplicity of argument by omitting a summation procedure 

 which leads to a generalized statement of Lambert's law. The effect 

 of introducing Lambert's law into the diffraction integrals will, however, 



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