INTRODUCTION 239 



be stated. Ciu'iously enough, Lambert's law leads to a simplification 

 of the diffraction integral for the total energy density in the image. 



The laws of microscopy may be derived from two different lines of 

 attack which lead to substantially the same conclusions. The first 

 attack was outlined by A))be but was not formulated analytically by 

 him. In Abbe's attack one selects an arbitrary point in the source of 

 light and computes the amplitude and phase distribution produced over 

 the plane conjugate to the source of light (the plane of the diffraction 

 plate) by the coherent light radiated from the selected point. This 

 computation or formulation takes into account the modifications which 

 result from the passage of the light through the object specimen. The 

 corresponding amplitude and phase distril^ution produced over any 

 selected image plane is now determined with the aid of Kirchhoff's law 

 from the known amplitude and phase distribution over the plane of the 

 diffraction plate. The selected image plane is not necessarily conjugate 

 to the object plane. The partial energy density is defined as the distribu- 

 tion of energy density produced over the selected image plane by the 

 coherent light radiated from the selected point in the source of light. 

 The partial energy density is proportional to the square of the absolute 

 value of the amplitude and phase distribution produced over the image 

 plane. Since dift'erent points in the source of light act as independent 

 radiators, the total energy density produced over the image plane by all 

 points in the source of light can be found by summing or integrating the 

 partial energy densities produced by all points in the effective area of the 

 source of light. Whereas Abbe's procedure can be outlined with ease, it 

 can become very cumbersome to formulate analytically unless the 

 effective area of the source of light is small and is centered upon the 

 optical axis. Abbe's procedure, moreover, gives more than the required 

 amount of information because the amplitude and phase distribution 

 produced over the plane of the diffraction plate is rarely of direct interest. 



We shall formulate the following attack because it is simpler and more 

 amenable to analysis than the attack outlined by Abbe. Beginning 

 with the coherent light radiated from an arbitrary point in the effective 

 area of the source of light, we state the amplitude and phase distribu- 

 tion over the light wave as it emerges from the object plane. We then 

 apply a transfer property of the primary diffraction integral to formulate 

 directly the corresponding amplitude and phase distribution produced 

 over the selected image plane. The partial energy density is propor- 

 tional to the square of the amplitude and phase distribution produced 

 over the image plane. The total energy density produced over the 

 image plane by all points in the effective area of the source of light is 

 obtained by integrating the partial energy density with respect to the 



