Three-dimensional diffraction theory of microscope image formation

Abstract

The Abbe theory of image formation for a plane object is extended to apply to the case of a three-dimensional object. The diffraction of light by such an object is treated by the standard methods applied to the diffraction of X-rays by crystals. The formation of an image of a three-dimensional periodic object is discussed, and it is shown that certain Fourier components of the structure of the object are reproduced in the image while others are left out. An expression is obtained for the minimum vertical separation between horizontal layers that can just be resolved by racking the microscope up and down; this depends on the scale of the detail in the layers.