Fourier Images: I - The Point Source

Abstract

The problem of designing a light or electron optical system specifically for the imaging of periodic objects, such as real crystals, is discussed. A qualitative appeal to communication theory suggests that it should be possible to devise systems of higher efficiency than the conventional microscope by using the a priori knowledge of periodicity. The possibility of deforming the incident wavefront in such a way that the periodic object acts as its own imaging system is considered and a formalism is set up. The particular case of the spherical wavefront is then examined in detail and it is predicted that a new type of image should be formed on certain planes. Since this image is in many ways analogous to the Fourier projection of crystallography, and since it can only be formed by periodic objects, it is named the Fourier image. Fourier images produced experimentally with light optics are presented and shown to be in agreement with theoretical predictions. Patterns on planes other than Fourier image planes are described briefly, but detailed treatment is deferred until Part II. The possibility of application to the imaging of crystal lattices by electron optics is discussed, but a quantitative treatment of the crucial problems of finite source size and coherence are deferred until Part III.