Most optical systems are used to create images: eyes, cameras, microscopes, telescopes, for example. These image-forming instruments use lenses or mirrors whose properties, in terms of geometrical optics, have already been discussed in Chapter 3. But geometrical optics gives us no idea of any limitations of the capabilities of such instruments and indeed, until the work of Ernst Abbe in 1873, microscopists thought that spatial resolution was only limited by their expertise in grinding and polishing lenses. Abbe showed that the basic scale is the wavelength of light, which now seems obvious. The relationship between geometrical and physical optics is like that between classical and quantum (wave) mechanics; although classical mechanics predicts no basic limitation to measurement accuracy, it arises in quantum mechanics in the form of the Heisenberg uncertainty principle.
This chapter describes the way in which physical optics is used to describe image formation by a single lens (and by extension, any optical system). The theory is based on Fraunhofer diffraction (Chapter 8) and coherence (Chapter 11) and leads naturally both to an understanding of the limits to image quality and to ways of extending them. We shall learn:
how Abbe described optical imaging in terms of wave interference;
that imaging can be formulated as a double process of diffraction;
what are the basic limits to spatial resolution;
how microscopes are constructed to achieve these limits;