Geometrical optics

Abstract

This chapter shall discuss the basics and the applications of geometrical optical methods in modern optics. Geometrical optics has a long tradition and some ideas are many centuries old. Nevertheless, the invention of modern personal computers which can perform several million floating-point operations in a second also revolutionized the methods of geometrical optics and so several analytical methods lost importance whereas numerical methods such as ray tracing became very important. Therefore, the emphasis in this chapter is also on modern numerical methods such as ray tracing and some other systematic methods such as the paraxial matrix theory. We will start with a section showing the transition from wave optics to geometrical optics and the resulting limitations of the validity of geometrical optics. Then, the paraxial matrix theory will be used to introduce the traditional parameters such as the focal length and the principal points of an imaging optical system. Also, an extension of the paraxial matrix theory to optical systems with non-centered elements will be briefly discussed. After a section about stops and pupils the next section will treat ray tracing and several extensions to analyze imaging and non-imaging optical systems. A section about aberrations of optical systems will give a more vivid insight into this matter than a systematic treatment. At the end a section about the most important optical instruments generally described with geometrical optics will be given. These are the achromatic lens, the camera, the human eye, the telescope, and the microscope. For more information about the basics of geometrical optics we refer to text books such as [2.1-8].