2.1 Introduction to Optical Design

In general, optical design includes a broad spectrum of topics, including geometrical optics, image formation, aberration theory, lens design, and image quality evaluation. Each topic is worth an entire book. This chapter will discuss only the necessary background on optical design. For more detailed discussions on optical design, please refer to Refs. 1-17.

2.1.1 Paraxial optics

This section will discuss the properties of the optical system in the region close to the optical axis called the paraxial region. In a practical system, most of the rays come from outside the paraxial region, but the basic properties of an optical system described in the paraxial region are applicable outside that region as well. The ideal behavior of an optical system in the paraxial region was first developed by Gauss, so it is referred to as "Gaussian optics" in many optical references.

Figure 2.1 is a schematic diagram of a simplified optical system showing the first and last surfaces. An optical system typically comprises one or more optical elements. The first-order properties of an optical system can be completely characterized by cardinal points, which are focal points (F,F′), principal points (P,P′), and nodal points (N,N′). When both the object and the image are in air, the nodal points coincide with the principal points.

The focal points of a lens system are the points at which an incident ray parallel to the optical axis of the optical system crosses the axis after passing through the system. The front focal point has the magnification of infinity, while the magnification of the rear focal point is zero. Nodal points have the unique property that a line passing through the front nodal point in the object space will emerge from the rear nodal point in the image space having the same angle with respect to the optical axis. The nodal points are thus characterized by unit angular magnification.