Thin-Lens Theory

Abstract

4.1 Definition of a Thin Lens A thin lens is a theoretical lens whose thickness is assumed to be zero and, therefore, negligible during thin-lens calculations. The thin lens is a design tool used to simulate a real lens during the preliminary stages of optical system design and analysis. The concept is particularly valuable because it enables the optical engineer to quickly establish many basic characteristics of a lens or optical system design. By assuming a lens form where the thickness is zero, the formulas used to calculate object and image relationships are greatly simplified. The drawback to the thin-lens approach is that it is not possible to determine image quality without including actual lens thickness (and other lens data) in the calculations. As a result, while it is possible to establish many valuable facts about an optical system by the application of thin-lens theory and formulas, the ultimate quality of the final image can, at best, only be estimated. 4.2 Properties of a Thin Lens Figure 4.1 is an illustration of a positive thin lens. Any lens system analysis must start with several known factors that will generally be provided by the end user, i.e., the customer. From these given starting factors it will be possible, using thin-lens theory and formulas, to generate the missing information required to completely describe the final lens system. In the case shown in Fig. 4.1, for example, it is given that the system detector (image size) will be 25 mm in diameter and that the full field of view of the lens will be 10 deg. Other system considerations dealing with detector sensitivity - thus required image brightness - dictate that a lens speed (f/#) of f/2.0 will be required. Since we know the image size and the field of view, applying the formulas shown in Fig. 4.1, we can calculate the effective focal length (EFL) of the lens. The image size dimension used for this calculation is measured from the optical axis and is designated as y1. In this case, the maximum value for y1 is 12.5 mm.