ABSTRACT
In order to follow the development and performance of refractive microlens elements, some rudimentary understanding of geometric optics is required. A number of references are given for the reader to consider. What we need here, at the very least, is an understanding of the basic terminology. It might be useful to bear in mind that there is really no conceptual difference in the optical principles relating to small refractive lenses as compared with large lenses; however, there is in the way one formulates the optical design. In the simplest case of paraxial ray tracing for large-diameter lenses, the so-called thin-lens approximation [1] is used, which simply means that the deviation of the rays through the lens thickness can be ignored. The paraxial specification means that Snell’s law can be written as fi¼nfr. Here fi and fr are the angles of incidence and refraction measured from the surface normal as shown in Fig. 2.1. When the lens thickness is comparable, or exceeds, the lens diameter, one has to resort to what is
often called the thick-lens formulation. Referring to Fig. 2.2, one has a set of definitions that derive from the desire to maintain the simple lens maker’s formula relating the focal length of the lens to the object and image distances
f ¼ 1 so þ 1 si
ð2:1Þ
Here, f represents the focal length of the lens, si is the image, and so is the object distance. In the thick-lens formulation, one must use a new set of definitions of the various common lens terms. These definitions are summarized in Table 2.1 based
on the description of Figs. 2.1 and 2.2. One can see that the principal planes, P1, P2, are defined in such a way as to make Eq. (2.1) valid if the object and image distances are measured from them and not the lens boundaries. One should realize from the expression in Table 2.1 that the position of the principal planes can lie outside the physical lens. We can see from the drawing of Fig. 2.2 how the principal plane is defined. The intersection of a parallel ray with the extension backward of a ray from the focus must lie on the principal plane.
