Abstract

Using the concept of a limiting lens and the matrix method of paraxial optics, we determine the maximum optical power which can be achieved given a particular lens diameter, length, and two refractive indices. The geometry for this analysis is shown in Figure 1. A series of k identical symmetric positive lenslets of diameter D, with zero edge thickness and index of refraction n₂ are positioned in succession with zero distance between adjacent lenslets. The center thickness of the positive lenslets is defined as t_α = D/α where the thickness parameter α is a real number, α ≥ 1.0. The surrounding media fills the remaining volume with index n₁ < n₂. The total length from the first to the last vertex of the assembly is L. As the number of lenslets approaches infinity while keeping L constant, the lens will have the maximum power attainable for the given volume and refractive indices. This infinite series of infinitesimally thin identical symmetric positive lenslets is defined as the limiting lens. For the limiting lens, both α and k must approach infinity.

© 1990 Optical Society of America