Segre says the diagram shows a failure to focus just visible at the cross over point. The graph was generated by Maple mathematics software. (Click for larger image).

Newly minted engineer Joel Segre and the organization he hooked up with have the worthy goal of making glasses affordable to people who earn less than $2 a day. Although precision machining equipment let Segre come up with several early prototype lenses, many produced images with a light haze, making them unacceptable. When he could not identify the problem, he turned for assistance to Marvin Weinstein, a theoretical physicist at Stanford University. Weinstein considered the problem and suggested that to understand the cause of the haze, they would have to develop better intuition for how sub-micron variations in the optical surfaces of each lens affect image quality.

For insight, Weinstein computer modeled each lens and ray-traced an expected image. The technique let them change the shape of the lens and quickly see what variations were causing the problem. While there are several expensive ray-tracing programs for designing lenses, Weinstein decided to implement a simple ray-tracing program in Maple mathematics software. (The ray tracing package is available at maplesoft.com) After putting the lens shape into the program, Weinstein identified the problem and helped Segre correct it. “Based on Weinstein's calculation, I went back to the lab and fixed the problem. Our lenses now produce crystal clear images,” says Segre.