Exploring fabrication tolerances of optical systems by solving inequalities

A scheme to study fabrication tolerances of optical components and systems is presented. By solving a set of non-linear inequalities an optimal set of lens parameters is found. Then, by selecting another, but strict, set of boundaries to the non-linear inequalities system, a new set of lens parameters is found. The fabrication tolerances are determined by the intersection domain of each lens parameters obtained by solving the set of non-linear equations, with a condition that one solution should come from a strict set on boundaries of the non-linear equation system. This scheme is applied to a classical triplet lens system, used as starting point, and is compacted in effective and back focuses lengths, showing the versatility to study the fabrication tolerances.