One-dimensional searches for finding new lens design solutions efficiently

A special structure is present in the lens design landscape that makes it different from a general global optimization problem: many local minimums are closely related to minimums of simpler problems and can therefore be found by decomposing the search for them in simple steps. We show here that in the design landscape of a wide-angle pinhole lens and in closely related optimization landscapes, all good local minimums found by other methods can be obtained easily with a succession of one-dimensional searches starting from simpler systems. By replacing high-dimensional searches with a succession of one-dimensional searches, the design efficiency can be increased significantly. By combining this method with conventional design methods, the wide-angle pinhole lens can be designed starting from a single lens.