Comparison of generalized simulated annealing and damped least-squares methods in lens design optimization

Abstract

A landscape lens (monochromatic, 22.5° FOV, f/10), photographic lens (polychromatic, 30° FOV, f/5), and a laser copying lens (monochromatic f/2.5, diffraction-limited over FOV) were designed using LASCO,1 ACCOSV, and CODEV2 from identical starting configurations. These were chosen to cover an example where the global minima are distinct and known (landscape lens), another with various local minima in a broad basin (photographic lens), and the third with a very steep minimum in the merit function space. It will be shown that the generalized simulated annealing (GSA) algorithm can find the global minimum from arbitrary starting configurations; however, with the starting configuration close enough to a local minimum, damped least squares (DLS) finds it faster. DLS is able to get to the local minimum only and can do so only if the starting configuration is the proper one and reasonably close to the local minimum. DLS is unable to find steep minima, whereas the GSA is able to do so; however, GSA has difficulty locating the exact minimum for this case. It appears that a combination of GSA and DLS algorithms with GSA being used for searching for the various minima and DLS used for reaching them quickly is a practical way to approach the lens design optimization problem.