Three types of merit functions were applied in automatic design of optical systems: mean square value of wave aberrations; variance of wavefront aberrations; and variance of an MTF based function suggested by H. H. Hopkins. They have proved to be very powerful in the final stages of optimization of well corrected systems and lend themselves readily to automatic control of minimization. The method of application and actual design examples are described.
Joseph Meiron, "The Use of Merit Functions Based on Wavefront Aberrations in Automatic Lens Design," Appl. Opt. 7, 667-672 (1968)