A new method for automatic lens design is described. Instead of finding the approximate solution to the system of simultaneous nonlinear equations, the solution is found to the system of simultaneous nonlinear inequalities. Thus, the aberrations are driven into the domains which have been set up around target values. The bandwidth of the domain is the allowable tolerance associated with each aberration. A relaxation method is used to solve the system of linearized inequalities and iterative cycles are used to find the solution to the system of nonlinear ones. This method allows a high degree of control of individual performance functions. Mechanical conditions can be treated in the same way as aberrations. The program was written for the IBM 7090 computer and satisfactory designs were obtained in general within a few minutes for gauss-type photographic lenses.
TATSURO SUZUKI and SEIJI YONEZAWA, "System of Simultaneous Nonlinear Inequalities and Automatic Lens-Design Method," J. Opt. Soc. Am. 56, 677-683 (1966)