We already know that DLS lens design optimization programs are, in most practical cases, unable to do more than find a local minimum in parameter space. Even in the simple case of the split doublet, a program can converge on the poor Gauss solution, even though the Fraunhofer solution is usually greatly superior. However, we also know that the capability of such programs to find a local minimum is of great value in lens design, as the optimization routines described in Chapter 1 are usually able to find this minimum quickly and effectively.
While there has been considerable progress in the development of so-called global optimization programs, they do not yet guarantee that the true global solution has really been found. Forbes has shown that a global optimization program, running on a computer tracing 1 million ray surfaces per second could take 10 seconds (about 10,000 years) to have any reasonable certainty of finding the true global minimum for the 15-parameter problem that was proposed for the 1990 International Lens Design conference. Since that time, global search programs have found solutions similar to the best one shown in Fig. 1.3, but not a better one. Lens systems often have many more than 15 variables; for practical purposes, therefore, the result of a lens design optimization remains critically dependent on the starting point given to the program.
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