Abstract

The core of the problem of lens design as a mathematical discipline is that of numerical optimization with the major difficulty being the basic nonlinearity of the variables used. The struggle with this nonlinearity can be divided into two parts. One is the part played by the designer, such as in choosing a favorable starting point, and generally acting in the role of what may be best described as the parent of a talented but unruly child, the child being the automatic part of the design team. This talk will be mainly concerned with the latter, namely the algorithmic procedure used in the design process, which is the second part of the two referred to above. Almost from the beginning of computerized lens design, the procedure of choice has been some variant of Newton’s method iteration, and progress has consisted mainly of refinements to this basic procedure, the most important being the addition of the ridge-regression procedure, otherwise known as damping, to cope with the ill-conditioning which is also a characteristic of this problem. One should also mention here that a large factor in the progress being made is due to the vastly improved hardware that keeps becoming available.

© 1990 Optical Society of America