A Brief History of Lens Design
8] `Ru5nd Since about 1960, the way lenses are designed has changed profoundly as a result of the introduction of electronic digital computers and numerical optimiz-ing methods. Nevertheless, many of the older techniques remain valid. The lens designer still encounters terminology and methods that were developed even in previous centuries. Furthermore, the new methods often have a strong classical heritage. Thus, it is appropriate to examine, at least briefly, a history of how the techniques of lens design have evolved.
5MR,UgT YlTaN, ?j A.2.1 Two Approaches to Optical Design
5X#E@3g5 >{wuEPA The equations describing the aberrations of a lens are very nonlinear func-tions of the lens constructional parameters (surface curvatures, thicknesses, glass indices and dispersions, etc.). Boundary conditions and other constraints further complicate the situation. Thus, there are only a few optical systems whose con-figurations can be derived mathematically in an exact closed-form solution, and these are all very simple. Examples are the classical reflecting telescopes.
" N 3) Qr This predicament has produced two separate and quite different approaches to the practical task of designing lenses. These are the analytical approach and the numerical approach. Historically the analytical dominated at first, but the numer-ical now prevails.
O#)jr-vXdV Neither approach is sufficient unto itself. A lens designed analytically using aberration theory requires a numerical ray trace to evaluate its actual perfor-mance. In addition, an analytically designed lens can often benefit significantly from a final numerical optimization. Conversely, a lens designed numerically cannot be properly understood and evaluated without the insight provided by ab-erration theory.
cL G 6(<L A|L'ih/ A.2.2 Analytical Design Methods
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