This article is also available in Japanese.

Tolerancing is a procedure to evaluate how the performance of a design degrades as a result of manufacturing defects such as element tip and tilts, surface irregularity, glass index errors etc.

The traditional design approach is a two-step process. First, the lens optimization stage produces some candidate designs, and then a tolerancing analysis is performed. This process is typically repeated several times until an acceptable design emerges.

The problem with this approach is that the initial optimization often tries to 'squeeze the last drop of performance' out of the lens, and can result in a sensitive design where performance degrades rapidly once lens parameters are perturbed from their optimal values. This is because the optimization takes place with no regard for the manufacturing tolerances that will be used to make the lens.

This article describes an optimization technique in which manufacturing tolerances are explicitly included in the merit function definition. This allows the manufacturing tolerances to directly influence the optimization, such that a manufacturable design results directly.