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Successful optimization usually involves the bounding of variables to ensure that optimized systems turn out to be physically realizable. Probably the most common variable type that requires bounding is thickness. Unbounded, thickness variables will generally produce either very thin, unmountable lenses or lenses that are unreasonably thick, heavy and expensive.

Thickness boundary constraints are so commonly used that they are built into the Default Merit Function dialog:

While these default constraints can be useful, there are also cases where they will not sufficiently bound the thickness of a given surface. As we will see, while not an issue for spherical and conically aspheric surfaces, polynomial aspheric surfaces generally cannot be successfully bounding using the default constraints.