Hi,

 From the article, it seems a general approach for all surface form. The approach  adds a flat phase surface prior to any surface that to be toleranced. if that’s a case, a curved phase surface which matches freeform surface substrate  will be more accurate?

If  you use more newer version of OpticStudio which support compound surface. Compound surface is another powerful feature you could use to tolerance most of any surface form.

This is a very important topic, and IMHO the Compound Surface approach is the right way to look at this class of problem.

When you design your system, you’ll use surface X, which might be a standard surface, polynomial surface, or any of the over 50 surface types that OS supports. You’ll design your system in terms of whatever the coefficients of that surface are.

When you come to tolerance though, the tolerances are usually not well expressed as tolerances of whatever the coefficients are. In other words, you could use TPAR to put a tolerance on each defining parameter: but the tolerances are not always expressible in that manner.

For example, imagine you have a rotationally symmetric freeform surface that you made using Chebyshev polynomials. It will be made by diamond turning a substrate. As a result, there are periodic errors introduced by the axis of rotation and the tool tip not being exactly coated. That may not be expressible as a deviation in the Cheby terms. You could use a periodic surface to model the sinusoidal errors introduced instead.

The point is to look at the manufacturing method and build a way to model the errors it produces. This is entirely separate to the properties of the functional set you chose when you selected the surface type to optimize. So if you design with a Chebyshev, the errors in manufacture are nothing to do with the Cheby: they are the errors introduced by the manufacturing process.

That’s why I think the Compound Surface is such a step forward in tolerancing aspheres, freeforms and ‘true’ freeforms in which there may be no functional basis for the surface. Split your surface into the nominal surface, and then use whatever other surface types best describe the error to add that on. 

To summarize: don’t tolerance the surface itself, tolerance other surfaces that best describe the errors in the manufacturing process. TEXI and TEZI were the first steps in this direction, but the Compound Surface is the Right Way to approach these problems 

BTW, I meant Composite, not Compound...