Hi Daoming,

Let me first give you my answer your questions, and then, some of my thoughts on how to solve your problem.

1. Norm Radius

Excerpt from the Help File: The normalization radius scales the X and Y intercept coordinates of the ray so that the polynomial terms are all dimensionless and the coefficients are all in lens units.

This definition isn’t clear to me, so to illustrate this concept, I’ve created a simple file (attached to this post) containing an Extended Polynomial surface with a single term (the x term) equal to one (or z = x). The aperture definition is Entrace Pupil Diameter = 10 mm. Therefore, the Semi-Diameter of the Extended Polynomial is 5 mm. By default, the Norm Radius = 100. If we look at the Surface Sag Cross Section, it looks like this:

As you can see, the sag is a linear function of the position. However, at a position of 1 mm, the sag isn’t 1 mm. In fact, at a position of 1 mm, the sag is 1 / 100 (the Norma Radius) mm and if you change the Norm Radius to 1 mm, you will obtain:

I think the Norm Radius is a mean to scale the sag depending on your fit.

2. a0

In your fit, a0 is a constant term. It doesn’t depend on x or y. Think of it as an offset. You can either ignore it or use the Thickness cell to emulate it (although it won’t show in the Sag Cross-Section).

Finally, I can see your x scale (in the cftool) varying from 0 to 500, and y scale varying from 250 to 700. What are the units? Is it millimeter? Micrometer? This will help you determine the Norm Radius. Also, note that in your case, you are missing the x^2 term (so it should be zero in OpticStudio), and you should use 5 terms.

Hope this helps, take care,

David