Hi Alberto,

I have question regarding Sag Table.

Do you know how sag table has calculated slope value? 

For the Surface Sag Cross Section try using the “Reverse Direction” option:

The result is not exactly the same as the Sag Table case, but it’s very close.

Hi Alberto,

You raise a good point, so out of curiosity I spent a bit more time looking into this problem. 

First, it looks like using the BFS Minimum Volume option within the Sag Table works properly.  I created a somewhat more general example by using a more aspherical axicon-like surface, and then used this surface for both a glass-to-air transition (defined in the direction of ray propagation) as well as a “reversed” air-to-glass version.  Note that in this context, selecting the “Reversed Direction” option for the BFS fit simply swaps the media around, it doesn’t flip the surface itself.  The model is attached, but here is an annotated screen shot:

In both cases, the fitting algorithm automatically selected the correct orientation for the aspherical surface (i.e., I did *not* need to manually select the “Reverse Direction” option), and it provided “Remove” numbers (which correspond to the BFS surface sag minus the asperical surface sag) that are positive, meaning one could start with the BFS surface and machine or polish material away, shown above in red, to generate the desired aspherical surface.  This is consistent with what the help documentation says:

However, when I tried to perform BFS (Minimum Volume) subtraction using the Surface Sag (or Sag Cross Section) tool, the results were significantly different.  In this case, with my more aspherical surface, the BFS option defaulted to a spherical surface having the base radius of curvature.  The “Reverse Direction” option made no difference at all. 

This seems like a bug.  Perhaps someone from Zemax can comment.  If not, then in a few days I may submit a tech support ticket.

Apparently the Sag Table and the Surface Sag tools use different versions of the BFS fitting algorithm.  At this point I would only trust the Sag Table version.

Regards,

Jeff

Hi Alberto,

Here is what I found, with some Matlab tests.

1- If you look at your Zemax layout, you will notice that the “sag table BFS” surface touches the original asphere at the edge. Note that in the text data, it says “Minimum Volume Removal”.

This is for machining, You want the sphere approximation to be always above the asphere, because you cannot put material back, only remove some. If you look at a circular profile that coincides with the asphere at the center and at the semi-diameter, there is only one and its radius of curvature is -22.088 (1 axis + 1 point define a unique circle).

2- If you ignore this constraint due to manufacturing and just want the closest sphere, you still can get 2 different mathematical values.

You can fit a 1 D profile H=f[r] and in that case, the best fit radius is -20.42, which you can obtain in the sag table with “Minimum RMS (no offset)”.

You can fit the 2D profile H=f(x,y) and in that case, the best fit radius is -20.63, which is what the Surface Sag Cross section returns. In a 2D geometry, there are way more points at the edge, so they get weighted higher than the ones close to the center.

Hi Hui,

Can you also please look at the model I attached above?  It demonstrates an aspherical surface for which the BFS Min. Volume Removal option shows dramatically different results when using the Sag Table version (BFS radius = -27.6 mm) compared to the Sag Cross Section version (BFS radius = -5.0mm). 

Thanks,

Jeff