Just answered my own question; 1/a and 1/b are the semi-minor axes of the ellipse.  The vertex is shifted from  z=0 to z=c in the ordinary expression for the ellipse x^2/a^2 + y^2/b^2 +z^2/c^2 =1.

Hi Charles!

Thanks for your post here, and I'm happy to hear that you were at least able to answer your question on this. I just wanted to comment that in terms of the a, b, and c values corresponding to major/minor axes, I suppose to be sure that we're clear, they're related to which axis the terms are working on (a on the x-axis, and so on). This you've shown in your equation above, but depending on the values you select for a through c, any one of these axes could be the 'major' axis, if it was longer than the others. But otherwise, your understanding of the terms seems correct.

Please let us know if you have any more questions here, and I hope you have a fantastic weekend ahead.

~ Angel

Angel, you are right, I should have been more careful.  Any of the axes could be the largest.  In my case, it was c.

There are a couple of good references by Roger Thomas, Applied Optics Vol 10, p 2029 (2004). and SPIE 4853 411 (2003).  Roger paid Focus Software Inc. to produce the elliptical grating code for Zemax.

Aha! I had no idea, about that -- thanks for sharing that info, Charles! I'll have to take a look at those references sometime! Some 'light' reading, perhaps :)

~ Angel

Roger's papers tell how to use the elliptical VLS code to treat toroidal VLS gratings.  The VLS option  is not available for the toroidal grating in Zemax.  Close to the vertex, the ellipsoid and the toroid are essentially the same, considering manufacturing tolerances.  The papers also give lots of insight on how to use the gratings at large magnifications.  These single optical element  designs are essential for spectroscopy in the EUV, where reflectivities are poor and transmittances are nil.