Hi Redbottle,

I’m not quite sure what you mean by this question. A Zernike polynomial is a generic term for a type of orthogonal polynomial set commonly used to model optical aberrations, while the Zernike Standard Sag is a specific type of surface that imposes deformations of a specific shape.

I think that you may have meant to ask about the difference between the standard and fringe Zernike terms, such as Zernike Standard Sag and Zernike Fringe Sag. The most detailed information about them is found in two help pages, for Zernike Standard Coefficients and Zernike Fringe Coefficients. Zernike polynomials are inherently two-dimensional, and a lot of the difference is in how terms numbered by (m,n) notation are mapped into a single index (i). The two pages have the first 37 fringe and 28 standard terms spelled out, and you can see that they follow a somewhat different ordering. If you see, for example, a term that looks like (6r^4-6r^2+1), it is an eleventh order standard, but a ninth order fringe. All terms in one version are also in the other if you look far enough. 

The other major distinction is the normalization. Standard terms have a bunch of square root coefficients in front of each term overall, while fringes do not. This is an aspect of the normalizing of the terms in Standard. There are, in fact, other schemes that can be used, but OpticStudio picked these two common ones. Standards are defined more fully in Born and Wolf’s textbook “Principles of Optics”, among other locations, and fringes are also called the “University of Arizona” notation Zernikes. I don’t know a particular reference off-hand, but that term and Google should provide plenty of background.

For your final question, there is no standard conversion tool between them in OpticStudio. I think the best option would be to create a macro to do it quickly, or just consult the tables if you just need to do it one time. Perhaps a community member has a macro to share?

If I’ve not addressed the question you meant, please don’t hesitate to post a follow-up.