Hi all.  It is frequently useful to have the Zernike Standard Polynomials available in Cartesian form, rather than just in the standard polar form.  The Cartesian forms can be used for a few different things, such as:

• Generating or fitting data that is sampled on a uniform XY grid
• Converting Zernikes into other surface shapes, such as Extended Polynomials.

Below, I’ve listed the first 37 Standard Zernike coefficients.  See the attached files for all 231 terms in text form and a Mathematica notebook that generates them. (See https://www.wolfram.com/player/ to read the .nb file.)