Jashcraf
commented
4 years ago Ye et al 2017 : Review of optical freeform surface representation technique and its application
Luckily for us someone thought to review the standard surfaces already. Here's a brief summary of the journal article:
Freeforms are theoretically very useful, but require a pretty incredible model in order to use correctly. So, people came up with some analytic functions for 2d orthogonal polynomials
What is Orthogonality?
The Zernike Circle Polyynomials
In theory, any surface can be described with sufficient zernike terms. But in practice the number of terms are commonly limited.
Q-Type Polynomials
These polynomials were created to reduce the computational burden on a greater number of surfaces via a recurrence relation.
Chebyshev Polynomials
Legendre Polynomials
Other non-orthogonal polynomials have been defined
XY Polynomials
Spline Surface
Radial Basis Function
And here's a really nice table showing a comparison of all the types
What qualifies as Freeform?
There are many answers to this question, but DWK's answer it is a surface described by an orthogonal and complete polynomial set where the constituent terms of the polynomial are not inter-related. In the case of an off-axis conic, using some polynomial set like the Zernikes will result in inter-related terms (e.g. Z6 is a function of Z4).
Your task - review what the standard for freeform polynomial conversion is
Our buddies in LOFT (hiya Trent and Joel, I assume you are working on Hyperion) must convert a freeform in Code V to one in Zemax. But if they don't use the exact same equation - the conversion is nontrivial (and maybe technically impossible) analytically. We need to discern how the industry can convert a Zernike freeform into a Q-type freeform, etc.