Support toroidal surfaces

[blefroy]

I'd like to be able to implement non-axisymmetric lenses (toroidal lenses) - for example, plano-cylindric lenses such as these: https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=2803

[HarrisonKramer]

Hi @blefroy,

Thanks for the question.

You can easily add support for toroidal/cylindrical surfaces by defining a custom surface type. The following tutorial shows you how this can be done: Tutorial 10a - Custom Surface Types. You will simply need the surface equation and the gradient of the surface equation.

For example, for a cylindrical lens, you can define the surface function as

$$ z(x, y) = \frac{x^2}{2R} $$

and the surface normal (via the gradient) as

$$ \hat{n}(x, y) = \frac{1}{\sqrt{\left(\frac{x}{R}\right)^2 + 1}} \left( \frac{x}{R},\ 0,\ -1 \right). $$

I can add a toroidal surface to the roadmap as well, but it does not have high priority currently. If you do implement this (or a cylindrical surface), please consider opening a pull request, or share the code here. I would be glad to add it to the codebase.

Regards,
Kramer