General formula for lenses without spherical abberation

[mfb]

TL;DR

Solution to a long-standing problem: How to make lenses without spherical abberation?

Publication: Rafael G. González-Acuña and Héctor A. Chaparro-Romo, "General formula for bi-aspheric singlet lens design free of spherical aberration," Appl. Opt. 57, 9341-9345 (2018)
Open access preprint: arXiv

Given one surface of a lens, how does the other surface has to look like to avoid spherical abberation? A question as old as the design of lenses. Computers found numerical approximations but an analytic expression is new. Just use this handy formula:

 

[jedishrfu]

Wow this is quite cool. It’s funny how there are still physics problems hanging out there that have been pretty much forgotten except by those in the field.

 

[nuuskur]

Very handy, indeed :D My hat's off to whomever typed that out, holy mother of ..

 

[mfb]

If you look into the expression there are many repeated elements. Replace them by other symbols and the equation gets more handy already. The preprint doesn't have the formula and I don't have access to the full publication (not even the usual approaches work) so the image is all I have.