# Is it possible to model a solar thermal concentrator using Zernike polynomials?

This question might seem a bit off-topic, but I guess there are a lot of people here that know about optics, telescopes, etc.

I would like to simulate solar thermal systems that focus solar radiation, e.g. heliostats or dish Stirling. Usually they are simulated using raytracing or Gaussian cone optics.

Basically, I would like to simulate the optical system and get the resulting image of the sun on some surface.

In the end I would like to calculate the "flux distribution" (~brightness) of the reflected radiation on some sort of receiver. The receiver could be a plate with heat pipes beneath or a Stirling motor. I would like to create images like http://solarenergyengineering.asmedigitalcollection.asme.org/data/journals/jseedo/929668/sol_136_03_031013_f002.png

So far, I read that Zernike polynomials can only be used to simulate optical systems with circular apertures. This is not the case for my application. Currently I am evaluating the optical system using Monte Carlo raytracing (GPU based) , which yields the very high accuracy that is needed.

We have not done any work on this so far, but for very large mirror arrays, e.g. 25000 heliostats, the raytracer takes quite a while to converge. And calculation time is a very critical point when in comes to optimizing the positions of the mirrors to avoid the shading and blocking amongst them.

This is why we are looking for faster ways to evaluate the optical performance of these systems while still getting highly accurate results.

Do you think it is possible to simulate them using Zernike polynomials? The simulation needs to consider surface errors of the mirrors, astigmatism and non-ideal focal lengths. Can one use Zernike polynomials only for arbitraty optical systems?

• Do you want to say 'approximate the surface using Zernike polynomials'? Else I can't make sense of what you're writing. – AtmosphericPrisonEscape Jan 10 '18 at 16:53