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

<p>I would like to simulate solar thermal systems that focus solar radiation, e.g. <a href="https://en.wikipedia.org/wiki/Solar_power_tower" rel="nofollow noreferrer">heliostats</a> or <a href="https://en.wikipedia.org/wiki/Solar-powered_Stirling_engine" rel="nofollow noreferrer">dish Stirling</a>. Usually they are simulated using raytracing or Gaussian cone optics.</p>

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

<p>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 <a href="http://solarenergyengineering.asmedigitalcollection.asme.org/data/journals/jseedo/929668/sol_136_03_031013_f002.png" rel="nofollow noreferrer">http://solarenergyengineering.asmedigitalcollection.asme.org/data/journals/jseedo/929668/sol_136_03_031013_f002.png</a></p>

<p>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.</p>

<p>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.</p>

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

<p>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?</p>

CC BY-SA 3.0
2018-01-10T16:53:35.900Z
Do you want to say 'approximate the surface using Zernike polynomials'? Else I can't make sense of what you're writing.
AtmosphericPrisonEscape
CC BY-SA 3.0
2018-01-10T17:18:23.023Z
Sorry, I added more info to the question.
Joe
CC BY-SA 3.0
2018-01-11T01:56:06.360Z
I think it would be great if optics questions could have their own SE site, but there isn't one. However, optics questions *sometimes get excellent answers* in Physics SE. It's helpful to formulate the question carefully and show as much prior work as you can. That helps define the level at which the answer is written. Also, the question shouldn't be just "is it possible" because an answer of "yes" may not be very helpful. Explain what you are trying to do, what level of math you are comfortable with, and what level of accuracy you need. Zernike polynomials may be overkill for a concentrator.
uhoh
CC BY-SA 3.0
2018-01-11T07:13:42.790Z
I also posted the question in physics, but no response so far. I will add some more info to the question.
Joe
CC BY-SA 3.0
2018-01-12T05:44:56.563Z
My guess is that ray tracing with GPUs is the only way to include all of the real-world effects that you need to include like pointing errors and deviations of all of the individual elements. Analytical methods will severely limit what bits of reality you can include. If you are computationally limited, maybe look for "short cuts" that are used in photorealistic rendering technology for movies. Possibly you can check out the [Blender SE site](https://blender.stackexchange.com/).
uhoh
CC BY-SA 3.0
2018-01-12T05:46:42.210Z
Here are some links related to "big science" simulations for the (really cool) [Large Synoptic Survey Telescope](https://en.wikipedia.org/wiki/Large_Synoptic_Survey_Telescope); [1](https://bitbucket.org/phosim/phosim_release/wiki/Home), [2](http://lsst-desc.org/FeaturedProjects/Phosim-v3.3), [3](http://astrostatistics.psu.edu/su11scma5/lectures/Connolly_scmav.pdf), [4](http://www.roe.ac.uk/roe/workshop/2011/presentations/mon-am1-andy-connolly.pdf), [5](https://docushare.lsstcorp.org/docushare/dsweb/Get/Publication-101/), [6](https://docushare.lsstcorp.org/docushare/dsweb/Get/Publication-72/)
uhoh
CC BY-SA 3.0
2018-01-12T05:56:18.363Z
Also see the [SST](https://www.cta-observatory.org/project/technology/sst/), [MST](https://www.cta-observatory.org/project/technology/mst/), [SCT](https://www.cta-observatory.org/project/technology/sct/) and [MST](https://www.cta-observatory.org/project/technology/lst/) designs of the  [Cherenkov Telescope Array](https://www.cta-observatory.org/project/) designed using ROOT-based simulator for ray tracing [ROBAST](https://robast.github.io/index.html) a "non-sequential ray-tracing simulation library developed for wide use in optical simulations of gamma-ray and cosmic-ray telescopes."
uhoh
CC BY-SA 3.0
2018-01-12T12:03:58.077Z
Thanks for your replies. I already looked into Blender and also Radiance (which is a daylight simulation tool). Blender won't work because we need forward raytracing, starting at the source (path tracing?) Radiance was used before for similar tasks and it seems to work. But it is not straight-forward to use and also not fast enough. see https://www.radiance-online.org/community/workshops/2008-fribourg/Content/Augsburger/GermainAugsburgerPresentation.pdf
Joe
CC BY-SA 3.0
2018-01-12T12:04:48.940Z
I looked through the links on Cherenkov telescopes you sent and the simulation software seems quite impressive. The calculations I am doing are not wavelength-dependent as we are just using the sun's intensity profile and the power in Watts per m2 as input. I am wondering if it might be possible to discretize a larger mirror and simulate the small parts "quasi-annular" with the Zernike equations. Stupid question: can one use the equations for off-axis problems (light source, mirror and target not on a line)?
Joe
<telescope><optics><mirror>
Is it possible to model a solar thermal concentrator using Zernike polynomials?
Joe
# Is it possible to model a solar thermal concentrator using Zernike polynomials?

(Asked by: username_0 on 2018-01-10)

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](https://en.wikipedia.org/wiki/Solar_power_tower) or [dish Stirling](https://en.wikipedia.org/wiki/Solar-powered_Stirling_engine). 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?

**Tags:** telescope, optics, mirror

> **Comments:**
> **username_1**: Do you want to say 'approximate the surface using Zernike polynomials'? Else I can't make sense of what you're writing.  
> **username_0**: Sorry, I added more info to the question.  
> **username_2**: I think it would be great if optics questions could have their own SE site, but there isn't one. However, optics questions *sometimes get excellent answers* in Physics SE. It's helpful to formulate the question carefully and show as much prior work as you can. That helps define the level at which the answer is written. Also, the question shouldn't be just "is it possible" because an answer of "yes" may not be very helpful. Explain what you are trying to do, what level of math you are comfortable with, and what level of accuracy you need. Zernike polynomials may be overkill for a concentrator.  
> **username_0**: I also posted the question in physics, but no response so far. I will add some more info to the question.  
> **username_2**: My guess is that ray tracing with GPUs is the only way to include all of the real-world effects that you need to include like pointing errors and deviations of all of the individual elements. Analytical methods will severely limit what bits of reality you can include. If you are computationally limited, maybe look for "short cuts" that are used in photorealistic rendering technology for movies. Possibly you can check out the [Blender SE site](https://blender.stackexchange.com/).  
> **username_2**: Here are some links related to "big science" simulations for the (really cool) [Large Synoptic Survey Telescope](https://en.wikipedia.org/wiki/Large_Synoptic_Survey_Telescope); [1](https://bitbucket.org/phosim/phosim_release/wiki/Home), [2](http://lsst-desc.org/FeaturedProjects/Phosim-v3.3), [3](http://astrostatistics.psu.edu/su11scma5/lectures/Connolly_scmav.pdf), [4](http://www.roe.ac.uk/roe/workshop/2011/presentations/mon-am1-andy-connolly.pdf), [5](https://docushare.lsstcorp.org/docushare/dsweb/Get/Publication-101/), [6](https://docushare.lsstcorp.org/docushare/dsweb/Get/Publication-72/)  
> **username_2**: Also see the [SST](https://www.cta-observatory.org/project/technology/sst/), [MST](https://www.cta-observatory.org/project/technology/mst/), [SCT](https://www.cta-observatory.org/project/technology/sct/) and [MST](https://www.cta-observatory.org/project/technology/lst/) designs of the  [Cherenkov Telescope Array](https://www.cta-observatory.org/project/) designed using ROOT-based simulator for ray tracing [ROBAST](https://robast.github.io/index.html) a "non-sequential ray-tracing simulation library developed for wide use in optical simulations of gamma-ray and cosmic-ray telescopes."  
> **username_0**: Thanks for your replies. I already looked into Blender and also Radiance (which is a daylight simulation tool). Blender won't work because we need forward raytracing, starting at the source (path tracing?) Radiance was used before for similar tasks and it seems to work. But it is not straight-forward to use and also not fast enough. see https://www.radiance-online.org/community/workshops/2008-fribourg/Content/Augsburger/GermainAugsburgerPresentation.pdf  
> **username_0**: I looked through the links on Cherenkov telescopes you sent and the simulation software seems quite impressive. The calculations I am doing are not wavelength-dependent as we are just using the sun's intensity profile and the power in Watts per m2 as input. I am wondering if it might be possible to discretize a larger mirror and simulate the small parts "quasi-annular" with the Zernike equations. Stupid question: can one use the equations for off-axis problems (light source, mirror and target not on a line)?  

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## 0 answers

