# Looking for trigonometric ray tracing software for optics

• difalcojr
difalcojr
TL;DR Summary
looking for possible ray trace software available

Is there an existing ray trace program that can trace planar light rays through this monocentric, model lens? Parameter values are given above. Input ray angles are all zero. Does some program give the output ray angle values at the second surface? How about for any arbitrary ray incoming to the lens, at any converging or diverging angle? Can the same program give the exit ray angles then? If so, what are the values of the output angles for your chosen input angles? And what is this software? Thank you.

Well, now I am puzzled. The viewer audience of 59 may too small a sample size expected to even know ray trace software in general. Much less have it available to them to test the above problem. If this might be the case, can you call an expert in? Call the ivory towers?

Otherwise, high school teachers, perhaps give this problem to your trigonometry class. Or geometry class. As a class exercise. This example can be solved by geometric methods pretty easily, using trigonometry too. The exit ray angles can be found, verified, probably in one class time. The analysis of the results, longer.

Remember that all the examples in the very first geometry classes in European universities were mostly of geometrical optics topics. Due light traveled in a straight line, as we see it. And geometry loves straight lines.

difalcojr said:
Is there an existing ray trace program that can trace planar light rays through this monocentric, model lens?
Simple graphical teaching software, that introduces students to optics, will not model your real world. In this case you have ignored the reflection from the front surface, the grazing incidence of the upper ray will result in reflection that reduces the aperture.

If you design optics, you must understand the geometry of the reflection and refraction coefficients. You should write your own program code for this analysis because it requires you to teach the software system, and the best way to learn, is to teach.

Is this a 2D or a 3D model ?
Will you consider only one wavelength ?
What about polarisation of the ray ?

2D. Only one wavelength. Just refraction checked. No reflection. No polarization.

Just the simplest conditions were wanted. Thick, monocentric model. Only theoretical at this time. Simple model.

However, I am contending the lens model is free of all spherical aberrations. That any arbitrary input ray angle will be reproduced at the second surface. My own trigonometric ray trace, homemade program confirms that this is true. I am looking for someone else to confirm this too. Or deny it. These are "perfect" spherical lenses, is my contention.

I would take seriously the absolute constraints of the etendue theorem. I suggest looking at long source and focal distances rather than infinite ones. I have used Zemax but it is proprietary: there are some here that are freeware.

https://en.wikipedia.org/wiki/List_of_ray_tracing_software

/

Dale
Well, you are probably right about the etendue theorem, but later in an analysis, maybe, I think, would be better. I know nothing about it. Here I am only trying to verify two refractions through spherical surfaces.

Also, my homemade software has been able to accurately find angles and lengths in the construction of a thick lens model. Certainly, I would need something more advanced to examine constraints of this theorem.

Perhaps it is completely out of my prerogative to ask others in a physics forum to verify my results. I really don't know who else to ask, though. Check what results? That the output angles are equal to the input angles.

Here's a source other than infinity. 30 degrees incoming wave. Source point is 2 units before the center of lens. Same parameter values. Diagram shows output angles equal input angles.

Who else may I ask to verity this? Or disprove it? I am just an independent researcher, unaffiliated with any company or university.

It is still unclear to me what you are attempting to show here. If you are correct, what is the novelty?
To show it correct you could try to trace one ray at the two interfaces. Maybe start with a symmetric one and show it in detail the refraction geometry at the two surfaces. How does your software do it?

The novelty is that it would be a spherical lens model completely free of spherical aberrations. Something that Hecht was correct in saying it probably couldn't be done.

Well, I have added more construction lines to the models I use than is shown here. Calculated more axis lengths and couple more angles. Well, if that's OK with you all, I'll provide the proof in diagrams. All trigonometry, law of sines equations a lot. I'll do it for the last diagram I posted here, if that's acceptable. It might take a little time to get a presentable package together, but I'll show all the angles and variable values needed. See if I can provide more proof, so you won't have to do the labor. I just had thought it could be verified easier. Is this OK?

But it would not be a singlet. So that is not what Hecht said. Am I missing something here?

Yes, possibly. Hecht did not speak of a singlet or doublet in particular, but said any "...real system comprising spherical surfaces." He says you probably can't get rid of all SA using only spherical surfaces. And I am trying to show that this model is the exception. That's novel.
I only refer to it as a singlet due the angles into it are the same as those that exit it. It would be a doublet in practice. I only want to show the equal angles property of the singlet. Little confusing, I think, for I've shown both.

hutchphd said:
But it would not be a singlet. So that is not what Hecht said. Am I missing something here?
Here's the same diagram sans the last doublet surface. Now a singlet again. (Running out of ink in my printer too.)

I'll prove this diagram trigonometrically, if that is OK. Or attempt to.

difalcojr said:
He says you probably can't get rid of all SA using only spherical surfaces. And I am trying to show that this model is the exception. That's novel.
When you read Born & Wolf's derivation of the thick lens, you see that the spherical aberrations come from the truncation of the power serie used to describe the interface, which then turns into a spherical surface. So it's not simply about how you combine them together.

But I'm a bit confused about your original drawing, are you using a different refractive index on each side of the lens? That's not very typical.

As for a raytracing program, I happen to have released an opensource one a bit over a year ago, so you could give it a try if you want to: https://aether.utt.fr/downloads

Other than that, there are plenty of commercial softwares that should work: Zemax, FRED, CodeV, Oslo, etc.

berkeman, hutchphd, difalcojr and 1 other person
KAHR-Alpha said:
When you read Born & Wolf's derivation of the thick lens, you see that the spherical aberrations come from the truncation of the power serie used to describe the interface, which then turns into a spherical surface. So it's not simply about how you combine them together.

But I'm a bit confused about your original drawing, are you using a different refractive index on each side of the lens? That's not very typical.

As for a raytracing program, I happen to have released an opensource one a bit over a year ago, so you could give it a try if you want to: https://aether.utt.fr/downloads

Other than that, there are plenty of commercial softwares that should work: Zemax, FRED, CodeV, Oslo, etc.
Yes, it actually is about exactly how you combine the radii and indexes together. Model rules. In the other post thread. This particular shape and combination of different indexes before and after a single, thick lens is unique in that regard. Only combination of shape and media that does it. For a spherical single lens, anyway.

Yes, refractive indexes are all different. Agree, not typical at all. But the singlet does become the doublet. You won't find this model in any textbook that I've seen.

Thank you for posting the link to your ray trace program. I will check it out. Perhaps you can check too, given the parameters and values I have provided in the first diagram. My hope was that this would have been an easy, 2D check on a couple of refraction surfaces for someone in a physics forum to do. That someone would be curious and try to check. But, no, now that it needs to be done, I will provide a full trigonometric proof in diagrams, for everyone to confirm. Take a few days. Maybe someone can beat me to a valid solution to show input/output angles are equal, or some existing software can do this.

hutchphd said:

It is still a doublet. A singlet lens has air on both sides. It may well be correct, but not novel in my opinion.
You're right, it is a doublet model. And you're right, a singlet is always thought of as one single lens having air on both sides. No one thinks of it in any other way, ever. Still, look at the Wikipedia definition, which says, "In optics, a simple lens or singlet lens is a lens consisting of a single simple element." That's all it says. Sounds too simple, almost dumb, to me. Maybe some other textbook has defined it the way we all think of it, I don't know.

So, my final argument then to you would be this. And this is all due to the fact of equal angles in, equal angles out. It would be, how about maybe for now, thinking of this theoretical model as a special case of singlet, where all three indices are different. Special case of singlet in theory, cemented doublet in practice. Might you agree to that? You don't have to. It's not even been proven valid yet! A novel doublet is OK too, but I am only going to prove, trigonometrically, what the input/output angles are for the single, 2D lens. I'll show you all the model variables I used in the calculations, the mechanical drawings. So far, I've only tried to keep all the diagrams as simple as I could. Give me a few days. I am still working too. Thks.

difalcojr said:
Perhaps you can check too, given the parameters and values I have provided in the first diagram. My hope was that this would have been an easy, 2D check on a couple of refraction surfaces for someone in a physics forum to do. That someone would be curious and try to check. But, no, now that it needs to be done, I will provide a full trigonometric proof in diagrams, for everyone to confirm. Take a few days. Maybe someone can beat me to a valid solution to show input/output angles are equal, or some existing software can do this.

Well, in this configuration things do seem to come out quite collimated:

Here is the output of the sensor with respect to the rays orientation (x,y,z, normalized) :

Here is the savefile if you want to play with it yourself:

difalcojr and berkeman
Nice. Very impressive software and diagram. You've proved it, apparently, too! Second time now software has worked to show equal in/out angles, the last time for a paraxial ray only, but your version works for all the rays in the planar wave, looks like.

Try the other lens diagram. 10, 20, and 30 degree rays from a source point 1 unit before the lens. Everything else the same. Check the output angles.

difalcojr said:
Nice. Very impressive software and diagram. You've proved it, apparently, too! Second time now software has worked to show equal in/out angles, the last time for a paraxial ray only, but your version works for all the rays in the planar wave, looks like.

Try the other lens diagram. 10, 20, and 30 degree rays from a source point 1 unit before the lens. Everything else the same. Check the output angles.

Unfortunately I don't have much spare time to split all the rays of a source point with and analyze the angles.

Instead, here's the case of the beam at a 30 degrees angle, this should convince you I think.

The output rays do seem to be quite parallel, although there's a small loss in precision:

difalcojr
Wow, that's very impressive. Beautiful color diagrams. Thank you. I don't need any convincing, but the scientific community does. This post was just looking for available software to ray trace the model. You've provided some now and shown proof, I think, too, of equal angles, in and out. Tremendous.

So, hopefully, now, someone else can verify this model too. If they are curious. Using your software, even. Not sure about Zemax, CodeV, Oslo, or other programs. Maybe try to trace a converging wave.

Model rules are on an attachment in the middle of the 'sine laws' thread, and they are very simple. You can keep these same values for radii, as well as media index values, for any incoming wave, planar or otherwise, that one might want to check further.

I will still do an old-fashioned trigonometry analysis with mechanical drawings of the 30 degree model now for a geometric proof. For the last diagram above. To have a redundant proof, if for nothing else.

difalcojr said:
However, I am contending the lens model is free of all spherical aberrations.
That is quite obvious in your model. First surface has a spherical aberration exactly matching with opposite sign the spherical aberration of the second surface.
Imagine raytracing refraction on the first surface gives your rays caustic. Now imagine backwards tracing of second surface refraction gives your the same rays caustic, which you can overlap.
I can raytrace it for you in Zemax when I back from vacation. Otherwise I suggest you to try a free OSLO EDU raytracing soft.

difalcojr

Thank you, that would be great if you are curious too. I'm going to post my trig program soon here. Sticking to it for now. It works.
Yes, and the aberrations patterns match for all the other waves too. The air-to-solid refraction pattern matches its inverse, the solid-to-air caustic. Here's that other diagram also showing what you are saying.

hutchphd said:
Maybe start with a symmetric one and show it in detail the refraction geometry at the two surfaces. How does your software do it?

Well, since you asked, and since I needed to provide a proof and not just diagrams, and since the post title even changed too, here it is. A trig proof that the angle in equals the angle out for this model. Long process, but not as long as Conrady's. TGIF and this homework assignment is turned in on time!

This is my model, and most all of the variables, a fully Cartesian model. All variables positive, but some can also be negative, and I put a sign showing that above each variable when needed, for it affects the sign of the equations. Ray angle with x-axis is positive divering, zero when planar, and negative converging. Axial lengths are negative left of the lens center, positive to the right. The beta angles with the radii are always measured counterclockwise. Only the positive side of the x-axis is calculated.

So, here's another proof for this model. What a contrast to that beautiful, multi-colored, computer-generated diagram shown above in the previous post!! With his own software!

KAHR-Alpha, hutchphd and Gleb1964
It turns out that the OP is trying to use PF for peer-review of his work, so this thread is closed per the PF rules.

## What is trigonometric ray tracing software used for in optics?

Trigonometric ray tracing software is used to simulate the propagation of light rays through optical systems. It helps in analyzing and designing lenses, mirrors, and other optical components by calculating the paths that rays of light take as they travel through different media. This is crucial for optimizing optical performance and identifying potential issues in optical designs.

## What are some popular trigonometric ray tracing software options for optics?

Some popular trigonometric ray tracing software options for optics include Zemax OpticStudio, Code V, TracePro, OSLO (Optics Software for Layout and Optimization), and LightTools. These programs offer a range of features for optical design, analysis, and optimization, catering to both simple and complex optical systems.

## Can trigonometric ray tracing software handle non-sequential ray tracing?

Yes, many advanced trigonometric ray tracing software packages can handle non-sequential ray tracing. Non-sequential ray tracing is used to model systems where rays can scatter, reflect, or refract in complex ways, such as in illumination systems, stray light analysis, and optical systems with multiple reflections or diffractions. Software like Zemax OpticStudio and TracePro have robust non-sequential ray tracing capabilities.

## What are the key features to look for in trigonometric ray tracing software for optics?

Key features to look for in trigonometric ray tracing software for optics include accurate ray tracing algorithms, support for both sequential and non-sequential ray tracing, a comprehensive library of optical materials, advanced optimization tools, user-friendly interface, and the ability to handle complex geometries and large-scale simulations. Additional features like polarization analysis, thermal effects modeling, and integration with CAD software can also be important depending on the specific application.

## Is there any free or open-source trigonometric ray tracing software available for optics?

Yes, there are free and open-source trigonometric ray tracing software options available for optics. One notable example is OpticsRayTrace, which is a simple, open-source ray tracing program. Another example is Python-based RayOptics, which provides basic ray tracing capabilities. While these tools may not offer the same level of sophistication and support as commercial software, they can be useful for educational purposes and basic optical design tasks.

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