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# Results for high frequency approximations (Wave propagation)

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Hello,

I am a new user of the OpticStudio software which arouses my curiosity!

The wave propagation can be solved with several models and the software offers several possibilities. The model based on the astigmatic Gaussian beams (beamlets) is very well interesting.

But, I found few years ago the relevant paper:

Gosse L., James F., Convergence results for an inhomogeneous system arising in various high frequency approximations, Numer. Math. 90: 721–753 (2002).

It is enough hard because the mathematics formulations are theoretic. However, the issue solving gives several possibilities to find the phase and the amplitude of the light wave together.

Numerical values for the phase and the amplitude of the smooth wedge.

Therefore, do we have this possibility with the OpticStudio? Compute the phase in order to see transparency images for instance?

Benoît.

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Best answer by Sandrine Auriol 27 September 2021, 11:30

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Hi Michael,

1. Yes, you are right. I not known this paper because I purchased the Pierre Pellat-Finet book (In French, unfortunately!). Strangely, the fractional Fourier transform is used also for the corpuscular physics. The relationships between the optical and corpuscular physics are closed. In the Gosse’s paper, you can remark that the author applies also his model for Schrödinger’s and Helmhotz’s equation, the wave physics stays very logical! It seems to me the programming with spherical surfaces as POP must be better for the simulation results.

2. Thank you for this detail of the POP programming. The Rayleigh length is the theory limit between the small and the large changes of the Gaussian beam width. The switch between the two models seems to me interesting relative to this limit.

3. The Lax-Friedrichs scheme is a finite difference time domain algorithm (FDTD). My programming is better now, but its is not very sure for all object types. The tool stays just a prototype to appreciate the power of the optics equations to solve simultaneous the phase and the irradiance and apply it to biological issues (see the image bellow).

In common use, it seems to me the principle of scalar field is correct when all partial derivative equations governing the electromagnetic field has the same expression. Indeed in this case, you can choose a field component (electric or magnetic) as the scalar field. Luckily, the asymptotic equations of the optics keep this vector property and we can extend the Gosse's algorithm to the vector format for instance. It would be surely not easy but it seems possible!

4. I will propose a letter in a journal concerning the Gosse’s algorithm, it is not obvious that this paper will be accepted. However, I wish to thank the Zemax team to ours fruitful exchanges in this paper. Do you have a particular formulation for the Zemax company?

Kind regards, Benoît.

Userlevel 5
+2

Hi Benoît,

Thank you for the sharing and discussion again.

POP hasn’t updated its fundamental algorithm for recent years but this makes me feel it might time to move forward. I will share this discussion to development team in case it’s useful to them.

For the reference, I have checked internally and it looks like we've never given specific instructions for citing Zemax in published papers. People will often reference the OpticStudio software by Zemax LLC as a tool used to produce some of the images in a paper. I have also seen some papers discussed the difference of its algorithm to that in OpticStudio in introduction.

I have also got some suggestions, but please consider these only if you are interested. The suggestions are that maybe you could post a summary about the paper on the community when it’s available, and host a “ask me anything” on thread for that. Otherwise, I think this discussion is already great. I’ve learnt a lot and believe it’s so to other readers too. Thank you!

Best regards,

Michael

Hi Michael,

I not know the benefice for the industrial partners but it would be great if the OpticStudio could introduce the Gosse’s algorithm.

Agreed, it is well the Zemax citation. I will see with the co-authors to ask the shared mode with the journal. In this way, I think the exchanges could be enlarged.

I stay ready to carry on our discussion, if you wish.

Best regards, Benoît.

Userlevel 5
+2

Thank you, Benoît!

I have forwarded this to development team for their information. Although I don’t think there will be an action any soon, but I think we should keep an eye on this kind of potential theories too. As the manufacturing method improves, diffractive optics or small structure would gradually become  commercially possible. And this kind of algorithm would be important to simulation in the future. I’m actually thinking this might be useful to the so-called diffractive lens simulation. But I don’t have enough knowledge about how it works, so I probably should not assume too much before I read it carefully.

And yes, that would be wonderful if you can share update when you have progresses to the paper or any publish!

Best regards, Michael

Great, Michael!

I know not very good as you the diffractive optics. However, the “Nature photonics” journal edited his “Volume 15 Issue 5” with a cover showing “Diffractive optical computing” (Nature Photonics volume 15, pages 367–373 (2021)).

I not read this paper but it must be interesting, the diffractive optics is surely future technology. I will look a bit this.

Our current study is nuclei inside the biological tissues which may act as micro-lenses (DD. Nolte, Optical interferometry for Biology and Medicine, 2012, Part of the Bioanalysis book series, Springer). I think this issue should be also diffractive optics as same way.

Warm regards, Benoît.

Userlevel 5
+2

Thank you, Benoît.

That’s interesting and I will try to have a read. I also forwarded this to one of my colleagues who is still a PhD student doing research related to optical neural network.

Yes, I agree this is related to diffractive optics. Normally I’m confident when I want to build the macro system for the biomedical optics related application, but it’s a little tricky when it comes to exactly modeling the light interaction with those micro structures, like nuclei. The book is very interesting. It’s a good reference to me if I want to understand the requirement of this kind of systems more, and thank you again for sharing the guidance.

Best regards, Michael

Hello Michael,

We advanced with the reconstruction of the biological tissue by using the Gosse’s algorithm.

The reconstruction of a image stack is possible lighting by a parallel ray beam. These images contain small structures. You have two 3D views (OpenGL), bellow:

Best regards, Benoît.

PS. They are fluorescence images.

Userlevel 5
+2

Hi Benoît,

Congratulation for the progress! This looks cool. Am I correctly understanding these are the irradiance of a collimated input beam at each “slice” as you mentioned before? The reason you say they are fluorescence image is because the excited light should be proportional to the irradiance, correct?

This looks interesting to me. It’s a 3D intensity distribution I(x,y,z) if I don’t mistook. We could convert it to a light source and simulate it in ray-tracing way with a real or ideal microscope model to know how it would look like in a microscope system. Just brainstorm for fun.

This looks nice and congratulation again!

Best regards,

Michael

Dear Michael,

The paper concerning our previous exchanges is published now in the “Scientific Reports” (https://www.nature.com/articles/s41598-022-24176-8). The authors thank the ZEMAX developer team for their help and especially to better know the OpticStudio Software (Thanks are in the paper).

But the adventure not stops, you will find a forum on WebSite of the Springer Nature to exchange if you wish. I will drop on the WebSite a new interesting reference to begin the exchanges.

Best regards,
Benoît.

Userlevel 5
+2

Hi Benoît,

That’s a great news and congratulation to the publish in Scientific Reports!!

And thank you for adding the information in Acknowledgements. I’m happy Zemax can help a little here.

I’m quite overwhelmed by many tasks now, but I really want to take time to read it. Congrats for the great work again and thank you for sharing it to us!

Best regards,

Michael

Userlevel 6
+2

Hi Benoit!

This is brilliant. Thank you.

Dear Sandrine and Michael,

It seems to the adding reference on the WebSite of the paper is not present. Its link is: https://www.sciencedirect.com/science/article/abs/pii/S1572100021000181?via%3Dihub.

Kind regards, Benoît.