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PSF broadening and beam width estimation

  • 2 September 2021
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Hi,
 

I am looking at a pint source, star, with a telescope system and I would like to understand how much my PSF broadened and what is the size of the observed point source on my detector. I am not sure what is the best approach to do this, as I get different results trying different type of methods for analysis. 

Method1: paraxial gaussian data. 

I set the input waist same as aperture value, as the input beam in collimated. Final value is 8.8mm beam size and beam waist of 5.5e-4mm. Looking at the PSF plot I donot see the 8.6mm. looking at the geometrical enclosed energy at above 85% energy, it is above 70um which does not go together with the beam size or beam waist estimated by paraxial beam.

 

Method2: Hygens PSF or FFT PSF cross section. They are much lower and not sure if they give a correct estimate when my system is not diffraction-limited.

 

Method3: Physical Optics propagation

I defined the beam as top hat with beam waist of aperture diameter for collimated entrance beam.Beam size and beam waist are very different in this case and much lower.

Method4: Geometric image analysis

Rough estimate of the beam size is 0.1mm, which again very different from other methods.

Method5: merit function report 

I tried using POPD, data=3, for beam size and GBPS for Gaussian beam size. Diffrent results in copare to above.

 

I would appreciate if you could shed light into how I should approach for understanding the point source bradening in my system and when to use these different methods.

 

Thank you in advance.

Fatemeh

 

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Best answer by Angel Morales 7 September 2021, 23:38

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Hi Fatemeh,

Thanks for posting on the community!

To get to your questions, I think at a high-level, we might need to just understand what specifically you’re trying to model. Do you expect the input illumination from your point-source to act like a top hat beam? Like a gaussian beam? I mention this because there is some discrepancy between your approaches. For instance, the Paraxial Gaussian Beam tool cannot consider something like a top hat beam, so I wouldn’t expect results to be that similar to a POP run with a top hat input, since the input distribution of light is fundamentally different. In addition, POP is a tool which requires attention to detail on the sampling of your beam from surface-to-surface, both for the irradiance distribution and the phase data. If there is any undersampling of your data, aliasing will limit the utility of the tool. We have a three-part Knowledgebase article series on this topic, which you can start reading (if you haven’t read them already) here: Using Physical Optics Propagation (POP), Part 1: Inspecting the beams – Knowledgebase (zemax.com)

As for using FFT/Huygens PSF, I think it might be okay to use, but without being able to see your system first-hand, it’s hard to say. The limiting factor with highly-aberrated systems and those analyses is that you would need very high sampling to ensure that your resulting data is accurate.

Without seeing your system, my inclination is to begin with the more geometric ray-based analyses. That way, you can get a baseline understanding of what’s happening with your system with the ray treatment, assuming that various settings for your aperture in the System Explorer is defined appropriately. Depending on the analyses used, you will get different perspectives on how your system performs. For example, a Spot Diagram will only show you specific field points (perfect point sources). The diffraction treatment analog here is going to be the FFT/Huygens PSF. You also would need to consider which of these two to choose from, as FFT is a faster computation but takes more assumptions on the nature of your system, whereas the Huygens does not make these same assumptions but requires some more computation time. We have some relevant articles here and here.

For extended sources, Geometric Image Analysis will allow you to define some finite size to the object you are imaging, but it’s important to understand the various settings and how they relate to the IMA file you end up using. As soon as you define some finite size, I think the comparison to something like the PSF is obfuscated, since you are fundamentally modeling a different thing between the two analyses. You could define an “off-axis” field point that defines the edge of your star (though it is a point source), and then compare the PSFs with each other. We have an article which details superimposing two PSFs using multiple configurations, though again, I think the value here would be capturing some diffraction effects that the Spot Diagram/GIA cannot report, which seems unclear if they would be observable if geometric aberrations dominate your performance anyway.

Otherwise, we do have analyses similar to GIA which can consider diffraction effects, like Image Simulation and Extended Diffraction Image Analysis. While there is a lot that can be discussed with respect to extended source imaging simulation, there is a webinar that you might find some value in looking through here: Simulating image quality in OpticStudio - webinar – Knowledgebase (zemax.com). One slide I noticed at about 32 minutes in mentioned Extended Diffraction Image Analysis being helpful for analyzing extended scenes with point sources:
 

 

Please let us know how these thoughts work out for you or if there are any lingering questions, and thanks again for the question!

Hi Angel,

 

Thank you very much for all the useful links and answer. It took me some time to go through them all. However I will not call my question solved yet. I am not sure I understand why should someone else than me say that my question is resolved if I still have the question ;-).

For the first part regarding illumination if it is Gaussian or top hat, I guess I am confused how to define it, you are right.  The source is a star with a Gaussian beam profile. However it is far away, so it is a wavefront,  arriving at the primary mirror as a collimated beam. Perhaps I will benefit from your advise here to how to define the input beam. I thought in POP BEam definition setting, it might make sense to define the beam as top-hat with Waist size of the aperture for the collimated beam.

 

My system is dominated by geometric aberrations and as I understand Geometric Image Analysis takes into account the aberration. So to my understanding radius for fraction of geometrical enclosed energy should give the same result as the beam width form GIA! Please let me know if that is correct.

 

I am interested in spectral resolution of the spectrometer which includes PSF broadening and detector pixel size.

Using GIA  I can see that the two adjacent line (5nm apart) can be resolved, which I interpret as 5nm Spectral resolution. I have set the pixel size as it should (0.013mm), but I am not 100% sure if this is pixel-limited resolution.

The left line corresponds to WL = 250 nm and the most right one is WL=350nm,  the spacing of WL is 5nm. 

 

However I was trying to use Huygens PSF Cross section (as I understood that I should not use FFT for tilted system)  to see the pixel-limited resolution following the guide below, by only having 2 WL of 250 and 255 nm.

https://support.zemax.com/hc/en-us/articles/1500005578862-How-to-build-a-spectrometer-implementation

Choosing the Image Delta as 13 (equivalent to 13um pixel size)  and full pixel number of 1024 pixels.

The lines do not look resolvable at all, as it does nicely on the GIA. That is why I am not sure what to do. 

 

 

For Image simulation, it is indeed very useful. I used it for imgaing part of my design. My main secion of design is a spectrometer and I am not sure it is useful to use Image Simulation analysis for spectrum analysis, as I am interested in Y-cross intensity over the full spectral range and spectral resolution.

For the Extended Diffraction Image Analysis, I wished the webinar where covering that. Setting it up it is really unclear for me. I have set the size and sampling to be the same as my detector, but the rest is not all clear for me. 

Thank you again and appreciate your help.

Fatemeh

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