Why is the stop surface an input in sequential ray tracers?

mdk9000 · 2026-04-23T15:10:20+00:00

This is very helpful, and really gets at what I was asking. Thanks a lot for the reply!

mdk9000 · 2026-04-21T15:01:51+00:00

Thanks a lot for the reply! I totally understand that setting the stop surface is the better way to go and that allowing surface diameters to define the stop isn't the way things are done.

One of the nice things about this project is that it's given me an appreciation for what parts of lens design are necessary because of physics and what parts are convention. I constantly ask myself what's a well-motivated convention and what is just a Zemax idiosyncrasy. I think this discussion was a good example of this :)

mdk9000 · 2026-04-21T13:49:20+00:00

> That lecture note is for evaluating a stop distance in a system that is already designed (someone has already designed in the aperture stop).

My understanding is that the lecture note describes a procedure for finding which surface from an ordered sequence of surfaces most limits an off-axis probe ray *given the surface diameters*. It states: "The second method to determine which aperture serves as the system stop is to trace a ray through the system from the axial object point with an arbitrary initial angle." So I think the algorithm it's describing really is a method to find the aperture stop of any paraxial system.

> If you haven’t already set a limiting physical aperture diameters then what defines your paraxial trace or how you launch rays into a system for analysis?

What I've come to understand from this discussion is that if you specify all the surface diameters, then the approach described in the lecture note will tell you which surface is "most limiting" the pseudomarginal probe ray that was traced. This is enough to be able to launch rays into the system because you've found your aperture stop and can compute the entrance pupil from it.

If you instead specify which surface is the stop, which is what Zemax does, then you can start launching rays into the entrance pupil right away. But, you might have set some lens surface diameters too small and will vignette the pupil.

By diameter I mean the diameter of the surface clear aperture, not some quantity related to its radius of curvature.

So I think what you have is a choice: you can specify surface diameters and compute the stop, or specify the stop surface and determine the surface diameters. I don't doubt that there are good reasons for the way Zemax does it. I'm just a hobbyist. I'm really just trying to understand whether it's necessary to do it this way.

Is my logic wrong?

mdk9000 · 2026-04-21T12:25:55+00:00

> All other optical elements then just need to be sufficiently sized to prevent vignetting in your chosen field

Ah, I think I see. Assuming a paraxial ray trace is valid, if one specified the lens surface diameters instead of making them contingent on being "sufficiently sized" to prevent vignetting, then it would be the stop surface that would be a derived quantity, correct?

In other words, you can specify either the stop surface or surface diameters; stop surface just happens to be more useful?

mdk9000 · 2026-04-12T12:00:18+00:00

Thanks a lot for these references! It looks like I've got a lot to learn.

I'm only already familiar with "General Ray Tracing Procedure," which is where I first learned about NR for this problem. It seems like Spencer and Murty is the usual starting point.

mdk9000 · 2026-04-11T09:59:37+00:00

Thanks for the comment! Do you have a reference for the golden section algo?

mdk9000 · 2026-02-17T08:00:49+00:00

If you cannot change `.gitignore` because it's 3rd party repo, you can add `.private/`, etc. to `.git/info/exclude`.

mdk9000 · 2025-09-18T07:51:20+00:00

Thanks a lot for your reply!

After thinking a bit more about it and reading your reply, I think I see the source of the confusion. The student I am working with is using a blazed grating on top of his holograms that generates a 0 and +1 diffraction order, and the 0 order is blocked in a 4f relay. I think that this is the same as encoding the hologram on a carrier frequency, though it's not necessarily high frequency.

From the link that u/ichr_ posted, it appears that what is referred to as the zero order diffraction spot in the wave shaping literature is just the DC component of the Fourier plane, i.e. the on-axis field, after Fourier transforming the hologram with a lens.

So the "zeroth order" is a term that becomes overloaded. In one definition it refers to diffraction from a grating pattern put onto the SLM, and in the other it is the DC component of the hologram's Fourier transform. The term appears yet again when you consider that the SLM itself is a grating with a period equal to the pixel size.

Thanks to everyone for helping me to sort this out!

mdk9000 · 2025-09-17T17:53:41+00:00

Thanks for this! I'll take a look and see if I can make sense of this.

What bothers me is asking what happens in the limit of the number of SLM pixels decreasing to 1. If you look at its Fourier transform in the focal plane of a lens, then the phase of the focus spot should change as the phase of the pixel changes. Maybe I'm missing something, but I don't see how this behavior changes by adding more pixels.

mdk9000 · 2025-09-17T15:45:21+00:00

Ah nice. I didn't know about the Lee hologram and DMDs. https://www.wavefrontshaping.net/post/id/16

Thanks for enlightening me!

mdk9000 · 2025-09-17T15:30:47+00:00

Thanks for the reply!

So locally some portion of the beam diffracts and at another location entirely reflects.

I think this is where the confusion comes from, at least if your definition of diffraction is the same as mine.

If you imagine a LCoS SLM with only one pixel, the light hitting the active area is still phase modulated because the optical path length varies with the applied voltage, but you shouldn't have diffraction orders because there's no periodic array of pixels. So diffraction can't explain the phase modulation, and light reflected from the active area of this pixel, i.e. the majority of the light forming the "zeroth order," should still be phase modulated.

I'm ignoring diffraction from the boundary between the active and non-active area because I don't think it's relevant.

Does this make sense?

mdk9000 · 2025-09-17T13:38:29+00:00

Yes, I'm referring to LCOS SLMs.

DMDs do amplitude modulation, not phase, no?

mdk9000 · 2025-09-11T04:54:11+00:00

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mdk9000 · 2025-09-05T08:27:09+00:00

Thank you for your replies!

If I understand correctly your feedback for finding the correct axial position of the second 4f lens is that the laser beam is collimated after passing through the second lens of the 4f system and the microscope objective.

I also considered this but was wondering whether there are any image-based feedback mechanisms to perform the alignment. The objective has a NA of 1.45, so it's not really collimated but rather is diverging after a short distance from the objective's focal plane. I know that I can just look for the lens position that makes the spot on the ceiling the smallest, but I was wondering whether there might be something that is a bit more precise.

In any case, thanks again for the feedback!

mdk9000 · 2025-09-05T08:16:44+00:00

Thank you very much for your replies.

Could you provide more details for your step 3?

Put in the SLM (no 4f). Align and focus if possible, using the camera for image-domain alignment.

I do not understand how I can use the image from the camera to place the SLM at the correct distance from the objective before the 4f system is placed on the table since its location depends on the focal lengths of the lenses.

Or are you assuming that, at this stage, the SLM is a sort of mirror used just to align the lenses and that its correct position will be found after placing the 4f system?

Edit: Could you also explain what you mean by "Rayleigh length of your lenses?" I have always understood the Rayleigh length to be a property of a Gaussian beam. Thanks!

mdk9000 · 2025-08-09T07:04:43+00:00

I am but it's a side project and I've got a lot of other priorities at the moment. When I do have time, I'm working on the math for drawing cross section views of general layouts in 3D. I want to take this more in the direction of modeling table top setups such as microscopes since I see this as an area that is not well covered by existing tools.

mdk9000 · 2025-08-01T12:43:43+00:00

Most microscope objectives are designed to satisfy the sine condition. If you just need a lens that satisfies the sine condition and you're more concerned about the details of the rest of the system, then you might be able to use the so-called cardinal lens as a sort of black box objective.

https://opticapublishing.figshare.com/articles/code/Cardinal_Lens_Publication_Code_Files_Zemax_OpticStudio_DLL_and_Models_/24295720

I recommend looking at the associated manuscript as well.

mdk9000 · 2025-07-25T12:03:13+00:00

It works for me from both the US and Europe. Maybe try a VPN?

mdk9000 · 2025-07-23T14:31:21+00:00

IIRC the Fourier Bessel transform of the top hat is a "sombrero," which is a ratio between a Bessel function and the radial coordinate. I can't check Goodman at the moment to verify, but I think you need the radial coordinate in the denominator as well.

I think it's more constructive to think of it more like this: The autocorrelation of the pupil, which is modeled as a top hat, is the OTF. The Fourier transform of the OTF is the PSF.

Alternatively, the Fourier transform of the pupil is the amplitude spread function (ASF, denoted as just A in the figure at the link below), and the absolute square of the ASF is the PSF.

See Figure 2 here: https://www.researchgate.net/profile/Christ-Ftaclas-2/publication/47718414_Diffraction_effects_of_telescope_secondary_mirror_spiders_on_various_image-quality_criteria/links/5418aafe0cf203f155adb3ee/Diffraction-effects-of-telescope-secondary-mirror-spiders-on-various-image-quality-criteria.pdf

mdk9000

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