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I Ideal lens calculated

  1. Mar 2, 2018 #1
    I have patent pending on this. I am publishing despite that. Patents last 20 years at the most, plus it can be researched already.

    I choose a focal point. I dirve rays from it in a fan fashion toward lens, which for now is in shape of mere segment. The segment has its position in horizontal plane and its given height. For each ray I can calculate what inclination will our now straight curve have in point of intersection so that refracted ray leads horizontally. I move points of the curve so that it corresponds with calculated derivatives.

    6sW8O.png

    But this moves the points into different distance from focal point and originally calculated derivatives will no longer refract the rays horizontally. I repeat the process with more and more exact curve, until I reach required tolerance.

    The script can be downloaded from github: https://github.com/jankokes/idealLens

    EDIT: This thread should have been called "recalculated". To me it was extremely dificult to find any info on the ideal lens, so I thought it would be nice if I explained where I was wrong and which post shows correct answer right at the top. Jan
     
    Last edited by a moderator: Mar 16, 2018
  2. jcsd
  3. Mar 2, 2018 #2

    berkeman

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    Staff: Mentor

    Welcome back to the PF. :smile:

    Your description is not very clear, and I don't think folks are going to want to run any scripts on their PCs to try to figure out what you are saying. What is different in your procedure compared to standard ray tracing techniques of lens design?

    Also, your figure is not very helpful -- do you have any PDFs of your technique? And how are you dealing with chromatic and spherical aberrations in your technique?
     
  4. Mar 2, 2018 #3

    Dale

    Staff: Mentor

    If you already filed then that is fine.
     
  5. Mar 2, 2018 #4
    Well, the main difference is that I calculated it. I firmly believe that someone wanting to understand this will not mind html as it is generally considered safe. Especially with no libraries included. Well, there is javascript, there is jquery... Programmers will understand.

    Yes, I filed already.

    This may sound little too selfish, but I think one day people will be amazed how this thread got moved from advanced to intermediate. I mean the lens has been known since old Babylonia and noone calculated the ideal lens before. Not even Newton. But that's an off topic. If you need it, you know where to find it. I have no pdfs yet and I am working on lens making machine since I need the lens for 3D printer, and I found it didn't exist. It exists now.
     
    Last edited: Mar 2, 2018
  6. Mar 2, 2018 #5

    Drakkith

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    Science Advisor

    I'm guessing your lens ends up being shaped like a parabola?

    How does your lens correct chromatic aberration, coma, and astigmatism?

    I'm not really a programmer, so I have no idea how to view your design, but I am an optical engineering student, the kind of person you'd want to easily be able to describe your lens to. Making it so that programmers are likely to be the only ones who will see your lens design runs counter to the idea of wanting to put your design out to the people who actually understand it. If you're not willing to put your design into a format that can be easily viewed by those people best able to evaluate and use it, why put it out at all? It's just lazy and it makes you look extremely bad.
     
    Last edited: Mar 2, 2018
  7. Mar 3, 2018 #6
    Unfortunately it is not parabola. It is ultimately unknown curve. I ruled out all the goniometric and exponential functions. I figured it is because of how it is created. If I had mathematical formula I would know the points of the curve directly, and I would approximate the derivatives. As is the case I calculate the derivatives first and approximate the curve from there. I create it. I made a set of functions and was testing which one it is. It is none. That is why I publish the program. It is html, you can view the curve in real time as you change the parameters, and in console you will find svg that can be imported into CAD or other software.
     
  8. Mar 3, 2018 #7

    berkeman

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    Staff: Mentor

    You have not addressed our aberration questions yet. Have you used your process on multi-element lenses and been able to correct for aberrations?
     
  9. Mar 3, 2018 #8
    Sorry. I made single interface of two materials, ie air and glass. This permits plano-covex or plano-concave lenses only. I can take it further, or anyone else, because first example is provided. I want to test it now. I imported it into Blender (3D software) and ran parallel rays through to see what Blender's internal engine thinks about the curve. I found the result satisfactory, so I am making the real lens now.
     
  10. Mar 3, 2018 #9

    Drakkith

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    I'm nearly certain that the shape should be a parabola. I know for a fact that, for a mirror, the only shape which works is a parabola. Since the only difference between a lens and a mirror is that the index of refraction of the mirror is negative, the shape should remain the same, just stretched differently. This is identical to how two lenses with the same focal length but different refractive indices must have different strengths for their curvatures, but both can remain spherical. Just changing the refractive index does not mean you must change the shape.

    What about aberrations? You still haven't addressed these.
     
  11. Mar 5, 2018 #10
    Blender confired the geometrical aberrations are taken care of. With monochromatic light, of course. Chromatic aberration is still present. The best I know that works to mitigate it is a focal point far away.
     
  12. Mar 5, 2018 #11

    Drakkith

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    Did you test for points not at the focal point?
     
  13. Mar 5, 2018 #12
    That is so. I started at focal point. It made debugging much easier.
     
  14. Mar 5, 2018 #13

    sophiecentaur

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    2017 Award

    An 'ideal' lens has to function over a range of object and image positions. You have written some code which produces a result but what is its significance in terms of a real lens? I cannot / will not try to run this code and nor will many readers of your posts. Is that a surprise to you? I am not sure what your aim is in this.
     
  15. Mar 5, 2018 #14

    Drakkith

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    A lens takes light emitted from different points in 'object space' and maps them to different points in 'image space'. The problem is that a single lens cannot do this perfectly for all points in object space and for all wavelengths. You will have aberrations. To minimize aberrations, lens designers have to optimize their lens designs. It is trivial to optimize a lens to function near-perfectly for a single point and a single wavelength, but lenses like these are not usually useful by themselves in the real world except in very specific, simplified cases.

    Also, please note that we already know an enormous amount about how lenses work and what shapes they should and shouldn't be. We've been working with lenses for more than 400 years, after all. If you're interested in optics and lens design, I recommend that you pick up a book on the subject. Here's one example, though there are many others.
     
  16. Mar 5, 2018 #15

    Khashishi

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  17. Mar 7, 2018 #16
    Thank you for your replies and for feedback. I just wanted to let you know that this can be done. I am fine with the idea noone will try the script. It represents ideal lens, which took long time to calculate, and I am glad I managed to do so.

    This lens can concentrate rays into a single point. I am well aware of the fact that there are many lenses that try to do the same.
     
  18. Mar 7, 2018 #17

    Drakkith

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    That what can be done? We already have lenses capable of bringing rays of a single wavelength emitted from a single point in object space to focus at a single point in image space (or as close as possible, limited by diffraction and lens imperfections).
     
  19. Mar 8, 2018 #18
    I don't think it is possible to get "as close as possible" without the actual knowledge of the curve. I will appreciate valid links.

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  20. Mar 8, 2018 #19

    sophiecentaur

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    We know it can be done because every decent lens you use will use ray tracing in its design (or some short cuts, no doubt). If you want more information about methods for this why no google "ray tracing lens design"? I did that and there were dozens of hits which would be much more relevant than I got with other search terms. Find one that is useful to you.
     
  21. Mar 8, 2018 #20

    Drakkith

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    My apologies, it appears the correct shape for a plano-convex lens is a hyperbolic shape, not a parabolic.
    Here's a link: http://httprover2.blogspot.com/2012/03/plano-convex-hyperbolic-lens.html
    Here's an example problem with solution by one of my professors where he requires that the shape of a perfect plano-convex lens be derived using both Fermat's principle and Snell's law. Both give you an exact shape in the form of a hyperbola. (if you can't access this link, let me know)
     
  22. Mar 9, 2018 #21
    Thank you both. I looked at mathematical derivation. It looks impressive.

    Section of hyperbola near peak could approximate the curve fairly well. However I must insist ideal lens is not hyperbic, because I must use only small section, as close to appex as possible, which disqualifies hyperbola in my eyes, as whole curve would have to produce the result. With hyperbola, the further I go, the more off I am. Which is the same as with sphere, only not as bad. Not an ideal lens.

    I downloaded pyOptTool and will see if I can import my lens in it. I will also try hyperbola and see how they compare.
     
  23. Mar 9, 2018 #22

    jbriggs444

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    Perhaps you need to rephrase. You are agreeing that a hyperboloid is optimal but complaining that a portion of a hyperboloid is not?
     
  24. Mar 10, 2018 #23
    Yes, this is the case. See my screencast below.
    One cannot use whole hyperbola, only infinately small part of it, such as

    Lim x -> 1 (y = 1/x)

    as shown here:


    As for the blog link I am not certain what the gentleman calculated and how he did it. Other people have already asked questions to no avail. The curve isn't too close to mine:
    screen-konkurence.png

    As for the mathematical paper, I am not all that good at diferential equations. Let me assume it is correct.

    I tested more recent OpticalRayTracer where hyperbolic lens can be simply chosen. The curve is much closer to what I have. The focal point is not ideal, but close:
    konkurence2.png
    screen-konkurence2.png
    I failed to install some libs for pyoptools yesterday (no internet at home), but I downloaded a showcase video about it which shows set of three lenses to bring rays into common points (yet it never shows the focus clearly).

    If I understand correcly, the situation up till today has been that someone theoretically calculated the curve and the calculation was obviously correct. The only problem was that whoever tried running it through ray tracers found out it wouldn't focus rays into a common point. The curve they got was close to what I get after my first approximation. I suspect I would end up with similar result if I didn't realize I need to repeat the processes recursively.

    So if I am correct we were all correct, except I was much more correct since I did actually have the curve and the algorithm. In addition I am presenting to your attention a mathematical formula that works. (However I don't think it is plausible to use it since it requires infinately small limits stretched out later on along with heavy usage of differential equations which I am yet to see used correctly, while my algorithm utilizes nothing but Snell's law.)
     
  25. Mar 10, 2018 #24

    sophiecentaur

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    You have 'an' algorithm and not necessarily 'the' algorithm. in post #20 there is a link which describes an algorithm that doe not agree with your result. That algorithm shows that the focus is 'very near' a point.
    Ray tracing methods are all subject to error so, perhaps you could re examine your algorithm and check before assuming you are 'right'.
     
  26. Mar 10, 2018 #25

    jbriggs444

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    The lens shown in the diagram following this passage showed a biconvex lens. The hyperbolic lens that is proven optimal is a plano-convex lens.

    There is no conflict between claims of optimality for both designs.
     
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