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Goodbye Aberration: Physicist Solves 2,000-Year-Old Optical Problem
- chroem- 7y agoWill this have any implications for astronomy?
- darkmighty 7y agoI don't see any figures comparing the error of the formula with the previous error from numerical methods. While mathematically the discovery seems significant, it isn't clear to me this will actually improve lenses.
- Quequau 7y agoFrom another comment in this thread: "The author’s have a paper from March 2019 (in arXiv) that uses the result to build some novel telescope geometries."
- perlgeek 7y agoNote that "build" doesn't mean they built a physical telescope, they came up with lense shapes. There are some serious problems when building large telescope lenses; if they get too heavy, they start to deform under their own weight, and non-spherical shapes are hard and expensive to produce. It would be awesome if this analytical solution inspired improvement in real applications, but I'm cautions about that.
- TheRealPomax 7y agoNot at the large scale - there aren't really any refracting telescopes left (based on lenses) when it comes to serious research, we replaced them with reflecting telescopes instead (based on mirrors). There's a few notable exceptions, like the Lick Observatory, but in terms of impacting the state or progress of astronomy, the research from this article is unlikely to have an impact outside of small scale labs and amateur astronomy. That's not to say the benefits there won't be appreciable for those who rely on optical telescopes, but you won't see this research make a difference for ground based arrays like NRAO, VLA, or in space telescopes.
- tomrod 7y agoThis was extremely well written. Not being a photographer myself, the mathematical discussion and subsequent impact to optics/photography are very accessible. Kudos to the author!
- a012 7y agoIt's good until the last sentence that circlejerks about 1 memory card slot.
- peterwwillis 7y agoI laughed when they tried to translate "Madres!", but a pissed off Latina mother running at you waving her sandal in the air like a medieval warrior swinging a truncheon is definitely an "Oh shit" moment.
- david-gpu 7y agoMy understanding is that centuries ago in Latin America "madre" became an euphemism for "madame of a brothel", while actual moms are called "mamá". In Spain it carries no such connotation.
- peterwwillis 7y agoMamá means mom, madre means mother. You use either depending on the context. (I'm only talking about the Mexican use) Madre is used more often in phrases, such as "Madre de dios!", Or "La madre putria," or "Pinche tu madre", or it's used as a formal to refer to one's mother. It's similar in English, such as "On my mother's side", "Mother fucker", "Mother of God!", etc. In Mexico, "tu madre" can be a general insult, probably shortened from "pinche tu madre", though in English we have a similar vulgar retort of "your mother". As a weird turn on the phrase, "de puta madre" is slang for a good thing. I'm not aware of an association with brothels in Mexico, but certainly in some Latin American country it could have.
- manuelisimo 7y agoIn México the word "Madrota" does carry that "madame of a brothel" connotation
- byebyetech 7y agoHopefully this will increase the sweet spot in the VR headsets.
- gfodor 7y agoVR headset lens already require software chromatic abberration correction -- I'm curious what constraints if any would limit the application of this new result for VR spherical aberrations. Would love some thoughts from an optics expert on this. I also wonder if this new knowledge could contribute to a software corrector.
- lux 7y agoHopefully it leads to software-based spherical aberration correction too, which may mean better perceived quality with the same lenses, or even thinner/cheaper lenses over time. Or maybe they'll find a way to apply it to make better lenses that need less software-based corrections. They struggle a lot not just with clarity at the edges but god rays and glare too.
- lux 7y agoNot an optical expert, just also interested in optics for VR/AR :)
- magicalhippo 7y ago> In this equation we describe how the shape of the second aspherical surface of the given lens should be given a first surface, which is provided by the user, as well as the object-image distance [...] (emphasis mine) I didn't check out the paper in detail, sounds like the shape of the correction surface depends on the distance to what you're imaging? Does it do so in a non-trivial way? If so, this sounds a bit more like an academic victory, no?
- anonymfus 7y agoSo it's useful if distance to your object changes predictably enough, like in astronomy, satellite imaging and many other kinds of space missions.
- magicalhippo 7y agoWell in astronomy you usually want your telescope to be able to observe different targets. So it depends on the details of how the correction surface has to change when the image-object distance. If it's just a mild deformation and offset, then yeah I guess technology similar to adaptive mirrors could work well.
- oh_sigh 7y agoDistances are usually treated as infinity, at least in astrophotography. I'd be surprised if this secondary lens was able to distinguish between light coming from 1ly and 1000ly
- magicalhippo 7y agoDoh, of course. Not sure what I was thinking.
- TehCorwiz 7y agoI used to be a photographer and have stared at the lens group diagrams from many a lens manufacturer, so take this with a grain of salt: In a lens there are multiple lens groups, it's often that the aberration correction is its own distinct group, with fixed input and output groups flanking it. I'd imagine that the distance to the projection surface, in this case the next lens group, can be fixed and thus distinct from the distance to your ultimate subject. A fun fact is that Helmholtz reciprocity says that regardless which direction light passes through an optical system you can reverse the distortion and reconstruct the input signal.
- jey 7y agoFulltext: https://www.researchgate.net/publication/328536020_General_formula_for_bi-aspheric_singlet_lens_design_free_of_spherical_aberration/download https://www.researchgate.net/publication/328536020_General_f...
- TheRealPomax 7y agoAnd to anyone who is averse to reading dense, long papers: it's only 4 pages long, and a quarter is pictures. It's heavy on the maths, because of course it has to be, but there isn't a single integral in the entire thing. It's remarkably accessible to anyone who took an introductory calculus course.
- JadeNB 7y agoOr on the arXiv: https://arxiv.org/abs/1811.03792 https://arxiv.org/abs/1811.03792 . It also looks like the first author wrote up a local article which seems to have substantially, umm, inspired the linked write up: https://transferencia.tec.mx/en/2019/02/21/eureka-they-find-the-formula-to-solve-an-old-optical-problem https://transferencia.tec.mx/en/2019/02/21/eureka-they-find-... .
- pizza 7y agoAwesome article, wild equation
- smitty1e 7y agoDon't such things always seem a bit obvious in retrospect? /joke
- thechao 7y agoThe paper is from Nov 2018, and is easy to find online. It’s a pretty amazing result; the examples they give in the paper are for some reasonable shaped primary surfaces and some really neat “exotic” stuff. The solution actually admits aberrant free solutions for any geometry that doesn’t include self-crossing rays. So, some of the ‘weird’ examples include a Bessel-function cross section, negative index of refraction, and lenses that focus at negative infinity. The author’s have a paper from March 2019 (in arXiv) that uses the result to build some novel telescope geometries.
- jhncls 7y ago[0] https://arxiv.org/abs/1811.03792 https://arxiv.org/abs/1811.03792 "Rigorous analytical formula for freeform singlet lens design free of spherical aberration" [1] https://arxiv.org/abs/1903.11129 https://arxiv.org/abs/1903.11129 "Single lens telescope"
- sdenton4 7y agoHmmm..... I have a 1/3rd hand-ground telescope mirror lying around... maybe I should see if I can apply some principles here...
- asark 7y ago> and lenses that focus at negative infinity. Any reasonable chance of of implications for projective geometry?
- readams 7y agoI'm not sure I really follow how this actually will result in better lenses. Is the precision of the numerical solution really the problem, or is the problem the actual precise manufacturing of the lens elements? I have a strong suspicion that the numerical solution is as precise as needed and the limiting factor is the manufacturing, but I would be interested to hear how this results in something new.
- Koshkin 7y agoYour suspicion is justified. The news here is the discovery of an analytical formula - which is "precise," sure, but whether using it directly in an actual computation could yield a more accurate and practically useful result is a good question, due to the complexity of the formula.
- samirm 7y agoI think the problem was being unable to solve a generalized version of the equation. Our old methods only made it economically viable to make "good enough" lenses and now this method makes it economically viable to make "perfect" lenses.
- themeiguoren 7y agoYour suspicion is right, as far as manufacturing goes. The real boon of this discovery is in designing lenses. For example, the authors have already used it to design a single-lens telescope for the first time [1]. I don't know much about the forefront of optics, but at least in my field having analytical models that you quickly iterate on and use to prime intuition are extremely useful. [1] https://arxiv.org/abs/1903.11129 https://arxiv.org/abs/1903.11129
- xondono 7y agoI have not checked the actual paper, but according to the article itself: > Moreover, the solution involved aspherical elements, which are harder to manufacture in a precise way and are thus more costly. > Their findings were published in the article General Formula for Bi-Aspheric Singlet Lens Design Free of Spherical Aberration, in the journal Applied Optics. I’m no expert in optics, but that does not sound like the kind of advancement that cheapens lenses, even if the math work is mathematically relevant
- kennyadam 7y agoHaven't read the paper, not an expert... but you still feel qualified to dismiss it?
- xondono 7y agoI have not read the original paper, I'm not an expert in optics, but the article clearly makes an argument that seems contradictory: - Current solution is expensive because it uses aspherical elements. - New solution promises cost reduction. - New solution uses aspherical elements as well. Either there's some hidden detail that the article fails to mention, or it's claims are overstated. If you actually know about optics, I'd be glad to know which is the true or if I'm missing anything here, otherwise I would appreciate to keep your snarkiness to yourself.
- TheRealPomax 7y agoIt also doesn't sound like the kind of advancement that makes camera lenses play mp3 files, but then: neither of those two things are even remotely relevant to the article? These people solved optical abberation. Even if their work leads to lenses that are twice as expensive as they are today, people whose research, or jobs, rely on perfect optics will be more than happy to pay what it costs to work with those. Anyone else can wait until one or more companies figures out how to make the manufacturing process cost effective at scale.
- russdill 7y agoCurrently abberation is dealt with by including multiple lenses. Even if the lens costs twice as much, it's still a wine from a price point. But yes, only for applications that care about abberation.
- joeberon 7y agoSlightly related: One thing I've learnt in Physics is that there are still a huge number of practical and fundamental problems to be solved. You might expect everything easy will already be done by now but that's just not true. Hence we still manage to write so many papers! In fact many Physicists have too many papers they want to write and not enough time to write them. This was a huge surprise for me coming in to my PhD. I had naively assumed that physicists were all scrounging for any morsel of content to publish!! Of course it depends on the field. It's a requirement here in the UK to publish a paper to get your PhD (at least I've been led to believe that), and many particle physics students really struggle to manage to fulfill this. On the other hand gravitational wave detectors have a huge amount of unexplored science as there are so many things that we still do not fully understand about the detectors themselves.
- michelpp 7y agoI agree with this big time. One of my favorite Feynman quotes is that science is an "expanding frontier of ignorance". There is always somewhere to go and something on the other side, that may change everything and invalidate deeply held convictions forever, all it takes is the guts to, again quoting Feynman, "be willing to stick your neck out".
- skybrian 7y agoOh, I'm sure there are lots of things to discover, but I think this underestimates what it takes to actually know enough to find the frontier and decide on a good problem to solve.
- godelski 7y agoWhile Feynman is correct on expanding the frontier of ignorance Asimov is also correct about the relativity of wrong (that we come asymptotically closer to the truth). This is why people think most of physics is solved, because in the context of what most people need it is extremely accurate.
- sleavey 7y ago> It's a requirement here in the UK to publish a paper to get your PhD Categorically false. I did my physics PhD in the UK and while I did publish a paper, it was not a requirement and I have plenty of friends who did not publish a paper and still got their physics PhD.
- TheRealPomax 7y ago"It is unclear whether he finished eating the Nutella bread." This article is alright.
- zaroth 7y agoTrying to figure out what voice you’re writing that in. I hope you mean alright alright, and not just _alright_ because I loved that line!
- TheRealPomax 7y agoIt is a most excellent line.
- dylan604 7y agoI read it as "This article is 'alright alright alright'".
- mykowebhn 7y ago> After months of working on solving the problem, Rafael González recalls, “I remember one morning I was making myself a slice of bread with Nutella, when suddenly, I said out loud: Mothers! It is there!” > He then ran to his computer and started programming the idea. When he executed the solution and saw that it worked, he says he jumped all over the place. It is unclear whether he finished eating the Nutella bread. This is my favorite quote from the article. Soon to be the most famous slice of Nutella bread?
- zaroth 7y agoGave me shivers reading it. Beautiful example of the incredible mystery of the human mind. Poof! And the solution materialized. Of course, all the groundwork had been laid. All the neurons primed. Just incredible. And that formula. Damn.
- ttul 7y agoThat was my thought. Why is it so damn complex? You’d think the solution would be simpler.
- rozap 7y agoSometimes complicated things are complicated.
- ben_w 7y agoIt is. Some parts are repeated, the one which caught my eye was (zₐ’(rₐ)²+1)
- paulpauper 7y agothe full equation for general relativity would take many pages to print, but Einstein notation makes it much shorter looking. This was not the case here.
- doelie_ 7y agoProbably looks a lot simpler in A-normal form, with intermediates factored out.
- amelius 7y agoIs the resulting lens rotationally symmetric?
- topspin 7y agoThe formula computes ZbRa; z axis vs radius. So yes, I believe this is symmetric around the center.
- amelius 7y agoDoes it solve chromatic aberration, or just spherical aberration?
- perlgeek 7y agoJust spherical.
- carlob 7y agoProud to see it was solved using Mathematica :)
- tambourine_man 7y agoI’m questioning my sense of humor because everyone here seemed to have enjoyed the tone of the article, while I was quite put off by it.
- adrianmonk 7y agoIt's a good article if you enjoy jokes and references about photographers and how they behave. It's not a good article if you want a minimum of fluff and just want to understand what the discovery is and why it might be significant.
- tambourine_man 7y agoI usually enjoy jokes intermingled with info, those didn’t hit the right note for me, for some reason.
- dentemple 7y agoNot every person finds every joke to be funny.
- mar77i 7y agoWhile I usually enjoy a good amount of fluff, I must say I, too, was underwhelmed by the amount of detail and/or substance reported. The formula makes no sense to me, and was apparently just thrown in in this form for a gag.
- pixelpoet 7y agoI also didn't like it, the title calls him a physicist and in the article it says mathematician, they did an experiment with 500 samples and got how many 9s, the presumption that Newton was the greatest scientist (von Neumann?), the comparison between such theoretical luminaries and someone who did a numerical optimisation of someone else's theoretical work, ... it reminds me of A Beautiful Mind, where the real accomplishments are obscured (and here greatly exaggerated) purely to tell a story to lay-people. More attention to the facts please, less attention to the sandwich.
- rahimiali 7y agoTo clarify: the innovation isn't that they design better lenses. It's that given the first surface of a lens, they have an analytical formula for the lens's second surface so that the lens doesn't exhibit spherical aberration. Traditionally, numerical methods are used to compute this second surface instead of an analytical formula. Also, as a practical matter, designers often use several spherical lenses instead of a few aspherics because the latter are harder to manufacture/more expensive.
- deleted 7y ago[deleted]
- gus_massa 7y agoIt's an interesting mathematical result, but note that gives a solution for the problem of the spherical aberration, but real lens have also chromatic aberration. I.E. the speed of light for each color inside the glass is slightly different, so the value n (refraction index) in the equation is different, so in the equation you get a different surface for each color. In the real lens you must pick one surface, so the effect is that one color is perfectly focused and the other colors are not focused and you get some rainbow-like effects. The solution is to use combination of a few lens of different glasses, to compensate the differences. It's not easy to design these kind of system, because they must compensante also for other types of aberrations. More details: https://en.wikipedia.org/wiki/Chromatic_aberration https://en.wikipedia.org/wiki/Chromatic_aberration https://kenrockwell.com/tech/lenstech.htm https://kenrockwell.com/tech/lenstech.htm
- visarga 7y agoUnrelated, but seems like optics use a different Arxiv format than ML papers, which are always double column.
- dylan604 7y ago12 nines? Yawn. Let me know when they get to 15. j/k That's some serious precision. I wonder if this would have been possible to calculate on a Pentium?[0] After last week, cloud service providers would be happy for 3 nines. [0]https://en.wikipedia.org/wiki/Pentium_FDIV_bug https://en.wikipedia.org/wiki/Pentium_FDIV_bug
- deleted 7y ago[deleted]
- mlevental 7y agohttps://petapixel.com/assets/uploads/2019/07/formula.gif https://petapixel.com/assets/uploads/2019/07/formula.gif definitely generated by mathematica
- amluto 7y agoThe article talks about the corners of an image being less sharp than the center. That’s not spherical aberration; that’s off-axis aberration. Spherical aberration causes the image to be less sharp at larger apertures. I wouldn’t be terribly surprised if this result helps indirectly with off-axis aberration, though — a closed-form solution to the spherical aberration problem may make it easier to optimize for lens shapes that minimize other aberrations.
- ricardobeat 7y agoWhat’s your background? In the photography field this is known as spherical aberration indeed: https://en.m.wikipedia.org/wiki/Spherical_aberration https://en.m.wikipedia.org/wiki/Spherical_aberration
- amluto 7y agoPhysics, but not optics. Also, I read and understood the paper. The Wikipedia link seems to agree with me too. Look at the diagram there, and compare it to the diagram for coma [0]. Spherical aberration causes the single point in the center of the object to focus to a different place depending on where the ray hits the lens. This means that the image of that single point is not fully sharp. If you restrict what parts of the lens can be hit by rays from that point (by closing the iris, for example), you reduce the area in the focal plane that the rays hit. [0] https://en.m.wikipedia.org/wiki/Coma_(optics) https://en.m.wikipedia.org/wiki/Coma_(optics)
- bariswheel 7y agoDoes this mean there’s hope for those of who had mild vertical diplopia (double vision) before and after lasik surgery? http://lee2see.com/double-vision-vs-ghosty-image/ http://lee2see.com/double-vision-vs-ghosty-image/
- ChuckMcM 7y agoThis is a seriously awesome piece of work. The mathematics in the paper are pretty dense but if you're ok with vector calculus its not too bad. The implication here is that you can build lenses that have a consistent focal plane across their entire surface. A pair of glasses made this way would have crystal clear vision regardless of your 'look' direction (as an example). It also suggests that you could build lenses for lasers that were much more consistent, so a laser projector could project an in focus image from edge to edge rather than "fuzzing out" at the corners. If there is a top prize in optics these guys clearly deserve it.
- noir_lord 7y agoThat would have pretty amazing applications (well everywhere) but in VR definitely, my Rift S is an amazing piece of kit but aberration is still noticeable on the outside edge (when aiming down a gun sight in Pavlov for example).
- deleted 7y ago[deleted]
- justinclift 7y agoIs this the kind of thing that will have an effect on optics in ray tracers? "Real world" simulation optics I'm meaning (eg for material design/prototyping), more than gamer oriented. ;)
- andygreenwell 7y agoExpect to see an implementation included in subsequent releases of Code V and Zemax.
- mindfulhack 7y agoCould this also be significant for super large lenses like giant telescopes?
- 6nf 7y agoThose tend to be mirrors instead I think
- tsss 7y agoHopefully video game makers will now finally stop putting that stupid chromatic aberration effect in their games.
- jonplackett 7y agoI wish there was a bit of insight into his mental process as he realised the solution. Like the description of Einstein sitting watching a clock and imagining what it would be like to move towards it as a ray of light
- kragen 7y agoThere are various people speculating on the economic significance of this solution, which, to me, is rather missing the point. It's like measuring the significance of the excavation of Tutankhamen's† tomb by the tourist revenues of museums. The point of economics is that it keeps us alive so we can do math and also think in other ways; the point of consciousness is not to make money. I don't think there is any economic significance. They found a closed-form formula, not a manufacturing process. They verified that it produces numerically correct results to 12 significant figures, but typical lens grinding is only accurate to about 100 nm; if your lens is 10 mm thick, that's an error in the 5th significant figure of any coordinate. Calculating a numerical solution to the Wasserman–Wolf problem to 5 significant figures is straightforward, and you could probably do it by hand if you didn't have a computer (although that would involve significant economic cost). In fact, it's not that hard to calculate it to 14 significant figures. The achievement is finding a closed-form solution rather than an iterative numerical approximation. † Or Tutankhaten, as we used to call him.
- VMG 7y ago> The point of economics is that it keeps us alive so we can do math The most hacker news comment I read all year
- MR4D 7y agoWhat wenT unsaid wasn’t anything about expensive camera gear, but that phone thingy we hold in our pocket. THAT device will get much better at photography in very quick order, and the price change will be largely immaterial. I fully believe this will be the death of all but professional cameras in 5 years or less. (Yes, I know cameras are already in sharp decline, but I’m talking true death - bankruptcies and firms leaving the market).
- p1esk 7y agoI fully believe Why? What makes you think this will be easier to implement than existing methods?
- MR4D 7y agoGut feel. To me, photography is now a software game. If you can put a reasonably cheap lens in front of a sensor and apply enough computing horsepower, I believe that the old one lens and one sensor will be like the mainframe of cameras. They will still be around, but smaller, modular ones put together via software will dominate.
- ur-whale 7y agoThe fact that there is an analytical solution to the problem is a really nice achievement, but I have to wonder: solving this problem numerically has surely been within reach of computers for a long time, and should therefore have made actually manufacturing such lenses somewhat straightforward. What am i missing?
- adammunich 7y agoCAD modeling is very slow when you need to use numerical simulation.
- nullc 7y agoI don't follow. I assume that if numerically solving for a correcting shape was burdensome you would model an element using a first surface and a 'dummy' second surface that your software just treats as magically correcting. ... then when you are happy with your design, you go ahead and compute the actual shape for that second surface... or similar. I would expect a closed form solution to more useful for meta analysis of the problem-- looking at its behaviors (and especially derivatives) in various external cases may suggest interesting and novel optical system designs. Like, "oh, foo changes cubically with with an infinite focal length that means if we could make lenses with cherry flavored unobtanium we could bounce a gravitation particle beam off the main deflector dish!".
- p1mrx 7y agoLooking at the picture... does this mean we'll all be using mustache-shaped lenses someday?
- linuxlizard 7y agoI would love/hate to read the LaTex that generated that equation.
- ernsheong 7y agoNobel-price worthy, you think? But perhaps only if they manage to derive a more beautiful formula...
- cellular 7y agoMan, that is a long formula! Not something that would pop into my head while spreading nutella.
- yagi 7y agoDoubtful that this paper is the first analytic solution. There's a light artist who exhibited lenses like this at NYC's Museum of Math several years ago. They turned flashlight beams into pictures. At the artist's talk he passed around a wavy lens and mentioned that one of the surfaces was solved in closed form. Looked like second-to-bottom lens on the page http://zintaglio.com/lens.html http://zintaglio.com/lens.html
- djmips 7y agoI voted for your comment because it's interesting but I don't agree that the example you linked is the same problem as solved in this post. But that is an opinion because I'm not informed enough to know for sure. Meanwhile I did dig up a paper related to mapping radiance with a shaped lens like the artist you linked. It's a cool topic! https://arxiv.org/pdf/1701.03076.pdf https://arxiv.org/pdf/1701.03076.pdf
- peter_d_sherman 7y agoBrilliant! Two thoughts: 1) The size of the equation is rather large. Nature tends to like simple equations, I wonder if this equation could be restated in a simpler format and not lose its efficacy. I also wonder if there are still simpler versions that trade off efficacy for degrees of error. 2) If the equation cannot be reduced, then this equation bears looking at from an information preservation perspective, that is, to people who study how the universe preserves information under various conditions, this is one of the equations they should add to their list of equations to study... But, overall a brilliant, laudable, commendable work with great applications and benefit to society! Well done!
- zaidukwahab 7y agoG Mga