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Math

Physicist Solves 2,000-Year-Old Optical Problem (petapixel.com) 153

Mexican physicist Rafael Gonzalez has found the solution to spherical aberration in optical lenses, solving the 2,000-year-old Wasserman-Wolf problem that Isaac Newton himself could not solve. Newton invented a telescope that solved the chromatic aberration, but not the spherical aberration. PetaPixel reports: Fast forward to 2018 when Hector A. Chaparro-Romo, a doctoral student at the National Autonomous University of Mexico (UNAM), who had been trying to solve this problem for 3 years, invited Rafael G. Gonzalez-Acuna, a doctoral student from Tec de Monterrey, to help him solve the problem. At first, Gonzalez did not want to devote resources to what he knew to be a millenary, impossible to solve problem. But upon the insistence of Hector Chaparro, he decided to accept the challenge. After months of working on solving the problem, Rafael Gonzalez 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. Afterwards, the duo ran a simulation and calculated the efficacy with 500 rays, and the resulting average satisfaction for all examples was 99.9999999999%. Which, of course, is great news for gear reviewers on YouTube, as they will still be able to argue about the 0.0000000001% of sharpness difference among lens brands. Their findings were published in the journal Applied Optics. They also published an article in Applied Optics that gives an analytical solution to the Levi-Civita problem formulated in 1900. "The Levi-Civita problem, which has existed without a solution for over a century, was also considered a mythical problem by the specialized community," reports PetaPixel.

"In this [algebraic] 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," explains Gonzalez. "The second surface is such that it corrects all the aberration generated by the first surface, and the spherical aberration is eliminated."
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Physicist Solves 2,000-Year-Old Optical Problem

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  • Translation (Score:2, Informative)

    by Anonymous Coward

    The article does not explain it, but that "Mothers!" is equivalent in spanish to a "Holy shit", if anyone was wondering

  • by jfdavis668 ( 1414919 ) on Monday July 08, 2019 @09:09PM (#58894008)
    Before the invention of optically clear glass?
    • Re:2000 years old? (Score:5, Informative)

      by jfdavis668 ( 1414919 ) on Monday July 08, 2019 @09:19PM (#58894030)
      Ok, I had to look that up. Diocles did work on the subject, but using mirrors, not lenses. And, I found out lenses were made of quartz crystal before the invention of clear glass. Diocles implied that lenses would have the same problem. Who knew?
    • Re:2000 years old? (Score:5, Informative)

      by Freischutz ( 4776131 ) on Monday July 08, 2019 @09:51PM (#58894100)

      Before the invention of optically clear glass?

      Euclid (325 BC–265 BC) wrote about geometrical optics and so did Hero of Alexandria (AD 10–70), Ptolemy actually wrote a book called 'Optics' and by he 980s Ibn Sahl was writing about lenses and focal points. Alhazen (965–1040 AD) who was known in the west under the name 'Alhacen' actually described a 'camera obscura' among other things in his work 'Book of Optics'. That work is credited with having extensively influenced the development of optics in Europe from the 13th century onwards (so if Ben Shapiro ever asks you what Islamic cultures ever contributed to science now you can name at least one very important thing). There is archeological evidence of rock crystal lens production on Gotland during the 10th century. At first these lenses seem to have been mainly for jewellery but the later examples of Viking age lenses evolved into a form that is actually useful for magnification and examination of small objects although I doubt the guys making them were aware of classical writing about Optics, they seem to have been clever enough to notice that these things had some very useful properties. Lenses were being used to create eyeglasses in Germany and Italy as early as the turn of the 12th/13th century.

      • Re: (Score:1, Troll)

        You should not be on Slashdot since you are referring to externally verifiable objective reality.

        Slashdot is meant for opinions and pseudo-reasoning presented as iron clad truth known by super-intellects who need not stoop to logical reasoning or mere facts. The certainty of egomania is the only standard here and by that criteria your post is a failure.

        You are in the wrong place and will be modded down to -1,000,000,000. Sorry about that, better luck next time.

      • On a side note, it's sadly humorous that, during the dark ages, Islamic scholars sometimes gave refuge to European scholars being hounded due to western religious oppression of scientific ideas - and now, in the present day, it's often Islamic scholars who are forced to flee their home countries for America and Europe in order to escape religious oppression of scientific ideas.

      • "if Ben Shapiro ever asks you what Islamic cultures ever contributed to science now you can name at least one very important thing"

        Like most political asides, this is idiotic.
        *Nobody* questions the massive contributions the Muslim world has made to science like astronomy, math, biology, medicine.

        The point is that they really haven't done anything meaningful since the 15th century.

        Which you (again) just sort of proved.

            I'm sure Ben would be proud of you.

        • by epine ( 68316 )

          The point is that they really haven't done anything meaningful since the 15th century.

          Rampant recentism strikes again.

          Just imagine how—after not accomplishing much for the last six million years—Mother Nature must be positively itching to introduce Homo chagrinus any day now.

          Nuclear facilities in Iran [wikipedia.org]

          Homo sapiens epitaph: two legs good, but far too much regression into cat and mouse.

          Final grade on project: B+

  • by fustakrakich ( 1673220 ) on Monday July 08, 2019 @09:16PM (#58894024) Journal

    Shouldn't we have something better by now [bbc.com]?

    • Designing a lens which takes light from one point and focuses it to a point on an image sensor is trivial. The problem is designing a lens which simultaneously takes light from all points in the scene, and focuses all light from each of those points to one (and only one) point on the sensor. The failure to do that for all points simultaneously is what leads to spherical aberration (you're trying to take light coming from a spherical scene and project it onto a flat image sensor). In fact one of the early [wikipedia.org]
    • I'm holding out for Time Cube.

      Wait, could we use 6 flat lenses to make 1 Time Cube? Genius!
    • Conventional lenses are either done by molding or grinding/polishing. Molding (usually plastic) allows somewhat arbitrary shapes, but the technology and materials to do it very well are only ten or 20 years old and still not universally accepted by premier lens makers. Grinding/polishing (usually glass) produces spherical surfaces unless the process is modified in a carefully controlled manner to produce other shapes -- usually paraboloids or hyperboloids, if I understand correctly.

      The lenses proposed by yo

  • by HotNeedleOfInquiry ( 598897 ) on Monday July 08, 2019 @10:06PM (#58894132)
    Designed in the 50's and was accepted as perfectly correcting chromatic and spherical distortion. And was manufactured in large quantities. I'm guessing that this physicist has done is come up with a math model for a perfectly corrected lens whereas Carl Zeiss came up with an empirically correct solution.
    • by hey! ( 33014 ) on Monday July 08, 2019 @10:25PM (#58894176) Homepage Journal

      According to the paper's abstract, the design is an aspheric *singlet* lens -- just one piece of glass ground on two surfaces.

      The Zeiss lenses you mention have eight or nine pieces of precisely ground glass. Given that complexity, I doubt very much they were just hacked together by trial-and-error.

      • You're correct. Even the fact that they are doing this with an aspheric singlet lens isn't really unique. Any optical designer can generate a custom aspheric singlet with complete correction of spherical aberration in under an hour, and you can buy lenses like this off the shelf. What is unique about Acuña and Romo's work is that they found a formula for finding the correct surface shape. Normally these kinds of lenses are designed by having a computer trace ray paths through the lens and tweak the sha
    • by Anonymous Coward

      Surprisingly enough, the summary even has the relevant quote:

      “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,” explains González. “The second surface is such that it corrects all the aberration generated by the first surface, and the spherical aberration is eliminated.”

      This is a fully general mathematical solution; not a one off numerical approximation. This should be a great help for lens design, and may allow bypassing of IP nonsense.

      • Re: (Score:2, Informative)

        by Anonymous Coward

        Indeed, and the formula is actually shown in the article linked first in the summary - and it is a doozy!!!

        I counted thirty odd large pairs of parenthesis and over sixty square-rooted quantities. Hell, I'd give a masters degree in programming to anyone who could write a computer program to compute it, and succeed on the first attempt.

        Hardly as elegant as E=mc^2, but impressive in a completely opposite way. Kudos to Rafael Gonzalez for having a brain big enough to contain this formula before breakfast.

        I ha

        • by dargaud ( 518470 )
          Just an empty comment to undo a mistaken mod. And to say you should be modded up.
        • by jabuzz ( 182671 )

          Nah, give me the LaTeX/TeX source that was used to typeset that and I can turn it into correctly functioning C first time :-)

  • ...why isn't an autonomous university solving these problems for itself without human interventionâ½

    • by jddj ( 1085169 )

      Boo Slashdot! No Interrobang support!!!!

    • "It is unclear whether he finished eating the Nutella bread."

      Have we examined the kitchen? Do we have fingerprint samples for everyone in the house at the time? Is it too late to get a warrant for a sewage DNA test? Answers must be had!

  • by phantomfive ( 622387 ) on Tuesday July 09, 2019 @01:00AM (#58894436) Journal

    Rafael Gonzalez 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!"

    Yeah right, you know he really said, "Puta madre, ahi está la chingada!"

  • That's literally a great achievement! I appreciate you modern Newton.
  • Sorry, that was the first optical 'problem' coming to my mind.

  • Would another chocolate hazelnut spread have worked as well or is it just Nutella?

    • Yeah, it appears we're getting product placement in scientific discovery announcements now. I wonder how much it costs to have your product name-dropped in a once-in-century scientific discovery?

    • by Anonymous Coward

      Nutella is a sugar/fat spread. It consists of 56.3% sugar, palm oil, 13% hazel nuts, 8.7% skimmed milk powder.

      If you want something that can rightfully be called a hazelnut spread, you'll probably have to make your own. (Some other brands contain like 33% percent hazel nuts, which still isn't gread.)

  • Dirac: I have an equation.

    Feynman: Well, I have an equation, too.

    Gonzalez: Hey guys, I have one, too!

    Feynman: Who are you and where did you come from?

    Dirac [dispensing with pleasantries]: So what's yours?

    Gonzalez whips a Tensegrity easel out of his pocket, unfurls it with a single snap, and winds the first "paper"-thin sheet of Euro A2 Buckyskin off a very thin spool onto the business end.

    * formula.gif [petapixel.com]

    Feynman [uneasily]: Nice easel.

    Dirac: My, that's a stiff membrane you have there.

    Gonzalez [absent mindedly]

"The whole problem with the world is that fools and fanatics are always so certain of themselves, but wiser people so full of doubts." -- Bertrand Russell

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