Relevant thread on the same topic <a href="https://news.ycombinator.com/item?id=20369960" rel="nofollow">https://news.ycombinator.com/item?id=20369960</a>
Opening sentence in the article:<p>> <i>It’s a problem that plagues even the priciest of lenses, manufactured to the most exacting specifications: the center of the frame might be razor-sharp, but the corners and edges always look a little soft.</i><p>The method in the article doesn't solve this. The method only give an analytic solution for the center and only for one color. All the other points of the frame and all the other colors look a little soft.<p>Previous discussion <a href="https://news.ycombinator.com/item?id=20369960" rel="nofollow">https://news.ycombinator.com/item?id=20369960</a> (845 points, 33 days ago, 210 comments)<p>I'll repost my previous comment:<p>It'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.<p>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.<p>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.<p>More details:<p><a href="https://en.wikipedia.org/wiki/Chromatic_aberration" rel="nofollow">https://en.wikipedia.org/wiki/Chromatic_aberration</a><p><a href="https://kenrockwell.com/tech/lenstech.htm" rel="nofollow">https://kenrockwell.com/tech/lenstech.htm</a>
I note that Roger Cicala over at lensrentals.com (in an interesting article showing disassembly of a fancy zoom unit) had this to say:<p>No, no it can't. It was really impressive mathematics (and according to several mathematicians, the formula was left more complex than necessary to make it look more impressive). In theory, it could improve ONE of the dozens of aberrations, but only in the center of the lens, not off-axis.<p>Not to take anything away from a very impressive intellectual effort, but basically it solved a problem nobody was particularly trying to solve (the stuff about '2,000 year old mystery' was so over-the-top it makes me wonder if the authors were having a bit of fun).
Does an analytical solution actually make any difference in practice though? I would guess that numerical approximations would have reached similar accuracy as modern manufacturing methods by this point.
Original article (in Spanish): <a href="https://transferencia.tec.mx/2019/02/21/resuelto-un-problema-optico-con-mas-de-un-siglo-sin-solucion/" rel="nofollow">https://transferencia.tec.mx/2019/02/21/resuelto-un-problema...</a>
I hope this can be used to improve eye glasses too. At higher powers the effect of chromatic aberration as you get away from the center of the lens really sucks.<p>I have aspheric lenses which are supposed to help, but I still see the problem and I’ve been complaining to my optometrist who basically says he can’t make anything better than what I’ve got.<p>It’s especially bad in computer interfaces which often have thin high contrast lines which just splay out into red/blue as you get to the edges of the monitor.
Does anyone here know any more details? I’m curious as to how this improves on the 2014 work by the same author and others: <a href="https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2014.0608" rel="nofollow">https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2014...</a><p>I think this is the new paper (from 2018): <a href="https://www.osapublishing.org/ao/abstract.cfm?uri=ao-57-31-9341" rel="nofollow">https://www.osapublishing.org/ao/abstract.cfm?uri=ao-57-31-9...</a><p>The introduction to the new paper gives a reasonably clear explanation of how it relates to previous work:<p>> The design of optical systems with aspheric surface has the goal to strongly reduce spherical aberration. Spherical aberration on lenses has been extensively studied by Ref. [1]. Luneberg [2] established a method for computing the shape of the second surface from an initial first surface that introduces spherical aberration, which he described just for special cases. Many authors proposed a lens design with two aspheric surfaces to correct spherical aberration [3,4].<p>> The problem of the design of a singlet free of spherical aberration with two aspheric surfaces is also known as the Wasserman and Wolf problem [5]. The problem has been solved with a numerical approach by Ref. [6]. Recently, Ref. [7] has shown a rigorous analytical solution of a singlet lens free of spherical aberration for the special case when the first surface is flat or conical. Since its publication, several works inspired by its solution have emerged [7–12], all of them free of spherical aberration. The solution has six different signs; therefore, it is a set of 2^6 = 64 possible solutions, where only one is right. We test the formula provided by those in Ref. [7], when the first surface is not flat or conic, and the equation system does not give correct answers.<p>> In this paper, we present a rigorous analytical solution for the design of lenses free of spherical aberration. The solution presented here has just one sign; therefore, it is a set of just two possible solutions. Our solution is robust because the set of solutions is valid for negative and positive refraction indices. The model allows use of continuous functions, such that the rays inside the lens do not cross each other. This model will compute the second surface in order to correct the spherical aberration produced by the first surface.<p>If I understand this correctly, the key difference is that the earlier paper (referred to as [7] above) only addresses the case where one of the surfaces of the lens is flat or conical. I’m not sure whether this is a serious limitation in practice: I would have thought naively that it’s easier to manufacture a lens with one flat surface.<p>The (new) paper also includes (in Appendix A) Mathematica code to compute and plot the lenses produced by this method.