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Mexican Physicist Solves 2,000-Year Old Problem That Will Lead to Cheaper and Sharper Lenses

In most lenses, the center of the frame might be razor-sharp, but the corners and edges always appear a little soft. It’s something that’s been a problem for thousands of years within optical devices, with many researchers giving up hope until a recent breakthrough from a Mexican physicist, who has now developed a formula that will change how lenses are manufactured.

On paper, a curved glass lens should be able to redirect all the rays of light passing through it onto a single target known as its focal point. But in the real world, it just doesn’t work that way. Differences in refraction across the lens, as well as imperfections in its shape and materials, all contribute to some of those light rays, especially those entering the lens near its outer edges, missing the target. It’s a phenomenon known as spherical aberration, and it’s a problem that even Issac Newton and Greek mathematician Diocles couldn’t crack.

Today’s lens-building procedures come close to producing uniformly sharp images, but the lenses don’t have a perfectly spherical shape and can be very expensive and difficult to manufacture and design. However, all could be about to change thanks to Rafael G. González-Acuña, a doctoral student at Mexico’s Tecnológico de Monterrey who has managed to produce an equation that provides an analytical solution for counteracting spherical aberration. It’s all rather technical.

Rafael G. González-Acuña's graphic equation

González-Acuña’s equation has been described as an “exact blueprint” for designing a lens that completely eliminates any spherical aberration. Regardless the size of the lens, the material it’s made from, or what it will be used for, this equation can decipher what is needed to design it to be optically perfect.

The breakthrough will revolutionize photographic equipment, as well as help improve scientific imaging, in devices like telescopes and microscopes. It’s said the advancement will allow companies to design and manufacture simpler lenses with fewer elements, benefiting the average consumer because it’ll mean lenses cost considerably less while offering improved image quality.

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Paul Casey's picture

Sharper I can believe. Cheaper? Not so sure on that one!

Carl Murray's picture

Cheaper to manufacture. Bigger profit margins.

Keith Meinhold's picture

"all of it is rather technical" yes, it does seem so.

Andrey Lutsenko's picture

I'll believe it when I see it.

Matt Williams's picture

Looking forward to my autofocus Otus pancake prime

(in seriousness I wish Zeiss would make a set of f/2.8 mini Otus lenses... maybe that's what the Loxias are... give them for Z mount please....)

Ivan Lantsov's picture

he did first, just use eye!
Galileo, Born: February 15, 1564, Pisa, Italy, Died: January 8, 1642, Arcetri

Viktor Wågman's picture

SO we will see in like 50 years if lenses get cheaper..

tyler h's picture

I just read the abstract and his other research paper on a single lens telescope. The formula gives you the second surface of the lens when the first surface is known. This does not make manufacturing any easier and the lens material still has to be free from defects.

Mark Sawyer's picture

"In most lenses, the center of the frame might be razor-sharp, but the corners and edges always appear a little soft." No, spherical aberration comes from the edge of the lens focusing on a different plane than the center of the lens. It is recorded across the whole image area, not "the corners and edges". The author knows nothing of what he's writing about.

Also, correcting only one of the seven principle aberrations at the expense of the other six does not make a better lens. This is a mathematical exercise of no practical value, nothing more.

Rod Kestel's picture

That's not a forumula I want to see before breakfast.

Manny Robalino's picture

There's an extra exponent on the fourth line.

Deleted Account's picture

I noticed a pair of errors in the equation…

Deleted Account's picture

Any peer reviews on that? Comments by optical engineers? Any practical value?

Fabio Di Lisa's picture

Thousands of years?

Gion-Andri Derungs's picture

Why 2000- year-old problem? Eyeglasses 13th century, microscopes and telescopes around 1600... What I'm missing?

Christian Lainesse's picture

Atlantis? Lemuria?

Gion-Andri Derungs's picture

Oh yes forgot about that. Controlled by the Reptilian Elite, of course!

Edward Anderson's picture

They made lenses thousands of years ago?

Paulo Macedo's picture

The Acuña-Romo equation for a Bi-aspherical lens has been around for at least two years now. And designed for Telescopes actually. Don't know if we will see any implementation on consumer grade optics, as the requirements are not as high as the ones required by the scientific comunity.
Also, the equation is for a single lens setup, again, telescopes, which usually do not use more than an extra element for focusing at the other end.
This might be used for space telescopes like the James Webb telescope, which launch is being postponed for a decade now.

Paolo Bugnone's picture

This is definitely not going to be used on the JWST, it has already been build and its Korsch optical scheme already corrects for spherical aberration (among others)

Karim Hosein's picture

“for space telescopes like…”

He never said it was for the JWST.

Nevertheless, I think most space telescopes will be made with mirrors, and not lenses, simply based on mass considerations for launch.

super steel_'s picture

pfew, now I can finally sleep well after so many years ive been wracking my brains out on why they couldnt remove spherical aberration

Spy Black's picture

The Mexican lenses will be detained at the border...

Joe Black's picture


Deleted Account's picture

Here is a much better report on that subject.

Gion-Andri Derungs's picture

Thank you, that explains the mystique 2000 years....

joseph cole's picture

Cheaper to develop just means greater profit margins from manufacturing company all the way down to the retailer. No we will not see a price drop on lenses, just like with every other new shiny toy in the beginning you will pay top dollar. New tech + higher quality + demand =BIG$$$$$$

Matthias Kirk's picture

The caveat is that a lens constructed according to this formular only works for a fixed focus distance. Great for microscopes, but not really for photography.