# The lens aberration problem that has plagued scientists for over 2000 years is finally solved

by

Takashi Hososhima

The history of optics dates back more than 2000 years, as the legend “Archimedes, an ancient Greek scientist, has collected sunlight with a concave mirror and burned an enemy ship”. It is reported that a graduate student in Mexico mathematically solved the difficult problem of “ cancellation of lens aberration ” that human beings could not solve for over 2000 years in the history of such optics.

OSA | General formula for bi-aspheric singlet lens design free of spherical aberration
https://doi.org/10.364/AO.57.009341

Mexicans solve problem unattainable for Newton
https://www.eluniversal.com.mx/english/mexicans-solve-problem-unattainable-newton

Goodbye Aberration: Physicist Solves 2,000-Year-Old Optical Problem
https://petapixel.com/2019/07/05/goodbye-aberration-physicist-solves-2000-year-old-optical-problem/

It is theorized that light incident on a reflector or lens converges to a point on the optical axis by refraction or reflection. However, since most lenses in reality have a surface that is part of a spherical surface due to processing problems, it is not possible to actually focus all the rays at one point. Therefore, if you increase the aperture of the lens to increase the resolution, the image may be blurred. The phenomenon that this light beam shift occurs is called 'spherical aberration'.

The spherical aberration of the lens was mentioned by

Diocres , a Greek mathematician over 2000 years ago. Also, 17th century mathematician Christian Hoygens stated in 1690 in his book 'On the Light ' that Isaac Newton and Gottfried Leibniz tried to solve the spherical aberration of the telescope's lens but could not You are

In fact, with the Newton-type reflection telescope invented by Newton , although color bleeding (chromatic aberration) does not occur, it was not possible to completely correct spherical aberration at that time because the reflector was used.

by

Internet Archive Book Images

In 1949, the question 'how should we analytically design a lens completely free of spherical aberration?' Was formulated in the mathematical world and treated as the 'Wasserman-Wolf problem'. The

Raphael Gonzalez, a Ph.D. student at the National University of Mexico in Mexico , has been one of the first to work mathematically on lens and aberration problems. According to Gonzalez, an idea came to mind when I was painting nutella on a piece of bread for breakfast one day. When Gonzalez shouted 'I understand!' He ran the idea he drew into the computer as it was and he was able to solve the spherical aberration. 'I was jumped to various places with great joy,' said Gonzalez. The following very complicated formula seems to be a formula that can analytically design the lens surface.

Gonzalez then simulated with 500 rays of light with fellow PhD student and research partner Hector Cappallo and calculated the effectiveness, and the average satisfaction rating for all results was 99.9999999999. That it was%. The following is an illustration (left of the image) of a lens with spherical aberration eliminated by Gonzalez (right of the image) analytically.

In addition, Gonzalez and Chapallo et al.'S research team said, ' General formula to design a freeform singlet free of spherical aberration and astigmatism' (a general formula for designing free-form surface singlets free of spherical aberration and astigmatism). It is also reported that the Levi-Civita problem formulated in 1900 has been solved.

The lens aberration has been solved mathematically, so we can expect to see the development of a better-performing lens and a major breakthrough in telescopes and spectrometers. PetaPixel says, “Even if a much better lens is made at a lower price, if the sticker for the photographer is put on the product, it will be priced many times higher for its added value. I wondered if it would lead to the activation of the lens market.

in Hardware,   Science, Posted by log1i_yk