# Thread: Lenses, Spherical Aberration and the Wasserman-Wolf Problem: Solved!

1. ## Lenses, Spherical Aberration and the Wasserman-Wolf Problem: Solved!

Student solves a centuries-old physics problem that baffled Newton, the Wasserman-Wolf Problem

RT
Thu, 04 Jul 2019 16:36 UTC

© Creativ Studio Heinemann via Global Look Press

Scientific luminaries like Isaac Newton could only create temporary solutions to the centuries-old problem of 'spherical aberration' but one Mexican student has finally solved it - while preparing his breakfast.
"I remember one morning I was making myself a slice of bread with Nutella and suddenly I said, 'Holy crap! It's there!'" Rafael González from the Institute of Technology in Monterrey, Mexico told his university paper.

"I went to my room, I started programming, it resolved and I jumped for joy with excitement."
The optical phenomenon was discovered approximately 2,000 years ago by Greek mathematician Diocles. Since then, scientists like Newton and Leibniz tried, and failed, to resolve the problem of maintaining the sharpness of images when passed through spherical lenses.

Newton managed to solve the chromatic aberration (the issue of focusing all the colors from a light source) but not the spherical aberration. The issue was formalized in 1949 in what became known in the scientific community as the Wasserman-Wolf problem, but no one could solve it, until now.

Industrial engineer Gonzalez, who is currently working on a PhD in nanotechnology, teamed up with his friend and colleague Alejandro to solve what they dubbed the "a mythical problem." Their work was published in the journal Applied Optics.

A previous quick-fix solution was the use of two aspheric lenses (only rounded on one side) but the calibration of such lenses depended on an imprecise calculation. However, thanks to Gonzalez and his solution, a precise result can now be derived regardless of changes to the variables with a 99.99 percent success rate.

The resolution of spherical aberration problem could revolutionize the field of optics and greatly improve the technology used in telescopes and cameras the world over.

Original article (Spanish)

Has it happened to you that, when you look through a photographic camera, a telescope, binoculars or a microscope, you see the images blurred or without sharpness? It is probably not that the lens is dirty or out of focus, but that it is an optical phenomenon called spherical aberration.

Aberration is a defect of the optical systems, which cause the image formed by a lens to be blurred or distorted, and the nature of the distortion depends on the type of aberration.

At the top there is a representation of a perfect lens without spherical aberrations: all incoming rays focus on the focal point. The lower example shows a real lens with spherical surfaces, which produces a spherical aberration: the different rays are not found after the lens at a focal point.

An optical imaging system that has an aberration will produce an image without sharpness. This is where the manufacturers of optical instruments must correct the devices to compensate for the aberration.

Spherical aberration is a type of optical aberration found in optical systems that use spherical surfaces, such as cameras, telescopes, binoculars, microscopes, and so on. The lenses and curved mirrors of these devices are generally made with surfaces that are spherical, because this shape is easier to form than the non-spherical curved surfaces. The rays of light that strike an off-center spherical surface are refracted or reflected more or less than those that impact near the center. This deviation reduces the quality of the images produced by the optical equipment.

Figure 1. At the top there is a representation of a perfect lens without spherical aberrations: all incoming rays focus on the focal point. The lower example shows a real lens with spherical surfaces, which produces a spherical aberration: the different rays are not found after the lens at a focal point.

The solution to the problem of spherical aberration (established by Wasserman-Wolf in 1949)

An aspheric lens is a lens whose surfaces are not a portion of a sphere, but have a freer form, for example, the lens of a photographic camera.

An aspheric lens can reduce or eliminate spherical aberration and also reduce other optical aberrations such as astigmatism, compared to a simple spherical lens. A single aspheric lens can often replace a much more complex multi-lens system. The resulting device is smaller and lighter, and sometimes cheaper than the design of multiple lenses.

In the design of optical systems, the aspheric surface aims to strongly reduce spherical aberration. Many authors proposed a design of lenses with two aspherical surfaces to correct the spherical aberration, but all the solutions are numerical in nature.

The problem of the design of a lens without spherical aberration is also known as the problem of Wasserman-Wolf, postulated by Wasserman and Wolf in 1949 in an article published in the Royal Society Proceedings, which explains the problem in a technical way, but does not give an analytical solution.

In a scientific paper called "General formula for bi-aspheric singlet lensdesign free of spherical aberration", which we recently published in the Applied Optics magazine, an analytical solution is provided.

2. ## The Following 16 Users Say Thank You to Hervé For This Post:

Alekahn2 (4th July 2019), avid (5th July 2019), Axman (5th July 2019), Bill Ryan (4th July 2019), Cara (5th July 2019), Constance (4th July 2019), Dennis Leahy (4th July 2019), Franny (4th July 2019), Inaiá (8th July 2019), Ioneo (6th July 2019), Mercedes (4th July 2019), mpennery (5th July 2019), Sadieblue (5th July 2019), Sunny-side-up (4th July 2019), Valerie Villars (4th July 2019), waree (4th July 2019)

3. ## Re: Lenses, Spherical Aberration and the Wasserman-Wolf Problem: Solved!

Highly abstruse! But for anyone with a bit of physics background, digging into the story of this discovery — by a young Mexican PhD student, no less — is fascinating.

4. ## The Following 11 Users Say Thank You to Bill Ryan For This Post:

Axman (5th July 2019), Constance (4th July 2019), Dennis Leahy (4th July 2019), Franny (4th July 2019), Hervé (4th July 2019), Ioneo (6th July 2019), Ken (4th July 2019), Mercedes (5th July 2019), Sadieblue (5th July 2019), Sunny-side-up (4th July 2019), Yoda (5th July 2019)

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