One of the oldest problems in optics has been solved. Rafael Gonzalez from Mexico's Tecnologico de Monterrey has come up with an almost comically dense equation that can be used to almost completely eliminate spherical aberration in optical lenses, and the effects could be widespread.

Camera lenses are insanely complex and extraordinarily precise devices, and one of the reasons for this is spherical aberration. This is distinct from chromatic aberration, or color fringing, which you get when a lens is unable to focus light from all parts of the visual color spectrum together. Spherical aberration is what causes some lenses to be sharp in the middle, but blurrier toward the outside edges.

Lens manufacturers have for years been building aspherical lenses to try to counteract this effect, modifying the sphere shape slightly to try to sharpen up the whole image. By and large, many have done a great job, as evidenced by the general optical sharpness of today's lenses. But rather than working to a precise mathematical formula that works to correct all spherical lens aberration, lens companies have had to work on each lens as a separate problem, finding solutions that worked, more or less, but forcing them to start over each time.

The following formula looks hilariously complex, but in effect it's the solution for the following problem: given a lens made of a certain material, and with a given shape on the front side, what shape does the back side need to be in order to completely remove all spherical aberration?

It's probably not the most memorable collection of symbols ever assembled, but having worked out the equation, Gonzalez ran tests simulating the behavior of 500 different light rays, and found that the formula met with real-life results with an average accuracy of 99.9999999999 percent.

What does it all mean? Well, Gonzalez's formula should vastly reduce trial and error in the lens making business. It could result in simpler, smaller, cheaper and sharper lenses with fewer elements. And optics, of course, isn't restricted to the camera game. There could be even more interesting effects at the tiniest end of the scale, with sharper microscope imaging, and at the biggest end of the scale with deep-space telescopy. Certainly, this kind of advance could make a wonderful contribution to many other research efforts.

The paper, titled "General Formula to Design a Freeform Singlet Free of Spherical Aberration and Astigmatism" was published in the Optical Society's Applied Optics journal.

View gallery - 2 images