A lens works by making rays of light converge on a point, called a focus. Properly converging light rays result in a sharp image, which is what every camera tries to achieve when seeking focus. This is also how our eyes and even telescopes work.
The problem, one that has apparently been puzzling mathematicians for nearly 2,000 years, is that the lenses do not focus the light rays perfectly. Rays of light in the center of a lens converge correctly, but rays closer to the edges do not. This results in what photographers see as distortion and colored stripes at the edges.
Lens design will never be the same again.
There are ways to reduce spherical aberration using more lenses, but this is still not a perfect solution and increasing the number of lenses increases the overall cost and complexity of a lens and camera system.
The image above shows how light rays are supposed to converge, the image below shows how they actually converge.
This problem was reduced to a complex mathematical problem, called the Wasserman-Wolf problem, in 1949. The Mexican mathematician Rafael G. González-Acuña has finally found an analytical solution to the problem.
The solution, pictured below, is incredibly complex but could revolutionize the way lenses are designed. Apparently (we’re not mathematicians here), when applied to lens design, the formula completely eliminates the spherical aberration problem, resulting in a lens system that is as sharp at the edges as it is at the center.
The formula is incredibly complex and solves a decades-old problem in lens design.
The solution has far-reaching consequences that will affect not only the way photographers shoot, but also astronomy, microscopy, laser design, and just about anything that involves lenses.
Hooray for math!
via GIPHY
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