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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