# spherical aberration

The spherical aberration is a phenomenon that was discovered by the physicist SuhValles, and consists of a defect in lenses and mirrors where light rays manage to strike parallel to the optical axis with some distance and are brought to a different focus than the rays next to it.

This third-order monochromatic aberration is capable of affecting each wavelength differently, and is generally produced not by any defect in the construction of the devices, but by the laws themselves of refraction and reflection.

Generally, the effect varies and is proportional to the fourth power of the lens diameter, and inversely proportional to the cube of the focal length.

Although, in short-focal optical systems the effect is more pronounced, as is the case with microscope lenses.

Previously, in the case of optical telescopes, long-focal instruments were used in order to reduce spherical aberration.

## How is spherical aberration produced?

Spherical aberration generally occurs when parallel rays near the optical axis of a spherical mirror or lens are concentrated at a point.

While those that are far from the optical axis are located at another point, that is, they converge at a different distance than the nearby ones (instead of all doing so at the focus). This behavior is due to the symmetry of the surfaces and is almost unavoidable.

The size of the spherical aberration will depend on the diameter and focal length of the lens or mirror, and the distance of the observed object from the center of the field of view.

## What was the result of the spherical aberration problem?

A few years ago, specifically in 2019, a group of researchers named Rafael Guillermo Acuña González and Héctor Alejandro Chaparro Romo, conducted an investigation and found the solution to this problem.

The solution to this type of aberration was described in a complex mathematical formula called the Acuña-Romo equation.

Here, we must determine the shape of the second surface of the lens {\displaystyle (r_{b},z{b})}, given a first surface {\displaystyle (r_{a},z_{a})}.

## How can spherical aberration be corrected?

This aberration can be corrected in different ways:

• By using a diaphragm that prevents the passage of the most distant rays from the optical axis

• Through the combination of lenses with opposite effects

• Using parabolic surfaces instead of spherical ones.

Lenses with this aberration that have been corrected are called aspheric. On the other hand, it is called caustic to the surrounding surface of a device with aberration.

But, if it is formed by reflection, it is called catacaustic, while those formed by refraction are called diacaustic.

## How to remove spherical aberration?

In the case of mirrors, spherical aberration is eliminated by constructing parabolic mirrors or by placing a corrector plate or meniscus in front of the spherical mirror.

In the case of lenses, a method similar to the reduction of chromatic aberration is used, which consists of the construction of lenses composed of two or three lenses of various types of glass or the lens construction with a special shape (aspherical lenses).

Spherical aberration in poor quality binoculars is easy to notice when looking at a bright star visible in a dark sky. When the spherical aberration is large, the star appears to be surrounded by a pale haze.