## Aspherical Elements

An

The problem with spherical lenses is that nearer to its edges, it refracts (bends) lights to a greater degree, thus, it's not able to bring the edges into perfect focus even when the centre is in perfect focus. This is known as spherical aberration.

In order to solve this problem, we need to construct lenses which are aspherical. The benefit of aspherical elementsis that they are able to replace complex systems of spherical lenses which were designed to avoid the problem of spherical aberration. Thus, in a practical sense, lenses with aspherical elements are able to be made smaller and lighter than lenses which are made purely from spherical elements. However, the downside is that

*aspherical*or aspheric element is one which is not constructed from a cross section of a sphere. Most optical elements are*spherical*, meaning they are constructed by taking a section of a sphere. The problem with spherical elements is that it is almost impossible to construct a perfect lens from them.The problem with spherical lenses is that nearer to its edges, it refracts (bends) lights to a greater degree, thus, it's not able to bring the edges into perfect focus even when the centre is in perfect focus. This is known as spherical aberration.

In order to solve this problem, we need to construct lenses which are aspherical. The benefit of aspherical elementsis that they are able to replace complex systems of spherical lenses which were designed to avoid the problem of spherical aberration. Thus, in a practical sense, lenses with aspherical elements are able to be made smaller and lighter than lenses which are made purely from spherical elements. However, the downside is that

**aspherical elements are expensive to manufacture**.## The Mathematics of Aspherical Elements

This is for the mathematical guys out there. Most people would encounter conic sections and this sort of mathematics in a early university-level analytic geometry course. Aspherical lenses are usually constructed from the following equation:

This function,

*z(r)*, represents the z-component of the displacement of the**surface**from the vertex. The most simple aspherical elements have the co-efficients alpha as zero, meaning that the lens surface is a axially symmetric quardic surface. The surface will have the shape of a conic section, depending on the value of*K.*The value of*R*refers to the radius of curvature.