Ball Lenses

Parameters of Ball lenses

There are four important parameters to keep in mind when working with ball lenses. These include the diameter of the ball lens (D), the effective focal length (EFL), the back focal length (BFL), and the index of refraction (n). 

The effective focal length is simply the distance between the beam focus and a plane through the center of the lens. It can  be calculated from the  diameter and the index of refraction using this simple equation:

EFL = nD/ 4(n-1)

The back focal length, on the other hand, is the distance from the focal point to the lens surface. This is always smaller than the effective focal length by the radius of the ball. 

A fifth important parameter related to the environment rather than the ball itself is the diameter of the input source, (d).  It is important to note that every ball lens will exhibit spherical aberrations, and these may become significant when working with small ball lenses where the diameter of the incident beam is scarcely smaller than the diameter of the ball itself. Because of this, you should not expect to attain your theoretical minimum spot size of focus. If these aberrations are not acceptable aspheric lenses can be used instead of optical glass balls. 

The numerical aperture of a lens depends on the size of the lens (D), the refractive index (n), and the diameter of the source. 

Examples of Ball Lenses in Fiber Optics

Ball lenses are a great choice when you want fiber to fiber coupling; coupling light from one fiber optic to another fiber optic that has a very similar numerical aperture. Use two identical ball lenses, and place them at BFL (back focal length) from the fibers. 

Ball lenses are also a good option for laser to fiber coupling. Here you’ll want to choose an appropriate size ball after looking at the cross-sectional diameter of the laser beam and calculating the NA of the ball lens in the system. This NA must be less than the NA of the fiber optic, or light will not be fully coupled.