# Ball Lenses Information

Ball lenses are spherical, light-refracting optical component that improve signal coupling between fibers, emitters, and detectors. They are made of glass or other transparent materials whose index of refraction is less than 2. This serves as a limitation for ball lenses, as materials with an index of refraction greater than 2 will have a focal length shorter than the radius of the ball lens.

## Physics

Light is refracted within the lens, and depending on the geometry of the input source a lens can either focus or collimate light. If the input is a collimated light source, such as a laser, the ball lens focuses the light at a given focal point. If the input source is a divergent beam, as is the case for light exiting fiber optics, the ball lens acts to collimate the light source. Two ball lenses can be used together to couple optical fibers, while a single ball lens can be used to couple a laser beam to an optical fiber.

### Numerical Aperture

The numerical aperture (NA) is a dimensionless number characterizing the range of angles over which a system can accept or emit light. The NA of the ball lens must be less than or equal to the NA of the optical fiber that it is coupled to. Since the NA of the ball lens is proportional to the ratio of the collimated light input beam diameter to the ball lens diameter, expressed as d/D, the diameter of the lens becomes an important specification when designing an optical system. The NA of a ball lens can be simplified when the refractive index outside of the balls lens is assumed to be 1 and can be expressed as:

### Spherical Aberration

Spherical aberration is a phenomenon that occurs due to increased refraction or reflection of light rays that strike the edge of a lens. This is the reason that NA increases as the ratio d/D increases. The increased refraction of incident light rays near the edge of the lens cause the size of the focal point at the back focal length to increase and when coupled to another optical component would require a device with a wider acceptance angle.

## Specifications

Common specifications used to select an appropriate ball lens for a given application include the following:

The effective focal length (EFL) is the distance from the center of the ball lens to the focal point. It is determined by the refractive index (n) of the material and the lens diameter (D).

The back focal length (BFL) is the difference between the radius of the ball lens and the EFL. Shorter BFL distances simplify fiber optic coupling.

The diameter of the ball lens should be selected based on the NA of the optical device the ball lens is coupled to and the diameter of the incident collimated light beam.

The materials of construction dictate the type of light with which it is compatible and may exhibit transmission of either ultraviolet (UV), infrared (IR), or visible (VIS) light. They will also exhibit a known index of refraction at a given wavelength. Manufactures offer a variety of ceramic, UV, and NIR materials while the most common materials used are:

• BK7 is a boro-crown glass (borosilicate glass) that is widely used in VIS applications where it exhibits an index of refraction of ~1.51.
• Sapphire is an aluminum oxide ceramic that exhibits superior optical transmission qualities and may be used for both UV and IR applications.
• UV grade fused silica exhibits excellent transmissions of UV light, a low coefficient of thermal expansion, and is used in UV, VIS, and NIR applications in a wavelength range of 200nm to 2.2μm.

Surface quality is determined by calculating the average defect size. A dig is a defect that is nearly equal in terms of its length and width. A scratch is a defect whose length is many times its width. Surface quality is represented by two numericals that together define the size of the average defects. The smallest value of 10 - 5 represents superior surface quality with an average dig diameter of .05 mm and an average scratch length of .10 mm. Values used to depict surface quality include:

• 10-5 Scratch / Dig
• 20-10 Scratch / Dig
• 40-20 Scratch / Dig
• 60-40 Scratch / Dig
• 80-50 Scratch / Dig

## Resources

Edmund Optics—Understanding ball lenses

Newport—Fiber optic basics

#### Image credit:

Knight Optical (UK) Ltd.