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# Ball Lenses

A Ball Lens consists of a highly transparent spherical ball, usually made of solid glass (fused silica) or another optical material with index of refraction less than 2. Most ball lenses are made with small diameters – a few millimeters or even less than a millimeter.  The optical physics can be understood by realizing these lenses are, equivalently, two plano-convex lenses separated by a parallel plane.

Ball lenses are often used as beam collimators for optical fibers and to improve signal coupling between emitters, detectors, and fibers. They have a high coupling efficiency and are easy to align. A single ball lens is used to couple a laser beam to an optical fiber, while two ball lenses are used to couple two optical fibers.

Other applications include objective lenses for endoscopy or optical sensors, and in the miniature optics used for barcode scanning.

The diameter, effective focal length, back focal length, and index of refraction of the ball are all parameters you will need to keep in mind as you design a setup that involves a ball lens. The effective focal length is equal to the index of refraction (denoted here by n) times the diameter of the ball lens (D), divided by 4(n-1). We can write this as EFL = [n D]/[4(n-1)]. The back focal length equals the effective focal length – D/2.

The numerical aperture of a spherical lens, abbreviated NA, can be calculated from the effective focal length and thediameter of the input source.  For collimated incident light, when the refractive index outside the ball lens equals one, you may use the equation

NA = 1/sqr[1+4(EFL/d)2]

Where sqr[] designates the square root of the expression between the brackets.

Spherical aberration is inherent in all ball lenses, but becomes a problem if light propagation isn’t restricted to a small fraction of the lenses cross-section.  The ratio of the diameter of the ball lens and the diameter of the input source is denoted as d/D, and when this number increases, the focus spot size at the back focal length of the lens also  increases.

Factory Standard

• Diameter: 2～50mm
• Scratch & Dig: 20/10
• Sphericity: 0.05mm
• Surface Quality: 40-20
• Diameter Tolerance: +/-0.05mm

Contact us for manufacturing limit or custom specifications.

## Selecting a Ball Lens for Fiber Optics Coupling

For laser to fiber coupling, the numerical aperture of the ball lens must be less than or equal to the numerical aperture of the fiber.  The spherical lens can then be placed a distance of the back focal length in front of the fiber in order to transmit the coupling light from laser to fiber.

For instance, if you were working with optical fiber with a numerical aperture of 0.22 you would need a ball lens of no more than 0.22 numerical aperture.

If you wish to couple two fiber optics, you will want to use two identical ball lenses. These can be placed in sequence between the fibers, with each lens a back focal distance from the fiber closest to it.

## Materials Used for Ball Lenses

The most common materials used in ball lenses are UV grade fused silica, sapphire, and BK7.  UV grade fused silica can be used for UV, VIS, and NIR applications, and is a stable substrate with a low coefficient of thermal expansion. BK7, a boro-crown glass, has an index of refraction of about 1.51 and is often used for visible light. Sapphire has a cost premium but does also provide better optical transmission. It is suitable for UV and IR applications.