Ball Lenses

Author: the photonics expert Dr. Rüdiger Paschotta (RP)

Definition: lenses which have the geometric form of a sphere

More general term: lenses

Category: article belongs to category general optics general optics

DOI: 10.61835/rf8 Cite the article: BibTex plain text HTML Link to this page LinkedIn

A special form of a thick biconvex optical lens is a ball lens, usually having the geometric form of a ball (sphere). They are manufactured from a single material, usually an optical glass with good transparency in the wavelength region of interest. A frequently used material is fused silica.

Another variant are half-ball lenses, which are obtained simply by cutting ball lenses in half.

Ball lenses are usually made with relatively small diameters of a few millimeters or sometimes even less than 1 mm (microlenses). Particularly for such small dimensions, they are easier to fabricate than lenses with traditional designs.

rays at ball lens — Figure 1: Focusing of light with a ball lens. While the paraxial rays have a focus position as indicated with the gray vertical line, the outer rays are more strongly refracted.

Ball lenses exhibit substantial spherical aberrations when light propagation is not restricted to a small fraction of its cross-section. Examples are shown in Figures 1 and 2.

A special kind of micro-ball lens is obtained by heating the end of a tapered fiber such that it melts.

Applications of Ball Lenses

Ball lenses are used particularly as beam collimators for optical fibers (fiber collimators) and for fiber-to-fiber coupling. They are also suitable for miniature optics with applications like barcode scanning, as objective lenses in endoscopy and for optical sensors. There are also microscope objectives (particularly immersion objectives) which have a hyperhemisphere (e.g., somewhat more than a hemisphere) as the first lens.

Focal Length

There are two different definitions of focal length of a ball lens. The effective focal length, which is the distance between a plane through the center of the lens and the beam waist (focus) of an initially collimated input beam, is given by the equation

$$f = \frac{{n\;D}}{{4(n - 1)}}$$

where <$D$> is the diameter of the lens ball and <$n$> its refractive index.

The back focal length is defined as the distance of the focal point from the lens surface, and is smaller than the effective focal length by half the diameter of the ball.

Optical Aberrations

Just as other spherical lenses, ball lenses exhibit optical aberrations and in particular spherical aberrations (see Figure 1 and 2) when operated with incident beams having a diameter which is not much smaller than that of the ball. Therefore, the minimum possible spot size of the focus is not obtained for the largest possible input beam size, as it would be for a perfect lens.

It is possible to produce aspheric lenses with much weaker aberrations, using spherical ball lenses as a preform which are then appropriately deformed.

Rainbows

Natural ball lenses in the form of small water droplets cause the phenomenon of rainbows. The color effects of the primary (most prominent) row arise from light paths with a single internal reflection in a droplet. Sometimes one can see a secondary rainbow, arising from beam paths with two internal reflections.

More to Learn

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Suppliers

The RP Photonics Buyer's Guide contains 30 suppliers for ball lenses. Among them:

Edmund Optics

Ball lenses are commonly used to improve signal quality in fiber coupling applications, or for use in endoscopy or bar code scanning applications. Our ball lenses feature short back focal lengths to minimize the distance needed from the ball lens to the optical fiber. Edmund Optics offers a variety of ball lenses in a range of substrates for performance in the ultraviolet to the NIR. Half-ball lenses are also available to ease mounting or system integration.

Shalom EO

Hangzhou Shalom EO provides ball lenses and half ball lenses made of various substrate materials including sapphire, ruby, BK7, UV fused silica, high index glass, and germanium, ZnSe, ZnS with AR coating. Our ball lenses and half-ball lenses are ideal for applications such as fiber communications, endoscopes, and microscopes.

Available diameters are between 0.3 mm and 300 mm, with surface roughness (Ra) <0.007 µm and a wide AR coating wavelength range. Custom ball and half ball module options are also available on request.

Avantier

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.

Knight Optical

Knight Optical provides a wide range of ball and half ball lenses which are ideal for endoscopy and fibre communications. We have a variety of material options available including quartz, sapphire, cubic zirconia, ruby, BK7 and other optical glass, fused silica, borosilicate, and many more. Our stock catalogue consists of 0.4 mm to 10 mm diameter ball lenses, but custom dimensions are available up to 100 mm.

Shanghai Optics

Shanghai Optics offers custom-made ball lenses. Please contact us for manufacturing limit or custom specifications. We can offer balls lenses e.g. with a diameter tolerance of ±50 μm, scratch & dig 20/10, surface quality 40-20, and with <50 μm deviation from a sphere.

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