What are Ball lenses and Half-ball lenses:

Ball lenses belong to a special form of biconvex lenses which have the geometry of a ball (sphere). Ball lenses are manufactured from a single optical material with good transmittance in the wavelength region of interest. The conventional applications of ball lenses include focusing light in the field of fibers(e.g. laser to fiber coupling, fiber to fiber coupling), emitters, and detectors, in major to collimate light depending on the geometries of the input light source. Also, ball lenses could be ball pre-forms of aspheric lenses where ball lenses are deformed on purpose to prevent spherical aberrations.

Half-Ball lenses are variants of ball lenses, obtained through cutting the ball lenses in half. Due to the ease of mounting derived from the one flat surface, half-ball lenses are more convenient for applications where space limitations exist and more compact designs are required, such as fiber communication, endoscopes, microscopes, optical pick-up devices, and laser measurement facilities.

There are three essential parameters of ball lenses and half-ball lenses. One is the effective focal length (EFL), which is the distance between a plane through the center of the lens and the beam waist (focus) of a collimated input beam. Another is back focal length (BFL), defined as the distance of the focal point from the lens surface, therefore half the diameter smaller than the EFL. The last is numerical aperture (NA), for collimated incident light, the numerical aperture (NA) of the ball lens is dependent on the size of the ball lens (D), its index of refraction (n), and the diameter of the input source (d). Numerical aperture is proportionate to the resolution of the lens, the larger the NA, the more the light is collected by the lens.

The calculation equations of the EFL, BFL, and NA and shown in the figure below:

1. Transmission of Sapphire at Infrared wavelength range (no coating)