Ball lenses are great optical components for improving signal coupling between fibers, emitters and detectors. They are also used in endoscopy, bar code scanning, ball pre-forms for aspheric lenses and sensor applications. Ball lenses are manufactured from a single substrate of glass and can focus or collimate light, depending upon the geometry of the input source. Half-ball lenses are also common and can be interchanged with (full) ball lenses if the physical constraints of an application require a more compact design.
Essential Equations for Using Ball Lenses
Figure 1: Key Parameters
There are five key parameters needed to understand and use ball lenses (Figure 1): Diameter of Input Source (d), Diameter of Ball Lens (D), Effective Focal Length of Ball Lens (EFL), Back Focal Length of Ball Lens (BFL) and Index of Refraction of Ball Lens (n).
EFL is very simple to calculate (Equation 1) since there are only two variables involved: Diameter of Ball Lens (D) and Index of Refraction (n). EFL is measured from the center of the ball lens, indicated by R in Figure 1. BFL (Equation 2) is easily calculated once EFL and D are known. Numerical Aperture NA (Equation 3) is dependent on EFL and d. It is a commonly referenced term and often used in lieu of d/D.
Since NA is often used, Figure 2 illustrates how it increases as the Diameter of the Input Source (d) also increases.
Figure 2: Numerical Aperture vs. Diameter for Ball Lens Glass Types offered by Edmund Optics®.