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Numerical Aperture

Numerical aperture (NA) is a basic optical characteristic of a specific fiber configuration. It can be thought of as representing the size or "degree of openness" of the input acceptance cone in Figure 2-4. Mathematically, numerical aperture is defined as the sine of the halfangle of the acceptance cone (sin θ).

The light-gathering power or flux-carrying capacity of a fiber is proportional to the square of the numerical aperture. This is the ratio between the area of a unit sphere within the acceptance cone and the area of a hemisphere (2p solid angle). A fiber with a numerical aperture of 0.66 has 43 percent of the flux-carrying capacity of a fiber with a numerical aperture of 1.0.

Snell’s law can be used to calculate the maximum angle within which light will be accepted into and conducted through a fiber (Figure 2-3):

In this equation, θ_MAX is the half-angle, n₀ the refractive index outside the fiber end (air =1.0), n_CO the refractive index of the core, and n_CL the refractive index of the clad.

As light emerges from the more dense glass medium into a less dense medium such as air, it is again refracted. The angle of refraction is greater than the angle of incidence, R > I, when emerging into a lower index media. Because R is by necessity less than 90 degrees, there must be a limiting value of I, the incident angle, beyond which no incident ray is refracted. This becomes the critical angle, and rays that strike at a greater angle are reflected. This is the principle behind Total Internal Reflection (TIR) in optical fiber.

It should be noted that this formula, for the calculation of numerical aperture, does not take into account striae, surface irregularities, and diffraction, all of which tend to decollimate the beam bundle. Decreasing the clad index and/or increasing the core index will increase the NA, which increases the Full Acceptance Angle and the Field of View.

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Figure 2-4 Numerical Aperture - Acceptance Cone