The meaning and the limitations of the numerical aperture of a perfect circular, cylindrical fiber are discussed. The light-collecting properties of the fiber due to skew rays collected beyond the meridional or nominal numerical aperture are shown. An effective numerical aperture which completely describes the light collection capacity of the fiber can be defined. It is shown that appreciably more light can be accepted by a fiber when all skew rays are considered than would be expected in a meridional approximation. The angular distribution of the emitted light has also been calculated for a typical case, and the effects of Fresnel reflection at the faces of the fiber are considered.
ROBERT J. POTTER, ERIC DONATI, and RICHARD TYNAN, "Light-Collecting Properties of a Perfect Circular Optical Fiber," J. Opt. Soc. Am. 53, 256-260 (1963)