Converting F# to NA  When an optical fiber is connected directly to the entrance slit of a spectrometer, the numerical aperture (NA) of the fiber should be smaller than the NA of the spectrometer to achieve a high throughput. The NA of a spectrometer can be calculated from its f-number (f/#) as: NA = 1/(2×f/#). The capability of an optical fiber for light collection is determined by its optical etendue GF = p×S×(NA)2 ,where S is the area of the core, NA is the numerical aperture of the fiber determined by the refractive index difference between the core (nco) and cladding (ncl) of the fiber, NA = (n2co- n2cl)1/2/nco. For a spectroscopy system that employs optical fiber for light delivery, the etendue of the fiber should be selected to match with the etendue of the light source and the spectrometer. About F# The f-number of an optical system expresses the diameter of the entrance pupil in terms of its effective focal length. The f-number is defined as f/# = f/D, where f is the focal length of the collection optic and D is the diameter of the element. The f-number is used to characterize the light gathering power of the optical system. The relation of f-number with another important optical concept, Numerical Aperture (NA), is that: f/# = 1/(2×NA), where the numerical aperture of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light.   Return to Econic Product page