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The number of bound modes, the mode volume, is related to the normalized frequency and thus to the numerical aperture. In multimode fibers, the term equilibrium numerical aperture is sometimes used. This refers to the numerical aperture with respect to the extreme exit angle of a ray emerging from a fiber in which equilibrium mode distribution ...
The f-number N is given by: = where f is the focal length, and D is the diameter of the entrance pupil (effective aperture).It is customary to write f-numbers preceded by "f /", which forms a mathematical expression of the entrance pupil's diameter in terms of f and N. [1]
Aperture real amplitude as estimated at focus of a half inch perfect lens having Fresnel number equal to 0.01. Adopted wavelength for propagation is 1 μm. The Fresnel number is a useful concept in physical optics. The Fresnel number establishes a coarse criterion to define the near and far field approximations.
The numerical aperture of a Gaussian beam is defined to be NA = n sin θ, where n is the index of refraction of the medium through which the beam propagates. This means that the Rayleigh range is related to the numerical aperture by z R = n w 0 N A . {\displaystyle z_{\mathrm {R} }={\frac {nw_{0}}{\mathrm {NA} }}.}
Memorial in Jena, Germany to Ernst Karl Abbe, who approximated the diffraction limit of a microscope as = , where d is the resolvable feature size, λ is the wavelength of light, n is the index of refraction of the medium being imaged in, and θ (depicted as α in the inscription) is the half-angle subtended by the optical objective lens (representing the numerical aperture).
The lens aperture is usually specified as an f-number, the ratio of focal length to effective aperture diameter (the diameter of the entrance pupil). A lens typically has a set of marked "f-stops" that the f-number can be set to. A lower f-number denotes a greater aperture which allows more light to reach the film or image sensor.
where k-factor depends on the truncation ratio and level of the irradiance, NA is numerical aperture, c is the speed of light, f is the photon frequency of the imaging beam, I r is the intensity of reference beam, a is an adjustment factor and is the radial position from the center of the beam on the corresponding z-plane.
In an optical fiber, the normalized frequency, V (also called the V number), is given by = =, where a is the core radius, λ is the wavelength in vacuum, n 1 is the maximum refractive index of the core, n 2 is the refractive index of the homogeneous cladding, and applying the usual definition of the numerical aperture NA.