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Numerical aperture is commonly used in microscopy to describe the acceptance cone of an objective (and hence its light-gathering ability and resolution), and in fiber optics, in which it describes the range of angles within which light that is incident on the fiber will be transmitted along it.
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]
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 aperture and angle of the light cone must be adjusted (via the size of the diaphragm) for each different objective lens with different numerical apertures. Condensers typically consist of a variable-aperture diaphragm and one or more lenses. Light from the illumination source of the microscope passes through the diaphragm and is focused by ...
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 .
2007-12-03 13:58 User A1 580×200 (52643 bytes) [[SVG]] Illustration of the Numerical aperture for an Optic fibre. Interior of the fibre is causing coupled light to undergo Total internal reflection due to Snell's law. 2007-12-03 13:57 User A1 744×1052 (51885 bytes) Illustration of the [[Numerical aperture]] for an [[Optic fibre]]. Interior of ...
The three-dimensional point spread functions (a,c) and corresponding modulation transfer functions (b,d) of a wide-field microscope (a,b) and confocal microscope (c,d). In both cases the numerical aperture of the objective is 1.49 and the refractive index of the medium 1.52.
Axial optical units are more complicated, as there is no simple definition of resolution in the axial direction. There are two forms of the optical unit for the axial direction. For the case of a system with high numerical aperture, the axial optical units in a distance z are given by: