In optical design, the finite distance between the object and the lens must often be considered. In these cases, the working f-number is used instead. The working f-number is defined by making the approximate relation above exact:

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Numerical apertureunit

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where λ0 is the vacuum wavelength of the light, and D is the diameter of the beam at its narrowest spot, measured between the 1/e2 irradiance points ("Full width at e−2 maximum"). Note that this means that a laser beam that is focused to a small spot will spread out quickly as it moves away from the focus, while a large-diameter laser beam can stay roughly the same size over a very long distance.

Fibers can be classified into G.651 fiber (gradient multimode fiber), G.652 fiber (conventional single mode fiber), G.653 fiber (dispersion-shifted fiber), G according to ITU-T recommendations for fiber type classification. .654 fiber (cutoff wavelength fiber) and G.655 (non-zero dispersion shifted fiber) fiber. Among them, G.652 and G.655 are widely used in current projects. G.652, also known as conventional single fiber, can operate at dual wavelengths with minimal dispersion at 1310 nM, with a typical attenuation of 0.34 dB/km. At 1550, the attenuation is at least 0.2 dB/km. G.652 fiber is relatively low in price and mature in technology. It is currently the largest fiber used, accounting for more than 90%.

Numerical apertureof lens

Optical fibers are classified into single-mode fibers and multimode fibers according to the transmission mode of light in the optical fiber.

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 has been established.

Numerical apertureof objective lens

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In most areas of optics, and especially in microscopy, the numerical aperture of an optical system such as an objective lens is defined by

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Numerical aperture definitionin optical

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When a light ray is incident from a medium of refractive index n to the core of index n1, Snell's law at medium-core interface gives

Light is an electromagnetic wave. The visible light partial wavelength range is 390-760 nm. The portion larger than 760 nm is infrared light, and the portion smaller than 390 nm is ultraviolet light. The applications in the fiber are 850 nm,1300 nm and 1550 nm.

Numerical apertureof microscope

where n is the index of refraction of the medium in which the lens is working (1.0 for air, 1.33 for pure water, and up to 1.56 for oils), and θ is the half-angle of the maximum cone of light that can enter or exit the lens. In general, this is the angle of the real marginal ray in the system. The angular aperture of the lens is approximately twice this value (within the paraxial approximation). The NA is generally measured with respect to a particular object or image point and will vary as that point is moved.

This has the same form as the numerical aperture in other optical systems, so it has become common to define the NA of any type of fiber to be

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Numerical aperture is not typically used in photography. Instead, the angular acceptance of a lens is expressed by the f-number, f/#, which for a thin lens imaging an object at infinity is given by

Numerical apertureformula

In microscopy, NA is important because it indicates the resolving power of a lens. The size of the finest detail that can be resolved is proportional to λ/NA, where λ is the wavelength of the light. A lens with a larger numerical aperture will be able to visualize finer details than a lens with a smaller numerical aperture. Lenses with larger numerical apertures also collect more light and will generally provide a brighter image.

Numerical aperture definitionphysics

The fiber can be divided into Step-Index Fiber (SIF) and Graded-Index Fiber (GIF) according to the difference in refractive index profile on the cross section.

Single mode fiber: The center glass core is thin (the core diameter is generally 9 or 10 μm), and only one mode of light can be transmitted. Therefore, the inter-mode dispersion is small, suitable for remote communication, but its chromatic dispersion plays a major role, so that single-mode fiber has higher requirements on the spectral width and stability of the light source, that is, the spectral width is narrower and the stability is better.

4) Light weight and small size. For example: 900 pairs of twisted pairs with 21,000 channels, 3 inches in diameter and 8 tons / KM. The cable with ten times the communication capacity is 0.5 inches in diameter and weighs 450 P/KM.

where n1 is the refractive index along the central axis of the fiber. Note that when this definition is used, the connection between the NA and the acceptance angle of the fiber becomes only an approximation. In particular, manufacturers often quote "NA" for single-mode fiber based on this formula, even though the acceptance angle for single-mode fiber is quite different and cannot be determined from the indices of refraction alone.

In laser physics, the numerical aperture is defined slightly differently. Laser beams spread out as they propagate, but slowly. Far away from the narrowest part of the beam, the spread is roughly linear with distance—the laser beam forms a cone of light in the "far field". The same relation gives the NA,

Multimode fiber: The center glass core is thicker (50 or 62.5 μm) and can transmit multiple modes of light. However, the dispersion between the modes is large, which limits the frequency at which digital signals are transmitted, and is more severe as the distance increases. For example, a 600MB/KM fiber has a bandwidth of only 300MB at 2KM. Therefore, the distance traveled by multimode fiber is relatively close, usually only a few kilometers.

In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. The exact definition of the term varies slightly between different areas of optics.

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Numerical apertureof optical fiber

Multimode optical fiber will only propagate light that enters the fiber within a certain cone, known as the acceptance cone of the fiber. The half-angle of this cone is called the acceptance angle, θmax. For step-index multimode fiber, the acceptance angle is determined only by the indices of refraction:

but θ is defined differently. Laser beams typically do not have sharp edges like the cone of light that passes through the aperture of a lens does. Instead, the irradiance falls off gradually away from the center of the beam. It is very common for the beam to have a Gaussian profile. Laser physicists typically choose to make θ the divergence of the beam: the far-field angle between the propagation direction and the distance from the beam axis for which the irradiance drops to 1/e2 times the wavefront total irradiance. The NA of a Gaussian laser beam is then related to its minimum spot size by

This approximation holds when the numerical aperture is small. The f-number describes the light-gathering ability of the lens in the case where the marginal ray before (or after) the lens is collimated. This case is commonly encountered in photography, where objects being photographed are often far from the camera.

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