Numerical aperture definition and formula
Note that the calculation is based on the paraxial approximation and therefore not accurate for cases with very high NA. A somewhat smaller spot size may be possible with correspondingly larger input beam radius, if the performance is not spoiled by aberrations. This shows that the numerical aperture depends on the location of some object plane determined by the designer according to the intended use.
Note, however, that a lens may not be designed for collimating light, but for example for imaging objects in a larger distance. There is a weak dependence of numerical aperture on the optical wavelength due to the wavelength dependence of the focal length, which also causes chromatic aberrations. The beam radius at the lens must be small enough to avoid truncation or excessive spherical aberrations.
The numerical aperture NA of an optical system e. 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. It is given by the simple expression: µ Numerical Aperture (NA) = n × sin (µ) or n × sin (α).
Typically, it will be of the order of half the aperture radius of the lens or perhaps slight larger , and in that case , with the beam divergence angle being only half the NA the achievable beam radius in the focus is. The numerical aperture, however, is a completely geometrical measure, which is not considering such aspects.
The numerical aperture of such a lens depends on its aperture and focal length, just as for the collimation lens discussed above.
The numerical aperture of an optical system is defined as the product of the refractive index of the beam from which the light input is received and the sine of the maximum ray angle against the axis, for which light can be transmitted through the system based on purely geometric considerations ray optics :. It is defined based on geometrical considerations and is thus a theoretical parameter which is calculated from the optical design.
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.
Figure (b) shows a lens and an object at point P. The NA here is a measure of the ability of the lens to gather light and resolve fine detail. The NA of a lens is defined as the sine of the angle made by the marginal ray and optical axis in image space, shown in Figure 1. Note: this box searches only for keywords in the titles of encyclopedia articles. f/# and Numerical Aperture It can often be easier to talk about the overall light throughput as the cone angle, or the numerical aperture (NA), of a lens.
Numerical Aperture
Note: the article keyword search field and some other of the site's functionality would require Javascript, which however is turned off in your browser. The meaning of NUMERICAL APERTURE is a number that indicates the . In the example case above, the numerical aperture of the lens is determined by its diameter and its focal length. The numerical aperture can be expressed and determined by the .
Numerical Aperture - Nikon’s MicroscopyU
In that case, one will consider rays coming from that object distance, and the obtained numerical aperture will be correspondingly smaller — sometimes even much smaller. See more. In case of doubt, one should ask the manufacturer what maximum input beam radius is appropriate for a certain lens. For the maximum incidence angle, it is demanded that the light can get through the whole system and not only through an entrance aperture.
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Another way to look at this is by the concept of numerical aperture (NA), which is a measure of the maximum acceptance angle at which a lens will take light and still contain it within the lens. For full-text searches on the whole website, use our search page. It is often not recommended to operate a lens or its full area, since there could be substantial spherical aberrations.
The extreme rays are limited by the size of the lens, or in some cases somewhat less if there is a non-transparent facet. Some lenses are used for focusing collimated laser beams to small spots. It cannot be directly measured, except in limiting cases with rather large apertures and negligible diffraction effects. Numerical Aperture (also termed Object-Side Aperture) is a value (often symbolized by the abbreviation NA) originally defined by Abbe for microscope objectives and condensers.
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