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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. By incorporating index of refraction in its definition, NA has the property that it is constant for a beam as it goes from one material to another, provided there is no ...
The near-field optical (NFO) microscope involved a sub-wavelength aperture at the apex of a metal coated sharply pointed transparent tip, and a feedback mechanism to maintain a constant distance of a few nanometers between the sample and the probe. Lewis et al. were also aware of the potential of an NFO microscope at this time. [14]
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).
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:
An imaging system may have many individual components, including one or more lenses, and/or recording and display components. Each of these contributes (given suitable design, and adequate alignment) to the optical resolution of the system; the environment in which the imaging is done often is a further important factor.
From this it is clear that a good resolution (small δ) is connected with a high numerical aperture. The numerical aperture of a lens is defined as = where α 0 is half the angle spanned by the objective lens seen from the sample, and n is the refractive index of the medium between the lens and specimen (≈1 for air). State of the art ...
It is NA that determines optical resolution, in combination with the NA of the objective. Different condensers vary in their maximum and minimum numerical aperture, and the numerical aperture of a single condenser varies depending on the diameter setting of the condenser aperture. In order for the maximum numerical aperture (and therefore ...
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} }}.}